Spin Hall-Magnetoresistancein FMI/NM/FMI-TrilayersDominik Bachelor... · in FMI/NM/FMI-Trilayers Dominik Irber ... realizable in everyday life as the fabricated one is quite diﬀerent

Technische Universität MünchenFakultät für Physik

Walther-Meißner-Institut für Tieftemperaturforschung

Bachelor’s Thesis in Physics

Spin Hall-Magnetoresistancein FMI/NM/FMI-Trilayers

Dominik Irber

Garching, 10 August 2013

Supervisor: Dr. Sebastian T.B. Goennenwein

First Reviewer (Supervisor): Dr. Sebastian T.B. Goennenwein

Second Reviewer: Prof. Dr. Christian Pfleiderer

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Spin Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 (Inverse) Spin Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Spin Hall Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 FMI|NM Heterostructures . . . . . . . . . . . . . . . . . . . . . . 62.3.2 Symmetric FMI|NM|FMI Heterostructures . . . . . . . . . . . . 8

2.4 Anisotropic Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . 9

3 Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1 Sample Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.2 Patterning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Thickness Dependent Measurements . . . . . . . . . . . . . . . . . . . 164.3 Inverse Bilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3.1 GGG|Pt|YIG Inverse Bilayer . . . . . . . . . . . . . . . . . . . . 184.3.2 YAG|Pt|YIG Inverse Bilayer . . . . . . . . . . . . . . . . . . . . 21

4.4 YAG|YIG|Pt|YIG Trilayer . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.1 Further Analysis Steps . . . . . . . . . . . . . . . . . . . . . . . . 345.2.2 Asymmetric FMI|NM|FMI Heterostructures . . . . . . . . . . . . 35

A Samples and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

iii

Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

iv

Chapter 1

Introduction

Figure 1.1: “I guess there’ll always be a gap between science and technology.”Taken from [1].

Fig. 1.1 shows a scene during the Stone Age, when a man tries to fabricate a wheel.At that time, the obviously new scientific development of the wheel was hardlyrealizable in everyday life as the fabricated one is quite different from the theorydrawing on the wall.

This illustrates, that the step from fundamental research to a broad applicationhas always been difficult. The computer is a good up-to-date example. On the onehand, all electronic components for data processing, are based just on the chargeas degree of freedom. The transport and manipulation of charge is quite an “old”technology. On the other hand, many components for storing data for a longer time,i. e. without permanent power supply, are based on the spin as degree of freedom.Early hard drives used the anisotropic magnetoresistance (AMR)[2] for disk readheads. With the introduction of the giant magnetoresistance (GMR)[3] “in around1997, storage capacities have increased approximately 100 times. The introductionof GMR sensors into HDDs was particularly fast because magnetoresistive sensorsbased on the [...] AMR had paved the way.”[4] But nevertheless, the step fromdiscovery to application took almost ten years. Current development is alreadybeyond the GMR, implementing read heads using the tunneling magnetoresistive

1

Chapter 1 Introduction

effect (TMR)[5, 6].

To sum up the actual situation, either the dynamic properties of charge or thestatic properties of spins are used in technology. Hence, another step to “increaseddata processing speed, decreased electric power consumption, and increased integra-tion densities compared with conventional semiconductor devices”[7] is the combi-nation of both the charge degree of freedom and the spin one. This research areais known as spintronics, which deals with the conversion of spin into charge infor-mation and vice versa, too. Commonly used effects, converting charge currents inspin currents and vice versa, are the spin Hall effect (SHE)[8, 9] and the inversespin Hall effect (ISHE)[10]. A recently discovered new effect is the spin Hall magne-toresistance [11–13], occurring in hybrids consisting of a normal metal (NM) on topof a ferro-/ferrimagnetic insulator (FMI), where “the resistance of a normal metalis influenced by the magnetization in the insulating magnet [attached to the normalmetal] even though non of the charge current is able to pass through the magnet”[14].This is a huge difference compared to other magnetoresistive effects like AMR, GMRor TMR. Therefore, “it enables direct electrical sensing of the magnetization in in-sulating magnets”[14] and studying “spin Hall effects in paramagnetic metals as wellas spin transfer to magnetic insulators via simple d.c. magnetoresistance measure-ments.”[12]

Another possible application of the SMR are spin valves [15, Ch. 6], in which theresistivity of the device is controlled magnetically by manipulating the spin currentflow with respect to the spin polarization. The SMR is interesting for spin valvesbecause of the conductive layer not having to be magnetic. However, conventionalSMR bilayers (substrate|FMI|NM hybrids) exhibit a very small effect amplitude.Therefore, trilayers (substrate|FMI|NM|FMI hybrids) are an interesting step towardsa technological application because theory predicts an SMR amplitude being morethan twice that of the bilayers’ [11].The arising question is, whether in some years the SMR will become as usual as theGMR is - or the wheel.

This bachelor thesis deals with the analysis of the SMR in trilayers. In chapter 2,the basics for the understanding of the SMR effect are summarized.In chapter 3, first a short summary of the sample growth process is given, which istopic of another bachelor thesis [16]. Then the process of preparing heterostructuresfor transport experiments is described shortly and at the end of this chapter, theexperimental set-up is explained, in which the data were taken.In the most important chapter 4, the obtained data are presented and discussed,considering several effects, which may give rise to deviations from theory.Finally, in chapter 5 a summary of the results is given. Afterwards, some topics arementioned which are of greater interest but not being covered by this thesis.

2

Chapter 2

Theoretical Background

2.1 Spin Currents

For the discussion of the SMR effect, spin currents are very important, as the SMRoccurs due to the interconversion of charge currents into spin currents and vice versa.Therefore a short introduction to spin currents is given in this section.In part (a) of Fig. 2.1, the very well known charge currents Jq = (J↑ + J↓) are

shown, with J↑ being the current, which represents all electrons with spin up, andJ↓ the current with spin down electrons (in a two spin channel model). In chargecurrents all electrons flow in the same direction, whereas the transported spins ofthe electrons are equally distributed to spin up or spin down. As a result, no netangular momentum is transported by pure charge currents.On the other hand, there are pure spin currents Js = − ~

2e(J↑−J↓) [17] (see Fig. 2.1c),which consist of particles carrying spins with different orientations, too, but flowingalso in opposite directions. Thus an effective transport of spin angular momentumarises while no effective charge is carried.Spin-polarized currents are a combination of Jq and Js. In this case, all charge

J↑

J↓

J↑

J↓

J↑

J↓

= = =Jq Jq

Js Js

(a) (b) (c)

Figure 2.1: Taken from [17]. (a) In a pure charge current, no angular momentum iscarried. (b) In a spin-polarized current there is a preferred orientation of spins, i. e.a net spin flow occurs. (c) For pure spin currents, charge carriers with different spinorientations move in different directions, so that the charge currents cancel each otherout.

3

Chapter 2 Theoretical Background

JqJs

Pt =N

s Jq

Pt =N

(a) (b)

Jsback

Figure 2.2: Taken from [12]. (a) Due to the spin Hall effect (SHE), a spin current Js,being perpendicular to the applied charge current Jq and the electron spin s, arises ina normal, paramagnetic metal (NM). (b) The inverse spin Hall effect (ISHE) convertsa spin current into a charge current.

carriers with same sign flow in the same direction but there is a preferred spinorientation which results in a non-vanishing spin transport.

2.2 (Inverse) Spin Hall Effect

As the SMR results of a combined action of spin Hall effect (SHE) and inverse spinHall effect (ISHE), both effects will be discussed briefly before presenting the SMR.In analogy to the ordinary Hall effect, which converts a charge current in anothercharge current perpendicular to the first one, the SHE converts a charge currentJq, applied to a normal paramagnetic material (NM), e. g. Platinum (Pt), to aperpendicular spin current Js [9]. Due to the nature of SHE the spins s of theelectrons contributing to Js are perpendicular to both, spin and charge current.

Js = αNM

(− ~

2e

)Jq × s (2.1)

αNM = σSHσ is the spin Hall angle, defined by the ratio of the spin Hall conductivity

σSH, which “has the side-jump contribution [...] and the skew-scattering contribu-tion”[18] (i. e. contributions due to spin dependent scattering) to the conductivity,and the electric conductivity σ. Therefore αNM gives information about the materialspecific conversion efficiency of the SHE.The SHE is caused by strong Spin-Orbit-Interaction (SOI) in paramagnetic materials,resulting in asymmetric scattering for different spin orientations (extrinsic SHE)[8].Another approach to explain SHE emanates from band structure details (intrinsicSHE)[19]. Therefore the SHE is independent of an applied external magnetic fieldand occurs even in the geometry shown in Fig. 2.2a. In analogy to the ordinary Halleffect, causing a charge accumulation perpendicular to the applied current (in opencircuit boundary condition), the SHE causes a spin accumulation at the surfaces ofa thin film sample, resulting in a gradient of the spin dependent chemical potentialµs along the direction of Js. Thus, in a simple picture electrons will be reflected at

4

2.3 Spin Hall Magnetoresistance

M ||

Jq

M

Jsback

´Pt =N

YIG=F

s M⊥

Jq

M

Jsback

Jsabs

´Pt =N

YIG=F

s(a) (b)

Figure 2.3: Taken from [12]. (a) When the magnetization M is parallel to the electronspin s, no angular momentum can be transferred. (b) Rotating M to a configurationperpendicular to s, angular momentum can be transferred, so that the spin is flipped.

the interface of the metal with vacuum because they can’t escape from the metaland also no angular momentum can be transferred into vacuum (open (spin current)circuit boundary condition). The reflected electrons are converted into a charge cur-rent via ISHE [10] again, which is oriented parallel to the original one. Hence, in thegeometry shown in Fig. 2.2, the SHE has no influence on the resistivity of the NM(when no spin-flips occur at the interfaces).


