high-entropy alloy
073902-3Huoetal.J.Appl.Phys.117,073902(2015)
HE-BMGareshowninFig.3(a).Temperatureintervalsof2Kand10KwereselectedfortheregionsinthevicinityofTCandfarawayfromTC,respectively.Asweknow,Arrottplotisausefultooltoidentifytheorderofthemagneticphasetransi-tion,25accordingtowhichtheslopeofM2versusH/Mcurvesindicateswhethertheobservedmagneticphasetransitionisofthe rstorder(negativeslope)orsecondorder(positiveslope).AsshowninFig.3(b),thepositiveslopesoftheArrottplotfortheHo20Er20Co20Al20Tm20HE-BMGsampledenoteasecondordermagnetictransition.
Tocharacterizethemagnetocaloriceffectofthesealloys,theirmagneticentropychanges(DSM)weremeas-ured.Inanisothermalprocessofmagnetization,thetotalDSMofthesystemcausedbyamagnetic eldcanbegivenbyintegratingtheMaxwellrelationoverthemagnetic eld10
ðHmax
@M
DSMðT;HÞ¼dH;(1)
@THHminwhereHminandHmaxrepresenttheinitialand nalvaluesof
magnetic eld,respectively.Inthiswork,Hmin¼0andHmax¼5T.ToderivethetemperaturedependenceofDSM,thenumericalapproximationoftheintegralisappliedinthiswork
ÐH
DSMðTi;HÞ¼
ÐH
MðTi;HÞdH–0MðTiþ1;HÞdH
:
Ti–Tiþ1
(2)
BycalculatingtheisothermalM-Hcurvesatvarioustemper-aturesasshowninFig.3(a),theDSMassociatedwiththeHvariationcanbecalculatedaccordingtoEq.(2).Figure4(a)displaystheDSMasthefunctionofthetemperatureandappliedmagnetic eldforHo20Er20Co20Al20Tm20.TheDSMreachesamaximumvaluenearTC.ThepeakvalueofthemagneticentropychangejDSpkMjforthisalloyincreasesalongwiththeexternal eldandreaches15.0JkgÀ1KÀ1at5T.Despitethedifferenttemperaturerange,thisvalueisapparentlylargerthanthoseofthemostrareearthbasedBMGs,aslistedinTableI.Figure4(b)showstheDSMasthefunctionofthetemperatureforthethreealloysunderamag-netic eldof5T.AllthealloyshavealargejDSpkMjvaluecomparedtootherrareearth-basedBMGsaslistedinTableI.ThejDSpkMjincreasesrapidlyandtheDSMpeaksnarrowdowngraduallywhenREchangesfromGdtoDyandTm,indicat-ingtheDSMalsocanbetunedbychangingtherareearthelements.
TheRCisanotherkeyparametertocharacterizetheef -ciencyofthemagneticrefrigerant,whichisproportionaltotheareaunderthecurveofDSMversusT.TheRCwascalcu-latedbytakingtheproductofthemaximumentropychangejDSpkMjandthefullwidthathalf-maximum(dTFWHM)oftheDSMpeak.26TheRCFWHMvaluesforthealloysRE¼Gd,
FIG.2.(a)TemperaturedependenceoftheZFCandFCmagnetizationunderamagnetic eldof200Oe,and(b)magnetictransitiontemperature(TC)asafunctionofthedeGennesfactorforHo20Er20Co20Al20RE20(RE¼Gd,Dy,andTm)HE-BMGs.TheinsetpresentsthecurvesofdM/dTversus
temperature.
FIG.3.(a)Isothermalmagnetizationcurvesand(b)ArrottplotsfortheHo20Er20Co20Al20Tm20HE-BMGmeasuredattemperaturesbetween2and70K.Temperatureintervalsof2Kand10Kwereselectedfortheregions2–20Kand20–70K,respectively.