Magnetic properties of amorphous Fe-Si-B glass-coated

Lappeenranta-Lahti University of Technology LUTSchool of Engineering ScienceComputational Engineering and Technical PhysicsTechnical physics

Essi Ristiranta

MAGNETIC PROPERTIES OF AMORPHOUS FE-SI-BGLASS-COATED MICROWIRES

Master’s Thesis

Examiners: Professor Erkki LähderantaJunior researcher Egor Fadeev

:

ABSTRACT

Lappeenranta-Lahti University of Technology LUTSchool of Engineering ScienceComputational Engineering and Technical PhysicsTechnical physics

Essi Ristiranta

Magnetic properties of amorphous Fe-Si-B glass-coated microwires

Master’s Thesis

2021

66 pages, 34 figures, 3 tables.

Examiners: Professor Erkki LähderantaJunior researcher Egor Fadeev

Keywords: ferromagnet, microwires, SQUID magnetometry

Microwires are fine wires with diameter in range of µm. These wires have attracted in-terest due to their outstanding magnetic properties, such as magnetic bistability. Theseproperties makes them prospective candidates for different applications, e.g. sensing el-ements for various sensors. In this thesis magnetic properties were investigated for theseamorphous glass-coated Fe-Si-B microwires. SQUID magnetometer was used for mag-netic measurements. Main objectives of the study were to evaluate the effect of tem-perature, nucleus diameter, thickness of the glass coating and removal of the coating onthe magnetic properties of the microwires. It was observed that before glass coating re-moval all microwires exhibited magnetic bistability at all measured temperatures. Afterthe glass coating removal microwires lost their bistable state due to partial reduction of in-ternal stresses. Exception for this was microwire with the biggest nucleus diameter, whichpreserved bistable state. Level of saturation for all samples decreased with temperaturedecrease. Reduction of nucleus diameter resulted in the increase of coercivity. Decreaseof relative thickness of glass coating resulted decrease in coercivity.

TIIVISTELMÄ

Lappeenrannan-Lahden teknillinen yliopisto LUTSchool of Engineering ScienceLaskennallinen tekniikka ja teknillinen fysiikkaTeknillinen fysiikka

Essi Ristiranta

Amorfisten Fe-Si-B lasipäällysteisten mikrolankojen magneettiset ominaisuudet

Diplomityö

2021

66 sivua, 34 kuvaa, 3 taulukkoa.

Tarkastajat: Professori Erkki LähderantaNuorempi tutkija Egor Fadeev

Hakusanat: ferromagneetti, mikrolangat, SQUID magnetometri

Mikrolangat ovat ohuita lankoja, joiden halkasija on mikrometrien luokkaa. Nämä langatovat kiinnostavia niiden magneettisten ominaisuuksien vuoksi, kuten esimerkiksi magnet-tinen bistabiliteetti. Näiden ominaisuuksien ansiosta ne ovat potentiaalisia materiaalejaerilaisiin sovelluksiin, joista eniten kiinnostusta on herättänyt käyttö antureissa erilais-ten parametrien havaitsijana. Tässä työssä tutkittiin amorfisten Fe-Si-B lasipäällysteistenmikrolankojen magnettiisia ominaisuuksia. Mittaukset suoritettiin käyttämällä SQUIDmagnetometria. Tavoitteena oli tutkia lämpötilan, langan metalliosan halkaisijan, lasi-päällysteen paksuuden ja sen poistamisen vaikutuksia. Ennen päällysteen poistoa kaikkitutkitut mikrolangat olivat bistabiilisia. Päällysteen poiston jälkeen mikrolangat menet-tivät bistabiilisen tilansa lukuunottamatta mikrolankaa, jolla oli suurin metalliosan hal-kaisija. Magneettinen saturaatio heikkeni lämpötilan laskun myötä. Metallisen sisuksenhalkaisijan pieneneminen lisäsi koersiviteettia. Suhteellisen lasipäällysteen paksuudenlisääminen johti koersiviteetin vähenemiseen.

PREFACE

I would like to thank my supervisors Erkki Lähderanta and Egor Fadeev for making thisthesis possible and guiding me through this work. I would like to thank also everyonewho had any contributions or are somehow related to this work.

I wish to thank my family for giving me their continuous support and friends who havemade my time at LUT so special. Special thank to a friend who spent a lot of time ona call with me while we were both working with our thesis. They gave me companyand support during these challenging times due to Covid-19 pandemic. There has beensome great moments and some challenging ones but now it is time to head towards newchallenges and see what the world has to offer.

Lappeenranta, July 15, 2021

Essi Ristiranta

5

CONTENTS

1 INTRODUCTION 81.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2 Objectives and delimitations . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Fundamentals of magnetism 102.1 Magnetic measurement units . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Diamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Antiferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.6 Magnetic hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.7 Demagnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 MICROWIRES 183.1 Properties of microwires . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.1 Magnetic domain structure . . . . . . . . . . . . . . . . . . . . . 183.1.2 Chemical properties . . . . . . . . . . . . . . . . . . . . . . . . 203.1.3 Mechanical properties . . . . . . . . . . . . . . . . . . . . . . . 213.1.4 Electrical properties . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Prominent effects of microwires . . . . . . . . . . . . . . . . . . . . . . 223.2.1 Giant magnetoimpedance (GMI) . . . . . . . . . . . . . . . . . . 223.2.2 Large Barkhausen effect and magnetic bistability . . . . . . . . . 23

3.3 Fabrication methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.1 Melt spinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.2 In-rotating-water spinning . . . . . . . . . . . . . . . . . . . . . 243.3.3 Taylor method . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.4 Glass-coated melt spinning . . . . . . . . . . . . . . . . . . . . . 263.3.5 Melt extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.6 Electrodeposition . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4.1 Sensing applications . . . . . . . . . . . . . . . . . . . . . . . . 283.4.2 Biomedical applications . . . . . . . . . . . . . . . . . . . . . . 293.4.3 Other applications . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 SQUID MAGNETOMETER 314.1 Working principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6

4.2 Structure of the SQUID magnetometer . . . . . . . . . . . . . . . . . . . 334.3 The recondensing cryostat and insert system . . . . . . . . . . . . . . . . 344.4 The magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 Temperature control of the VTI . . . . . . . . . . . . . . . . . . . . . . . 354.6 Superconducting detection system . . . . . . . . . . . . . . . . . . . . . 364.7 Electronic rack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5 EXPERIMENTS 395.1 Description of experiments . . . . . . . . . . . . . . . . . . . . . . . . . 39

6 RESULTS AND DISCUSSION 406.1 Sample 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2 Sample 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.3 Sample 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.4 Comparison between the samples . . . . . . . . . . . . . . . . . . . . . . 536.5 Current study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.6 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7 CONCLUSION 58

REFERENCES 59

Tables 63

Figures 64

7

LIST OF ABBREVIATIONSθ Weiss constantλ Magnetostriction constantµ0 Permeability of free spaceΦ Magnetic fluxχ Magnetic susceptibilityAC Alternative currentB Magnetic flux densityC Curie constantd Nucleus diameter of wireD Wire diameterDC Direct currentemu Unit of magnetic momentFe-Si-B Iron-Silicon-BoronGMI Giant magnetoimpedanceH Magnetic field strengthH∗ Switching fieldHc Coercive fieldm Magnetic momentM MagnetizationMr Remanent magnetizationMs Saturation magnetizationSQUID Superconducting quantum interference devicet TimeT TemperatureTC Curie temperatureTN Néel temperatureVTI Variable temperature insert

8

1 INTRODUCTION

1.1 Background

Microwires are thin wires with diameter in the range of micrometers. The microwirescan be either bulk wires or consist of an inner core and a glass coating which is shieldingthe core. They possess different mechanical, chemical, electrical and magnetic prop-erties. Especially magnetic microwires posses magnetic properties, like giant magne-toimpedance (GMI) effect and magnetic bistability, which allows highspeed propagationof domain wall through the entire microwire. These magnetic properties are desirablefor applications such as sensing elements in various sensors. They can be used to detectdifferent parameters, for example, temperature, tensile stress or magnetic field. Due totheir small size they are very sensitive to environmental changes.

Amorphous state is favourable for GMI effect and magnetic bistability. It is known thatGMI effect is strong in Co-rich amorphous microwires and magnetic bistability is inherentfor amorphous glass-coated wires with positive magnetostriction. In order to fabricatemicrowires with these magnetic properties they are drawn together with molten glassand then quenched rapidly to obtain amorphous state. This technique was developed insixties [1].

1.2 Objectives and delimitations

The aim of this thesis is to investigate magnetic properties of amorphous Fe-Si-B glass-coated microwires. The objectives of this thesis are:

• Since changes in magnetic domain structure affect magnetic properties, it is nec-essary to estimate influence of glass coating removal to magnetic domain structureand therefore, to magnetic properties by measuring dependencies of magnetizationon magnetic field (M (H)).

• To investigate influence of the temperature on magnetic properties.

• To investigate how changes in metallic core diameter and glass coating thicknessaffect magnetic properties of the microwires.

9

Length of microwire has also an influence on the magnetic properties [2]. However, inthis thesis the influence of the length is not studied.

1.3 Structure of the thesis

Chapter 2 introduces fundamentals of magnetism including types of magnetic ordering,measurement units and description of demagnetizing process. Chapter 3 describes mi-crowires, their properties, fabrication methods and possible application. Chapter 4 givesan overview of SQUID magnetometer, which is used to conduct the measurements in thisthesis, and its working principle. Descriptions of experiments is presented in Chapter 5.Results and discussion are provided in Chapter 6. The last Chapter 7 contains conclusionsof the thesis.

10

2 Fundamentals of magnetism

Since the discovery of magnetism and magnetic materials in the ancient world, humankindhas always been baffled and fascinated by its mysterious properties. Nowadays magnetsare widely used in different areas ranging from industry to medicine. Magnets are used ineveryday life in variety of electric devices such as household appliances [3, 4]. There arefive main types of magnetic ordering: paramagnetism, diamagnetism, ferromagnetism,ferrimagnetism and antiferromagnetism. All materials exhibit some type of magneticordering [5].