This behaviour changes when adding an adjacent insulating layer with intrinsic mag-netisation (ferromagnetic or ferrimagnetic insulator, FMI) like yttrium iron garnet(Y3Fe5O12, YIG). Now the boundary conditions for the electrons at the surfacePt|YIG still do not allow electrons to escape from the Pt-layer, but angular momen-tum can be absorbed as a spin-transfer torque (STT) in the ferrimagnet [11] (closed(spin current) circuit boundary condition). This means that the electrons spin isflipped and the magnetization of the YIG-layer compensates the change in angularmomentum by generating magnons.However, a STT is not possible if the magnetization of the YIG-layer1 is parallel tothe spin orientation of the electrons, that is parallel to t (cf. Fig. 2.4 and Fig. 2.3a).Rotating the magnetization direction m = M

|M| to a configuration perpendicularto s (such that m is perpendicular to both s and Jq, i. e. in a plane perpendicularto t) angular momentum can be transferred. As the electron spin is flipped, it willnot contribute to the original charge current via ISHE [10]. Therefore, the longitu-dinal resistivity of the Pt-layer increases, which is the spin Hall magnetoresistance

1from now on “YIG” and “FMI” are used synonymously referring to the sample layer, i. e. “YIG-layer”, same for “Pt” and “NM”

5


Figure 2.4: Taken from [13]. Anew Cartesian coordinate systemis defined by the unit vectors j,aligned with the direction of theapplied charge current, n, be-ing perpendicular to the surfaces,and t = n × j. The definitionfor the used measurement scheme(esp. Vlong) is also shown.

n

t

j

YAG (111)

Pt

YIG

Vlong

l

Iq

wVtrans

tPt

^

^

^

(SMR).2 The change in resistivity due to the SMR can be described by the followingequations, taken from [13]:

ρlong = ρ0 + ρ1m2t , (2.2)

ρtrans = ρ2mn + ρ3mjmt. (2.3)

where mi is the projection of the normalized magnetization onto the axis i. ρlong isthe measured specific resistivity3 of the Pt-layer along the Hall bar (cf. Fig. 2.4) andρ1 is the absolute amplitude of the SMR effect.4 It is important to note that thequite simple formulae (2.2) and (2.3) are just series expansions in α2

NM, i. e. thereare terms of higher order in α2

NM, which are neglected for the moment (see [11] forfurther details of this calculation).Another crucial point is the dependence on mi. In experiments, however, one

applies an external magnetic field H. Assuming that the magnetization is saturated,m is aligned to the external field, and the SMR is in fact independent of the mag-netization value. Thus, the H-orientation can be used for m.

2.3.1 FMI|NM Heterostructures

For a quantitative description of the SMR, the crucial value is −ρ1ρ0 . Chen etal. [11] developed a SMR theory starting with Ohm’s law for metals with Spin-Orbit-

2As this thesis mainly deals with the longitudinal resistivity-change, all phrases like SMR, magni-tude etc. refer to the longitudinal resistivities, etc.

3See Sec. 4.1, how the specific resistivity is calculated from the measured potential drop.4ρ1 < 0, i. e. the specific resistivity without SMR is ρ0 − ρ1

6


-180° -90° 0° 90° 180°

406.3406.4406.5406.6406.7

ρ long

(10-9

Ωm

)

α

-10010203040

ρ trans

(10-1

1 Ωm

)

-90° 0° 90° 180° 270°

406.3406.4406.5406.6406.7

ρ long

(10-9

Ωm

)

β

0

5

10

ρ trans

(10-1

1 Ωm

)

-90° 0° 90° 180° 270°

406.3406.4406.5406.6406.7

ρ long

(10-9

Ωm

)

γ

0

5

10

ρ trans

(10-1

1 Ωm

)

h||t h||-th||j h||t h||-th||n h||-j h||jh||n

1 T 1 T 1 T

ρlong

ρtrans

ρlong

ρtrans

ρlong

ρtrans

(a)

ip oopj oopt

(b) (c)

j

t

n

α

m

^

^

^

βm

j

t

n^

^

^

γ

m

j

t

n^

^

^

Figure 2.5: Taken from [13]. Expected dependencies of the longitudinal (black) andtransverse (red) resistivities on m for different rotation planes. The expected depen-dencies of the AMR (cf. Sect. 2.4) is shown by the dashed lines. (a) In in-plane (ip)configuration the magnetization is rotated in the film plane. A cos2(α)-dependenceis expected for the longitudinal resistivity, where α is the angle between j and m, asdefined in the graphic belonging to (a). (b) In out-of-plane configuration perpendicularto j (oopj), i. e. m is rotated around j, a cos2(β) dependence is expected, too. Here, βis the angle between n and m as illustrated in the graphic in (b). (c) In oopt geometrySMR theory predicts no dependence on the rotation of m.

Interaction5 and the spin-diffusion equation6 in normal metals to first calculate thespin diffusion process in a FMI|NM bilayer and the spin accumulation at the Ptsurfaces. The resulting formula, describing the longitudinal SMR magnitude, is

−ρ1ρ0

=α2NM

(2λ2NMρNM

)(tNM)−1Gr tanh2

(tNM2λNM

)1 + 2λNMρNMGr coth

(tNMλNM

) (2.4)

with the crucial parameters αNM the spin Hall angle, and λNM the spin diffusionlength in the NM, describing the mean free path for spins. ρNM is the specificresistivity of the NM (Pt for our samples), tNM the thickness of the NM-layer andGr is the real part of the spin mixing interface conductance [20], which describesthe spin transfer at the interface YIG|Pt via spin flips around the magnetization

5 jcjsxjsyjsz

= σ

1 αNMx× αNMy× αNMz×

αNMx× 1 0 0αNMy× 0 1 0αNMz× 0 0 1

−∇µ0/e−∇µsx/(2e)−∇µsy/(2e)−∇µsz/(2e)

,

“where µs = (µsx, µsy, µsz)T − µ01 is the spin accumulation, i.e. the spin-dependent chemical

potential relative to the charge chemical potential µ0, σ is the electric conductivity, αNM is thespin Hall angle.”[11]

6 ∇2µs = µsλ2

7


0 5 1 0 1 5 2 00

5 x 1 0 - 4

1 x 1 0 - 3

0 5 1 0 1 5 2 00 . 05 . 0 x 1 0 - 41 . 0 x 1 0 - 31 . 5 x 1 0 - 32 . 0 x 1 0 - 32 . 5 x 1 0 - 3

YY50

a

−1/

0

t P t ( n m )

λ= 1 . 4 5 n mαS H = 0 . 1 1 N M = 4 0 0 n Ω mG r = 4 x 1 0 1 4 Ω - 1 m - 2

YIG12

0a

( a )

Y I G | P t

T r i l a y e r Y I G | P t | Y I G

2 x B i l a y e r B i l a y e r

Y I G | P t

( b )

−1/

0

t P t ( n m )Figure 2.6: Dependence of the SMR amplitude at room temperature, using Eq. (2.4),on the thickness of the Pt-layer tPt for (inverse) bilayers (a) and trilayers (b). Inpanel (a) vertical lines indicate thicknesses of the samples discussed in Sect. 4.3. Theparameters used for calculations were obtained by simulations with experimental data[13].

conventionalbilayer

substrateFMINM

inversebilayer

substrate

FMINM

trilayersubstrate

FMI 1NM

FMI 2

Figure 2.7: Layer scheme of the used samples. Conventional bilayer means a sub-strate|FMI|NM hybrid, etc.

direction of the FMI. Equation (2.4) applies only in the limit of Gi << Gr with Gibeing the imaginary part of the spin mixing conductance.The SMR magnitude decreases with lower values for Gr and αNM and higher valuesfor λNM. −ρ1

ρ0is also sensitive to the thickness tNM of the NM. In Fig. 2.6a this

dependence is shown with typical values for the other parameters. The graph showsthat the largest SMR amplitude occurs at about two times λNM and goes to zero forinfinite thickness.

2.3.2 Symmetric FMI|NM|FMI Heterostructures

The theoretical step from bilayers to trilayers is not very big, at least with someassumptions.In asymmetric trilayers there are two FMI-layers with magnetizations M and M

′

being able to point into different directions (see Fig. 5.1). In the deduction for −ρ1ρ0the second boundary condition just has to be changed from open circuit (vacuum)to an m′ dependent one. However, this is quite a big step in the complexity of the

8

2.4 Anisotropic Magnetoresistance

calculations, so that a complete symmetric trilayer has been assumed first. Thatmeans, that both magnetizations are aligned with the external magnetic field, theirmagnetic properties (coercive field and saturation magnetization) are identical andboth interfaces FMI1|NM and NM|FMI2 are identical, too. This is (up to now -compare [16]) a quite idealistic assumption, just as the assumption that the NM isnot influenced by the growth of the second FMI-layer. Chen et al. [11] also deducedan equation for symmetric trilayers, which looks quite similar to the one calculatedfor FMI|NM bilayers (2.4).

−ρ1ρ0

=α2NM

(4λ2NMρNM

)(tNM)−1Gr tanh2

(tNM2λNM

)1 + 2λNMρNMGr tanh

(tNMλNM

) (2.5)

Considering the thickness dependence of −ρ1ρ0 , in a naive picture, a behaviour likethat of a bilayer with an amplitude twice as large is expected, since a symmetrictrilayer can be imagined as a stack of a “classic” FMI|NM bilayer with an inverseone (NM|FMI) on top, in a first approach. However, theory [11] (Fig. 2.6b) shows adifferent result for a thickness smaller than two times the spin diffusion length. Theamplitude is a bit larger than two times the bilayer one and the maximum is shiftedslightly to smaller values. For a larger thickness the simulation is in accordance withtwo times a bilayer. This is not surprising as the SMR is a surface effect and spinsaren’t able to cover this long distances. Therefore, both surfaces can be treated asindependent just like two bilayers in samples with large tPt.

2.4 Anisotropic Magnetoresistance

For the discussion of the results, it will be helpful to know some basic featuresof another type of magnetoresistance - the anisotropic magnetoresistance (AMR)[2].The AMR is a more typical magnetoresistance, for it just occurs when the conductivelayer is also magnetic like in the GMR[3] and the TMR[5, 6] in contrast to the SMR,where the magnetic layer is attached to the conductive layer. The origin for the AMRis again the spin-orbit-interaction, which can result in non-spherical-symmetricalorbitals [15]. Therefore, in Ohm’s law E = ρJ the resistivity is no more longer ascalar but a tensor [21]

ρ =

ρ‖ −ρH 0

ρH ρ‖ 0

0 0 ρ⊥

. (2.6)

Comparing the dependence on the magnetization of the AMR (2.7)7 with those forthe SMR (2.2), they appear at first glance very similar for a polycrystalline magnetic

7 Again, as in the corresponding equations for the SMR, there are higher-order terms, which areneglected.

9


metal. The AMR reads

ρlong = ρ0 + ∆ρm2j (2.7)

ρtrans = ρ2mn + ∆ρmjmt (2.8)

Actually, in ip-geometry (with m being in the plane of the magnetic thin film (seeFig. 2.5)) the distinction between SMR and AMR isn’t possible. Hence, out-of-plane-measurements are necessary because the SMR disappears at oopt, while the AMRdisappears at oopj rotations.Another subtle difference is ∆ρ > 0 (in conventional AMR), while ρ1 < 0 for theSMR. Thus, the resistivity due to AMR has a minimum for m ‖ n while the SMRhas a maximum.

