Separation of the first- and second-order contributions in magneto-optic Kerr effect magnet

a r X i v :c o n d -m a t /0311278v 1 12 N o v 2003

Separation of the ?rst-and second-order contributions in magneto-optic Kerr e?ect

magnetometry of epitaxial FeMn/NiFe bilayers

T.Mewes ?

Department of Physics,1077Smith Laboratory

Ohio State University

174W 18th Ave,Columbus,OH 43210,USA

H.Nembach

Fachbereich Physik and Forschungsschwerpunkt MINAS

Technische Universit¨a t Kaiserslautern

Erwin-Schr¨o dinger-Str.56,67663Kaiserslautern,Germany

M.Rickart

INESC Microsistemas e Nanotecnologia

Rua Alves Redol,91000-029Lisboa,Portugal

B.Hillebrands

Fachbereich Physik and Forschungsschwerpunkt MINAS

Technische Universit¨a t Kaiserslautern

Erwin-Schr¨o dinger-Str.56,67663Kaiserslautern,Germany

(Dated:February 2,2008)

The in?uence of second-order magneto-optic e?ects on Kerr e?ect magnetometry of epitaxial exchange coupled Fe 50Mn 50/Ni 81Fe 19-bilayers is investigated.A procedure for separation of the ?rst-and second-order contributions is presented.The full angular dependence of both contribu-tions during the magnetization reversal is extracted from the experimental data and presented using gray scaled magnetization reversal diagrams.The theoretical description of the investigated system is based on an extended Stoner-Wohlfarth model,which includes an induced unidirectional and fourfold anisotropy in the ferromagnet,caused by the coupling to the antiferromagnet.The agree-ment between the experimental data and the theoretical model for both the ?rst-and second-order contributions are good,although a coherent reversal of the magnetization is assumed in the model.

I.

INTRODUCTION

Since its discovery in 1877by J.Kerr 1the magneto-optic Kerr e?ect (MOKE)has evolved into a very power-ful tool for characterization of magnetic materials.Due to its high sensitivity MOKE magnetometry is widely used for thin ?lm and multilayer analysis.The high lat-eral resolution of modern MOKE magnetometry enables the study of individual magnetic nanostructures 2,3,4,5.Recent developments using stroboscopic magneto-optic techniques achieved high time resolution 6,7,8,9,thus en-abling the study of the magnetization dynamics on a picosecond-time https://www.sodocs.net/doc/e83886117.html,ing second harmonic genera-tion in MOKE measurements results in a high sensitivity to the magnetization at the interfaces between di?erent materials 10,11,12,13,14.

The origin of magneto-optic e?ects is the spin-orbit interaction.In many cases it is su?cient to treat the magneto-optic response in ?rst order,i.e.take into account only contributions linearly proportional to the

magnetization.However as ?rst shown by Osgood et al.15second-order magneto-optic e?ects can be impor-tant in thin ?lms with in-plane anisotropy.In particular for magnetization reversal measurements using MOKE magnetometry the second-order contributions can lead to asymmetric hysteresis loops 15,16,17,18,19,which are not observed using other magnetometry methods.On the other hand in exchange bias systems,which consist of a ferromagnet exchange coupled to an antiferromagnet,asymmetric hysteresis loops have been reported inde-pendently of the magnetometry method 20,21,22,23,24,25,26.Therefore special care is necessary when investigating ex-change bias systems using magneto-optical Kerr e?ect magnetometry in order to distinguish between the e?ects caused by second-order magneto-optics and those caused by the broken symmetry due to the exchange bias e?ect.In this article we use the epitaxial Fe 50Mn 50/Ni 81Fe 19exchange bias model system to show how second-order magneto-optic e?ects a?ect the magnetization reversal observed in MOKE magnetometry.By utilizing a sim-

2

ple procedure described in this article both the?rst-and second-order e?ects can easily be separated.The exper-imental data is summarized and compared with an ex-tended Stoner-Wohlfarth model using magnetization re-versal diagrams.Our approach builds upon a method to extract the linear and the quadratic Kerr contributions from Kerr e?ect measurements,which has recently been proposed by Mattheis et al.,and in which a magnetic?eld of constant?eld strength is rotated about the axis normal to the sample surface,(”ROTMOKE”method,32,33).In contrast to this method,which is reminiscent to a torque measurement,the method proposed in the current article is based on the analysis of the magnetization reversal of the sample under investigation.