The phenomenon of magnetism can not be fully explained using classical physics, alsoquantum mechanical approach is needed in order to understand fundamentals of mag-netism. The origin of magnetism arises from orbital angular momentum of electrons andelectrons spin angular momentum [6].

2.1 Magnetic measurement units

The International System of Units (SI) is widely accepted by most nations. It is an agree-ment on which units are used as a standard. However, both SI and cgs systems are utilizedfor magnetic measurements. The cgs system stands for "centimeter-gram-second". In cgssystem emu is an unit for magnetic moment. Magnetization M is defined as a vectorsum of magnetic moments by volume, mass or moles of the sample as a counting base.Magnetic quantities with respective units in cgs and SI systems are represented in Table1.

Table 1. Magnetic quantities with cgs and SI units [5].

Quantity Symbol cgs units SI unitsMagnetic flux density B G (gauss) T

Magnetic field strength H Oe (oersted)Am

Magnetic moment m emu Am2 ,JT

Magnetization Memucm3

,emu

g,

emumol

Am

,Am2

kg,

Am2

mol

Magnetic susceptibility χ 1,cm3

g,

cm3

mol1,

m3

g,

m3

mol

One gauss corresponds to 10−4 T and one oersted corresponds to103

4π

Am

. Gauss and

11

oersted have same dimensions meaning that 1 G = 1 Oe. Magnetic quantities B, H andM are related to each other in cgs system by equation

B = H + 4πM. (1)

The same relation using SI system is defined as

B = µ0(H +M), (2)

where µ0 represents permeability of free space. Measuring a direct magnetization re-sponse to the applied magnetic field gives

χ =M

H, (3)

where χ represents magnetic susceptibility. Magnetic susceptibility plays an importantrole on classifying materials [5].

2.2 Paramagnetism

Every material posses some value of magnetic susceptibility χ. Paramagnetic materialshave positive values of susceptibility (χ > 0). Paramagnetic susceptibility values are rel-atively small, commonly in the range of 10−6 to 10−1. The total magnetization dependson applied magnetic field and temperature (M ∝ B

T). The paramagnetic material which

is not exposed to the external magnetic field has randomly oriented intrinsic magneticmoments due to thermal agitations. Illustration of magnetic moments of paramagnetic or-dering is shown in Figure 1a. When no magnetic field is applied, these magnetic momentscancel each other out and the net magnetization is zero. When the material is exposed toan external magnetic field, the magnetic moments begin to align parallel to the field inorder to decrease the Zeeman energy. However the Zeeman energy is small compared tothermal energy, hence the total magnetization is very small. Positive χ values indicatesthe direction of the moments to be same as the field direction [5, 7].

The χ of many paramagnetic materials follows the equation

12

(a) paramgagnetism (b) ferromagnetism (c) antiferromagnetism

(d) ferrimagnetism (e) canting ferromag-netism

Figure 1. Illustration of magnetic moments of different types of magnetic ordering [5].

χ =C

T, (4)

whereC represents the Curie constant. The equation is known as the Curie law. The Curielaw does not apply for metallic paramagnets as their susceptibility is not temperaturedependent [4]. These materials close to temperature independent type of paramagneticsusceptibility are referred as materials that exhibit Pauli paramagnetism [6]. Examples ofmetallic paramagnets are palladium and platinum. Paramagnetic materials can be solids,liquids or gases. For example, elements sodium and oxygen are paramagnets [8].

2.3 Diamagnetism

The material is diamagnetic, when there is no innately existing magnetic moments inthe material. Diamagnetic materials have negative magnetic susceptibility (χ < 0) [5].The susceptibility values are commonly relatively small, usually in the range of −10−6

to −10−2 [7]. When an external magnetic field is applied to the diamagnetic material,it induces magnetic dipoles, which are aligned to the opposite direction of the field dueto Lenz’s rule. The magnetic field penetrates into diamagnetic materials although thematerial tends to repel it as illustrated in Figure 2a [5].

13

Diamagnetic materials are, for example, materials containing ions or atoms with closedelectronic shell and inorganic compounds, such as benzene rings [6]. In addition, mostof the nonmetal materials are diamagnets [8]. Superconductors are categorized as perfectdiamagnets. In a superconducting state they exhibit the Meissner effect meaning magneticflux inside of the material is zero (B = 0) even in the presence of the external magneticfield as illustrated in Figure 2b [5].

(a) diamagnet (b) perfect diamagnet = super-conductor

Figure 2. Illustration of magnetic flux inside of diamagnets [5].

2.4 Ferromagnetism

Ferromagnetism is the form of magnetism that people normally consider as a magnet inour everyday life. Iron is a good and well-known example of the ferromagnetic material.Materials which have similar magnetic properties to iron such as nickel and cobalt arealso ferromagnets. In addition, alloys of aforementioned elements tend to exhibit ferro-magnetic behaviour [8]. Moreover, alloys with no ferromagnets as constituent elementscan possess ferromagnetic behavior [9].

Ferromagnetic materials have a critical value of temperature known as the Curie temper-ature TC . Below TC material behaves like ferromagnet with a spontaneous magnetizationand above the TC material exhibits paramagnetic behaviour. The Curie law was intro-duced above in Section 2.2 describing paramagnetism, however, it does not take intoaccount any of the magnetic moment interactions. For this reason Curie-Weiss law isintroduced

χ =C

T − θ, (5)

14

where θ represents a correction term and is called the Weiss constant. The unit of θ isKelvin (SI system). Positive values of θ indicates that magnetic moments have a highprobability to align parallel to the external magnetic field. The alignment of the magneticmoment is illustrated in Figure 1b [5].

The origin of ferromagnetism arises from the spins of electrons [6]. The spontaneousmagnetization is possible in the temperature range of 0 K to TC [3]. Ferromagnetic mate-rials exhibit magnetic hysteresis, which describes dependence of magnetization versus theapplied magnetic field [4]. The hysteresis and magnetization of ferromagnets is describedmore in details in Section 2.6.

Susceptibility values of ferromagnets are commonly in the range of 10 to 107. Great val-ues of χ indicates that the total magnetization of ferromagnets in the presence of magneticfield is large [7]. The susceptibility is theoretically infinite at TC and drops to the rangeof paramagnets above TC [3].

2.5 Antiferromagnetism

Antiferromagnets have two magnetic sublattices with magnetic moments oriented antipar-allel to each other in the presence of an external magnetic field alongside of the spin axis.Illustration of antiparallel ordering of the magnetic sublattices is shown in Figure 1c. Themagnetic moments of sublatices are equal, therefore, they cancel each others out leadingto only weak net magnetism. The case of nonequivalent antiparallel magnetic sublatticesis called ferrimagnetism and is presented in Figure 1d [3]. If an external magnetic field isapplied perpendicular to the spin axis, the magnetic moments starts to turn with the fieldin the way, which is illustrated in Figure 1e. Both ferrimagnetism and canted ferromag-netism are special cases of antiferromagnetism [5,6]. In the absence of the magnetic fieldantiferromagnetic material has a zero net magnetization [7].

The susceptibility range of antiferromagnets is similar to that of paramagnets [7]. Thedifference between them is that antiferromagnets possess ordered structure of magneticmoments. The ordered structure starts to deteriorate with the temperature increase, lead-ing to rise of susceptibility. Like ferromagnets, antiferromagnets also have a critical tem-perature. This temperature is called The Néel temperature, TN . Above TN the orderedstructure is completely destroyed and the material behaves like paramagnet. The suscep-tibility of antiferromagnets reaches its peak at TN and starts to decrease as the material’sstate changes to paramagnetic [6].

15

Examples of antiferromagnetic materials are manganese and chromium [7]. Antiferro-magnets can also be fabricated artificially. These materials are called synthetic antifer-romagnets. These materials are formed by stacking thin-films on top of each other. Themultilayered structure of synthetic antiferromagnets is made of alternating ferromagnet(e.g., cobalt) and nonmagnetic metal (e.g., ruthenuim). In this structure the ferromagneticlayers are coupled. The structure of the synthetic antiferromagnet is illustrated in Figure3 [4, 10].

Figure 3. Structure of a synthetic antiferromagnet [4].

2.6 Magnetic hysteresis

Ferromagnetic materials exhibit magnetic hysteresis. Ferromagnetic materials have anirreversible nonlinear response to the applied magnetic field, and as a result they forma hysteresis loop of magnetization versus the applied magnetic field as shown in Figure4. If a ferromagnetic material has not been exposed to a magnetic field, its magneticdomains are oriented randomly. In this case the material is in so-called virgin state. Whenmagnetic field is applied, the magnetic domains starts to align with the field. When themagnetic domains have aligned parallel to the applied field, the material reaches a levelof saturation magnetization, which is referred in Figure 4 as Ms. When the magnetic fieldis reduced back to zero, the material will remain in the magnetized state. In Figure 4The remanent magnetization is denoted as Mr. In order to have zero magnetization in thematerial, it is needed to apply an opposite magnetic field of the value, which is denotedas Hc in Figure 5. This value of magnetic field is called coercive field.

16

Figure 4. Illustration of a ferromagnetic hysteresis loop [4].

Broad loops shaped like square are characterized as hard magnetic materials. These ma-terials remain in a magnetic state even after the field is removed once they are magnetizedto Ms in a magnetic field. They have high coercive field values, meaning the magnetizedstate is not sensitive to changes in ambient fields. Therefore these materials are suitablefor permanent magnets, which are used, for example, in electric motors. Materials withnarrow hysteresis loops shaped like letter S are soft magnetic materials. These materialshave small coercive fields. As a result, in these materials it is easy to change the sign ofmagnetization [4, 8].

2.7 Demagnetization

As mentioned in Section 2.6, ferromagnetic materials exhibit magnetic hysteresis. Theresidual magnetization in once magnetized ferromagnets can be eliminated using demag-netization methods also referred as degaussing [11]. For some applications it is necessaryto demagnetize the material, for example, magnetic recording is dependent on the demag-netization.

