中科大材料的磁性课件08稀磁半导体简介

一、稀磁半导体简介5/11/2026Page1HefeiNationalLaboratoryforPhysicalSciencesatMicroscale以半导体材料为支撑的大规模集成电路和高频率器件在信息处理和传输中扮演着重要的角色，在这些技术中极大的利用了电子的电荷属性；而信息技术中另一个不可缺少的方面——信息存储（如磁带、硬盘等）则是由磁性材料来完成的，它们极大的利用了电子的自旋属性。如果能同时利用电子的电荷和自旋属性，无疑将会给信息技术带来崭新的面貌，稀磁半导体DMS(Diluted

Magnetic

Semiconductors)就可以实现上述功能。常见的半导体材料都不具有磁性，如：Si、GaAs、ZnO、GaN等，具有磁性的材料如：Fe、Co、Ni等及其化合物不具有半导体的性质，而且它们与半导体材料的表面势垒不能很好地相容，因此人们想到了通过掺入磁性离子来获得磁性的方法，在GaAs、GaN、InP、ZnO等化合物半导体中掺杂引入过渡金属(或稀土金属)等磁性离子。DMS材料具有优异的磁光、磁电性能，使其在磁感应器、光隔离器和自旋量子计算机等领域有广阔的应用前景，已成为材料领域中新的研究热点。5/11/2026Page2HefeiNationalLaboratoryforPhysicalSciencesatMicroscale通常情况下，当3d过渡金属磁性离子取代宿主阳离子，磁性离子的3d轨道就会和近邻宿主阳离子p轨道发生强烈的杂化，影响了其电子结构。该杂化使得局域3d自旋和宿主价带载流子之间发生强烈的磁交换作用。1998年，Science期刊报道了居里温度达110K的铁磁性(GaMn)As薄膜，但较低的铁磁转变温度限制了它的应用。根据Dietl等的预测，半导体材料的居里温度随着带隙的增加而升高，因此近年来以宽禁带半导体ZnO和GaN为基的DMS广受关注。5/11/20263HefeiNationalLaboratoryforPhysicalSciencesatMicroscale随着Mn含量的增加，3eV中间带形成，吸收边向高能侧移动，带隙变大。主要的带间吸收是由于6A1→4T2跃迁