10

Chapter 3

Experimental Techniques

3.1 Sample Fabrication

3.1.1 Growth

As F. Schade grew both inverse substrate|YIG|Pt bilayers and the YAG|YIG|Pt|YIGtrilayer for his bachelor thesis, we refer to his thesis [16] for a much more detailed de-scription. In this section just some fundamental differences between optimal growthconditions and the used ones will be summarized.In [22] ideal parameters were figured out to grow “normal” bilayers, i. e. sub-strate|FMI|NM hybrids. The YIG-layer was first grown in (111)-orientation on a(111)-oriented GGG or YAG substrate in an oxygen atmosphere1 of 25 µbar viapulsed laser deposition (PLD) at 550 C (GGG) or 500 C (YAG) as substrate tem-perature. Afterwards, the Pt-layer was deposited in-situ, i. e. without breaking thevacuum, via electron beam evaporation at room temperature, resulting in a polycrys-talline layer. This parameters were used by Althammer et al. [13] for their samples.For the growth of inverse bilayers, i. e. substrate|Pt|YIG (see Fig. 2.7), the param-eters for Pt remained unchanged. However, the YIG-layer on top of Pt was nowgrown in an argon atmosphere at 25 µbar but at a lower substrate temperature of450 C (YAG), which was figured out to fit best to an argon atmosphere to avoidoxidation of the Pt-layer [16]. The YIG growth conditions for conventional bilayersand for inverse bilayers thus are quite different.

3.1.2 Patterning

For transport experiments, a Hall bar structure was patterned in the plain multilayersample by first using photolithography2 and subsequent argon ion beam milling3.

1An oxygen atmosphere was used to avoid oxygen vacancies.2First, the sample was covered with the fotoresist AZ 5214E and put on a hot plate for 70 s at

110 C. Afterwards the resist was exposed to light of a mercury vapour lamp for 42 seconds anddeveloped in AZ 726 MIF developer for up to 40 seconds.

3It is very likely that the etching process even etched into the substrate, but due to unknownetching rates for YIG, no quantitative statement can be given.

11

Chapter 3 Experimental Techniques

During this process, the sample was cleaned with acetone p.a. and isopropanol p.a.several times.The resulting Hall bar has a length lHB of 1000 µm and a width w of 80 µm. Thedistance between the transverse pads along the Hall bar is 200 µm, so that the dis-tance covered by the Vlong measurement l is 600 µm (see Fig. 2.4).The finished samples were glued with GE-varnish4 on a block of copper5 which inturn is part of a chip carrier. The pads were connected to the carrier’s pads withaluminium wires via wedge bonding (cf. Fig. 4.5).

3.2 Experimental Setup

All data presented in this thesis were taken in the “Moria”-cryostat, an Oxford In-struments SM4000-8 cryostat. The magnetic field is generated by a superconductingsplit coil magnet, being able to generate fields up to µ0H = 7T at a coil temper-ature of 4K. The cryostat is cooled with liquid helium (He), and, to enhance thetemperature isolation, there is an outer tank with liquid nitrogen (N2). The cryostatis controlled via LabView based software.The sample is mounted on a dipstick (see Fig. 3.1), which is placed in a variabletemperature insert (VTI), being in the centre of the cryostat. The temperature inthe VTI (TVTI) is controlled by an Oxford Instruments Intelligent Temperature Con-trol (ITC) 503S, and can be regulated by the flow of helium through a needle valveand a heater. The samples were placed on a small block of copper, which in turnis thermally connected to the dipstick. Thus, after a thermalization process, thesample’s temperature corresponds to the dipstick temperature T , which was set bya LakeShore temperature controller (LS 304).The applied current Iq was supplied by a Keithley K2400 SourceMeter and the po-tential drops Vlong and Vtrans (cf. Fig. 2.4) were measured with Keithley K2182Nanovoltmeters. Each potential drop value was obtained by averaging of 10 singlemeasurements via an internal digital moving filter. The single measurements werein turn taken using the delta method6[23].The dipstick can be rotated around an axis perpendicular to the magnetic field witha stepper motor (Owis DMT 100), which is placed at the VTI top flange. Also thestepper motor was controlled via LabView based software.

For the ADMR measurements (angle dependent magnetoresistance) presented in this

4VGE-7031 varnish5about 9mm× 9mm× 3mm6The method records the voltages V1 and V2 for two currents with equal magnitude but differ-ent directions being applied along the Hall bar (DC current-reversal technique). A result iscalculated via V = V1−V2

2.

12

3.2 Experimental Setup

Figure 3.1: The lower end of the dipstick, where the chip carrier can be mounted.In this picture, it is mounted in oopj geometry. Upon rotating the sample (the chipcarrier) by 90, it can be mounted in oopt. To measure in ip geometry, the chip carriercan be placed on the other mounting position, which appears as a whitish square dueto heat conducting past residues.

thesis, data points7 were taken in 2 steps from −20 to 380.8 To vary the pro-jections of m onto the axes, the absolute value of the external magnetic field wasconstant at |H| = H = 7T to minimize the impact of magnetic anisotropy, but thedirection h = H

H was rotated. Measurements were carried out with the three differentrotation geometries ip (rotation around n), oopj (around j) and oopt (around t) (seeFig. 2.4 and Fig. 2.5). The applied current was Iq = 100 µA.9 For the temperatureseries presented in Fig. 4.4 and 4.6, first the sample and the VTI were cooled downto T = 10K and TVTI = 5K, respectively. Then an ADMR measurement was car-ried out via a rotation of the sample. To achieve stable temperature, the systemwas thermalized for 15min between taking data at the next (higher) temperature.However, in this time the temperature had to be increased, too.

7Each data point includes the stepper motor angle (α, β or γ), the longitudinal and transversalvoltage (Vlong and Vtrans), the temperatures of the sample and of the VTI (T and TVTI), theexternal magnetic field (H), the pressure within the VTI and a timestamp.

8These angles are not comparable to Fig. 2.5, since the 0 mark of the stepper motor was notaligned with the external magnetic field.

9except for the samples YIG112 and YIG113, where Iq = 500 µA

13

Chapter 4

Results and Discussion

In this chapter, the results of the measurements will be shown and discussed. Atfirst, we describe how the “raw” measurement data were processed to obtain thedata shown. We then analyse a possible dependence of the SMR amplitude on thethickness of the YIG-layer, and discuss the ADMR measurements for the inversebilayers and the trilayer.

4.1 Data Processing

As mentioned in Sect. 3.2, the measured quantity is the potential drop V betweentwo pads of the Hall bar. To obtain the specific resistivities1 of the Pt, Eq. (4.1) wasused:

ρlong =VlongIq

wtPtl

(4.1)

with Vlong being the measured potential drop along j, Iq the applied charge currentand w, l, tPt the dimensions of the Hall bar (cf. Fig. 2.4).For the quantity most important in this thesis, the SMR effect magnitude −ρ1ρ0(Eq. (2.4)), each value of an ADMR measurement was divided by the maximumof this dataset to obtain ρlong

ρ0.2 In this way of presenting the data, the relative am-

plitude −ρ1ρ0 can be seen easily because it is the difference between 1 and the y-valueof the lowest datapoint.A further step in data processing was the correction of the angles, because the 0

mark of the stepper motor typically is no perfectly aligned with the direction of theexternal magnetic field and it was also hardly possible to align the dipstick perfectlywith the 0 mark. To get rid of this misalignment, two ADMR curves for each mea-surement geometry3 taken at different temperatures were fitted with a sin2 angular

1Exept Fig. 4.2, in all figures, it doesn’t matter, whether the measured voltage is used for thequotient ρlong

ρ0or the specific resistivities.

2In this thesis, ρ0 is the maximum of each dataset, which is in accordance to [13]. However, in[11], ρ0 is the minimum.

3ip, oopj, oopt; cf. Fig. 2.5

15

Chapter 4 Results and Discussion

Figure 4.1: Panel (a) shows the Pt thick-nesses (blue squares), obtained via sim-ulation of XRD data by [24], of allfour GGG|YIG|Pt hybrids discussed inSect. 4.2. Panel (b) shows the ob-tained relative amplitudes (red circles) formeasurements taken in oopj geometry at300K, µ0H = 1T and Iq = 100 µA in caseof the samples YIG105 and YIG106 andIq = 100 µA in case of the other two sam-ples. In panel (b), the black rectanglesalso illustrate the theoretical value for therelative amplitudes from Eq. (2.4) for thePt thicknesses, including Eq. (4.2) to ac-count for the dependence of the specificresistivity on tPt.

0 50 100 150 2002.62.83.03.23.4

t Pt(n

m)

(a)GGG|YIG|Pt

0 50 100 150 2001.1x10-3

1.2x10-3

1.3x10-3

1.4x10-3

1.5x10-3

YIG

113

YIG

112

YIG

106

(- 1/ 0)exp

tYIG (nm)

-1/

0

(- 1/ 0)theory

YIG

105

(b)

dependence in Origin with fixed period of 180, and the calculated offset was sub-tracted from the rotation angle of the original data.As mentioned in Sect. 3.2, data were taken for a range of H orientations from −20 to380(clockwise) and back (counter-clockwise).4 However, the data presented in thisthesis correspond to 360 extracts from the ones obtained during the backrotation,because the data taken during the clockwise rotation show thermal drift in some ofthe measurements taken.

4.2 Thickness Dependent Measurements

As it is quite hard to grow trilayers with two YIG-layers of the same thickness, i. e.a “geometrically” symmetric trilayer, a first approach towards trilayers is the studyof a possible dependence of the SMR signal on the thickness of the YIG-layer.For this purpose, four substrate|FMI|Pt hybrids were analysed, which were grownonto (111)-oriented GGG-substrates by M. Schneider using standard growth param-eters [24]. The samples consist of Pt with similar thicknesses tPt in a range of 2.8 nmto 3.3 nm on top of YIG. All samples thus have tPt close to the value for which weexpect the maximum SMR effect (cf. Fig. 2.6a). Hence, a relative amplitude −ρ1ρ0of slightly more than 1× 10−3 is expected. The YIG thicknesses of the samples arevery different in a range from 16 nm to 200 nm. All thicknesses were obtained bysimulating XRD (x-ray diffraction, [25]) data [24]. The error of the YIG-thicknesses

4These angles refer to the stepper motor’s scale.