II.EXPERIMENT

The samples were prepared in an UHV system with a base pressure of5×10?11mbar.In order to epitaxially grow Fe50Mn50/Ni81Fe19bilay-ers single crystalline MgO(001)substrates were used,?rst depositing a bu?er layer system consisting of Fe(0.5nm)/Pt(5nm)/Cu(100nm)described in detail elsewhere27.The samples consist of a10nm thick Fe50Mn50layer and a5nm thick Ni81Fe19layer covered by2nm Cu in order to ensure symmetric interfaces and by1.5nm Cr to prevent oxidation.The di?erent ma-terials were evaporated using either an e-beam evapora-tor(Fe,Pt,Ni81Fe19,Cr)or Knudsen cells(Cu,Mn), with typical evaporation rates ranging from0.01nm/s to0.1nm/s.The layer composition and crystallographic structure was characterized using a combined low energy electron di?raction(LEED)and Auger system.Further structural investigation was performed using re?ecting high energy di?raction(RHEED)and in-situ scanning tunneling microscopy(STM).The samples were heated after deposition in UHV slightly above the bulk N′e el-temperature of Fe50Mn50(500K),while a magnetic?eld of500Oe was applied along the in-plane[100]-direction of Ni81Fe19during cool down.

III.RESULTS AND DISCUSSION

A Fe50Mn50layer deposited on top of the Cu(001) bu?er layer by co-evaporation of Fe by e-beam evap-oration and Mn from a Knudsen cell also grows in (001)orientation,with[100]F eMn||[100]Cu.The surface morphology consists of rather large terraces with small monoatomic islands on top.These small islands have a large

size distribution,as can be seen in the STM image in Fig.1(a).Ni81Fe19deposited on Fe50Mn50(001)also grows in(001)orientation but shows a broadening of the LEED spots due to formation of small islands with an average size of10nm,while the larger terraces of the un-derlying Fe50Mn50are still visible,as can be seen in Fig. 1(b).FIG.1:(a)STM image of a10nm thick(001)-oriented Fe50Mn50-layer grown on MgO(001)/Fe/Pt/Cu,the scan area is0.4μm×0.4μm,with a full height scale of2nm.The inset shows the LEED pattern of the same surface at a primary en-ergy of109eV.(b)STM image of a5nm thick(001)-oriented Ni81Fe19-layer grown on top of a10nm thick Fe50Mn50-layer, the scan area is0.4μm×0.4μm,with a full height scale of 2nm.The inset shows the LEED pattern of the same surface at a primary energy of128eV.

The magnetic properties of a Fe50Mn50(10 nm)/Ni81Fe19(5nm)bilayer are measured using Kerr e?ect magnetometry.The magnetic?eld is applied collinear to the plane of the incident s-polarized light. The angleαH of the in-plane[100]-direction of the Ni81Fe19layer relative to the plane of the incident light is varied from0to360degree in1degree steps by rotating the sample.For all experimental data obtained from this rotation the decreasing?eld branch is shown in Fig.2,using a magnetization reversal diagram with a grayscale proportional to the Kerr-rotation.This kind of data visualization enables the presentation of the whole angular dependence of the magnetization reversal in a single diagram and was described in detail elsewhere28. As can be seen in this?gure the magnetization reversal diagram of the Fe50Mn50/Ni81Fe19exchange bias system shows an asymmetry,which is characteristic for

3 FIG.2:Magnetization reversal diagram for the branch of the

hysteresis curve with decreasing external magnetic?eld of an

epitaxial Ni81Fe19/Fe50Mn50sample,as measured using Kerr

e?ect magnetometry.The grayscale is proportional to the

Kerr-rotation.The regions where the asymmetry discussed

in the text is most obvious are marked’A‘and’B‘.

quadratic contributions to the Kerr rotation,as will

be shown in the following.This asymmetry impedes a

correct determination of the angular dependence of the

coercive?eld and the exchange bias?eld from the raw

data causing those quantities to be asymmetric with

respect to the in-plane angleαH.