ZnO

是一种铅锌矿结构的宽带隙(3.35eV)II-VI族化合物半导体。它具有大的电子质量，因此有望在运动载流子和局域磁性离子之间显示强的磁耦合。ZnO在可见光区透明，使得透明磁体可行。ZnO是一种很有前途的紫外激光器件材料，使得基于单一化合物的磁光器件成为可能。JAP72,041301(2005)5/11/20264HefeiNationalLaboratoryforPhysicalSciencesatMicroscale由M(H)曲线在5-300k温度范围内观察到了铁磁性，矫顽力非常小，只有几高斯。由M(T)曲线可知铁磁居里转变温度约为300K。铁磁－顺磁转变显而易见，表明铁磁性不是由Co团簇引起的。由较低的饱和磁矩(0.7μB/molCo)可知Co的价态接近Co+2APL82,34905/11/20265HefeiNationalLaboratoryforPhysicalSciencesatMicroscale在x=0.02时薄膜具有弱负磁阻效应，它是由载流子的弱局域化引起的，说明载流子和磁性离子的s-d交换作用微弱。在x=0.15时薄膜具有正磁阻效应，表明随着Co含量的增加，s-d交换作用占据了主导地位，它已经压制了弱局域化和自旋无序散射。而在x=0.10时，当H<Hkink时具有负磁阻效应，它也是由弱局域化引起的，当Hkink<H<Hmax具有正磁阻效应，表明s-d交换作用导致了自旋劈裂，当H>Hmax时显示负磁阻效应，表明自旋无序散射降低。5/11/20266HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleAPL81,4212.XRD显示该多晶粉末属于纯六方ZnO，当Fe掺杂浓度改变时，XRD峰位移动，晶格参数改变。数据精修表明随着Fe掺杂浓度增大，晶格常数a加大。X射线吸收谱表明Fe的氧化态为Fe+2。当x=0.05时，Zn1-xFexO具有最大饱和磁化强度(Ms)，其值为0.025μB/Fe，然而该值太小而不能认为是室温铁磁性。然而，随着掺Cu量的增加，Ms急剧增大，在1%Cu时其值是未掺杂Cu的30倍。Cu起着空穴掺杂的作用，这样就有利于载流子调制铁磁性的产生。5/11/20267HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleM-T曲线表明由铁磁到顺磁的转变温度为550K，这对于制备室温铁磁器件来说已足够。此外，转变曲线相当尖锐，偏离了平均场描述。零场电阻曲线显示了典型的半导体输运行为。在100K下样品具有较大的正磁阻，高于100K，磁阻效应消失。5/11/20268HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleAPL87,202507TEM研究表明5%Ni-注入GaN样品包含了岛状Ni3Ga晶粒，它被离子注入损伤引起的无定型区包围。高能和长时间的离子轰击使Ga-N键分解，N脱离表面，自由Ga原子和Ni反应形成纳米晶粒Ni3Ga。随着退火温度的增加，样品的磁性质增加，当800oC退火时已展示了明显的铁磁行为。5/11/20269HefeiNationalLaboratoryforPhysicalSciencesatMicroscale场冷和零场冷的M(T)曲线相似，都展示了铁磁行为，磁滞回线表明样品具有室温铁磁性。随着退火温度的增加，空穴浓度增加，铁磁居里转变温度提高。铁磁性是由由载流子调制的近临过渡金属离子之间的RKKY引起的。5/11/202610HefeiNationalLaboratoryforPhysicalSciencesatMicroscale(a)自旋场效应晶体管(SFET)的示意图(b)基于GaN半导体系统的自旋场效应晶体管使用自旋输运的器件比使用电荷输运的器件好，主要体现在(1)数据处理快速(2)功率损耗小。在GaN中引入Mn，由于Mn3d和N2p轨道的杂化，形成了100%自旋极化的1.5eV宽的杂质带，GaMnN材料半金属化，使其非常适合于自旋注入应用。在SFET中，通过晶体管的电流依赖于电子自旋的相对取向和源、漏区的磁矩，当他们平行时电流最大。栅极偏压导致电场和载流子自旋进动的相互作用，可以对电流的净自旋极化进行空间调制，若载流子的自旋取向不成一直线，电流可以有效的关闭。5/11/202611HefeiNationalLaboratoryforPhysicalSciencesatMicroscale由于3d过渡金属较高的固溶度(30%对Mn和Co)，ZnO也是实现高效自旋极化注入的材料。第一性原理计算表明ZnMnO的基态为反铁磁，可通过在栅极加负偏压，引入空穴掺杂实现半金属铁磁态。使用铁磁性的ZnCoO作源和漏，可实现自旋极化的电子在半金属中流动。GaAs基自旋发光二极管(SLED)示意图基于ZnO的自旋场效应晶体管该结构由p型铁磁半导体GaMnAs和n型非磁性GaAs组成。在正向偏压下，自旋极化空穴从GaMnAs一侧注入非磁性区，和非磁性InGaAs量子井中的自旋非极化电子复合，穿过厚为d的空间层，产生极化电致发光。5/11/202612HefeiNationalLaboratoryforPhysicalSciencesatMicroscale二、FundamentalKnowledgeonMagnetismandPhenomenologicalModelinFerromagneticShapeMemoryAlloyNi2MnGa5/11/2026Page13HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleOutlineIntroductionFundamentalknowledgeonmagnetismField-inducedstraininNi2MnGaCrystallographyandmagnetizationinNi2MnGaModelforfield-inducedstraininNi2MnGa5/11/202614HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleI.IntroductionAnattractive5%shearstraininH=4kOeatroomtemperaturewithpre-stressinNi2MnGaalloy.Currentresearchesonthreeaspects. 1.InvestigatingnewalloyswithhighstrainathighT 2.Modelingthemechanismforthefield-inducedstrain 3.AttemptingtoputthealloysintopracticaluseMainaspectsinNi2MnGa:crystallographyandmagnetism.5/11/202615HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleII.FundamentalKnowledgeonMagnetismOriginsofmagnetisminmaterialsClassificationofmagneticmaterialsMagnetocrystallineanisotropyMagnetostrictionWeissdomainsMagnetizationinamultidomaincrystalCGSandSI

