N ELSEVIER Journal of Magnetism and Magnetic Materials 133 (1994) 74-76

journal of magnetism and magnetic

~ H materials

Influence of domain wall stabilization on dynamic losses in amorphous ribbons

E. Ldpez "'*, C. Aroca ~, M. Maicas a, M.C. Sfinchez a, p. Sfinchez b " Dpto. Fisica de Materiales, Facultad F[sica, Unit,ersidad Complutense, 28040 Madrid, Spain

b Dpto F[sica, ETSI Telecommunicacidn, Univ. Politdcnica Madrid, 28040 Madrid, Spare

Abstract

Dynamical hysteresis losses in amorphous magnetic materials depend mainly on the micro eddy currents. This effect can be enhanced by domain wall (DW) stabilization phenomena, since the anisotropy modulation induced by a stabilized DW behaves like a pinning plane. The irreversible displacement of a DW that overcomes this kind of defect produces an increase of micro-eddy currents that can be an important part of the total hysteresis losses.

1. Introduction

It is well known that Joule heating by eddy currents is the predominant loss mechanism in magnetic metal- lic alloys undergoing cyclic magnetization, even under quasistatic conditions [1,2]. Moreover, domain wall pin- ning produced by local changes in anisotropy or the existence of impurities contribute to increase static and dynamic losses. Such kind of situations produce an anomalous increase of domain wall velocity just when it overcomes the defect, increasing the micro-eddy currents.

Under sufficient stress high magnetostrictive amor- phous ribbons show magnetization processes with few domain walls. Even more, it is possible to get magneti- zation processes with just one domain wall by applying a large enough stress, since the domain wall character- istics such as energy and width are easily controllable in a wide range by the applied stress. In this way we have a very simple experimental situation that can be accurately simulated to understand the mechanism of magnetic losses.

In previous works [3,4] we have simulated the inter- action of a domain wall (DW) with several kinds of anisotropy modulations. In this paper we use these

* Corresponding author. Fax: +34 (1) 394 4547.

techniques for studying the hysteresis losses in samples with a single DW that moves cyclically and interacts with helical anisotropy induced by DW stabilization (IHA).

2. Simulat ion

The main parameters that control the magnetiza- tion processes in a sample with a single DW, interact- ing with an IHA are the propagation field, Hp, the stabilization field, H~, and the demagnetizing field H a. The propagation field (average value of magnetic field necessary to produce domain wall displacement in the sample) is dependent on internal factors such as sam- ple surface roughness, nonmagnetic inclusions, ctc., and on external factors such as anisotropy induced by the applied stress and the temperature of the sample [5]. The stabilization field (the minimum field neccs- sary to overcome the anisotropy modulation produced by the domain wall stabilization, IHA) depends on the maximum anisotropy in annealing conditions and ap- plied stress. The demagnetizing field depends on sam- pie geometry and magnetization state. During the in- teraction the susceptibility decreases abruptly because of the domain wall pinning.

A numerical method has been used to study the influence of applied stress on H~ by simulating the static and dynamic interaction between a domain wall

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E. L6pez et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 74-76 75

Hs(Am -1)

50.

<P I.H.A. width

40 i t 1.2 1.9 2.6

D.W. width (10"~m)

Fig. 1. Stabilization H~ fields versus DW width (with IHA).

and an IHA, in the case of similar widths. This method is based on the minimization of the total energy of the system D W - I H A [4]. Fig. 1 shows the H s dependence on domain wall width. It has been seen that the H S reaches its minimum value when the DW and the IHA widths coincide.

Magnetization processes can be modelled by assum- ing that the domain wall movement is controlled by the magnetic fields mentioned above. These assumptions allow us to obtain minor hysteresis loops and hysteresis losses from simulation based on the supposition that the domain wall velocity, when there is no interaction between the DW and the IHA, is:

( V=~w" H - H p - , (1) a

where P~w is the DW mobility, H is the applied field, N is the demagnetizing factor, 2a is the sample thick-

...-. E <[

4 0 -

20-

0-

-20-

-40

1

-3 -1 1 Magnetic Field H (Am "1)

Fig. 2. Hysteresis for IHA sample.

hess and x is the DW position with respect to the IHA. During the interaction v = 0 until

__N'x'M~ > [Hs]. JI4-I-Ip a

The hysteresis loop obtained from this study is shown in Fig. 2.

3. Experimental method

Metglas 2826 ribbon samples were prepared by an- nealing under a saturating applied magnetic field and at zero field in order to have samples with or without IHA. We have studied the D W - I H A interaction by comparing the measured magnetic losses in these sam- ples.