Material can be demagnetized by exposing the material to alternating magnetic fields. Theamplitude of the alternating magnetic field is gradually decreased down to zero as shownin Figure 5. As the magnetic field is decreasing, the magnetization reduces with it to itsminimum value. This demagnetization method is based on the hysteresis behaviour [11].

Demagnetization can be attained using other methods as well. For example, annealing

17

Figure 5. Illustration of hysteresis loops during demagnetization process [11].

the material above its TC changes its magnetic state to paramagnetic, and material losesits magnetization. After the annealing material should be cooled down in a zero magneticfield [12]. For a very rapid demagnetization effective lasers can be used to induce anultra-fast demagnetization [13].

18

3 MICROWIRES

Microwires are very fine wires with diameter in the range of micrometers. Commonly,the core consist of a metal alloy, which is coated with thin layer of glass. Microwires arebarely visible for a human eye, very thin, pliable, and resembling hairs.

Microwires are promising materials for a great variety of different applications, for ex-ample, in the field of sensors and biomedicine. Due to variety of properties and pos-sible applications especially ferromagnetic microwires have gained ever increasing in-terest among the scientist and companies all over the world during the last couple ofdecades [14].

3.1 Properties of microwires

Microwires have promising mechanical, electrical, chemical and magnetic properties.This section describes amorphous magnetic microwires, which is the main focus of thisthesis.

3.1.1 Magnetic domain structure

The magnetic domain structure of rapidly quenched wires is interesting and complex. Thequenching rates differs between the centre and the surface of the wire leading to complexinternal stress distribution, which usually have axial, radial and circular components. Thedomain structure is determined by the magnetostriction constant, λ. The magnetostrictioncan have positive or negative values, which is an important parameter to consider whendetermining the domain structure.

Amorphous wires with positive values of λ have commonly longitudinal easy axis in theinner core and radial easy axis in the outer shell, like shown in Figure 6. The cylindricalinner core with axial domain structure covers usually around 70-90 % of the volumeof the wire. This kind of domain structure enables large Barkhausen jump, which isbeneficial for many applications, and also shows magnetic bistability. For instance, Fe-based microwires have positive values of λ [15, 16].

Amorphous wires with negative values of λ have commonly axial domains in the inner

19

Figure 6. Schematic illustration of domain structure of wire with positive magnetostriction coef-ficient [15].

core of the wire and circular in the outer shell as shown in Figure 7. As the inner cylin-drical core has similar domain structure to the wires with positive values of λ, it is alsopossible for wires with negative values of λ to exhibit large Barkhausen jump. However,in the case of amorphous glass-coated wire with large negative values of λ the circularouter domain shell covers practically the whole volume of the wire. For instance, Co-based microwires have negative values of λ [15].

Figure 7. Schematic illustration of domain structure of wire with negative magnetostriction coef-ficient [15].

Amorphous wires with values of λ close to zero have very complex domain structure,and it is extremely difficult to precisely define domain structure of them. Due to that thedomain structure is most often considered to be very similar to wires with negative valuesof λ. For instance, wires with composition of Co-Fe-Si-B have λ values close to zero [15].

The domain structure of wires, which have been fabricated by rapid quenching, can beeasily modified by exposing the wire to mechanical and thermal treatments. For example,the domain structure can be significantly modified by removing the glass coating, since it

20

has a significant effect on the internal stress distribution of the wire. For amorphous glass-coated wires with positive values of λ the removal of the glass coating leads to growth ofthe outer domain shell and to decrease of inner core, nevertheless, the whole configurationdoes not change. This is illustrated in Figure 8. The glass coating removal reduces signif-icantly axial tensile stress, which might soften the material in terms of magnetism [15].

(a) With glass coating

(b) Glass coating removed

Figure 8. Schematic illustration of the effect of glass coating removal on the magnetic domainstructure of the wire with positive value of λ. OS denotes outer shell and IC denotes inner core[15].

For amorphous glass-coated wires with negative values of λ the removal of the glasscoating leads the change of domain structure from radial to axial as illustrated in Figure9. The shell configuration remains unchanged, however, the volume of the outer shelldomain increases. It is possible to restore the domain structure, that the microwire hadbefore the glass coating removal, by applying tensile stress [15].

3.1.2 Chemical properties

The amorphous wires have high resistance for corrosion due to their chemical and struc-tural homogeneity as there is no grain boundaries to help the corrosion. Corrosion resis-tance even higher than in stainless steel can be obtained in amorphous Fe-based wires withaddition of chromium. In addition, for glass-coated wires the coating provides protectionagainst the corrosion [16].

21

Figure 9. Schematic illustration of the effect of glass coating removal on the magnetic domainstructure of the wire with negative value of λ. OS denotes outer shell and IC denotes inner core[15].

3.1.3 Mechanical properties

Amorphous microwires are found to be very strong and ductile. Some of their mechanicalproperties are stronger than those of their crystalline counterparts. They have high valuesof fracture strength approaching the theoretical values. For instance, Fe-based amorphouswires have fracture strength values up to 3.5 GPa, which is higher than of steel [15, 16].

A phenomenon called size effect is observed in glass-coated wires. The size effect meansthat tensile strength and thermal coefficients of glass coating and inner core alloy areconnected. Meaning the wire diameter has an influence on the tensile strength. The sizeeffect is not observed if the thermal expansion coefficients of the glass and alloy are inthe same range meaning changes in nucleus diameter does not have an impact on thetensile strength. However, if the thermal expansion coefficients of glass and alloy differsignificantly from each other, the size effect is observed. As the diameter decreases, thevalue of the tensile strength increases. The size effect was observed not only in amorphousglass coated wires, but also in crystalline glass coated wires [16].

Annealing of the wires can cause some notable changes in their mechanical properties.For instance, Fe-based amorphous wires exhibit thermal embrittlement. The embrittle-ment can be a significant problem for some applications. Annealing can also lead togeneration of nanocrystallites. On the contrary, cold-drawing can also be used to modifythe mechanical properties of the wires. For instance, plasticity and tensile strength canbe modified by the cold-drawing process. It can also improve a giant magnetoimpedance(GMI) effect in wires, which is desirable for sensors [15].

22

3.1.4 Electrical properties

Amorphous metallic wires have significantly higher electrical resistance compared to theircrystalline counterparts with similar chemical composition. For instance, Fe-Si-B amor-phous glass-coated microwire has 20 % higher electrical resistance than its crystallinecounterpart. In addition, the resistance is less temperature dependent. High electricalresistance is favorable for high frequency applications, but it is not for the GMI effect.The resistance can be lowered by annealing the wire up to point of nanocrystallization.The resistance can also be modified by external magnetic fields, by changing the chemicalcomposition, by increasing pressure or by applying mechanical stress [15, 16].

3.2 Prominent effects of microwires

Microwires exhibit many interesting phenomena. This makes them very prospective ma-terials for a great variety of different applications in all walks of life and industry. Thissection presents brief overview of two of the effects.

3.2.1 Giant magnetoimpedance (GMI)

The giant magnetoimpedance (GMI) is a fairly recent discovery. The GMI effect is changeof AC impedance of a soft ferromagnetic conductor under the influence of an applied mag-netic field. For a cylindrical object (e.g., microwires) the GMI effect can be understood asthe result of an increase of skin depth up to the radius of the wire by means of reductionof circumferential permeability. Choosing a material with high values of circumferentialpermeability leads to reduced skin depths resulting in higher values of GMI, which isbeneficial for sensor applications. The magnitude of the GMI effect can be modified bychanging frequency.

The GMI effect can be observed in both glass-covered and conventional wires. However,for example, wire with value of λ close to zero shows a significant decrease of the GMIvalue after the glass coating removal. The glass coating removal decreases the value ofthe circumferential permeability. In addition, glass coating thickness affects the valueof GMI. Observed GMI value decreases, as the thickness of the glass coating increases.Amorphous wires with positive values of λ do not exhibit GMI effect. However, if thewire is annealed up to the point of nanocrystallization, it starts to exhibit the GMI effect

23

[17].

3.2.2 Large Barkhausen effect and magnetic bistability

The large Barkhausen effect is possible in microwires with large positive values of λdue to the magnetic domain structure, which includes the axially magnetized inner core.Materials exhibit the Barkhausen effect due to magnetization reversal in the core at acertain value of axial magnetic field, which is called the switching field (H∗). The effectis visible in hysteresis loop as a vertical step (See Figure 10). In Figure 10 the left looprepresents the full effect and then the completeness of the effect decreases towards theright side. In the last hysteresis loop on the right side of Figure 10 the effect is completelyvanished [18, 19].

Figure 10. Degree of the large Barkhausen effect from perfect to nonexistent [18].

The vertical jump in the hysteresis loop is also described as magnetic bistability, meaningthat the magnetization switches from one stable state to another at critical value of thefield. As mentioned in Chapter 3.1.1, the inner core of amorphous glass-coated wireswith positive values of λ occupies large percentage of the volume therefore the magneti-zation of the core dominates the magnetization of the wire. The inner core has two stablemagnetization states which are parallel and antiparallel to the wire [18, 19].

3.3 Fabrication methods

There are several methods for microwire fabrication. This chapter introduces the mostcommon fabrication methods: melt spinning, in-rotating-water spinning, Taylor method,glass-coated melt spinning, melt extraction and electrodeposition. Metallic amorphous

24

wires without glass coating are fabricated using the first two methods. Glass-coated amor-phous wires can be fabricated using Taylor or glass-coated melt spinning methods. Theamorphous glass-coated microwires are the most promising for technical applications e.g.sensing elements in sensors. Wires fabricated using electrodeposition also attract someinterest among scientists due to uniform magnetic properties.

Sometimes it is needed to remove the glass coating. This usually causes changes in mag-netic and mechanical properties of a wire. The removal can be done mechanically or usingchemical etching. Chemical etching usually causes less changes in magnetic, electricaland mechanical properties compared to mechanical glass coating removal. However, oneshould gradually decrease concentration of acid and rinse the metal with water in order toavoid etching of the metal part [20].