The Kerr rotationθKerr,s in longitudinal geometry

with s-polarized light and the sample magnetized in

the plane of the sample surface,can be written as

follows19,32,33,34,35:

θKerr,s=?long

Kerr M +?quad

Kerr

M M⊥,(3.1)

where M and M⊥are the in-plane magnetization com-ponents parallel and perpendicular to the plane of inci-

dence of the light.?long

Kerr and?quad

Kerr

are the longitudinal

and quadratic proportionality factors of the Kerr rota-tion.The second order term proportional to the product of the longitudinal and transverse component is the re-?ection analogy of the Voigt e?ect19,29,30,31and gives rise to the asymmetry observed in Fig.

2.The two contribu-tions to the Kerr rotation can be separated by making use of the symmetry of the problem as follows.As illus-trated in Fig.3,if the in-plane angleαH of the sample with respect to the plane of the incident light is changed by180deg and the sign of the magnetic?eld H is re-versed the same magnetization reversal process should be observed.However by doing so the?rst term in equation (

3.1)proportional to M changes sign while the second term proportional to M M⊥will have the same sign for both sample orientations.This leads to apparently di?er-ent magnetization reversal curves observed in Kerr e?ect magnetometry,an example of which is shown in Fig.4 (a).

By calculating the di?erence of the magnetization re-versal forαH andαH+180deg the Kerr rotationθlong

Kerr FIG.3:Geometry used to separate the di?erent contribu-tions to the Kerr rotationθKerr,s.(a)Situation for an angle αH of the[100]-direction with respect to the plane of the inci-

dent light(characterized by the wavevector k).(b)Equivalent situation with rotation of the sample by180deg and reversed direction of the applied magnetic?eld.The?lled circle marks the orientation of the sample.

caused by the longitudinal component of the magnetiza-tion M can be reconstructed:

θlong

Kerr

:=[θKerr(αH)?θKerr(αH+180?)]/2(3.2)

=?long

Kerr

M .

This is shown in Fig.4(b)for the magnetization rever-sals shown in part(a)of the same?gure.On the other

hand the quadratic contributionθquad

Kerr

to the Kerr rota-tion can be obtained by calculating the average of the Kerr rotation atαH andαH+180deg:

θquad

Kerr

:=[θKerr(αH)+θKerr(αH+180?)]/2(3.3)

=?quad

Kerr

M M⊥,

as shown in Fig.4(c).

By carrying out the same kind of analysis for all angles

αH the magnetization reversal diagram forθlong

Kerr

,i.e.for the longitudinal component of the magnetization,can be

4

FIG.4:(a)Magnetization reversal for two equivalent angles

αH=90deg(open symbols)andαH=270deg(line).Note

that the sign of the magnetic?eld for the magnetization re-

versal atαH=270deg was reversed,so that the reversal is

equivalent to that atαH=90deg.In(b)the linear longitu-

dinal contributionθlong

Kerr to the Kerr rotation of the magneti-

zation reversal in(a)is shown,while in(c)the second-order contributionθquad

Kerr

is shown.

reconstructed,as is shown in Fig.5(a).Consequently in this?gure the asymmetry that was observed in Fig.2 is no longer present.Note however,that the symmetry

04590135180225270315360

FIG.5:a)Measured magnetization reversal diagram forθlong

Kerr caused by the longitudinal component of the magnetization M .In b)the corresponding reversal diagram of the second-order contributionθquad

Kerr

caused by M M⊥is shown.In both graphs the grayscales are chosen di?erently in order to?t the respective data range.

breaking e?ect of the exchange bias e?ect is still visible in this diagram.A similar diagram can be constructed

for the quadratic contributionθquad

Kerr

to the Kerr rotation, as shown in Fig.5(b).As this diagram contains infor-mation about the product M M⊥it re?ects the corre-sponding symmetry(see also Fig.7(b)discussed later).