5/11/202616HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleOriginsofMagnetisminMaterials1.Conductorscarryingcurrentsproducedmagneticfields5/11/202617HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleOriginsofMagnetisminMaterials2.AtomicmagneticmomentOrbitalmagneticmomentofanelectron.Effectivespinningmagneticmotionofanelectron.Anuclearmagneticmoment.Note:Therefirstandsecondtermsarethetwomajorcontributionstothemagneticmomentofanatom.Thelastoneisoftheorderof10-3ofthatoftheBohrmagneton(

B)andisoftenomitted.5/11/202618HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleClassificationofMagneticMaterialsFivetypesofmagneticmaterialclassifiedbytheirmagneticsusceptibilities

.1.Diamagnetic2.Paramagnetic3.Ferromagnetic4.Antiferromagnetic5.Ferrimagnetic

:permeability

r:relativepermeabilitywithdimensionlessquantity5/11/202619HefeiNationalLaboratoryforPhysicalSciencesatMicroscale1.Diamagneticmaterials

~-10-6,verysmall

negative.Examples:inertgases,hydrogen,manymetals,mostnon-metalsandmanyorganiccompounds.Asmallnetmagnetizationisinducedinasenseopposingtheappliedfield.Note:Intheseinstancestheelectronmotionsaresuchthattheyproducezeronetmagneticmoment.ClassificationofMagneticMaterials5/11/202620HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleClassificationofMagneticMaterials2.Paramagneticmaterials

~10-3–10-6

positive

small.Importantfeature:obeyingCurie’slaw

1/T,Examples:compoundscontainingtransitionmetalorrareearthionsandferromagneticsandferritesabovetheirCurietemperatures(TC).5/11/202621HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleClassificationofMagneticMaterials3.FerromagneticmaterialsAtT>TCobeyingCurie-Weiss’slaw

1/(T-TC);atT<TCthematerialsarespontaneouslymagnetizedand

ispositiveandverylarge.Examples:Fe,Co,NiandGdmetalsandalloys,somemetaloxides,etc.5/11/202622HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleClassificationofMagneticMaterials4.AntiferromagneticmaterialsAtT>TN,

1/(T+TN);atT<TNthemagnetizationsneutralizeoneanotherandtheoverallmagnetizations,and

ispositiveandverysmall(~10-3).TN:Néeltemperature.Examples:MnO.5/11/202623HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleClassificationofMagneticMaterials5.FerrimagneticmaterialsThemagnetizationofonesublatticeisantiparalleltothatofanothersublattice.Twomagnetizationsareofunequalstrengthleadingtoanetspontaneousmagnetization.Thetemperaturedependenceofferrimagnetic

showsclosesimilaritytothatofferromagneticone.5/11/202624HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleMagnetocrystallineAnisotropyEasyaxis:Spin–orbitlatticecouplingresultsinorientationofthespinsrelativetothecrystallatticeinaminimumenergydirection.Anisotropyenergy

EK:Aligningthespinsinanyotherthaneasyaxisdirectionleadstoanincreaseinenergy.Anisotropyconstants

K1andK2.Anisotropymagneticfield

HA, where

theanglebetweenHAandMS.5/11/202625HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleMagnetostrictionMagnetostriction:changesinthespindirectionsresultinchangesintheorientationoftheelectronorbitswhich,becausetheyarerestrainedbythelattice,havetheeffectofslightlyalteringthelatticedimensions.Magnetostrictionconstant

m(10-3~10-6)isdefinedasthestraininducedbyasaturatingfield.5/11/202626HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleWeissdomainsBelowTCaferromagneticbodyconsistsofalargenumberofsmalldomains,eachspontaneouslymagnetizedtosaturation.Eachgrainorcrystallitemaycontainanumberofdomainswithdifferentdirectionofmagnetizationandtheoverallmagnetizationcanbezero.