3.3.1 Melt spinning

The melt spinning method is widely used to fabricate amorphous metallic alloys. Thecooling rate of this method ranges from 104 to 106 K/s. Using this method it is possi-ble to fabricate wires with a diameter ranging from 1 to 300 µm. The method is basedon the pressure ejection of melt stream through an outlet into a coolant, after which thisstream solidifies rapidly before disintegrating into droplets. In order to fabricate the wiresdirectly from the melt with rapid solidification several conditions must be met. First,the melt stream should solidify at high cooling rates within the certain "stability" dis-tance from the outlet. Second, the coolant must have low viscosity and surface tension.Third, the coolant must have non-turbulent and stable flow with high velocities. However,in practice it is difficult to maintain simultaneously cooling capacity of the melt streamwithout the precipitation of crystalline phases in the range from melting to glass transitiontemperature. Due to these difficulties it is challenging to to fabricate glass-coated metallicalloy wires using the melt spinning method [20].

3.3.2 In-rotating-water spinning

To overcome the limitations of the melt spinning method, the in-rotating-water spinningmethod was developed. The main difference is that the melt stream is guided straight intorotating water instead of impinging on the inner parts of the rotating drum. The devicebased on this method is presented in Figure 11. Some adjustments are needed dependingon the alloy being cast. For instance, it may be necessary to adjust the ejection angle, the

25

distance between the nozzle tip and coolant surface, and the temperature of the coolantor the depth of the coolant layer. The cooling rate of this method is commonly around105 K/s. The diameter of amorphous metallic wires fabricated using this method rangescommonly from 30 to 300 µm, however, also thinner and thicker diameters have beenreported. This method can be used to fabricate wires with alloy compositions which arehard to obtain using conventional methods [20].

Figure 11. A cross-section illustration of microwire fabricating device using in-rotating-waterspinning method [20].

3.3.3 Taylor method

Taylor method was first introduced in 1924 by G.F. Taylor. In this method a metallic bodyis placed in a glass tube and then treated by induction heating. The heating causes themelting of the material. Contact with the molten metal leads to softening of the glass.The softened glass can then be drawn. The drawn glass acts as mould for the solidifyingmetal core and provides uniform surface and diameter of the wire. The cooling rate ofthis methods varies from 103 to 106 K/s. The diameter of the wires can be in the rangeof 2 to 100 µm. A great variety of different metallic wires has been successfully fabri-cated using this method, including steels, noble metals and coppers. The challenges of

26

the Taylor method are finding a suitable sheath material which has a sufficient chemicalinertness towards the used molten metal and finding a softening temperature consistentwith the melting temperature of the metal. To avoid the contamination of the metal by thesheath, it is crucial to use a glass which is compatible with the metal in terms of meltingtemperature, viscosity and chemical properties [20, 21].

3.3.4 Glass-coated melt spinning

The glass-coated melt spinning method is also known as Taylor–Ulitovsky method [22].This method is an alteration to the Taylor method allowing alloy systems with low wireforming capacity to be fabricated without any major difficulties. The schematic illustra-tion of the glass-coated melt spinning method is shown in Figure 12. The metal alloyis annealed using induction coils up to its melting point. Melting metal forms a dropleton the bottom of the Pyrex glass tube and softens the glass tube which is envelopingthe droplet. This softened glass around the droplet allows the drawing of the capillaryto take place. The molten metal fills up the glass capillary and solidifies rapidly in thesolidification zone as it is cooled with the coolant jet [20, 23].

Figure 12. Schematic illustration of the glass-coated melt spinning method used for microwirefabrication [23].

The diameter of the metallic core obtained using the glass-coated melt spinning method iscommonly in the range of 0.8 to 30 µm and the thickness of the glass coating ranges from

27

2 to 15 µm. This method has cooling rate from 104 to 107 K/s, which is higher than thatof the in-rotating-water spinning method. The cooling rate is considered as an advantagesince it eases the fabrication process of amorphous wires. Additional significant advan-tages compared to the other methods are suitability for the mass production, possibility tofabricate continuous long wires up to 10 km, and possibility to vary wide range of bothgeometrical and physical parameters [20].

3.3.5 Melt extraction

The melt extraction method has recently been widely used to fabricate magnetic mi-crowires. The schematic illustration of this fabrication method is presented in Figure13. This method is based on the annealing of metal alloy up to its melting point. Al-loy rod is inserted to crucible to provide molten alloy. Then a wheel with sharp edge,spinning at high-speed, is contacted to the molten metal alloy droplet surface. As a re-sult wire is extracted and cooled rapidly from the alloy. Using melt extraction methodthe cooling rates are in the range from 105 to 106 K/s, which is even higher than ofthe Taylor-Ulitovsky method. Advantages using the melt extraction method are the highquality surface, smooth circular geometry of the wires, and significantly improved softmagnetic properties of the materials. The diameter of the fabricated wires commonlyranges from 30 to 60 µm. These diameters are quite big compared to the other methods.One of the major disadvantages of this method is that the diameter of the wires can not beprecisely controlled [20].

3.3.6 Electrodeposition

Using electrodeposition fabrication method uniform wires with non-magnetic inner coreand magnetic outer shell layers can be produced. The layers are obtained by moving theinner core through electrolyte baths and smoothing the surface with rotating rollers. Thethickness of the layers can be varied by the deposition time when the value of the currentis fixed. The diameter for the inner core is commonly around 20 µm and the magneticlayer thickness ranges from 2 to 7 µm, but the total diameter can vary from 20 to 1000µm. The advantageous possibilities of electrodeposition method are: 1) to use wide rangeof materials (e.g., alloys, metals, composites), 2) to use continuous and batch processing,3) to produce materials with different grain shape and size, and 4) to produce a productin the form of coating or bulk material. In addition, electrodeposition method can becombined with melt spinning method [20].

28

Figure 13. Schematic illustration of the melt extraction method used for microwire fabrication[20].

3.4 Applications

Microwires have a huge potential to be utilized in great variety of applications due totheir versatile properties. Majority of the possible applications are related to some type ofsensing. However, nowadays, microwires are not produced commercially in great quanti-ties due to higher cost compared to conventionally produced wires and design engineers’lack of knowledge regarding the properties and availability of the microwires. Taylor wirefabrication method is cheaper fabrication technique compared to mechanical die-drawingmethods [24].

3.4.1 Sensing applications

Magnetic microwires have useful properties for sensing elements in sensors. Magneticmicrowires can be used as tensile stress, temperature or magnetic field sensors. One ofthe advantages of using microwires as sensors is their small size and mass [25].

For instance, amorphous glass-coated microwires with positive values of λ are greatchoice for sensors as they exhibit magnetic bistability. Working principle of the sen-sors is based on the switching of the direction of the magnetization from one stable stateto another. Several external factors affect the switching field (e.g., mechanical stress,

29

and temperature). Temperature influences the switching field due to different thermal ex-pansion coefficients of the glass coating and the alloy. The tensile stress inside the wireincreases as the wire gets warmer leading to the changes of the value of the switchingfield [25].

Temperature sensors can be used, for example, for meteorological or environmental sens-ing. Stress detection sensors can be used for structural monitoring of an aircraft. Magneticfield sensors, for example, can be used for navigation purposes and to monitor magneticfield which arise from electrical sources [25].

GMI effect is also widely used in sensor applications. GMI sensors can detect magneticfield, current (both ac and dc) and stress. Main advantages of GMI sensors are highsensitivity, low energy consumption and good thermal stability. The GMI sensors can beused, for example, in computer disk heads, antitheft systems and car traffic monitoring[17].

3.4.2 Biomedical applications

Magnetic glass-coated microwires are possible solutions for different biomedical appli-cations. Utilizing the wires in biomedical applications is related to sensing properties.There is a need for biomedical sensors to improve healthcare and life science. With im-proved sensing it may, for example, be possible to detect diseases in early state allowingearly treatment. The wires have a huge advantage over the conventional sensing devicesas wires do not need separate elements for sensing and transmitting. The glass coatingmakes wires bio-compatible and due to their tiny size they will not cause any defects tothe structure of implants. They are also very sensitive to detect different parameters dueto their size. The wires can be used, for example, for sensing stress and temperature inmuscles, spinal cord or bones [26, 27].

3.4.3 Other applications

Due to good mechanical properties of the amorphous wires, such as tensile strength, theycan be used for reinforcement of composites or as material for cutting utensils. In addi-tion, it was observed that amorphous wires added in polymer matrix composites shows aclear reinforcement effect. That can be utilized, for example, in tyres to improve their sus-tainability [16]. Another example is silicons microwires, which have been used in solar

30

cells [28].

31

4 SQUID MAGNETOMETER

A superconducting quantum interference device (SQUID magnetometer, "Cryogenic S700X")was used to measure the static magnetic properties of the studied microwires in the cur-rent thesis. SQUID can be used in a variety of fields including geophysics, materialsscience, astronomy and biomagnetism [29]. SQUID magnetometer is the most sensitiveequipment available up to date for magnetic properties measurements [30].

Figure 14. The "Cryogenic S700X" SQUID magnetometer, which has three main components(from left to right): cryostat, electronics rack and computer.

32

"Cryogenic S700X" SQUID magnetometer can detect 10−6 flux quanta variations in mag-netic flux. Magnetic field up to 7 T can be achieved using a superconducting magnet.Temperature of the sample can be varied continuously from 1.6 K to 400 K.

There exist several operation modes, however, the measurements were conducted usingonly one mode, which is called extraction magnetometry. This is the most widely usedmode, which records total magnetic moment of the sample. The sample is moved throughthe set of superconducting pick-up coils, which detect a magnetic flux. Compared toother extraction magnetometers this is a significant advantage as the pick-up coil systemproduces the electric DC/AC signal based on the magnetic flux Φ, not the changes in the

fluxdΦ

dt. Therefore, it is not necessary to move the sample with a high speed through the

pick-up coil system.

