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Paramagnetic anisotropic magnetoresistance in thin films of SrRuO3

Paramagnetic anisotropic magnetoresistance in thin films of SrRuO3
Paramagnetic anisotropic magnetoresistance in thin films of SrRuO3

a r X i v :c o n d -m a t /0311343v 1 [c o n d -m a t .m t r l -s c i ] 14 N o v 2003

Paramagnetic anisotropic magnetoresistance in thin ?lms of SrRuO 3

Isaschar Genish,Yevgeny Kats,and Lior Klein

Department of Physics,Bar-Ilan University,Ramat-Gan 52900,Israel

James W.Reiner ?and M.R.Beasley

T.H.Geballe Laboratory for Advanced Materials,Stanford University,Stanford,California 94305SrRuO 3is an itinerant ferromagnet and in its thin ?lm form when grown on miscut SrTiO 3it has T c of ~150K and strong uniaxial anisotropy.We measured both the Hall e?ect and the magnetoresistance (MR)of the ?lms as a function of the angle between the applied ?eld and the normal to the ?lms at temperatures above T c .We extracted the extraordinary Hall e?ect that is proportional to the perpendicular component of the magnetization and thus the MR for each angle of the applied ?eld could be correlated with the magnitude and orientation of the induced magnetization.We successfully ?t the MR data with a second order magnetization expansion,which indicates large anisotropic MR in the paramagnetic state.The extremum values of resistivity are not obtained for currents parallel or perpendicular to the magnetization,probably due to the crystal symmetry.

I.

INTRODUCTION

The phenomenon of anisotropic magnetoresistance (AMR)in magnetic conductors expresses the dependence of the resistivity ρon the angle δbetween the current J and the magnetization M .In polycrystals the AMR ef-fect is commonly found to follow:ρ=ρ⊥+(ρ ?ρ⊥)cos 2δwhere ρ⊥is the resistivity when J ⊥M ,and ρ is the resistivity when J M [1].This simple relation is not expected to hold in crystalline samples where both the current orientation relative to the lattice as well as the magnetization orientation relative to the lattice play an important role.

Here we present AMR measurements of thin ?lms of the 4d itinerant ferromagnet SrRuO 3above T c (T c ~150K).Those ?lms are epitaxial and characterized by large uniaxial magnetocrystalline anisotropy (MCA)[2].In our measurements,we study the AMR in uncommon conditions:(a)while in most AMR measurements the orientation of M is changed without changing its mag-nitude,here,because of the large MCA both orientation and magnitude of M are changing;and (b)while in most AMR measurement the applied ?eld H is parallel to M ,here,because of the large MCA M ?H except for the cases where H is along the easy or hard axes.Therefore,to explore the AMR in SrRuO 3it is not su?cient to mea-sure magnetoresistance (MR)as a function of angle,but we need to independently determine both the magnitude and orientation of M .

Our ?lms are grown on miscut (2?)SrTiO 3substrates using reactive electron beam epitaxy.The ?lms have orthorhombic structure (a =5.53?A ,b =5.57?A ,c =7.85?A )and they grow uniformly (without twinning)with the c axis in the ?lm plane and the a and b axes at 45?out of the plane (see Fig.1)[3].The MCA is uniaxial

10]

https://www.sodocs.net/doc/4d8159905.html,bining the two measurements we show that the MR can be ?t very well with a second order magnetization expansion.

Both HE and MR measurements were performed as a function of the angle φbetween the applied ?eld H and the easy axis,where H is rotating in the (001)plane.Each ?lm has two kinds of patterns:a pattern with cur-rent along the [1

-3.5-3

-2.5-2

-90

-45

04590

p r e d i c t e d M R (%)

α

(deg.)

FIG.3:The expected MR at 170K and H =8T as a function of the angle αbetween M and b ,assuming M is constant,for P c (solid curve),and P ab (dashed curve).

?tting parameters in case there is di?erence between the instrumental φand the actual φof up to 2?.

The ?ts of the MR data based on Eq.1allow us to determine the ”clean”AMR e?ect;namely,how would the resistivity change if we could rotate M in the (001)plane without changing its magnitude.Figure 3shows the expected behavior at T =170K for P ab and P c for a value of magnetization obtained with H =8T along the easy axis.

