high-entropy alloy
073902-4Huoetal.J.Appl.Phys.117,073902(2015)
FIG.5.(a)FielddependenceofthemagnetizationofHE-BMGsat2K.(b)Maximummagneticentropychanges(jDSpkMj),(c)fullwidthathalf-maximumoftheDSMpeak(dTFWHM),and(d)RCasafunctionofspontane-ousmagnetization(M0)fortheHo20Er20Co20Al20RE20(RE¼Gd,Dy,andTm)HE-BMGs.
FIG.4.(a)3-dimentionalmagneticentropychangesasafunctionofthetem-peratureandappliedmagnetic eldforHo20Er20Co20Al20Tm20HE-BMG.(b)Magneticentropychangesasafunctionoftemperatureunder5TforHo20Er20Co20Al20RE20(RE¼Gd,Dy,andTm)HE-BMGs.TheinsetpresentsthemagnetichysteresisofHo20Er20Co20Al20Tm20HE-BMG.
Dy,andTmweredeterminedtobe627JkgÀ1,468JkgÀ1,and375JkgÀ1,respectively.ThehighRCFWHMshouldbeattributedtothelargeDSMandtheparticularglassyandmagneticstructurewhichextendsthelargeDSMtoawidertemperaturerange.Inthespin-glassphase,magneticmomentsarefrozenintotheequilibriumorientations,butthereisnolong-rangeorder,27whichmakesitmoredif culttobefrozenthantheferromagneticmaterials.Therefore,thespinglassandcomplicatedcompositionofthesehighen-tropyBMGscanwidenthemagnetictransitiontemperaturerange,whichthenbroadentheDSMpeakandthusincreasethevalueofRCFWHM.
TheDSMhasbeenshowntobecorrelatedwiththemag-neticmomentofthematerialinotheralloysystems.28–30ToinvestigatewhethersucharelationshipholdsbetweenjDSpkMjandthemagneticmomentoftheHE-BMGs,the eldde-pendenceofthemagnetizationoftheHE-BMGswasmeas-uredat2Kfor eldsupto5T,asshowninFig.5(a).Extrapolationofthemagneticmomenttozero eldgivesthelowtemperaturespontaneousmagnetization(M0)valuesof148emu/g,120emu/g,and109emu/gforRE¼Gd,Dy,andTm,respectively.M0isaparameterrepresentingthetotalmagneticmomentsofthematerials.Fortheferromagneticamorphousalloys,28–30thejDSpkMjareusuallyproportionalto
M0.However,forthepresentspinglass-likeHE-BMGs,the
jDSpkMjdecreasesalongwiththeincreaseofM0,asshowninFig.5(b).Thisabnormalbehaviorcanbeinterpretedasfol-lowing.Forthespinglassphase,thejDSpkMjrepresentstheamountofmagneticmomentsfrozenclosetoTC,whichisonlyapartofthetotalmagneticmoments.Theportionisrelatedtothetransitiontemperaturerange.Forferromagneticphasetransitions,thetransitiontemperaturerangeisnarrowandsimilarfordifferentmaterials.Butforspinglass-likephasetransitions,thetransitiontemperaturerangeisverywideandvarieswithmaterials.ForthepresentHE-BMGs,thedTFWHMincreasesalongwiththeincreaseofM0,asshowninFig.4(c).AlargedTFWHMdenotesthatasmallamountofmomentsgetfrozennearTC,whichyieldsasmall
pk
jDSpkMj.Thus,thenegativedependenceofjDSMjonM0ismainlyderivedfromthechangeofdTFWHM.Ontheotherhand,theRCrepresentsthecompleteentropychangeoverthetotalspinglasstransitiontemperaturerange,whichshouldhaveagoodproportionalrelationwithM0.Thisisveri edinFigure5(d).Sowecanconcludethat,fortheHE-BMGswiththespin-glassmagnetictransition,theRC,ratherthanDSM,hasagoodcorrelationwithM0.
Themagnetic elddependenceofjDSpkMjandRCFWHMforthethreealloysisshowninFigs.6(a)and6(b),respec-tively.Onecan ndthattheHo20Er20Co20Al20Tm20hasthehighestjDSpkMjundertheapplied eldfrom0.5Tto5T,andtheHo20Er20Co20Al20Gd20hasthehighestRC.Accordingtothemean eldtheory,thejDSpkMjandRCcanbeexpressedpk
approximatelyasjDSMj/HnandRC/HN.30Theexpo-nentsnandN,controlledbythecriticalexponentsofthealloyseries,canbeextractedthrough ttingtheexperimentaldatainFigs.6(a)and6(c)withtherelationsabove.ForthealloyRE¼Gd:n¼0.8560.01,andN¼1.1260.01;thealloyRE¼Dy:n¼0.9060.01,andN¼1.2060.01;thealloyRE¼Tm:n¼0.7260.01,andN¼1.2060.01.TheexponentsnnearthetransitiontemperaturefortheseHE-BMGsarelargerthanthoseofFe-based($0.75),Gd-based($0.81),andDy-based($0.87)BMGs,30,31which
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