The distance of a sample moving up and down through the pick-up coils can be var-ied from 2 to 120 mm. For all of the measurements the distance was set to be 40 mm.All of the measurements are conducted in a short-circuit mode of the superconductingsolenoid. All of the measurements were carried out using direct current (DC) measure-ments, meaning DC current is used to generate magnetic field. In DC measurements theapplied magnetic field is quantized and can have only strictly fixed values during a scan.In order to detect magnetic hysteresis it is essential to have fixed values of the appliedmagnetic field during the scans [30].

4.1 Working principle

The SQUID magnetometer converts magnetic flux into electrical voltage. The SQUIDmagnetometer is based on the Josephson and field quantization effects. The SQUID mag-netometer has a superconducting ring with two very narrow pieces of insulator, calledJosephson junctions, parallel to each other as shown in Figure 15 [31].

Josephson effect is a quantum tunneling effect where the superconducting current (Cooperpairs) is able to tunnel through the Josephson junctions. Electrons posses wave properties.In the ring electrons are divided equally into two branches and when those branches meetagain electrons converge. If there is no applied field they will meet on the other side ofthe ring without any phase difference. When magnetic field is applied to the system, itwill induce superconducting current in the circuit. This circulating current will add to thebias current flowing through one of the junctions and subtract from that flowing throughthe other junction. As a result, the branches have no more the same current and there will

33

Figure 15. Schematic illustration of SQUID magnetometer working principle [31].

be some phase difference [29].

4.2 Structure of the SQUID magnetometer

The whole system can be divided into three main parts, which are the cryostat, the elec-tronic rack and the computer. The cryostat is liquid helium reservoir with variable tem-perature insert (VTI) in it. All the electronics components are stored in the rack. Themagnetometer is controlled using a computer via the LabVIEW software [30].

34

4.3 The recondensing cryostat and insert system

The recondensing cryostat with the VTI in it is shown in Figure 16. The cryostat hasan outer aluminium shell. The shell contains the liquid helium reservoir with VTI, thecryocooler and the recondensing loop system. The liquid helium reservoir has a thermalradiation shielding. Volume of the reservoir is 40 liters and it is fabricated from weldedaluminium with the neck and tail sections made from glass fibre composite. The cry-ocooler is located at the top of the cryostat and it provides the cooling power for thesystem. The cryocooler liquefies helium gas using the recondensing loop. It is crucial tomaintain low temperatures in the system in order to preserve superconducting parts in asuperconducting state and prevent undesirable helium gas boil off. The cryostat also hasa Mu metal shielding to prevent ambient magnetic fields like the Earth’s magnetic fieldpenetrating into the system.

The VTI houses superconducting magnet and pick-up coils. Sample space is also in theVTI. The sample is inserted and removed via airlock, which is located at the top of theVTI. The sample is attached to a rod, which is used to lower the sample to the level wherethe pick-up coils are located. Stepper motor, which is also located at the top of the VTI,is used to move the rod (and the sample) vertically through the pick-up coils during themeasurements [30].

4.4 The magnet

Schematic illustration of the superconducting magnet is shown in Figure 17. It can gen-erate magnetic field up to 7 T. The generated field is highly homogeneous and has lowdrift. The whole magnet can be divided into internal and external parts. The internal partgenerates the bulk of the magnetic field. The external part minimizes stray fields and itfine-tunes homogeneity of the axial magnetic field.

To change the value of the magnetic field it is needed to change the value of the currentin superconducting magnet. This can be done by driving the superconducting bridge to anormal state, where the current can no longer flow without resistance. The change to thenormal state can be achieved using a heater. Once the current is changed and stabilized,the system can be driven back to the superconducting state by switching off the heater.In the superconducting state the current can flow without any losses, therefore it is notrequired to apply current to the system [30].

35

Figure 16. The structure of the recondensing cryostat [30].

4.5 Temperature control of the VTI

Schematic illustration of the VTI is shown in Figure 18. Liquid helium moves through aneedle valve, which causes a very sharp drop of the pressure cooling down and vaporizingthe helium. As the cold helium gas passes through a heat exchanger, it is warmed to thedesired temperature before entering a sample chamber. Auxiliary heater, which is located

36

Figure 17. Schematic illustration of the magnets [30].

in the sample chamber, is also used to support the heating. There are two thermometers tomonitor the temperature. Thermometer A is located at the heat exchanger and monitorsthe temperature of the helium gas entering to the sample chamber. Thermometer B is posi-tioned just above the sample and once the thermal equilibrium is reached the temperaturegiven by the thermometer B is the same as the temperature of the sample [30].

4.6 Superconducting detection system

Superconducting pick-up coil detect magnetic flux. It is located outside of the samplechamber in the middle of the magnet as shown in Figure 17. The pick-up coil is partof a flux transformer, which is connected to input coils of the SQUID detection system.

37

Figure 18. Schematic illustration of the VTI [30].

Due to quantum effects the flux changes cause a voltage change. The SQUID detectoris positioned above the magnet and it is shielded by a niobium can. The niobium can isshielding the SQUID detector from environmental noises and stray fields from the magnet.The SQUID measures relative changes in magnetic flux, therefore it is needed to movethe sample through the pick-up coils. This induces a screening current to flow in theflux transformer circuit, which opposes the resultant change in flux through the pick-upcoil. This current is detected by the SQUID and it is proportional to the induced magneticmoment. In the SQUID electronics the output voltage is directly proportional to the signal,which is detected by the SQUID detector [30].

4.7 Electronic rack

The electronic rack, shown in Figure 14 consist of several parts, which are from top tobottom [30]:

38

• Temperature Controller: Controls the temperature of the VTI heat exchanger andmonitors the thermometers.

• Level gauge and DC SQUID interface: Measures helium level in the liquid heliumreservoir. SQUID output available via a BNC connector and displayed on the panelmeter.

• Stepper motor controller: Controls the sample positioning within the pick-upcoils.

• Data acquisition unit/Valve block indicator panel: Controls all digital and ana-logue outputs and inputs apart from the temperature controller and magnet powersupply. Green LED of the front panel indicates that the computer is properly con-nected and red LED indicates power to the data acquisition unit. Front panel alsohas a schematic illustration of the helium circuit including electrically controlledvalves. Red LED indicates that the valve is closed and green LED that the valve isopen.

• Computer: Controls multiple electronic systems and runs the S700X software.

• Superconducting Magnet Power supply/Controller: Controls the current in thesuperconducting magnet.

• Mains power ON/OFF and Valve block: Houses electronically controlled valveswhich operate gas systems and also a pressure gauge for the VTI.

• Electronic filter unit and power supplies: Houses the electronic filtering circuitsfor all of the electrical services, which are connected to the insert, the power sup-plies for the VTI heaters, and SQUID/magnet detection circuit

39

5 EXPERIMENTS

The samples studied in the current thesis were Fe75Si10B15 amorphous glass-coated mag-netic microwires. The wires were fabricated using the glass-coated melt spinning method,described in details in Section 3.3.4. In total, three samples with different total diameter(D) and diameter of the nucleus (d) were studied. Diameters of the samples, length of thesamples (L), and ratios of nucleus diameter to total diameter (d/D) are presented in Table2.

Table 2. Dimensions of the Fe75Si10B15 microwire samples

Sample D (µm) d (µm) L (mm) d/D1 19.4 6.8 6.0 0.35052 26.8 10.8 5.4 0.40303 27.3 14.0 5.8 0.5128

5.1 Description of experiments

The sample was attached to a copper wire using a Teflon tape (PolytetrafluoroethylenePTFE) as shown in Figure 19. The copper wire was attached to a rod in order to place thesample in the SQUID magnetometer.

Figure 19. The sample attached to a copper wire using PTFE tape.

Magnetic hysteresis loop measurements for all three samples were performed at 10, 40,70, 100 and 300 K. The magnetic field range was ± 50 mT. All samples were firstly mea-sured with glass coating and then without. The glass coating was removed mechanicallyby placing the sample between two microscope slides and carefully pressing the slides.

40

6 RESULTS AND DISCUSSION

In this chapter magnetic measurement results for each sample are introduced and dis-cussed. Comparison for all of the three samples at 10 K is presented. Possible futurework is also discussed at the end of this chapter.

6.1 Sample 1

Hysteresis loops of sample 1 with glass coating (d = 6.8 µm, D = 19.4 µm, d/D = 0.3505,L = 6.0 mm) at 10, 40, 70, 100 and 300 K are presented in Figure 20. Figure 20b isan enlargement of Figure 20a to get a closer look at the hysteresis loops. Magnetic fieldvalues given in the units of T are on the x-axis and values of magnetization given inarbitrary units (a.u.) are on the y-axis. The hysteresis loops for each temperature arenormalized by dividing the measured magnetization values by the maximum value ofmagnetization. However, there were magnetization fluctuations in magnetic fields closeto the maximum measured value. Therefore, the maximum value used to normalize thedata was taken just before the noisy parts.

The hysteresis loops at all measured temperatures have somewhat rectangular shapes. Therectangular shape indicates magnetic bistability of the wires, which originates from thespecific magnetic domain structure. The unique domain structure is a result of stressesinduced in the fabrication process, which in this case was the glass-coated melt spinningmethod [32]. The domain structure, which causes magnetic bistability is observed inmaterials with positive values of magnetostriction coefficients, as described in Section3.1.1.

It can be seen from the Figure 20b that the squareness of the hysteresis loops increasesas the values of temperature gets higher. The squareness is a consequence of the magne-tization reversal of the axial magnetic domain. The increase of the squareness indicatesgrowth of axial magnetization meaning at higher temperatures the axial magnetizationis larger. The saturation magnetization increases with temperature increase. The systemaims to minimize magnetostatic energy, which is the origin of closure domains. In thiscase, the magnetostatic energy is decreasing with temperature decrease. This leads todecrease of the volume of the closure domains [32].

As can be seen from Figure 20, coercive field is independent on temperature. This also

41

(a) Hysteresis loops of sample 1

(b) Enlargement of hysteresis loops of sample 1

Figure 20. Hysteresis loops of sample 1 with the glass coating (d = 6.8 µm, D = 19.4 µm, d/D =0.3505) at 10, 40, 70, 100 and 300 K.

indicates that preferential magnetization mechanism and domain structure are the same[32].