16

4.2 Thickness Dependent Measurements

- 9 0 0 9 0 1 8 09 4 6 . 4

9 4 6 . 8

9 4 7 . 2

9 4 7 . 6

Y I G 1 0 5 a o o p j 1 0 0 0 m T 3 0 0 K 1 0 0 µ A

long (n

Ωm)

β ( ° )

Y I G 1 0 5 o o p j 1 T 3 0 0 K~ 1 . 4 n Ω m

l o n g

Figure 4.2: ADMR data, taken inoopj geometry for sample YIG105(GGG|YIG(16 nm)|Pt(2.8 nm)). Theblack arrow illustrates the SMR mag-nitude ρ1 and shows therefore whichdata are presented in Fig. 4.1. Iq was100 µA for this sample and for the sampleYIG106. For the samples YIG112 andYIG113, Iq was 500 µA.

are assumed to be ±10 percent. Note that for thicknesses of more than 100 nm, XRDthickness analysis is not very precise.As just the effect of tYIG on the SMR was to be analysed, data were only takenin oopj configuration at 300K. An example of the “raw” measured data is shownin Fig. 4.2. From the measured longitudinal potential drops, −ρ1 was extracted bysubtracting the lowest value from the largest. Note that the largest ρ value is ρ0. Toobtain the relative amplitude, the quotient −ρ1ρ0 was calculated.The obtained relative amplitudes spread in a range of 1.2× 10−3 to 1.4× 10−3 (seeFig. 4.1b, red circles) and all values are above the expected values of about 1× 10−3.To explain these data, the simulation for the Pt thickness dependence has to bemodified. In the simulation presented in Fig. 2.6, a constant value for the specificresistivity of Pt ρPt is assumed. However, ρPt does depend on tPt for these verythin metal films. We thus take the thickness dependence of ρPt into account, usingFischer’s-Equation [26]

ρPt(tPt) = ρ∞

(1 +

3

8(tPt − h)(l∞(1− p))

)(4.2)

with the parameters from [13]: The specific resistivity ρ∞ = 328 nΩm at infinitethickness, the mean free path l∞ = 4.1 nm at infinite thickness and the surfaceroughness h = 0.8 nm. p describes the scattering at the interface and is set to be 0(diffusive limit). With this parameters, the maximum SMR amplitude increases to1.4× 10−3 and it is shifted slightly to a smaller thickness of 2.3 nm (see Fig. A.1).The relative amplitudes, as function of the Pt thicknesses of the samples obtainedfrom the simulation including Eq. (4.2), are presented in Fig. 4.1b, too (black rectan-gles), and reproduce the measured trend with an average deviation of less than 5%.Therefore, we conclude that the SMR amplitude is not related to the YIG-thickness.The deviation from theory can be caused by an inevitable spread in SMR measure-ments and experimental uncertainties at the thickness determination. Furthermore,slight changes in the parameters for Eq. (4.2) can change the theoretical curve to

17


some extent.For the analysis of the inverse bilayers and the trilayer in the following sections, thesimulation for the SMR amplitude will be used, which does not take the dependenceof ρPt on the thickness into account because the roughness will be quite differentfor YIG on top of Pt. Furthermore, the simulation for the trilayer diverges with theparameters above, so that new parameters have to be obtained, which is not possiblewith just one trilayer sample available at the moment.

4.3 Inverse Bilayers

Whereas in SMR theory, there is no difference between a sample with Pt on topof YIG and another one with YIG on top of Pt (cf. Sect. 2.3), material propertiesforced us to grow YIG on Pt with non-ideal parameters (cf. Sect. 3.1.1, [16]). Hence,an important step towards trilayers is the analysis of inverse bilayers5 and thereforethe interface of YIG grown on top of Pt.

4.3.1 GGG|Pt|YIG Inverse Bilayer

In this section, the results obtained from the sample YIG 120a, aGGG|Pt(6 nm)|YIG(43 nm) hybrid, will be discussed.From the dependence of −ρ1ρ0 on the Pt thickness (see Fig. 2.6a), a relative SMRmagnitude of 7× 10−4 is expected for YIG 120a, considering a Pt thickness of 7 nm,obtained by simulating XRD data of this sample6[16]. This magnitude is expectedto be seen when rotating the magnetization from a configuration perpendicular tot (α = 0 for an ip rotation and β = 0 for oopj; see Fig. 2.5) to a configurationparallel to t (α = 90, β = 90), so that for ip and oopj configuration the magnitudesare expected to be the same.Let us first discuss the data of the ADMR measurement taken with the sampleYIG120a (GGG|Pt|YIG) at 300K (cf. Fig. 4.4d-f, red symbols) and compare theseto data of a “conventional” GGG|YIG|Pt hybrid (cf. Fig. 4.4a-c), i. e. Pt on topof YIG, as discussed in [13]. We start with the oopt data. In this H rotationplane, the angle dependent signal is constant within observational errors, which isin accordance with SMR theory and experiments carried out by Althammer et al. [13].

In ip and oopj, a signal with cos2(α) and cos2(β), respectively, shape is observedwith almost the same relative amplitude of 5.3× 10−4 and 5.2× 10−4, respectively,obtained by fitting the data with Origin. According to Fig. 2.6a, this implies a Ptthickness of about 10 nm. In fact, YIG120a was fabricated with a maximum Pt

5Both inverse bilayers were grown by F. Schade during his bachelor thesis [16].6This data don’t fit the experimental results well.

18


thickness of about 7nm, so that a thickness of 10 nm appears overestimated.As YIG 120a is an inverse bilayer, the surface between Pt and YIG is not supposedto be very “clean” in the sense of epitaxial growth and interface intermixing [16].One issue might be the occurrence of a platinum-oxygen-layer (PtOx) in betweenYIG and Pt. By simulating XRD data with the assumption of a further layerbetween Pt and YIG with the density of PtO, a Pt thickness of 1.4 nm and a PtOthickness of 9.3 nm are obtained [16]. PtOx is an insulating material for x ≥ 2, andfor lower x, it becomes conductive [27]7. A thin PtO2-layer of this thickness willchange the possibility of spin transfer torques in the FMI as now the tunnel effecthas also to be taken into account, decreasing the effective spin mixing conductanceand the total number of transferred spins, too. Actually, with such a PtO2-layer theSMR signal is expected to vanish completely. Unfortunately, a PtO-layer is muchmore likely, because the YIG was not grown in an oxygen atmosphere, but in Argon.Quantitative statements about a PtO-layer are difficult at this point, because [27, 28]refer to Pt-films with thicknesses of at least 200 nm. But a qualitative comparison tomeasurements with an inserted copper-layer can be made. Such a layer between YIGand Pt has a great influence on SMR-amplitudes, despite copper being a very goodconductor. With a thickness of about 7 nm for Pt and 9 nm for Cu, the SMR-signaldecreases to less than 1

6 of the expected amplitude for a sample without Cu [13,Fig. 8c, d]. Hence, it is very likely, that also a PtO-layer decreases the resistivitymore than 50%, and so we suppose that this layer, if existent, doesn’t consist of justPtOx.Another reason for the low relative amplitude can be the behaviour of Pt being ontop of GGG while heated up to 450 C. In his bachelor thesis, [16] F. Schade alsogrew a single Pt-layer on top of GGG and annealed this sample at 450 C. Theatomic force microscopy image taken of the Pt afterwards (see Fig. 4.3) shows avery rough surface with many tall spikes with heights of up to 88 nm, exceedingthe original Pt thickness of about 7 nm and even the YIG-thickness of the sampleYIG120a. Since the sample is still conductive, at least a thin Pt film has to existbetween the spikes. As related to SMR, electrons moving normal to the film surfacedue to SHE, located “under” a spike, cannot transfer their angular momentum intoYIG. With the assumption of spikes covering about a quarter of the surface, therelative amplitude being about 75% of the expected relative value can be explained(a decrease down to 75% could correspond to a 10 nm Pt thickness instead of 7 nm).This spike forming process occurs just when using GGG as substrate. Hence, forthe data of the second inverse bilayer and the trilayer, grown on a (111)-oriented

7In [27], the resistivity of a 500 nm thick sample was measured with a varying fraction of oxygenin PtOx. Thus, and because the total resistivity was given, and not the specific one, the resultscan’t be directly transferred to thin layers. Therefore, just the statement of a conductive PtO-layer is used, however, the specific resistivity is supposed to be at least one order larger thanthe one of pure Pt, which is also supported by [28].

19


Figure 4.3: Taken from [16].Atomic force microscopy image ofa sample (PTG#3) consisting ofa Pt-layer on top of GGG, whichwas annealed at 450 C after de-positing the Pt-layer. The rootmean square of the surface rough-ness is RRMS = 13.7 nm.

substrate (YAG), this is no problem.

Taken together, the 300K ADMR data of the sample YIG120a appear reasonable,although a rough surface might be an issue. However, ADMR measurements werenot only taken at 300K but also at various lower temperatures (see Fig. 4.4d-f).SMR experiments in [13] showed no change in angular dependence, but a reductionin the amplitude by 34% at 5K compared to 300K.However, the ADMR curves of the sample YIG120a show a quite different behaviour.In all geometries, the data taken at 250K and 200K are similar to the ones takenat 300K, within experimental fluctuations. In fact, the ADMR data from 300K to200K are undistinguishable in Fig. 4.4d-f. In oopt the data taken at temperaturesbelow 200K, i. e. 10K, 50K and 100K all of a sudden show a clear angular depen-dence, which is cos2(γ)-like but not as “smooth” as a cos2(γ).A likely explanation for this behaviour is the occurrence of an AMR-like effect.Therefore, a both conductive and magnetic layer is needed. One possibility is alayer between Pt and YIG, consisting not of PtOx but of PtFex or another mixtureof Pt with some - or all - atom types forming YIG. Such a layer is supposed to havea Curie temperature between 100K and 200K, because the AMR-like behaviourappears only below 200K in our experiments. Another possibility for a conductivemagnetic layer is conductive YIG. To not destroy the Pt-layer’s conductivity, theYIG-layer is grown at lower substrate temperatures compared to the ideal one (seeSec. 3.1.1, resp. [16]). In [16], it is also figured out, that YIG grown at even lowertemperatures looses it’s magnetization. In addition, the YIG’s surface can becomeconductive, [29] which might also be the case in this sample. But also this possibleeffect has to exhibit a critical temperature below which the layer is both magneticand conductive. Above it, the layer is at least just magnetic, because without amagnetic behaviour at higher temperatures, the SMR signal clearly resolved in ipand oopj measurements would not exist.To sum up, this oopt-behaviour is quite interesting due to it’s AMR-like effectwith the possibility to be switched on and off by changing the sample temperature.

20


However, a problem with this interpretation is the angular dependence of the data.According to Eq. (2.7) with ∆ρ > 0, the AMR is to show a sin2(γ) behaviour andnot the recorded cos2(γ) one. Thus, at least an unconventional AMRmust be present.

In ip (see Fig. 4.4d), the ADMR measurements taken at 10K, 50K and 100Khave a much larger amplitude of up to 2.8× 10−3 at 10K, increasing with decreasingtemperature. Furthermore, there is a phase shift of 90, i. e. the cos2(α) becomes asin2(α).In the oopj rotation this phase shift is also noted, while the amplitude doesn’t changemuch. A possible explanation for this behaviour is given by equation (2.2) being justa series expansion in α2

NM as mentioned in Sect. 2.3. Hence, there can be terms ofhigher order having a big effect on the SMR signal and resulting in a deviation ofthe simple cos2(α) behaviour.In ip, a distinction between SMR and AMR is not possible, but the ip behaviour isat least consistent with the out-of-plane data, because the ip relative amplitude isto be the “sum” of the out-of-plane ones, including phase contributions.8 Therefore,the phase shift arises as a result of the oopt behaviour, changing with decreasingtemperature.