For P c we note that although J ⊥M there is a sig-ni?cant AMR (β=1),and that γ=0is within our

experimental accuracy,as could be expected from sym-metry considerations.These results exhibit strong de-pendence of the MR not only on the angle between M and J (which remains constant)but also on the direction of M relative to the crystal.For P ab we note that the extremum values are not obtained for J M or J ⊥M but at intermediate angles.In fact,the extremum values for P ab are in between those obtained in P c (along the a and b axes)and those observed in polycrystals (parallel and perpendicular to J ).This shows that in our case the AMR related to the orientation of M with respect to the lattice is of the same order of magnitude as the AMR due to the relative orientation of M and J .We also note that for α=45?,which corresponds to M perpendicular to the plane the MR is di?erent in P ab and P c despite the fact that in both cases J ⊥M .This illustrates the dependence of MR on the direction of J relative to the crystal.

In conclusion,we have presented AMR investigation of SrRuO 3with simultaneous measurements of M and MR in the same pattern thus enabling accurate deter-mination of its AMR behavior despite the change in the magnitude of M and in its relative angle with H .The re-sults indicate signi?cant AMR even in the paramagnetic state,where M is relatively small,and large e?ect of the orientation of M and J relative to the crystal axes.

We acknowledge support by the Israel Science Foun-dation founded by the Israel Academy of Sciences and Humanities.

[1]T.R.McGuire and R.I.Potter,IEEE Trans.Magn.,

MAG-11,1018(1975).

[2]L.Klein et al .,J.Phys.:Condens.Matter 8,10111(1996).[3]A.F.Marshall et al .,J.Appl.Phys.85,4131(1999).[4]As the sample is rotated in applied magnetic ?eld,jumps

in magnetoresistance which correspond to magnetization reversal occur at angles consistent with a uniform direction

of the easy axis throughout the sample.[5]J.Smit,Physica XXI ,877(1955).

[6]L.Klein et al .,Phys.Rev.B 61,7842(2000).

[7]Even for a saturated magnetization (which is far from the

case of 170K,6?8T),the demagnetizing ?eld is less than 5%of the ?elds we apply here.

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ansysworkbench设置材料属性

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FLUENT控制步长时间courant数的有效的经验

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它们与温度T的关系为 $xi_{ab}(T)=xi_{ab}(0)(1-T//T_c)^{-1/2}$ $xi_c(T)=xi_c(0)(1-T//T_c)^{-1/2}$ 这篇各向异性相干长度(anisotropiccoherencelength)百科小物理,你推荐给朋友了么?

A plasticity and anisotropic damage model for plain concrete

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二十多种材料特性 Isotropic Elastic: High Carbon Steel MPMOD,1,1 MP,ex,1,210e9 ! Pa MP,nuxy,1,.29 ! No units MP,dens,1,7850 ! kg/m3 Orthotropic Elastic: Al203 MPMOD,1,2 MP,ex,1,307e9 ! Pa MP,ey,1,358.1e9 ! Pa MP,ez,1,358.1e9 ! Pa MP,gxy,126.9e9 ! Pa MP,gxz,126.9e9 ! Pa MP,gyz,126.9e9 ! Pa MP,nuxy,1,.20 ! No units MP,nuxz,1,.20 ! No units MP,nuyz,1,.20 ! No units MP,dens,1,3750 ! kg/m3 Anisotropic Elastic: Cadmium MPMOD,1,3 MP,dens,3400 ! kg/m3 TB,ANEL,1 TBDATA,1,121.0e9 ! C11 (Pa) TBDATA,2,48.1e9 ! C12 (Pa) TBDATA,3,121.0e9 ! C22 (Pa) TBDATA,4,44.2e9 ! C13 (Pa) TBDATA,5,44.2e9 ! C23 (Pa) TBDATA,6,51.3e9 ! C33 (Pa) TBDATA,10,18.5 ! C44 (Pa) TBDATA,15,18.5 ! C55 (Pa) TBDATA,21,24.2 ! C66 (Pa) Blatz-K Rubber MPMOD,1,5 MP,gxy,1,104e7 ! Pa Mooney-Rivlin: Rubber MPMOD,1,8 MP,dens,1,.0018 ! lb/in3 MP,nuxy,1,.499 ! No units TB,MOONEY,1