Domainwall:theboundarybetweentwoadjacentdomains,sometimescalledBlochwall.Magnetizationcannotchangediscontinuouslyatadomainboundary.ItcanmovewiththeapplicationofH.Domainsizecanbeupto1mandwallswidthsintherange10–100nm.5/11/202627HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleWeissdomainsIdealizedmagneticdomainconfigurationsanddomainwallantiparalleldomainsfluxclosuredomainschangeinspinorientationacrossthewidthofadomainwall5/11/202628HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleMagnetizationinamultidomaincrystalMagneticB–H

hysteresisloop5/11/202629HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleMagnetizationinamultidomaincrystalHysteresisloopsillustratingthedistinctionbetweenmagnetically‘soft’and‘hard’or‘permanent’materials5/11/202630HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCGSandSI

1.MagneticMomentm(emu=G•cm3=erg/G)2.Magnetization(Magneticmomentperunitmass)s(emu/g=J/T.kg=erg/G.g)3.Magnetization(magneticmomentperunitvolume)M(emu/cm3=G)4.Magnetization(magneticmomentperformulaunit)

m=s

formulaunitmass(ing/mol)/NA

mB

m

=s

f.u.(ing)/5582Morm(mB/f.u.)5.MagneticSusceptibility(perunitmass)

cg=s/Ba

cg(emu/g.G=cm3/g)6.MagneticSusceptibility(perunitvolume)

c=cg

densityc(cm3/g

g/cm3)dimensionless

7.MagneticSusceptibility(permole)

cm=cg

formulaunitmass(ing/mol)cm(cm3/mol)8.EffectiveMoment

meff=Z-0.5(C/0.12496)0.5=Z-0.5(3CkB/NA)0.5mB

C:experimentalCurieconstant(1/slopeofcm-1(T))

Z:formulaunitperunitcellmeff(inmB)5/11/202631HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCGSandSICGSB=H+4

M,B(Gauss,G),H(Oersted,Oe),M(G)

SIB=

0(H+M),B(Tesla,T),H(A/m),M(A/m)

0=4

10-7H/mAppliedFieldBa=Ha(CGS),1T=104

Oeor104G

Ba=

0

Ha(SI)

5/11/202632HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleIII.Field-inducedstraininNi2MnGaDiscovery:0.2%field-inducedstrainalong[001]inunstressedcrystalsNi2MnGawithH=8kOeappliedat265K(Ullakko,etalAPL69,1966(1996)).Mechanism:associatedwiththesuperelasticmotionoftwinboundariesinthemartensiticphase.Advantage:easierandfastertobecontrolledviamagneticfieldthanthoseinconventionalshapememorymaterialslikeNiTialloyscontrolledviachangesintemperature.5/11/202633HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleField-inducedstraininNi2MnGa--5/11/202634HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleIV.CrystallographyandMagnetizationinNi2MnGaHightemperatureausteniticphase,cubicHeuslercrystalstructure,spacegroupL21,latticeconstanta=5.825Å5/11/202635HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCrystallographyandMagnetizationinNi2MnGaLowtemperatureMartensitephase,tetragonalcrystalstructure,spacegroupI4/mmm,latticeconstanta=b=5.90Å,c=5.44ÅVB:variantboundariesDB:domainboundariesTB:twinboundaries.5/11/202636HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCrystallographyandMagnetizationinNi2MnGaa0a0aacaacAusteniteMartensitevariantsSketchofthetwinnedmartensitemicrostructureSketchofshape-memorybehaviorduetovariantrearrangement5/11/202637HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCrystallographyandMagnetizationinNi2MnGaM

vs

Halongthe[001]

directionintheparentphase(299K)

andinthemartensiticproductphase(265K).High-temperature,MS=47emu/g(382G)at1kOe.Low-temperature,twinnedphaseMS=58emu/g(475G),saturationismoredifficultwithHS=8kOe.DiscontinuitiesintheslopeofM–Hat265K.5/11/202638HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCrystallographyandMagnetizationinNi2MnGaMagnetizationloopsoftheNi2MnGasingle-variantmeasuredparallel(//)andnormal(

)tothecontractiondirection([001]axis)Strongmagneticanisotropy.Easymagnetizationalongthe[001]direction.Hardmagnetizationalongtheextension[010]direction.5/11/202639HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCrystallographyandMagnetizationinNi2MnGaTemperaturedependenceofthemagnetizationforNi52Mn24.5Ga23.5recordedatH=1G.MartensitestarttemperatureMS