Figure 21 shows the same hysteresis loops of glass-coated sample 1 as in Figure 20, how-ever, here relative magnetization is normalized by the maximum value of magnetization

42

achieved at T = 10 K. Figure 21 shows that at 300 K the saturation takes place already atvery small fields. This indicates sudden switching from one stable state to another. Sat-uration magnetic field at 10 K is much higher than at 300 K. Such behaviour is commonfor ferromagnetic materials.

Figure 21. Hysteresis loops of sample 1 with glass coating (d = 6.8 µm, D = 19.4 µm, d/D =0.3505) at 10, 40, 70, 100 and 300 K normalized by Ms at 10 K.

Hysteresis loops of sample 1 after glass coating removal at 10, 40, 70, 100 and 300 K arepresented in Figure 22. Figure 22b is an enlargement of Figure 22a to get a closer lookat the hysteresis loops. Hysteresis loops are normalized the same way as in Figure 20 forthe same sample before glass coating removal.

After glass coating removal the shape of the loops changes significantly for all measuredtemperatures. As can be seen from Figure 22, the magnetic bistability vanishes after theremoval of the glass coating. The disappearance of the magnetic bistability is a resultof partially reduced stress caused by the removal of the glass coating. Interface betweenmetallic nucleus and glass coating has a significant amount of thermoelastic tensile stress,which is caused due to difference in thermal expansion coefficients of metallic nucleusand glass coating. As the glass coating is removed, the stress is released to some extentchanging the internal stress distribution [33]. Changes of internal stress distribution af-fects the domain structure. The volume of the axially magnetized domain decreases andthe volume of periphery domains increases [32].

43

(a) Hysteresis loops of sample 1 without glass coating

(b) Enlargement of hysteresis loops of sample 1

Figure 22. Hysteresis loops of sample 1 after glass coating removal at 10, 40, 70, 100 and 300 K.

Coercive field becomes temperature dependent after removal of the glass coating. Thisindicates that the domain structure and preferential magnetization mechanism are not any-more similar. The domain wall no longer propagates easily through the sample, insteadof that the magnetic moment vectors begins to rotate with the applied magnetic field.Coercive field values increases as the temperature decreases. This may be a result fromthermal expansion resulting an increase of axial magnetization or decrease of radial mag-

44

netization [32].

In Figure 23 hysteresis loops normalized by magnetic saturation Ms value at 10 K arepresented for sample 1 after removal of the glass coating. Ms is a maximum value ofmagnetization, which is achieved when magnetization is no longer increasing despite ofthe increase of the magnetic field. Like hysteresis loops normalized by Ms 10 K forsample 1 with the glass coating in Figure 21, also loops for sample without the glasscoating shows saturation drop with temperature decrease.

Figure 23. Sample 1 after removing the glass coating (d = 6.8 µm) at 10, 40, 70, 100 and 300 Knormalized by Ms at 10 K.

In Figure 24 normalized hysteresis loops are presented for sample 1 at 10 K before andafter the removal of the glass coating in order to investigate the influence of the glass coat-ing removal. The main visible difference between the loops observed in Figure 24 is theshape difference. Magnetic bistability state vanishes with the removal of the glass coating.Hysteresis loop of sample 1 without the glass coating is broader, meaning coercivity in-creases with glass coating removal. The remanent magnetization gets considerably lowervalues for sample without the glass coating. Sample with the glass coating saturates atrelatively low field compared to sample without glass coating and has bigger squarenesscoefficient (see Table 3). Saturation magnetization is higher for sample with the glasscoating.

45

Figure 24. Sample 1 at 10 K with and without the glass coating.

6.2 Sample 2

Normalized hysteresis loops of sample 2 with glass coating (d = 10.8 µm, D = 26.8 µm,d/D = 0.4030, L = 5.4 mm) at 10, 40, 70, 100 and 300 K are presented in Figure 25.Figure 25b is an enlargement of Figure 25a.

It can be observed from Figure 25a that hysteresis loops have rectangular shapes at allmeasurement temperatures indicating initial magnetic bistability [32]. The same be-haviour was observed with sample 1 as rectangular hysteresis loops are typical for glass-coated Fe-based microwires [34]. This is possible due to unique magnetic domain struc-ture, which is also exhibited by sample 1.

The enlarged Figure 25b gives a closer look of squareness of the loops and coercive fields.The squareness of the loops increases with higher values of temperature meaning that thesample begins to show saturation at lower fields. Saturation magnetization increases withtemperature increase. Coercive fields shows only little evidence of temperature depen-dence as the coercivity does not increase much with decrease of temperature. In facttemperatures 10 K and 40 have the same coercive field values.

Figure 26 Shows hysteresis loops of sample 2 with the glass coating for whole range ofmeasurement temperatures normalized by Ms at 10 K. Level of saturation decreases astemperature decreases. Same behaviour was observed with sample 1. This is characteris-

46

(a) Hysteresis loops of sample 2 with the glass coating

(b) Enlargement of hysteresis loops

Figure 25. Hysteresis loops of sample 2 with the glass coating (d = 10.8 µm, D = 26.8 µm, d/D= 0.4030) at 10, 40, 70, 100 and 300 K.

tic behaviour for ferromagnetic materials.

Hysteresis loops of sample 2 after removing the glass coating for the whole range of mea-surement temperatures are presented in Figure 27. Figure 27b is an enlargement of Figure27a. Behaviour exhibited by sample 1, losing the rectangular shape of hysteresis loops

47

Figure 26. Sample 2 with glass coating (d = 10.8 µm, D = 26.8 µm, d/D = 0.4030) at 10, 40, 70,100 and 300 K normalized by Ms at 10 K.

after removal of the glass coating indicating disappearance of bistable state, is observedalso for sample 2 after the glass coating removal. This is also a result of changes in in-ternal stress distribution caused by the partial reduction of stresses by removing the glasscoating. The changes in internal stress distribution leads to changes in magnetic domainstructure decreasing volume of the axial domain and increasing volume of the peripherydomains.

Coercive field values are increasing with the decrease of temperature. Coercivity increasesat all measurement temperatures compared to results before glass coating removal (seeTable 3). This indicates that preferential mechanism of magnetization reversal changesfrom the high speed magnetic domain wall propagation through the wire to rotation ofmagnetic moment vectors with the applied external magnetic field.

Figure 28 is a comparison normalized by Ms at 10 K. Saturation drops with the tempera-ture. This observation is in the line with results observed with sample 1.

Figure 29 shows hysteresis loops of sample 2 before and after glass coating removalat 10 K. Before glass coating removal sample shows magnetic bistability. The bistablestate is lost after glass coating removal, due to changes in magnetic domain structurecaused by partial stress reduction. More precisely, volume of axial domain decreases andperiphery domains increases. Squareness coefficient is bigger for sample before glass-

48



Figure 27. Hysteresis loops of sample 2 after removing the glass coating at 10, 40, 70, 100 and300 K.

coating removal. Saturation magnetization values are higher for sample with the glasscoating. Coercivity increases with the glass coating removal.

49

Figure 28. Sample 2 after removing the glass coating (d = 10.8 µm) at 10, 40, 70, 100 and 300 Knormalized by Ms at 10 K.


6.3 Sample 3

Normalized hysteresis loops of sample 3 with glass coating (d = 14.0 µm, D = 27.3 µm,d/D = 0.5128, L = 5.4 mm) at 10, 40, 70, 100 and 300 K are presented in Figure 30.Figure 30b is an enlargement of Figure 30a.

50

As can be observed from Figure 30a hysteresis loops of the third sample are rectangularfor the whole range of measurement temperatures indicating magnetic bistability. Sameobservations were done with the first and second sample. This is also caused by the sameunique magnetic domain structure. Remanent magnetization increases with the increaseof temperature.

One can observe from the enlarged Figure 30b that coercivity differs between the tem-peratures. A little increase of coercivity is observed with increase of temperature. How-ever, all the coercive field values are very close to each other. Therefore, the preferentialmagnetization mechanism and domain structure can be considered to be the same. Thismeans that magnetization reversal happens with high speed propagation of the domainwall through the entire wire.

Hysteresis loops of sample 3 after removing the glass coating for the whole range ofmeasurement temperatures are presented in Figure 31. Figure 31b is an enlargement ofFigure 31a.

The shape difference of hysteresis loops observed in Figure 31a compared to ones withglass coating presented in Figure 30a is well visible. The loops in Figure 31a are broaderloops with smaller squareness coefficients (see Table 3). One key observation is that thesample preserves the bistable state after the removal of the glass coating unlike the firstand second samples. This is observed most clearly at higher temperatures and bistabilitybegins to fade away with the decrease of temperature. Bistable state indicates similarmagnetic domain structure, which is exhibited by all of the samples before the glass coat-ing removal.

The squareness increases with the increase of temperature. Coercive field achieves highervalues with decrease of the temperature. The coercive field also gets higher values com-pared to the same sample before the glass coating removal. This fact indicates some minorchanges in magnetic domain structure. These changes are a result of the small changesin internal stress distribution, which is caused by the removal of the glass coating. Thechanges causes small movement of the domain wall between axially magnetized domainand periphery domains. The volume of the axially magnetized core decreases a little andperiphery areas volume increases, respectively. Also the volume of the closure domainsincreases. This change can be considered insignificant in terms of changing the wholedomain structure drastically causing the disappearance of the bistable state [32, 35]. Itis worth to mention that sample 3 has the biggest nucleus diameter out of the studiedsamples and also the biggest d/D ratio.

51

(a) Hysteresis loops of sample 3 with the glass coating


Figure 30. Hysteresis loops of sample 3 with the glass coating (d = 14.0 µm, D = 27.3 µm, d/D= 0.5128) at 10, 40, 70, 100 and 300 K.