梯度向量流的各向异性扩散分析

ISSN1000—9825,CODENRUXUEW JournalofSoftware,V01.21,No.4,April2010,PP.612—619 doi:10.3724/SEJ.1001.2010.03523 @byInstituteofSoftware.theChineseAcademyofSciences.Allrightsreserved. 梯度向量流的各向异性扩散分析牛 宁纪锋1,2+,吴成柯1,姜光1,刘侍刚3 1(西安电子科技大学综合业务网国家重点实验室,陕西西安710071) 2(西北农林科技大学信息工程学院,陕西杨凌712100) 3(西安交通大学电子与信息工程学院,陕西西安710049) AnisotropicDiffusionAnalysisofGradientVectorFlow NINGJi.Fen91’2+,WUCheng.Kel,JIANGGuan91,LIUShi.Gan93 1(StateKeyLaboratoryofIntegratedServicesNetworks,XidianUniversity,Xi’an710071,China) 2(CollegeofInformationEngineering,NorthwestA&FUniversity,Yangling712100,China) 3(SchoolofElectronicsandInformationEngineering,Xi’allJiaotongUniversity,Xi’an710049,China)+Correspondingauthor:E-mail:jifeng_ning@hotmail.corn E—mail:jos@iscas.ac.锄http://www.jos.org.cnTel/Fax:+86.10—62562563 Ning JF,WuCK,JiangG,LiuSG.Anisotropicdiffusionanalysisofgradientvectorflow.JournalofSoftware,2010,21(4):612—619.http://wwwdos.org.cn/1000—9825/3523.htm Abstract:Anewexternalforcefieldforactivecontourmodel,calledanisotropicgradientvectorflow,ispresentedtosolvetheproblemthatgradientvectorflow(GVF)isdifficulttoentertheindentation.ThediffusiontermofGVFistheisotropicandhighlysmoothLaplacianoperatorwiththesamediffusionspeedalongtangentandnormaldirections.ThediffusionofLaplacianoperatorisactuallydecomposedintothetangentandnormaldirectionsbythelocalimagestructures.Diffusionalongthetangentdirectionenhancestheedge,whilediffusion alongthenormaldirectionremovesnoiseandpropagatestheforcefield.This paperdevelopsananisotropic gradientvectorflowbasedontheanalysisofdiffusionprocessofGVFalongtangentandnormaldirections。Inthe proposedmethod,thediffusion speedsalongthe normaland tangentdirectionsareadaptivelyobtainedbythelocal structureoftheimage.TheexperimentalresultsshowthatcomparedwithGVF,theproposedmethodconsideringthesetwodiffusionactionscanenterlong,thinindentationandimprovethesegmentation. Keywords:gradientvectorflow;anisotropicdiffusion;Laplacianoperator;activecontourmodel;imagesegmentation 摘要:为了解决梯度向量流力场(gradientvectornow,简称GVF)难以进入目标凹部的问题,提出了一种新的主动轮廓模型外力场一一各向异性梯度向量流.GVF的扩散项是各向同性且光滑性强的拉普拉斯算子,它在各个方向的扩散速度相同.拉普拉斯算子根据图像的局部结构可分为沿边界法线和切线方向的扩散,沿切线方向的扩散具有增 ?SupportedbytheNationalNaturalScienceFoundationofChinaunderGrantNos.60532060,60775020,60805016(国家自然科学基金);the“lllProject”ofChinaunderGrantNo.B08038(高等学校学科创新引智计划);theChinaPostdoctoralScienceFoundationunderGrantNo.20080430201(中国博士后基金);theChineseUniversityScientificFundunderGrantNo.QN2009091(中央高校基本科研业务费专项资金) Received2008?04-07;Revised2008-08—07;Accepted2008—1l?lO 万方数据

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