=285K.ReversetransformationstarttemperatureAS

=289K.Anotherintermartensitictransformation,atTI=205Kduringcooling,reverseatTR=240Kduringheating,hysteresisof35K.5/11/202640HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleCrystallographyandMagnetizationinNi2MnGaEasyaxisincaxis(a).Martensitetwinswithcompatiblemagnetizationdirections(b).Twinboundariesmotionundermagneticfield.OnemechanismforFSMAsbehaviorinNi2MnGaisshown5/11/202641HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleV.

Modelforfield-inducedstraininNi2MnGaExperimentalobservations:Magnetic-field-inducedstrainsinNi2MnGaassociatedwithaprocessoftwin-boundarymotionratherthanmagnetostriction.Dependenceofstrainonmagnetization,e(M),generallyshowingalinearrelationship(ratherthanquadratic)

inMbelowsaturation.5/11/202642HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGaBasisofthemodel:Giantmagneticstrainsinmartensites,MandHconfiguration.Drivingforcefortwin-andphase-boundarymotion.Supposingthesampleiscomposedofonlytwotwinvariantsforsimplicitywithoutneglectoftheessentialpoint.Fromenergypoint:minimizingthemagneticfreeenergydensity.5/11/202643HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGaResultsfromthemodel:Accountforphase-andtwin-boundarymotion.Presentthelinearityobservedinbothe(H)andM(H)belowsaturation.Describethenonlinearitiesobservedinbothe(H)andM(H)closetosaturation.5/11/202644HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGa(a)high-symmetryparentphase(shaded).(b)

theslipstrainor(c)

twinningmartensitedeformation.Note:(b)couldberuledoutbecauseitneedsmoreenergythan(c)does.(c)isfavored.Phase-boundariesin(c)isduetotheincompletedeformationfromaustenitetomartensite.5/11/202645HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGaWeakanisotropy,Ku<<Zeemanenergy(MSH),twin-andphaseboundarymotions.NosignificantpressureonthetwinboundaryregardlessofH.Stronganisotropy,Ku>>MSH,twin-andphaseboundarymotions5/11/202646HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGaZeemanenergydifferencebetweenthetwinvariantsZeemanenergydifferenceoneithersideofthetwinvariantsandDrivingpressureonthetwinboundaryforKu>>MSHcaseMagneticenergychangewiththeapplicationofHforKu>>MSHcase5/11/202647HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGaElasticenergychangeduetothetwin-boundarymotionwiththeapplicationofHforKu>>MSHcaseC:elasticstiffnessconstant,aneffectivestiffnessagainstwhichthetwin-boundarymotionisoccurring.e0isthestrainassociatedwithtransformation.5/11/202648HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGaStronganisotropy(ha<<1,ha=MSH/2Ku,dimensionlessfieldparameter;he=MSH/C

,reducedfield)5/11/202649HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGa5/11/202650HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGa2.Intermediateanisotropy(ha~1,difficultcase)Onesimpleconfiguration:

=90oand

=0,wewillgetNote:m=f1+f2cos:theanglebetweenM2andH5/11/202651HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGa5/11/202652HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleModelforfield-inducedstraininNi2MnGa3.ComparisonwithexperimentalresultsNote:Left,twingeometryanddirectionofstrainmeasurement.Right,dependenceofreducedmagnetizationandstrainoninternalfield,Hi(demagnetizingfieldremovedfromdata)andmodelpredictionsforKu=2.2

106andC/2=0.9

106erg/cm3.5/11/202653HefeiNationalLaboratoryforPhysicalSciencesatMicroscale三、Magnetomechanicaltrainingeffectonthestrain-inducedchangeofmagnetizationinaNi-Mn-Gasinglecrystal