Figure 32 shows hysteresis loops of the third sample before and after glass coating re-moval at measurement temperature 10 K. The Figure 32 illustrates well the transforma-tion of the hysteresis loop from a narrow to a broader one as the glass coating is removed.The sample before glass coating is in a bistable state. After the glass coating removalthe bistable state is still preserved to some extent. The switching field is higher after the

52



Figure 31. Hysteresis loops of sample 3 after removing the glass coating at 10, 40, 70, 100 and300 K.

glass coating removal. Hysteresis loop of the sample without the glass coating has lowervalues for remanent magnetization compared to one with the glass coating and squarenesscoefficient is also smaller.

53


6.4 Comparison between the samples

Normalized hysteresis loops of all three samples with glass coating (d1 = 6.8 µm, D1 =19.4 µm, d1/D1 = 0.3505; d2 = 10.8 µm, D2 = 26.8 µm, d2/D2 = 0.4030; d3 = 14.0 µm,D3 = 27.3 µm, d3/D3 = 0.5128) at 10 K are presented in Figure 33. Figure 33b is anenlargement of Figure 33a. Loops are very narrow in general, which indicates that thematerial can be classified as a soft ferromagnet. The softer the magnet is, the easier it isto change the sign of magnetization [36].

All three samples have rectangular hysteresis loops, which is common for Fe-based mi-crowires covered with glass coating. This indicates that magnetic bistability is exhibitedby each wire at low temperatures, which in this case was 10 K.

The coercive field values differs slightly between the samples. The field value is thesmallest for the third sample with just a small difference compared to the second sample.The first sample has the biggest coercive field value. The first sample has the smallestnucleus diameter and in comparison the third sample has the biggest nucleus diameter.In conclusion the coercivity increases with the decrease of the nucleus diameter. Also asthe ratio of d/D increases, the coercivity decreases. The ratio of d/D influences on theamount of internal stress, which can be seen as the consequence of different coercive fieldvalues. Increase of the ratio d/D decreases internal stresses. The broader the hysteresisloop is the harder the magnet is considered to be. In other words, the increase of the ratio

54

(a) Hysteresis loops of all samples with the glass coating


Figure 33. Comparison between all of the samples with the glass coating at 10 K

d/D softens the magnet [37].

It is worth to emphasize that length also effects the properties of the wires. The effect oflength is more significant for thicker wires. However, the effect of length is not consideredin more detail in the current thesis.

55

Normalized hysteresis loops of all three samples after removing the glass coating at 10 Kare presented in Figure 34. Figure 34b is an enlargement of Figure 34a.

(a) Hysteresis loops of all samples without the glass coating


Figure 34. Comparison between all of the samples (d1 = 6.8 µm; d2 = 10.6 µm; d3 = 14.0 µm)after the removal of the glass coating at 10 K

From the enlarged Figure 34b one can observe that coercivity is highest for sample 1and smallest for sample 3. Coercivity is bigger for samples with smaller nucleus radius.

56

For amorphous materials increase of magnetic field amplitude or frequency is known toincrease coercivity [37].

As a summary, coercive field (Hc), remanent magnetization (Mr) and saturation magne-tization (Ms) values of each sample with and without glass coating are listed in Table 3.Also the squareness coefficients SQ = Mr/Ms are calculated for each sample with theirrespective temperatures.

Table 3. Coercive field (Hc), remanent magnetization (Mr), saturation magnetization (Ms), andsquareness coefficients (SQ) of each sample at each measuring temperature.

Sample Glass T (K) Hc (mT) -Hc (mT) Mr (a.u.) Ms (a.u.) SQ = Mr/Ms

1 Yes 10 0.250 0.250 0.8865 0.9998 0.886740 0.250 0.250 0.9136 0.9992 0.914370 0.250 0.250 0.9247 0.9992 0.9254100 0.250 0.250 0.9402 1.0000 0.9402300 0.250 0.250 0.9745 0.9996 0.9749

No 10 1.154 1.164 0.3177 0.9891 0.321240 1.001 0.998 0.3246 0.9927 0.327070 0.925 0.924 0.3342 0.9932 0.3365100 0.862 0.859 0.3563 0.9997 0.3564300 0.465 0.465 0.5136 0.9961 0.5156

2 Yes 10 0.170 0.189 0.7254 0.9997 0.725640 0.170 0.189 0.7330 0.9994 0.733470 0.130 0.150 0.7527 0.9963 0.7554100 0.130 0.189 0.7773 0.9996 0.7776300 0.070 0.130 0.8573 0.9993 0.8579

No 10 0.247 0.270 0.1922 0.9993 0.193640 0.208 0.206 0.1941 0.9943 0.195270 0.183 0.202 0.2144 0.9999 0.2144100 0.139 0.151 0.2356 0.9989 0.2359300 0.089 0.030 0.4327 0.9986 0.4333

3 Yes 10 0.030 0.043 0.4090 0.9964 0.410540 0.042 0.043 0.4270 0.9999 0.427070 0.029 0.029 0.4880 0.9988 0.4886100 0.028 0.068 0.5480 0.9998 0.5481300 0.086 0.050 0.8488 1.0000 0.8488

No 10 0.235 0.237 0.2219 0.9908 0.224040 0.149 0.233 0.2246 0.9935 0.226170 0.227 0.228 0.2376 0.9930 0.2393100 0.167 0.168 0.2405 0.9991 0.2407300 0.029 0.030 0.3960 0.9999 0.3960

57

6.5 Current study

In the study following results were observed to answer the objectives of the thesis:

• The removal of the glass coating had a significant effect on magnetic properties ofthe wire. The hysteresis loop shapes changed from rectangular to S-shaped. Thewires lost magnetic bistability or it was drastically weakened. These changes aredue to changes in magnetic domain structure.

• All of the samples followed the same trend: saturation decreased with the decreaseof temperature, meaning squareness of the loops increased with higher values oftemperature. Coercivity of the samples increased with the decrease of the tem-perature, excluding sample 1 before glass coating removal, which had coercivityindependent on temperature.

• Coercivity was stronger for samples (before and after glass coating removal) withsmaller nucleus diameter. Increase of the d/D ratio resulted to decrease in internalstress leading to decrease of the coercivity.

There exist some studies conducted on the same subject. Composition of the samples andmain goal of the study are close to this thesis. For instance [32] is close to this thesis. Themain results are mainly in line with the already existing studies.

6.6 Future work

There was some peculiar behaviour observed with samples 1 and 2, especially with sam-ple 2, after the glass coating is removed. The samples exhibit strange jump in the middleof the hysteresis loops at whole range of measurement temperatures. This would needsome further investigation as no clear explanation was found.

58

7 CONCLUSION

Magnetic properties of amorphous Fe-Si-B microwires were studied. Common trend ob-served in samples was that before the glass coating removal all samples had rectangu-lar hysteresis loops indicating magnetic bistability, which is desired property for severalsensing applications. The bistable state was observed due to the wires’ unique magneticdomain structure with axially magnetized core, radially magnetized periphery areas andclosure domains at the end of the wire. After the glass coating of microwires was re-moved samples had S-shaped hysteresis loops and they lost their bistable state due to apartial stress reduction. Exception for this was the third sample, which maintained rect-angular hysteresis loops preserving the bistable state. The preserved state of bistabilitywas strongest at high temperatures and gradually started to fade away with decrease ofthe temperature. It was also observed that nucleus diameter, d/D ratio and temperaturechanges had an influence on magnetic properties of the microwires by affecting coercivityand squareness of the loops.

59

REFERENCES

[1] A. Zhukov, M. Ipatov, P. Corte-León, L. Gonzalez-Legarreta, J.M. Blanco, andV. Zhukova. Soft magnetic microwires for sensor applications. Journal of Mag-

netism and Magnetic Materials, 498:166180, March 2020.

[2] A.P. Zhukov, M. Vázquez, J. Velázquez, H. Chiriac, and V. Larin. The remagnetiza-tion process in thin and ultra-thin Fe-rich amorphous wires. Journal of Magnetism

and Magnetic Materials, 151(1-2):132–138, November 1995.

[3] K. H. J. Buschow and F. R. de Boer. Physics of Magnetism and Magnetic Materials.Springer US, 2003.

[4] J. M. D. Coey. Magnetism and Magnetic Materials, page 1–23. Cambridge Univer-sity Press, 2010.

[5] Mathias. Getzlaff. Fundamentals of Magnetism. Springer-Verlag Berlin Heidelberg,Berlin, Heidelberg, 2008.

[6] Soshin Chikazumi. Physics of ferromagnetism. International series of monographson physics ; 94. Oxford University Press, 2nd ed. edition, 1997.

[7] Hanmin Jin and Terunobu Miyazaki. Magnetism of solids. In The Physics of Ferro-

magnetism, pages 97–173. Springer Berlin Heidelberg, 2012.

[8] Richard M. Bozorth. Concepts of ferromagnetism. In Ferromagnetism. IEEE, 2009.

[9] Tanja Graf, Claudia Felser, and Stuart S.P. Parkin. Simple rules for the understandingof heusler compounds. Progress in Solid State Chemistry, 39(1):1–50, May 2011.

[10] Michael Forrester and Feodor Kusmartsev. The nano-mechanics and magnetic prop-erties of high moment synthetic antiferromagnetic particles. physica status solidi (a),211(4):884–889, January 2014.

[11] Boris Livshitz and Jason S. Goldberg. Degaussing of write heads in perpendicularmagnetic recording. IEEE Transactions on Magnetics, 47(10):3403–3406, October2011.

[12] D.W. Collinson, K.M. Creer, and S.K. Runcorn. Methods in Palaeomagnetism:

Proceedings of the NATO Advanced Study Institute on Palaeomagnetic Methods,

Held in the Physics Department of the University of Newcastle upon Tyne, April

1–10, 1964. Elsevier Science, 2013.

60

[13] A Eschenlohr, M Battiato, P Maldonado, N Pontius, T Kachel, K Holldack,R Mitzner, A Föhlisch, P M Oppeneer, and C Stamm. Ultrafast spin transport askey to femtosecond demagnetization. Nature materials, 12(4):332–336, 2013.

[14] Faxiang Qin and Hua-Xin Peng. Ferromagnetic microwires enabled multifunctionalcomposite materials. Progress in Materials Science, 58(2):183–259, 2013.