4.3.2 YAG|Pt|YIG Inverse Bilayer

This section deals with the sample YY50a (YAG|Pt(3nm)|YIG(22 nm)), which isalso an inverse bilayer like the sample discussed in the previous section (YIG120a).However, YY50a was grown on YAG as substrate instead of GGG (see [16] fordetails). As the trilayer, of which the ADMR results will be discussed in Sect. 4.4,was also grown on YAG, this inverse bilayer is even one step closer towards it,compared to the one above. The data of this inverse bilayer is quite different from

8Assuming a simultaneously occurrence of the SMR and the AMR, both equations (2.2) and (2.7)have to be added. As in both formulae, ρ0 describe the same “offset”, they do not need to beadded. The resulting equation is

ρlong = ρ0 + ∆ρm2j︸︷︷︸

AMR amplitide

+ ρ1m2t︸︷︷︸

SMR amplitide

With mi being the projections of a unit vector onto different axes of a Cartesian coordinate system,1 = m2

j +m2t +m2

n. As just ip geometry is to be considered, mn = 0, and thusm2t = −m2

j . Thereforeit applies

ρlong = ρ0 + (∆ρ− ρ1)︸︷︷︸ip amplitide

m2j

As in the used definition, ρ1 < 0 and ∆ρ > 0, both amplitudes add up in ip geometry.

21


90180

270360

0.997

0.998

0.999

1.000

90180

270360

180270

360450

0.997

0.998

0.999

1.000long/ 0

(a)ip1T

GG

G|YIG

|Pt

GG

G|YIG

|Pt

GG

G|YIG

|Pt

(b)oopj1T(c)oopt1T

-900

90180

0.997

0.998

0.999

1.000

-900

90180

-900

90180

0.997

0.998

0.999

1.000d)

YIG

120aip

7T

long/ 0

α(°)

GG

G|P

t|YIG

GG

G|P

t|YIG

e)Y

IG120a

oopj7T

β(°)

300K250K200K150K100K

50K10K

GG

G|P

t|YIGγ

(°)

f)Y

IG120a

oopt7T

j t

nα

m

^

^^

βm

j t

n ^

^^

γ

mj t

n ^

^^

Figu

re4.4:

Inall

graphs,results

ofADMR

(angle-dependentmagnetoresistance)

measurem

entsare

shown,

takenin

differentorientations,

i.e.ip

(a,d),

oopj(b,

e),oopt

(c,f),

seeinsets.

Allpresented

datashow

normalized

longitudinalspecific

resistivities,thatis

themeasured

longitudinalresistivityρlongwas

dividedby

themaxim

umvalue,w

hichisρ0 .

In(d)-(f)

dataare

presented,which

were

obtainedat

varioustem

peratureswith

theinverse

GGG|Pt|Y

IGhybrid

YIG

120awith

anapplied

chargecurrent

ofIq

=10

0µA

.In

(a)-(c)the

longitudinalresultsofa

conventionalGGG|Y

IG|Pthybrid

at30

0K,presented

in[13,F

ig.5],areshow

nas

areference.

The

insetsare

inanalogy

to[13].

22


the YIG120a one.

Again we start the discussion with the data taken at 300K. While the relativeamplitudes of the sample YIG120a were smaller than expected, here they exceedexpectations. Both ip and oopj show a relative amplitude of more than twice themaximum value expected from theory (cf. Fig. 2.6a and Fig. 4.6a,b) with 2.7× 10−3

and 2.3× 10−3 respectively, being the values obtained by fitting these curves inOrigin. Also the oopt data are, with a relative amplitude of 0.4× 10−3, already ina comparable range, despite no angular dependence is expected. The shape of asin2(γ) is in accordance with an AMR.

For the calculation of ρlongρ0

it does not matter whether to use the specific resis-tivities, for whose calculation the Pt thickness in needed, or the measured potentialdrop. Therefore an “SMR-thickness” can be inferred from the dependence of theSMR on tPt as shown in Fig. 2.6. For the sample YY50a this is not possible, sincethe SMR amplitude exceeds theory. Nevertheless, statements about the thicknessof the Pt-layer can be made. In [16] XRD measurements were carried out for thissample and a simulation was used to obtain values for the layer thicknesses. Withthe assumption of just a Pt and a YIG layer, a Pt thickness of 6.9 nm reproduces theXRD data best, but the agreement between XRD and fit is not satisfactory. Withan additional layer with the density of PtO in between, a thickness of 0.4 nm for Ptand 8.8 nm for PtO follows, which quite nicely reproduces the XRD data [16], butdeviates from experimental expectations.We carried out another very naive thickness determination by measuring the resis-tivity along the Hall bar9 in absence of an external magnetic field, and thus withoutSMR. Using Eq. (4.3), a thickness was calculated, with R being the measured resis-tivity of 1.24 kΩ, ρ the specific resistivity of Pt being assumed to be 450 nΩm [13]and lHB = 1000 nm, w = 80 nm, tPt the dimensions of the Hall bar (see Fig. 2.4).

R = ρlHB

w · tPt(4.3)

From this calculation tPt is supposed to be 4.5 nm, which seems to be realisticcompared to growth parameters [16]. Due to this resistivity, a Pt thickness of 0.4 nmunder PtOx is not possible.

An explanation for the very high measured relative SMR amplitude can again bea possible interlayer being magnetic and conductive, suggested by the occurrence ofan AMR in oopt. Such a layer changes the boundary condition for the electrons,

9For this measurement, the longitudinal pads were used, which are used for the insertion of thecharge current in ADMR measurements, and not transverse ones.

23


which now are not only able to transfer their angular momentum into the layeradjacent to Pt, but also able to enter this layer because of it’s conductance. This isa much stronger boundary condition, as the decrease in the measured voltage dropis in this case the sum of electrons just transferring their angular momentum andof electrons passing the interface. Hence, this is more close to a spin current closedcircuit boundary condition, which is important for the SMR effect. Such a layer doesnot only change the boundary conduction, but a charge current flowing in it canalso contribute to SMR at the interface with YIG. However, SMR in magnetic layersis not discussed in literature yet. The question arises if the magnetization of theconductive layer has a much stronger influence on the electrons than the adjacentYIG-layer. We suppose the spin diffusion length to decrease, so angular momentumcan be transferred already within this layer. If the spin diffusion length is longenough to let the electrons transfer spins mostly when they move perpendicular to j,we presume a big increase in an SMR-like effect. However, also SMR in conductiveand magnetic layers is not discussed in literature properly yet.

Now also the data taken at lower temperatures will be discussed. Starting withoopt configuration (see Fig. 4.6c), a monotone increase in relative amplitude withdecreasing temperature is noted from Fig. 4.6f. For the data taken at the lowesttemperature (10K) in this set of measurements, the relative amplitude rises up to4.7× 10−3, obtained by a fit in Origin. This big amplitude can again be attributedto the AMR. For a further discussion of the AMR effect, see Sect. 4.4.

In oopj configuration (see Fig. 4.6b) a phase shift of 90, turning the cos2(β) into asin2(β), is noted as previously observed in the inverse bilayer YIG120a. However, theshifted curves have, like the curves taken at higher temperatures, a bigger relativeamplitude compared to YIG120a and the phase shift starts at lower temperatures,because the data taken at 100K still show no phase shift. Furthermore, at theselow temperatures the curves are no longer “pure” sin2(β) functions, but ones withmany additional wiggles. This oopj behaviour can be caused by different reasons. Afirst one is Eq. (2.2) being just a series expansion (already mentioned in Sect. 4.3.1).Another and very simple one is a possible tilt in the sample plane, i. e. the sampleis not perfectly oriented in oopj configuration. This tilt can e. g. be a result of thesample not being perfectly aligned on the chip carrier. Therefore a photo of the chipcarrier with glued sample was taken (see Fig. 4.5), and the angle between the Hallbar and the pins, being plugged in the dipstick, was measured. This angle is smallerthan 2, which corresponds to an oopt contribution in oopj of sin(2) ≈ 3.5%, whichimplies a decrease in the oopj amplitude of up to (−ρ1)oopt,10K · 3.5% = 0.05 nΩm.This does not explain the change in the absolute amplitude of about 1.5 nΩm betweenthe data taken at 10K and 300K in oopj.

24

4.4 YAG|YIG|Pt|YIG Trilayer

Figure 4.5: To test the hypothe-sis of a tilt in sample mounting,a photo was taken and the an-gle between the Hall bar and thepins plugged in the dipstick (high-lighted by red lines) was measuredto be smaller than 2. On theright is a European 1 Cent coinas a size reference.

The ip (see Fig. 4.6a) data show an increase in relative amplitude with temperaturedecreasing to 150K and a decrease for even lower temperatures. This behaviour isagain consistent with the out-of-plane data (see end of Sect. 4.3.1).


After two approaches towards trilayers, the analysis of the YIG thickness depen-dence of the SMR and the analysis of inverse bilayers, this section deals with thesample most important in this bachelor thesis, the trilayer. It is the first symmetricsubstrate|FMI|NM|FMI hybrid fabricated at Walther-Meißner-Institute, and it wasgrown by F. Schade for his bachelor thesis [16].The discussion of the results will be in a different order, compared to the inversebilayers, starting with the comparison of relative amplitudes to theoretical ex-pectations. Afterwards the behaviour of ip, oopj and oopt geometry at differenttemperatures will be discussed.

At first, the data taken at 300K in ip and oopj geometry are analyzed (seeFig. 4.6d,e, red symbols). Fitting these curves with Origin,10 relative amplitudesof 2.5× 10−3 and 1.6× 10−3, respectively, were obtained. Compared to theoreticalcalculations (cf. Fig. 2.6b), 2.5× 10−3 slightly exceeds the maximum of 2.4× 10−3

for a Pt thickness of about 2.7 nm. A relative SMR amplitude of 1.6× 10−3 impliesa thickness of either about 0.9 or 6.6 nm.As for the inverse bilayers, XRD data of this sample were fitted with different as-sumptions about existing layers in [16]. With just YAG|YIG|Pt|YIG, a Pt thicknessof 6.4 nm was obtained, which does not fit the curve properly. With an additionallayer with the density of PtO, i. e. YAG|YIG|Pt|PtO|YIG, the results are 1.4 nm forPt and 7.5 nm for PtO. As a third way, the resistivity over the whole Hall bar wasmeasured with a digital voltmeter, resulting in R = 864 Ω. This corresponds to aPt thickness of 6.5nm via Eq. (4.3), with the specific resistivity of Pt being again

10The curves were fitted with a sin2 with fixed period of 180.