The losses were measured using a typical double- winding system. The magnetic field applied consists of a dc signal for centering the hysteresis loop where the IHA is present and an ac signal for describing the hysteresis loop. B~ and By, phase and quadrature of the first harmonic of magnetic induction B, are ob- tained by measuring the induced electromotive force at the pickup coil by a lock-in amplifier synchronized with a square signal in phase with the current through the exciting winding (proportional to H, so that the quadrature component Hv = 0). Magnetic losses can then be obtained using the expression [6]:

P = - H x .By . (2)

4. Results

Fig. 3 shows the hysteresis losses obtained from the simulation for both samples with and without IHA, while Fig. 4 shows experimental results. As it was expected losses increase clearly when the DW have to jump over the IHA.

Changes in stresses applied on the sample produce anisotropy variations and therefore changes in the DW width. Fig. 5 shows the magnetic losses measured for different applied stresses and thus different domain wall widths. We can see how the losses are minimum when the DW and IHA widths are the same. This situation is in good agreement with the results of Fig. 1, except for the H~ values, which are higher because of different simulation conditions [4].

The effect of the IHA in magnetic losses is very important because it behaves like a pinning plane. The whole domain wall surface is pinned when it interacts with the IHA and the differential susceptibility is al- most zero during the interaction. When the domain wall overcomes the IHA the whole DW surface moves at high velocity until it reaches the next almost stable

76 E. L6pez et al. / Journal of Magnetism and Magnetic Materials 133 (1994) 74-76

4-00 ] Hp=!Am -1

x o

200

o

Ld

O+ ~ , ~ , - - , 0 40 80

Mognetic Induction (roT) 450

8

-~ 350 o

o 250

©

150 4O

Hp= 0.6Am -~

Hp=O.4Arn -~

/ H,=I .SAm-l/'" H,= 0.BArn -1

~ H~=O (no I.H.A.)

9 /

60 8'0 ~ ~ 60 M o g n e t i c I n d u c ~ T o n ( n o T )

Fig. 3. Simulated losses for samples (a) without and (b) with IHA.

si tuation. It p roduces very large losses because eddy cur ren ts are p resen t in the zone swept by the domain wall ( the whole domain wall). In normal in terac t ions

2 4 0

E

180 ©

o

~h 120 £z

S o I ~ 6o © c

L:J

!.H,A.

NON I.H.A.

r ] 1 y ~ = T ~ i - - q

0 0 40 80 ! 20 ! 60 Magnetic Induction (m [ )

Fig. 4. Experimentally measured losses.

~- 30

28-~

o 26

(b

L!;

24

/ , * f - -

t O'o f o r I .~t .A. w i d t h

0(} 20(} ,590 4 O0 stress (MPo)

Fig. 5. Losses in sample with IHA versus stress.

be tween D W and pinning cent res the susceptibili ty is still large because there are some unp inned areas in the DW. W h e n the domain wall overcomes these pin- ning cent res eddy cur ren ts are only res t r ic ted to these small areas and the losses are lower. In the s imula ted hysteresis loop losses have been implicitly t aken into account in the p ropaga t ion field. This makes losses increase almost linearly with the maximum induction.

5 . C o n c l u s i o n s

General ly , a m o r p h o u s mater ia l s are thermal ly t rea ted in o rder to reduce in ternal stresses. In these t rea tments , if no magnet ic field is applied, the sample is not sa tura ted . Since the domain walls tend to be stabil ized in the posi t ions they occupied dur ing the annea l ing IHAs will appea r in them. It is thus highly r e c o m m e n d e d to annea l the samples with a sa tura t ing magnet ic field appl ied or to annea l over the Curie t e m p e r a t u r e in o rder to avoid those p inning planes and so to reduce losses.

Acknowledgement. This work was suppor ted by CI- CYT of the Minis ter io de Educaci6n (TAP92-0851- mat93-0322).

R e f e r e n c e s

[1] J.E.L. Bishop, J. Magn. Magn. Mater. 49 (1984) 241. [2] C. Aroca et al., Phys. Rev. B 34 1 (1986) 490. [3] M. Maicas et al., J. Magn. Magn. Mater. 104-107 (1992)

319. [4] M. Ma~cas et al., Phys. Rev. B 47 6 (1993) 3180. [5] P. Sfinchez et al., IEEE Trans. Magn. 26 (1990) 1139. [6] C. Aroca et al., J. Phys. E: Sci. Instrum. 22 (1989) 185,