The reversal data of the longitudinal component of the magnetization in Fig.5(a)is used to derive the angular dependence of the exchange bias?eld H eb(see Fig.6(a))and the coercive?eld H C(see Fig.6(b)) of the Fe50Mn50/Ni81Fe19double layer system.These angular dependencies are then?tted assuming a coher-ent rotation of the magnetization and using the perfect-delay convention36within the framework of an extended Stoner-Wohlfarth model28,37.The experimental data can be reasonably well described by including a unidirectional anisotropy K1and a fourfold anisotropy K4contribution to Gibb’s free energy g of the system,which in turn can

FIG.6:Angular dependence of(a)the exchange bias?eld and(b)the coercivity.The experimental

data is shown as solid symbols,while the?t using equation3.4is shown as open symbols.

be written as:

g=?K1cos(αM)+K4sin2(αM)cos2(αM)(3.4)?HM S cos(αM?αH).

A?t of the experimental data shown in Fig.6using the Gibb’s free energy given by equation3.4results in a unidirectional anisotropy K1=(2.7±0.1)erg/cm3and a fourfold anisotropy K4=(4.9±0.2)erg/cm3.Note that the appearance of an induced fourfold anisotropy in addition to the unidirectional anisotropy in epitax-ial Fe50Mn50/Ni81Fe19-bilayer systems has recently been shown theoretically using a vector spin model38.The resulting angular dependence of the exchange bias?eld H eb and the coercive?eld H C predicted by the extended Stoner-Wohlfarth model is also shown in Fig.6.

In order to complete the picture of the magnetization reversal that results from these anisotropies within the extended Stoner-Wohlfarth model in Fig.7the reversal diagrams are given for both M and M M⊥.These two diagrams correspond to the expected linear and second-FIG.7:Magnetization reversal diagrams of the decreasing ?eld branch,as predicted by the extended Stoner-Wohlfarth model using equation3.4,with K1=2.7erg/cm3and K4= 4.9erg/cm3.In a)the longitudinal component M is shown, while in b)the grayscale is proportional to the product M M⊥.

order contribution to the magneto-optic Kerr e?ect re-spectively and can therefore be directly compared with the experimental results in Fig. 5.Given the simpli?-cation of a coherent magnetization reversal process as-sumed in the extended Stoner-Wohlfarth model and the small number of?tting parameters the agreement be-tween the model and the experimental results is sur-prisingly good.However one notices di?erences between the model calculations and the experimental results es-pecially along the axis parallel to the easy direction of the unidirectional anisotropy,i.e.around0deg and 180deg.Similar deviations have been observed in epi-taxial NiFe/FeMn bilayers28(i.e.in a system with re-versed layer sequence)and may be related to thermal activation37or to domain formation and propagation, which are not taken into account in the Stoner-Wohlfarth model.

IV.SUMMARY

In summary we have shown that second-order magneto-optic e?ects are present in exchange coupled epitaxial Fe50Mn50/Ni81Fe19-bilayers.By using the method described in this article it is possible to sepa-rate the?rst-and second-order contributions.Thereby the asymmetry related to magneto-optics can also be sep-arated from the one associated with the exchange bias ef-fect.The experimental data can thus be analyzed within an extended Stoner-Wohlfarth model,which describes well the overall angular dependence of the magnetization reversal.The observed di?erences between the exper-imental data and the Stoner-Wohlfarth model may be caused by thermal activation or domain formation and propagation.

Acknowledgments

We would like to thank R.Lopusn′?k for stimulating and helpful discussions.

?Electronic address:mewes@https://www.sodocs.net/doc/e83886117.html,

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