25


0.9940.9950.9960.9970.9980.9991.000

0.9940.9950.9960.9970.9980.9991.000

-900

90180

0.9940.9950.9960.9970.9980.9991.000

-900

90180

-900

90180

0.9940.9950.9960.9970.9980.9991.000

YAG|Pt|YIGa) YY50a ip 7T

l o n g / 0

YAG|Pt|YIGb) YY50a oopj 7T

YAG|Pt|YIGc) YY50a oopt 7T

YAG|YIG|Pt|YIG

l o n g / 0

α (°)

d) YY55a ip 7T

YAG|YIG|Pt|YIGe) YY55a oopj 7T

β (°)

300K 250K 200K 150K 100K 50K 10K

Y A G | Y I G | P t | Y I G

f) YY55a oopt 7T

γ (°)Figu

re4.6:

In(a)-(c),A

DMR

resultsobtained

with

thesam

pleYY50a,an

inverseYAG|Pt|Y

IGhybrid,taken

atdifferent

orientationsand

temperatures

areshow

n.(d)-(f)

showthe

correspondingdata

fromthe

sample

YY55a,

atrilayer,

i.e.a

YAG|Y

IG|Pt|Y

IGhybrid.

Alldata

were

takenwith

Iq

=100

µA.

26


Table 4.1: Results for the Pt thickness of the trilayer. The values were obtained byanalysing SMR data, XRD data [16] and the resistivity.

method of measurement rel.amplitudee. g. resistivity

Pt thickness (nm)

SMRip 2.5× 10−3 2.4oopj 1.6× 10−3 6.6 or 0.9

XRDYIG|Pt|YIG 6.4YIG|Pt|PtO|YIG 1.4

tPtO = 7.5

resistivity864 Ω 6.5

assumed to be ρ = 450 nΩm [13].Comparing all these results, a thickness of about 6.5 nm appears to be very likely,even though this a close to the maximum possible value of the Pt thickness, since athickness of about 7nm was set for the Pt deposition.

As the in-plane amplitude is supposed to be the “sum” of both out-of-plane ones(see end of Sect. 4.3.1), the non-vanishing oopt amplitude also contributes to the ipdata. Therefore, the in-plane results are also consistent with this thickness, despitethe high relative amplitude.Considering the whole temperature series taken in ip geometry, it appears to be sim-ilar to the YY50a one. However, now the relative amplitude increases monotonouslywith decreasing temperature and has no more a local minimum. This temperaturedependence of the SMR signal is also consistent with the out-of-plane data at lowtemperatures.

Not only the ip data, but also the ones taken in oopj (see Fig. 4.6e) are similarto the YY50a data at a first glance. Again, the relative amplitude stays almostconstant when decreasing temperature down to 150K, and at lower temperatures, aphase shift of 90 is noted in the neighbourhood of β = 90, i. e. the magnetization isparallel to t in the sample plane. Yet in the vicinity of β = 0, that is a configurationnormal to the sample plane, almost no change is noted even at low temperatures,except 10K. Therefore the possibility of a tilted sample, which would result ina contribution of the oopt geometry to oopj, mentioned in Sect. 4.3.2, is ratherunlikely, also because the measured tilt is again lower than 2, which cannot cause asufficient change. Therefore again Eq. (2.2), being just a series expansion to second

27


order, can be a reason for this strange behaviour.

Furthermore, the oopt data show a much more regular behaviour. At any mea-sured temperature, a sin2(γ) like shape of the data is noted with a period of 180.Compared to the inverse bilayer YY50a, the data show a monotonically increasingrelative amplitude, too, but each one is bigger than the corresponding YY50a data,e. g. at 10K the relative amplitude reaches almost 6.5× 10−3. Even at 300K arelative magnitude of 1.5× 10−3 is noted.

Yet this oopt data is not a “pure” sin2(γ). At high temperatures just changes ofthe resistivity around 0 ± 180 are noted, which corresponds to m ‖ n, while thesignal is almost constant between 45 and 135 (m ‖ j in the sample plane), in away that the maximum at 90, which occurs at lower temperatures, vanishes11. Sucha behaviour is a strong indicator for anisotropy. A crystalline magnetic anisotropyin the YIG appears unlikely. Indeed, no strong crystalline anisotropy was observedin all our epitaxial YIG samples (compare [13], for example). Thus, a strong shapeanisotropy of the YIG magnetization is quite likely to occur, especially in this tri-layer, consisting of two magnetic thin films. The magnetization always tends tominimize its potential energy, which results in a preferred orientation in plane forthin films [30], e. g., a hard magnetic axis along n. When rotating the external mag-netic field, the magnetization is expected to stay as long in the sample plane as thisis the configuration which minimizes the energy. This can cause the plateaus in ooptrotation. The strength of the external magnetic field, respectively it’s componentnormal to the sample plane, at which the magnetization will not stay any more in thesample plane, is determined essentially by the saturation field µ0Hsat in the directionnormal to the thin film.The SQUID magnetometry data of Fig. 4.7a support the notion of an anisotropicmagnetization, showing an unusual magnetization behaviour. Two different coercivefields are noted12; one at some ten mT and the other one at more than 2T. Theappearance of two different values can be explained by the trilayer consisting of twoYIG-layers. We suppose the lower coercive field belonging to the lower YIG-layer(YIG on YAG; grown under “optimal” conditions), and the bigger one to the upperlayer (YIG on Pt - or another Pt-YIG-mixture). A typical coercive field value forYIG is µ0Hc = 3mT and also the saturation field µ0Hsat is in a comparable range[13]. In contrast, µ0Hsat > 3T at this sample, measured at room temperature. Asthis data was taken with µ0H in plane, the needed external field is very likely to beeven bigger if it is normal to the sample. The average saturation magnetization of

11same for −90

12As in this curve, the whole magnetization of the sample is shown, i. e. the sum of all magneticlayers, just one zero-crossing can be seen.

28


- 6 - 4 - 2 0 2 4 6- 1 0 0- 5 0

05 0

1 0 0

µ0 H ( T )

M (kA

/m)

Y Y 5 5 a i pT = 3 0 0 K

( a )

4 0 4 2 4 4 4 6 4 8 5 0 5 2 5 41 0 0

1 0 2

1 0 4

Y Y 5 5 a( b )

Pt (11

1)

2 θ (°)

I (cps

) YAG

(444)

YIG (4

44)

Figure 4.7: Both taken from [16]. (a) Magnetization curve of the trilayer, via SQUIDmagnetometry [25]. A very high external magnetic field µ0Hsat is noted to be neededfor the YIG magnetization being saturated. (b) XRD 2θ-ω scan of the trilayer, cf. theanalysis of Bragg-reflections. At 2θ ≈ 40 a peak is noted, which can be attributed toa crystalline Pt-layer.

about Msat ≈ 120kAm is comparable to the literature value of 143kA

m [31].However, considering also data taken in oopj rotation at “high” temperatures, uni-axial anisotropy, as the shape anisotropy for thin films is, is not possible, becausethe data do not show plateaus or similar behaviour. The fact that the sample has alonger edge of 5mm being parallel to j and a shorter one, being half as long, is veryunlikely to have an effect on the anisotropy.

Yet not only the YIG layers can contribute to anisotropic effects, but also thePt. In Sect. 4.3.1 the behaviour of Pt to form spikes when annealed on GGG wasdiscussed. As the trilayer was grown onto YAG no such behaviour is expected.Unfortunately, there is another behaviour of Pt. The Pt-layer grown via electronbeam evaporation [16] is polycrystalline and becomes (partly) textured along the(111)-orientation when heated up to temperatures necessary for growing YIG (cf.Fig. 4.7b). By contrast, SMR theory assumes a polycrystalline NM-layer. Dueto a preferred magnetization orientation, anisotropic behaviour is expected, too.However, no quantitative statements can be given, because the SMR in crystallinemetals has not yet been observed.Hence, again the occurrence of an AMR-like effect is possible, as discussed in theprevious sections for the inverse bilayers. Since also a trilayer consists of an inversePt|YIG interface, where YIG is grown onto Pt, the discussion of possible conductivelayers is applicable for this sample, too.

In the following section, the effects observed in oopt in both inverse bilayers and the

29


trilayer, will be discussed with respect to XMCDmeasurements13[25] carried out withdifferent samples. As already mentioned in Sect. 4.3.1, for a possible AMR, a bothconductive and magnetic layer is needed. Lu et al. [32] reported an AMR in YIG|Pthybrids, i. e. “normal” bilayers, too, and attributed their result, also consideringXMCD data, to a static magnetic proximity effect in Pt. This means that the YIG,adjacent to the Pt-layer, causes the Pt to become magnetic (i. e. to show a finitespin polarization). In contrast to this result is the data, obtained also via XMCDof YIG|Pt hybrids, published by Geprägs et al. [33], who reported an upper limitfor the magnetization in Pt, so that an AMR due to magnetic proximity effects canbe ruled out. In an additional comment on Lu et al. [34], Geprägs et al. claim thatthe magnetization, observed by Lu et al., might be caused by a contamination ofthe Pt with atoms from YIG. Suggested reasons are a sputtered Pt-layer14 onto theYIG-layer, after breaking the vacuum, and therefore contaminations at the YIG|Ptinterface might occur, for example by forming a PtOx-layer, which is suggested in[34] based on differences in the whiteline intensity at the Pt L3 edge in XANESmeasurements.The samples used for this bachelor thesis also show AMR-like behaviour, whichappears consistent with the suggestion of by Geprägs et al., because in case of oursamples, a reason for the contamination of the Pt is quite obvious: A YIG-layer wasgrown on top of the Pt. During this process, the Pt was heated up, which resultsin a large kinetic energy of the sample’s atoms. Therefore, their ability to mix witheach other is greatly enhanced, and the occurrence of a “mixed layer” at the interfaceseems possible. This layer can be both magnetic and conductive, depending on theatoms, forming this layer, and thus might give rise to an additional AMR.

13XMCD (x-ray magnetic circular dichroism) allows a separation between different elements, con-tributing to a magnetization.

14Also Vlietstra et al. [35] noted differences between the deposition of the Pt-layer by sputteringand by electron beam evaporation.

30


0 5 1 0 1 5 2 00 . 05 . 0 x 1 0 - 41 . 0 x 1 0 - 31 . 5 x 1 0 - 32 . 0 x 1 0 - 32 . 5 x 1 0 - 3 T r i l a y e r

2 x B i l a y e r B i l a y e r

−1/

0

t P t ( n m )

Y Y 5 0 a

Y Y 5 5 a

Y I G 1 2 0 a

Figure 4.8: Dependence of the SMR sig-nal on the Pt thickness for bilayers andtrilayers. The red squares symbolize theused inverse bilayer samples and the bluesquare symbolizes the trilayer. For eachsample the value for −ρ1

ρ0is the measured

amplitude in oopj geometry at room tem-perature with errors of about the size ofthe squres. To estimate the Pt thick-nesses, values from SMR, XRD and resis-tivity measurements were taken into ac-count. In addition, the maximum thick-nesses from growth perspective were con-sidered, too.