5/11/2026Page54HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleAbstractThestrain-inducedchangeinmagnetizationinaNi50.3Mn28.7Ga21singlecrystalisstudiedinanorthogonalmagneticfieldundermagnetomechanicaltraining.Effectofthepresenceofmagneticfieldduringferromagticandmartensitictransformationsonboththemechanicalandthemagneticbehaviorofthemartensiticsampleisexamined.Theinitialmagnetomechanicaltraininginducesastrongcouplingbetweenthemagnetizationandthemartensitevariant,resultinginreversiblechangeofmagnetization(∆M),theincreasedreversiblestrainandmagnitudeof∆M,andboththemechanicalandthemagneticbehaviordependingstronglyonthedirectionoftheappliedmagneticfield.Thisphenomenoncanbeunderstoodfromthatthemagnetomechanicaltrainingresultsinastablepreferentialorientationofmartensitevariants.Suchinvestigationhelpstoidentifymajorinfluencingfactoronthemagnetizationpropertyofferromagneticshapememoryalloys(FSMAs)andtounderstandtherelatedmechanism.ThepresentresultsareusefulforoptimizingboththemechanicalpropertyandthemagnetizationpropertyoftheFSMAs.5/11/202655HefeiNationalLaboratoryforPhysicalSciencesatMicroscale1.实验安排Fig.1ExperimentalconfigurationsTheingotfromwhichthesamplewasmanufacturedwithaBridgman-typecrystalgrowthfurnaceandhomogenizedinvacuumquartzampouleat1000

Cfor48h,thendirectlyannealedat800

Cfor72h.Thefacesofthesamplewereparallelto{100}planeswithdimensionof6.933.072.09mm3.5/11/202656HefeiNationalLaboratoryforPhysicalSciencesatMicroscale2.实验结果Fig.2DSCmeasurements

Transformationtemperaturesweredeterminedonadifferentialscanningcalorimetry(DSC)fromTAinstrumentandand

acsusceptibilitymeasurement.(Ms=43ºC,Mf=39ºC,As=47ºC,Af=51ºC)

5/11/202657HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleFig.3Curvesof(a)compressivestress(Comp.Stress)vs.compressivestrain(Comp.Strain),(b)thechangeinmagnetization(

M)vs.strain,(c)strainvs.timeand(d)M

vs.time.Thesamplewasfirstfield-freeheatedupto80ºCandthenfield-freecooledtoroomtemperature.Mshowsanearlylineardependenceonstrainandnegligiblehysteresis,anditsaturateswhenthestrainisexceedingacertainlimit,referto(b)and(d),respectively.

5/11/202658HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleFig.4Curvesof(a)Comp.Stressvs.Comp.Strain,(b)

Mvs.strain,(c)strainvs.timeand(d)M

vs.time.Thesamplewasfirstfield-freeheatedupto80ºCandthencooledinamagneticfieldof3kGausstoroomtemperature.Thereversiblestrainisgreatlyenhancedinthefieldcoolingmode.5/11/202659HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleFig.5Curvesfor0

configuration

of(a)Comp.Stressvs.Comp.Strain,(b)strainvs.timeand(c)M

vs.time.Thesamplewasfirstfield-freeheatedupto80ºCandthencooledinamagneticfieldof3kGausstoroomtemperature.Thereversiblestrainisgreatlyenhancedinthefieldcoolingmode.5/11/202660HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleFig.6Curvesfor45

configuration

of(a)Comp.Stressvs.Comp.Strain,(b)strainvs.timeand(c)M

vs.time.Thesamplewasfirstfield-freeheatedupto80ºCandthencooledinamagneticfieldof3kGausstoroomtemperature.Thereversiblestrainisgreatlyenhancedinthefieldcoolingmode.5/11/202661HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleFig.7Curvesfor0

configuration

of(a)Comp.Stressvs.Comp.Strain,(b)strainvs.timeand(c)M

vs.time.Thesamplewasfirstfield-freeheatedupto140ºCandthencooledinamagneticfieldof3kGausstoroomtemperature.Thereversiblestrainisgreatlyenhancedinthefieldcoolingmode.5/11/202662HefeiNationalLaboratoryforPhysicalSciencesatMicroscaleH.E.Karaca,I.Karaman,B.Basaran,Y.I.Chumlyakov,andH.J.Maiser,Acta

Mater.54,233(2006).

Fig.8Istheresomeexplanationincommonwhenthesampleistrainedtoformasinglevariantfromatwo-variantparentphasebymagneticfield