[15] Hua-Xin Peng, Faxiang Qin, and Manh-Huong Phan. Domain structure and prop-erties of GMI materials. In Engineering Materials and Processes, pages 21–37.Springer International Publishing, 2016.

[16] H. Chiriac and T.A. Óvári. Amorphous glass-covered magnetic wires: Preparation,properties, applications. Progress in Materials Science, 40(5):333–407, January1996.

[17] Manh-Huong Phan and Hua-Xin Peng. Giant magnetoimpedance materials: Funda-mentals and applications. Progress in Materials Science, 53(2):323–420, February2008.

[18] K. Mohri, F.B. Humphrey, K. Kawashima, K. Kimura, and M. Mizutani. Largebarkhausen and matteucci effects in FeCoSiB, FeCrSiB, and FeNiSiB amorphouswires. IEEE Transactions on Magnetics, 26(5):1789–1791, 1990.

[19] J. Kravcák, L. Novák, and A. Zentko. Czechoslovak Journal of Physics, 52(2):175–178, 2002.

[20] Hua-Xin Peng, Faxiang Qin, and Manh-Huong Phan. Fabrication of ferromagneticwires. In Engineering Materials and Processes, pages 9–20. Springer InternationalPublishing, 2016.

[21] G. F. Taylor. A method of drawing metallic filaments and a discussion of theirproperties and uses. Physical Review, 23(5):655–660, May 1924.

[22] A. Zhukov. Design of the magnetic properties of Fe-rich, glass-coated microwiresfor technical applications. Advanced Functional Materials, 16(5):675–680, March2006.

[23] Y. Y. Zhao, H. Li, H. Y. Hao, M. Li, Y. Zhang, and P. K. Liaw. Microwires fabricatedby glass-coated melt spinning. Review of Scientific Instruments, 84(7):075102, July2013.

[24] I. W. Donald. Production, properties and applications of microwire and related prod-ucts. Journal of Materials Science, 22(8):2661–2679, August 1987.

61

[25] Katarína Draganová, Josef Blažek, Dušan Praslicka, and František Kmec. Possi-bile applications of magnetic microwires in aviation. Fatigue of Aircraft Structures,2013(5):12–17, August 2014.

[26] D. Kozejova, L. Fecova, P. Klein, R. Sabol, R. Hudak, I. Sulla, D. Mudronova,J. Galik, and R. Varga. Biomedical applications of glass-coated microwires. Journal

of Magnetism and Magnetic Materials, 470:2–5, January 2019.

[27] Veeradasan Perumal, N. Amil, N. Aiman, and U. Hashim. Fabrication and charac-terization of metal microwire transducer for biochip application. In RSM 2013 IEEE

Regional Symposium on Micro and Nanoelectronics. IEEE, September 2013.

[28] Morgan C. Putnam, Shannon W. Boettcher, Michael D. Kelzenberg, Daniel B.Turner-Evans, Joshua M. Spurgeon, Emily L. Warren, Ryan M. Briggs, Nathan S.Lewis, and Harry A. Atwater. Si microwire-array solar cells. Energy & Environ-

mental Science, 3(8):1037, 2010.

[29] John Clarke. Squid fundamentals. In SQUID Sensors: Fundamentals, Fabrication

and Applications, pages 1–62. Springer Netherlands, 1996.

[30] Cryogenic Limited. S700X SQUID Magnetometer USER MANUAL. CryogenicLimited.

[31] Antonio Palacios, John Aven, Patrick Longhini, Visarath In, and Adi R. Bulsara.Cooperative dynamics in coupled noisy dynamical systems near a critical point: Thedc superconducting quantum interference device as a case study. Physical Review

E, 74(2), August 2006.

[32] I. A. Baraban, A. V. Emelyanov, P. N. Medvedskaya, and V. V. Rodionova. Lowtemperature magnetic properties of amorphous ferromagnetic Fe–Si–B glass-coatedand glass removed microwire. Physics of the Solid State, 60(6):1158–1162, June2018.

[33] I. Baraban, L. Panina, A. Litvinova, and V. Rodionova. Effect of glass-removal onthe magnetostriction and magnetic switching properties in amorphous FeSiB mi-crowires. Journal of Magnetism and Magnetic Materials, 481:50–54, July 2019.

[34] V. Rodionova, I. Baraban, K. Chichay, A. Litvinova, and N. Perov. The stress com-ponents effect on the Fe-based microwires magnetostatic and magnetostrictive prop-erties. Journal of Magnetism and Magnetic Materials, 422:216–220, January 2017.

[35] M. Vázquez, A.P. Zhukov, K.L. García, K.R. Pirota, A. Ruiz, J.L. Martinez, andM. Knobel. Temperature dependence of magnetization reversal in magnetostrictive

62

glass-coated amorphous microwires. Materials Science and Engineering: A, 375-377:1145–1148, July 2004.

[36] A. Zhukov. Domain wall propagation in a Fe-rich glass-coated amorphous mi-crowire. Applied Physics Letters, 78(20):3106–3108, May 2001.

[37] A. Zhukov, M. Vázquez, J. Velázquez, A. Hernando, and V. Larin. Magnetic prop-erties of Fe-based glass-coated microwires. Journal of Magnetism and Magnetic

Materials, 170(3):323–330, June 1997.

63

List of Tables

1 Magnetic quantities with cgs and SI units [5]. . . . . . . . . . . . . . . . 10

2 Dimensions of the Fe75Si10B15 microwire samples . . . . . . . . . . . . . 39

3 Coercive field (Hc), remanent magnetization (Mr), saturation magneti-zation (Ms), and squareness coefficients (SQ) of each sample at eachmeasuring temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

64

List of Figures

1 Illustration of magnetic moments of different types of magnetic ordering [5]. 12

2 Illustration of magnetic flux inside of diamagnets [5]. . . . . . . . . . . . 13

3 Structure of a synthetic antiferromagnet [4]. . . . . . . . . . . . . . . . . 15

4 Illustration of a ferromagnetic hysteresis loop [4]. . . . . . . . . . . . . . 16

5 Illustration of hysteresis loops during demagnetization process [11]. . . . 17

6 Schematic illustration of domain structure of wire with positive magne-tostriction coefficient [15]. . . . . . . . . . . . . . . . . . . . . . . . . . 19

7 Schematic illustration of domain structure of wire with negative magne-tostriction coefficient [15]. . . . . . . . . . . . . . . . . . . . . . . . . . 19

8 Schematic illustration of the effect of glass coating removal on the mag-netic domain structure of the wire with positive value of λ. OS denotesouter shell and IC denotes inner core [15]. . . . . . . . . . . . . . . . . . 20

9 Schematic illustration of the effect of glass coating removal on the mag-netic domain structure of the wire with negative value of λ. OS denotesouter shell and IC denotes inner core [15]. . . . . . . . . . . . . . . . . . 21

10 Degree of the large Barkhausen effect from perfect to nonexistent [18]. . . 23

11 A cross-section illustration of microwire fabricating device using in-rotating-water spinning method [20]. . . . . . . . . . . . . . . . . . . . . . . . . 25

12 Schematic illustration of the glass-coated melt spinning method used formicrowire fabrication [23]. . . . . . . . . . . . . . . . . . . . . . . . . . 26

13 Schematic illustration of the melt extraction method used for microwirefabrication [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

14 The "Cryogenic S700X" SQUID magnetometer, which has three maincomponents (from left to right): cryostat, electronics rack and computer. . 31

65

15 Schematic illustration of SQUID magnetometer working principle [31]. . 33

16 The structure of the recondensing cryostat [30]. . . . . . . . . . . . . . . 35

17 Schematic illustration of the magnets [30]. . . . . . . . . . . . . . . . . . 36

18 Schematic illustration of the VTI [30]. . . . . . . . . . . . . . . . . . . . 37

19 The sample attached to a copper wire using PTFE tape. . . . . . . . . . . 39

20 Hysteresis loops of sample 1 with the glass coating (d = 6.8 µm, D = 19.4µm, d/D = 0.3505) at 10, 40, 70, 100 and 300 K. . . . . . . . . . . . . . 41

21 Hysteresis loops of sample 1 with glass coating (d = 6.8 µm, D = 19.4µm, d/D = 0.3505) at 10, 40, 70, 100 and 300 K normalized by Ms at 10 K. 42

22 Hysteresis loops of sample 1 after glass coating removal at 10, 40, 70,100 and 300 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

23 Sample 1 after removing the glass coating (d = 6.8 µm) at 10, 40, 70, 100and 300 K normalized by Ms at 10 K. . . . . . . . . . . . . . . . . . . . 44

24 Sample 1 at 10 K with and without the glass coating. . . . . . . . . . . . 45

25 Hysteresis loops of sample 2 with the glass coating (d = 10.8 µm, D =26.8 µm, d/D = 0.4030) at 10, 40, 70, 100 and 300 K. . . . . . . . . . . . 46

26 Sample 2 with glass coating (d = 10.8 µm, D = 26.8 µm, d/D = 0.4030)at 10, 40, 70, 100 and 300 K normalized by Ms at 10 K. . . . . . . . . . . 47

27 Hysteresis loops of sample 2 after removing the glass coating at 10, 40,70, 100 and 300 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

28 Sample 2 after removing the glass coating (d = 10.8 µm) at 10, 40, 70,100 and 300 K normalized by Ms at 10 K. . . . . . . . . . . . . . . . . . 49


30 Hysteresis loops of sample 3 with the glass coating (d = 14.0 µm, D =27.3 µm, d/D = 0.5128) at 10, 40, 70, 100 and 300 K. . . . . . . . . . . . 51

66

31 Hysteresis loops of sample 3 after removing the glass coating at 10, 40,70, 100 and 300 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52


33 Comparison between all of the samples with the glass coating at 10 K . . 54

34 Comparison between all of the samples (d1 = 6.8 µm; d2 = 10.6 µm; d3 =14.0 µm) after the removal of the glass coating at 10 K . . . . . . . . . . 55

Documents

Magnetic properties of amorphous Fe-Si-B glass-coated