31

Chapter 5

Conclusions and Outlook

5.1 Conclusions

In summary, in the framework of this thesis we systematically studied the spinHall magnetoresistance (SMR) in substrate|FMI|NM|FMI trilayers,1 especially fo-cussing on differences in surface effects at an inverse surface, i. e. YIG on topof Pt, due to different growth conditions in comparison to “conventional” bilayers(substrate|YIG|Pt). We recorded data at different magnetic field orientations and atdifferent temperatures and found out, that there is a SMR-like effect in trilayers, too,which is larger compared to bilayers, but consistent with the SMR theory calculatedfor trilayers. Furthermore, we recorded an AMR-like effect in oopt rotations withvery large amplitude (even larger than the SMR-signal in oopj at specific tempera-tures), increasing with decreasing temperature, which we contribute to difficulties insample growth. Our discussions included several attempts to explain this behaviourby taking into account possible interlayer formations.

We found out that the SMR is independent of the YIG-layer thickness. Thisis important for symmetric trilayers because it is very difficult to fabricate twoidentically thick YIG-layers.Furthermore, as the SMR is an interface effect, we analysed inverse bilayers, i. e.substrate|Pt|YIG hybrids at first. While theory predicts no differences comparedto a substrate|YIG|Pt interface, we found quite big variations between “conven-tional” bilayers and inverse ones, what we noted also in case of the trilayer, aYAG|YIG|Pt|YIG hybrid.To analyse our samples, we rotated an external magnetic field H, and thus theYIG magnetization M, in three different geometries (ip, oopj, oopt; see Fig. 2.5for the definition of the rotational axes and the related angles). In oopj geometry,where just effects of SMR are to be seen, we recorded a qualitative change withdecreasing temperature in our inverse bilayer samples and our trilayer sample. At100K to 150K, the SMR-like sin2(β) behaviour changes to a cos2(β) one. Anotherobservation is that the data taken at lower temperatures are no longer “smooth”

1See table A.3 for the used abbreviations.

33

Chapter 5 Conclusions and Outlook

functions. However, the samples differ in the relative SMR amplitude, being eithertoo low compared to theory (YIG120a; on GGG), too high (YY50a; on YAG) orin a good agreement to theory (YY55a, trilayer; on YAG). However, the thicknessdetermination of the normal metal layer is not straight forward because thicknessvalues for the same sample obtained via different methods vary in a range muchbigger than experimental uncertainties.In oopt geometry, we observed a sin2(γ)-like behaviour with very large relativeamplitudes, increasing with decreasing temperatures (up to 6.5× 10−3 at 10K forthe trilayer sample).2

The observed ip behaviour for both inverse bilayers and the trilayer is not consistentwith pure SMR theory, too, because of too large relative amplitudes. However, withthe assumption that the signals measured in the oopj and oopt geometry add up tothe ip signal (see end of Sect. 4.3.1), the ip behaviour can be explained.

We attributed these differences from SMR theory especially to more difficultgrowth conditions for YIG on top of Pt, which can cause an interlayer between Ptand YIG. Such an interlayer can consist of some mixtures of Pt with the atomsforming YIG. We suppose this interlayer to be magnetic to some extent. This canbe a reason for differences in thickness determinations and it is also supposed togive rise to the AMR, which would explain the oopt behaviour. We mentionedalso some anisotropic effects, e. g. a (partly) crystalline Pt-layer, while SMR theoryassumes a polycrystalline one. Another approach to explain the deviations fromtheory is formula (2.2), expressing the explicit “angular” dependence, being just aseries expansion to first order in α2

NM. We propose that this is not sufficient for thedescription of the SMR in case of an inverse Pt|YIG interface.

To conclude, like in case of the wheel in the Stone Age, still much research has tobe done until the SMR will be broadly used in technology (some further steps arementioned in Sect. 5.2.1).

5.2 Outlook

5.2.1 Further Analysis Steps

As many of the reasons for the differences to theory, given in this thesis, are justspeculations, confirming experiments have to be carried out. A first and very simpleexperiment is the analysis of the sample YY51 (Pt on top of YIG on YAG), whichwas grown by F. Schade with the same parameters for each layer than the inverse

2The oopt behaviour of the sample YIG120a differs from the other samples as cos2(γ)-like be-haviour is noted, but just below 200K.

34

5.2 Outlook

bilayer YY50a (also on YAG). The study of this layer can help to exclude possiblynon-ideal parameters for growing YIG as reason for the deviations. If this sampleshows a behaviour which is compatible with the ones in [13], problems with theinterface YIG on top of Pt are much more likely.As related to growth, there is much space for optimization. One aim in F. Schade’sbachelor thesis [16] was to find an optimal temperature for growing YIG in an argonatmosphere, so that further steps will be the optimization of the other parameters,e. g. the argon pressure within the growing chamber or to try different laser-energies.

Further steps in the research of the SMR in trilayers are analysing proposedeffects mentioned in this thesis. Firstly, this is the analysis of the SMR in crystallinePt-layers. Therefore, theory needs to be changed and recalculated because SMRtheory is just applicable for polycrystalline NM layers. Then, we suggest to growsome “normal” bilayers and anneal them to such high temperatures that the Pt-layerwill become crystalline. We suggest normal bilayers for these experiments becausesome possible problems, for example a interlayer between YIG and Pt, won’t existto this extent.

Secondly, another very important experiment wil be the characterization of apossible interlayer. Thus, we suggest to carry out element specific XMCD measure-ments with the inverse bilayers and the trilayer to get detailed information about apossible magnetic interlayer.Thirdly, a related issue are additional SMR experiments with conductive layersthat are magnetic for sure. For this measurements pure Pt is not suitable, but alsoreplacing Pt by a completely different conductor is difficult because of the strongSpin-Orbit-Coupling needed for the SMR. Thus, we suggest to replace Pt with e. g.PtFex. However, at first an appropriate value for x has to be figured out.

Last but not least, comparative experiments with further trilayers have to be donein the future because for this bachelor thesis just one trilayer sample was available.

5.2.2 Asymmetric FMI|NM|FMI Heterostructures

Another very interesting approach to trilayers, and to a technological use as spinvalves, is leaving the symmetric case by pinning one layer, i. e. to fix the magneti-zation of one FMI layer, likely the upper one via adding an antiferromagnet on topof the second FMI. As a result, the boundary condition at this surface is fixed, i. e.M′ can’t rotate any more for H < Hexchangecoupling (see Fig. 5.1).Pinning M′ in a configuration parallel to t (open spin current circuit boundarycondition) a bilayer behaviour is expected [11]. For M′ ⊥ t (closed circuit boundarycondition) a bilayer-like behaviour is expected, too, but with an offset due to the

35

Chapter 5 Conclusions and Outlook

Figure 5.1: In analogy to [13].In a more general approach to tri-layerrs, the lower and the upperYIG-layer can have different mag-netizations M and M′. YAG (111)

Pt

YIG

n

t

jM’

M

second dissipation channel at the NM|FMI interface.Considering Fig. 4.7a, asymmetric experiments can be tried already with the trilayersample analysed above, by taking advantage of the two different coercive fields. Forthis measurements an initial external magnetic field µ0H > 4T should be appliedat a defined H orientation (e. g. H ‖ j or H ‖ t). Afterwards measurements can becarried out with µ0H at a much smaller absolute value in a range of some hundredmT and with reversed direction. The problem of rotations at such low fields mightbe an anisotropy occurring also in the layer with the lower coercive field.

36

Appendix A

Samples and Parameters

Table A.1: In this table, the important parameters of the used samples are summarized.The thicknesses, especially for the lower three samples grown by F. Schade, exhibit largepossible errors. A possible interlayer isn’t listed. For results including errors, see Fig. 4.1and Fig. 4.8.

sample name layers (thickness (nm)) grown byYIG105 GGG|YIG(16)|Pt(2.8) M. Schneider [24]YIG106 GGG|YIG(44)|Pt(3.3) M. SchneiderYIG112 GGG|YIG(74)|Pt(2.8) M. SchneiderYIG113 GGG|YIG(197)|Pt(2.9) M. SchneiderYIG120a GGG|Pt(6)|YIG(43) F. Schade [16]YY50a YAG|Pt(3)|YIG(22) F. SchadeYY55a YAG|YIG(43)|Pt(6.5)|YIG(27) F. Schade

0 5 1 0 1 5 2 00 . 0

5 . 0 x 1 0 - 4

1 . 0 x 1 0 - 3

1 . 5 x 1 0 - 3

−1/

0

t P t ( n m )

B i l a y e r B i l a y e r

i n c l u d i n g E q . ( 2 6 )

Figure A.1: Dependence of the SMR amplitude at room temperature for bilayers withconstant ρNM = 400 nΩm (red solid line), and the dependence including Eq. (4.2) forρNM (black dasched line).

37

Appendix A Samples and Parameters

Table A.2: Summary of the standard parameters used for taking temperature seriesdata. When numbers for Hall bar pads are given, they refer to Fig. A.2.

parameter value Hall bar padsµ0H 7000mTTVTI T − 5KIq 100 µA pads 5+ − 15−

Vlong pads 4+ − 14−

Vtrans pads 11+ − 12−

11214

151311

24

53

Figure A.2: The numbers at the Hall bar pads are related to the standard bondingscheme.

38

Used Abbreviations

Table A.3: Used Abbreviationsρ specific resistivityαNM spin Hall angle (see Sect. 2.2)λNM spin diffusion length (see Sect. 2.3.1)Gr spin mixing conductance (see Sect. 2.3.1

and [20])AFM atomic force microscopeADMR angle dependent magnetoresistance (see

Sect. 3.2)AMR anisotropic magnetoresistance (see

Sect. 2.4 and [2])FMI ferro-/ferrimagnetic insulatorGGG gadolinium gallium garnet (Gd3Ga5O12)GMR giant magnetoresistance [3]ip in-plane geometry (see Fig. 2.5)ISHE inverse spin Hall effect [10]MBE molecular beam epitaxyNM normal metaloopj out-of-plane geometry with rotation of h

or m, respectively, around j (see Fig. 2.5)oopt similar to oopj but with t as rotation axisPLD pulsed laser depositionPt platinumSHE spin Hall effect [8, 9]SMR spin Hall magnetoresistanceSOI Spin-Orbit-InteractionSQUID superconducting quantum interference de-

vice [25]STT spin-transfer torque [11]TMR tunneling magnetoresistive effect [5, 6]VTI variable temperature insert (see Sect. 3.2)XMCD X-ray magnetic circular dichroism [25]XRD X-ray diffraction [25]YAG yttrium aluminum garnet (Y3Al5O12)YIG yttrium iron garnet (Y3Fe5O12)

39

Bibliography

[1] http://www.sciencecartoonsplus.com/gallery/physics/galphys2d.php#.

[2] T. McGuire and R. Potter, Anisotropic magnetoresistance in ferromagnetic 3dalloys, IEEE Transactions on Magnetics 11, 1018 (1975).

[3] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, Enhanced magnetore-sistance in layered magnetic structures with antiferromagnetic interlayer ex-change, Physical Review B 39, 4828 (1989).

[4] P. Grünberg, Nobel Lecture, 2007.

[5] J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Large Magnetore-sistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions,Physical Review Letters 74, 3273 (1995).

[6] S. Mao, Y. Chen, F. Liu, X. Chen, B. Xu, P. Lu, M. Patwari, H. Xi, C. Chang,B. Miller, D. Menard, B. Pant, J. Loven, K. Duxstad, S. Li, Z. Zhang, A.Johnston, R. Lamberton, M. Gubbins, T. McLaughlin, J. Gadbois, J. Ding, B.Cross, S. Xue, and P. Ryan, Commercial TMR heads for hard disk drives: char-acterization and extendibility at 300 gbit/in2, IEEE Transactions on Magnetics42, 97 (2006).

[7] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár,M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Spintronics: A Spin-Based Electronics Vision for the Future, Science 294, 1488 (2001).

[8] J. E. Hirsch, Spin Hall Effect, Physical Review Letters 83, 1834 (1999).

[9] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observationof the Spin Hall Effect in Semiconductors, Science 306, 1910 (2004).

[10] E. Saitoh, M. Ueda, H. Miyajima, and G. Tatara, Conversion of spin cur-rent into charge current at room temperature: Inverse spin-Hall effect, AppliedPhysics Letters 88, 182509, 182509 (2006).

[11] Y.-T. Chen, S. Takahashi, H. Nakayama, M. Althammer, S. T. B. Goennenwein,E. Saitoh, and G. E. W. Bauer, Theory of spin Hall magnetoresistance, PhysicalReview B 87, 144411 (2013).

41

http://www.sciencecartoonsplus.com/gallery/physics/galphys2d.php#

http://dx.doi.org/10.1109/TMAG.1975.1058782

http://dx.doi.org/10.1103/PhysRevB.39.4828

http://www.nobelprize.org/nobel_prizes/physics/laureates/2007/grunberg-lecture.html

http://dx.doi.org/10.1103/PhysRevLett.74.3273



http://dx.doi.org/10.1126/science.1065389


http://dx.doi.org/10.1126/science.1105514

http://dx.doi.org/10.1063/1.2199473

http://dx.doi.org/10.1063/1.2199473



Bibliography

[12] H. Nakayama, M. Althammer, Y.-T. Chen, K. Uchida, Y. Kajiwara, D. Kikuchi,T. Ohtani, S. Geprägs, M. Opel, S. Takahashi, R. Gross, G. E. W. Bauer,S. T. B. Goennenwein, and E. Saitoh, Spin Hall Magnetoresistance Inducedby a Nonequilibrium Proximity Effect, Physical Review Letters 110, 206601(2013).

[13] M. Althammer, S. Meyer, H. Nakayama, M. Schreier, S. Altmannshofer, M.Weiler, H. Huebl, S. Geprägs, M. Opel, R. Gross, D. Meier, C. Klewe, T.Kuschel, J.-M. Schmalhorst, G. Reiss, L. Shen, A. Gupta, Y.-T. Chen, G. E. W.Bauer, E. Saitoh, and S. T. B. Goennenwein, Quantitative study of the spin Hallmagnetoresistance in ferromagnetic insulator/normal metal hybrids, PhysicalReview B 87, 224401 (2013).

[14] A. Brataas, Insulating Magnets Control Neighbor’s Conduction, Physics 6, 56(2013).

[15] R. Gross, Lecture Notes on Spintronics, 2005.

[16] F. Schade, Fabrication and Characterization of Y3Fe5O12|Pt|Y3Fe5O12 Trilay-ers for Spin Current Based Experiments, Bachelor’s Thesis (Technische Uni-versität München, 2013).

[17] F. Czeschka, Spin Currents in Metallic Nanostructures, PhD thesis (TechnischeUniversität München, 2011).

[18] S. Takahashi and S. Maekawa, Spin current, spin accumulation and spin Halleffect, Science and Technology of Advanced Materials 9, 014105 (2008).

[19] J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDon-ald, Universal Intrinsic Spin Hall Effect, Physical Review Letters 92, 126603(2004).

[20] A. Brataas, Y. V. Nazarov, and G. E. W. Bauer, Finite-Element Theory ofTransport in Ferromagnet-Normal Metal Systems, Physical Review Letters 84,2481 (2000).

[21] S. Meyer, Magneto-thermogalvanische Experimente an (Ga,Mn)As Dünnfil-men, Diploma Thesis (Ludwig-Maximilians-Universität München, 2012).

[22] M. S. Wagner, Epitaktisches Wachstum dünner ferromagnetischer Schichtenaus Y3Fe5O12 mittels gepulster Laserdeposition, Bachelor’s Thesis (TechnischeUniversität München, 2011).

[23] Model 2128 Nanovoltmeter, Third Printing, Keithley Instruments, Inc. (28775Aurora Road Cleveland, Ohio, U.S.A., 1998).

[24] M. Schneider, Herstellung und Charakterisierung von Y3Fe5O12-Pt Bilagenfür Spinstrom basierte Experimente, Bachelor’s Thesis (Technische UniversitätMünchen, 2013).

42





http://dx.doi.org/10.1103/Physics.6.56

http://dx.doi.org/10.1103/Physics.6.56

http://www.wmi.badw.de/teaching/Lecturenotes/index.html

http://www.wmi.badw-muenchen.de/publications/theses/Czeschka_Doktorarbeit_2011.pdf

http://stacks.iop.org/1468-6996/9/i=1/a=014105





http://www.wmi.badw-muenchen.de/publications/theses/Meyer,Sybille_Diplomarbeit_2012.pdf

http://www.wmi.badw-muenchen.de/publications/theses/Meyer,Sybille_Diplomarbeit_2012.pdf

http://www.wmi.badw-muenchen.de/publications/theses/Wagner_Bachelorarbeit_2011.pdf

http://www.wmi.badw-muenchen.de/publications/theses/Wagner_Bachelorarbeit_2011.pdf

Bibliography

[25] K.-W. Nielsen, Ursache der magnetischen Kopplung in Kobalt-dotiertem ZnO ,PhD thesis (Technische Universität München, 2008).

[26] G. Fischer, H. Hoffmann, and J. Vancea, Mean free path and density of con-ductance electrons in platinum determined by the size effect in extremely thinfilms, Physical Review B 22, 6065 (1980).

[27] H. Neff, S. Henkel, E. Hartmannsgruber, E. Steinbeiss, W. Michalke, K. Steen-beck, and H. G. Schmidt, Structural, optical, and electronic properties ofmagnetron-sputtered platinum oxide films, Journal of Applied Physics 79, 7672(1996).

[28] K. Kuribayashi and S. Kitamura, Preparation of Pt-PtOx thin films as electrodefor memory capacitors, Thin Solid Films 400, 160 (2001).

[29] S. Geprägs, private communication.

[30] R. Gross and A. Marx, Festkörperphysik (Oldenbourg Wissenschaftsverlag,2012).

[31] P. Hansen, P. Röschmann, and W. Tolksdorf, Saturation magnetization ofgallium-substituted yttrium iron garnet, Journal of Applied Physics 45, 2728(1974).

[32] Y. M. Lu, Y. Choi, C. M. Ortega, X. M. Cheng, J. W. Cai, S. Y. Huang, L. Sun,and C. L. Chien, Pt Magnetic Polarization on Y3Fe5O12 and MagnetotransportCharacteristics, Physical Review Letters 110, 147207 (2013).

[33] S. Geprägs, S. Meyer, S. Altmannshofer, M. Opel, F. Wilhelm, A. Rogalev,R. Gross, and S. T. B. Goennenwein, Investigation of induced Pt magneticpolarization in Pt/Y3Fe5O12 bilayers, Applied Physics Letters 101, 262407,262407 (2012).

[34] S. Geprägs, S. T. Goennenwein, M. Schneider, F. Wilhelm, K. Ollefs, A. Ro-galev, M. Opel, and R. Gross, Comment on “Pt magnetic polarization onY3Fe5O12 and magnetotransport characteristics”, ArXiv e-prints (2013).

[35] N. Vlietstra, J. Shan, V. Castel, B. J. van Wees, and J. Ben Youssef, Spin-Hall magnetoresistance in platinum on yttrium iron garnet: Dependence onplatinum thickness and in-plane/out-of-plane magnetization, Physical ReviewB 87, 184421, 184421 (2013).

43

http://www.wmi.badw-muenchen.de/publications/theses/Nielsen_Doktorarbeit_2008.pdf


http://dx.doi.org/10.1063/1.362341

http://dx.doi.org/10.1063/1.362341

http://dx.doi.org/http://dx.doi.org/10.1016/S0040-6090(01)01503-6

http://books.google.de/books?id=4BY31IukHI8C

http://dx.doi.org/10.1063/1.1663657

http://dx.doi.org/10.1063/1.1663657


http://dx.doi.org/10.1063/1.4773509

http://dx.doi.org/10.1063/1.4773509

http://adsabs.harvard.edu/abs/2013arXiv1307.4869G



Acknowledgements

This bachelor thesis wouldn’t exist without the help and support of many people.Thus, I would like to thank

• Prof. Dr. Rudolf Gross for having given me the opportunity to do my bachelorthesis at the Walther Meißner Insitut für Tieftemperaturforschung (WMI).

• Dr. Sebastian T. B. Goennenwein for supervising this bachelor thesis, for hisimprovement proposals and for proofreading this thesis.

• Dr. Hans Huebl for giving me the opportunity to give a seminar talk aboutthe topic of my bachelor thesis. This was a good start to develop a sensiblestructure for this thesis.

• Dr. Stephan Geprägs for his support concerning questions about the growthof the samples and related topics like SQUID data, etc.

• Dr. Matthias Opel for his support, too, especially concerning conductive PtOx.

• Sibylle Meyer for her great support and advice during my whole time at theWMI. Not only that without her, I wouldn’t have been able to take data atlower temperatures than room temperature because the cryostat started to dowhat it wants shortly after starting working for this thesis. She also proofreadthis thesis and I could always turn to her when having problems or questions- in case I found her in one of several possible rooms/labs :-)

• Felix Schade for growing the important samples for this thesis. Without histrilayer, I would not have been able to keep to the original title of this thesis.

• Marc Schneider for growing the samples for the YIG thickness series.

• Richard Schlitz for being a great fellow bachelor student. With you, it wasnever boring to refill the cryostat, etc.

• Friedrich Witek for his many tips concerning writing a thesis.

• All the other students in the bachelor room for the good atmosphere and forhelping me with some troubles, e. g. LATEX ones.

45

• Last but not least, I want to thank all the other people at the WMI, whosupported this thesis, either by helping to fix technical stuff like the ion beametcher, by giving some advice or just by contributing to the good workingatmosphere.

46

Documents

Spin Hall-Magnetoresistancein FMI/NM/FMI-TrilayersDominik Bachelor... · in FMI/NM/FMI-Trilayers Dominik Irber ... realizable in everyday life as the fabricated one is quite diﬀerent