Magnetic and Magneto-Optical Properties of Fe75-xMn25Gax Heusler-like Compounds

ma e ials A icle Magne ic and Magne o-Op ical P ope ies o Fe75−xMn25GaxHeusle -like Compounds Daniel K ál1, Lukáš Be an 1, Ma in Zelený1,2 , Jan Zemen 3, Roman An oš 1, Ja osla Ham le 1, Jakub Záz o ka 1, Michal Rameš 4, K is ýna Onde ko á4, Oleg Heczko 4,* and Ma in Veis 1,* 1Facul y o Ma hema ics and Physics, Cha les Uni e si y, Ke Ka lo u 5, 12 16 P ague 2, Czech Republic; daniel.k al@ka lo .m .cuni.cz (D.K.); [email p o ec ed] (L.B.); [email p o ec ed] (M.Z.); an os@ka lo .m .cuni.cz (R.A.); ham le@ka lo .m .cuni.cz (J.H.); [email p o ec ed] (J.Z.) 2Facul y o Mechanical Enginee ing, Ins i u e o Ma e ials Science and Enginee ing, B no Uni e si y o Technology, Technická2896/2, 616 69 B no, Czech Republic 3Facul y o Elec ical Enginee ing, Czech Technical Uni e si y in P ague, Technická2, 166 27 P ague, Czech Republic; [email p o ec ed] 4 Ins i u e o Physics o he Czech Academy o Sciences, Na Slo ance 1999/2, 18221 P ague 8, Czech Republic; [email p o ec ed] (M.R.); [email p o ec ed] (K.O.) *Co espondence: [email p o ec ed] (O.H.); eis@ka lo .m .cuni.cz (M.V.) Recei ed: 6 Janua y 2020; Accep ed: 25 Janua y 2020; Published: 4 Feb ua y 2020   Abs ac : Fe 75−x Mn 25 Ga x Heusle -like compounds we e in es iga ed in a wide ange o Fe/Ga a ios while keeping he Mn con en cons an and equal 25 a % in o de o elucida e he in e play be ween magne ic p ope ies and composi ion. Ma e ials we e p epa ed by a c-mel ing om pu e elemen s and subsequen ly annealed. Expe imen al in es iga ions we e ocused on magne iza ion beha io in a wide empe a u e ange om 4 o 1000 K and magne ic ield up o 9 T. Op ical and magne o-op ical (MO) measu emen s we e employed o shed mo e ligh on he magne ic s a e and elec onic s uc u e o in es iga ed ma e ials. Magne iza ion measu emen s indica ed ha in he icini y o s oichiome y (Fe 2 MnGa) he compounds a e e o/ e imagne ic, whe eas he Fe-de icien compound is pa amagne ic and a high Fe concen a ion he an i e omagne ic in e ac ion p e ails. Theo e ical calcula ions o co esponding o de ed and diso de ed s oichiome ic compounds we e ca ied ou and compa ed o he expe imen on he le el o ne magne ic momen as well as magne o-op ical spec a. This compa ison sugges s ha he Heusle c ys al s uc u e, L2 1 , is no p esen e en close o s oichiome y. Mo eo e , he compa ison o densi y o s a es (DOS) o o de ed and diso de ed s uc u es allowed us o explain missing ma ensi ic ans o ma ion (MT) in in es iga ed ma e ials. Keywo ds: Heusle compounds; Fe-Mn-Ga; ma ensi ic ans o ma ion; Cu ie poin ; magne o-op ics; ab ini io 1. In oduc ion Some Heusle compounds unde go ma ensi ic ans o ma ion (MT), which is essen ial o shape memo y and calo ic beha io [ 1 ]. Mo eo e , he winned low symme y phase can exhibi magne ically induced eo ien a ion ha mani es s i sel as a huge magne ic ield-induced s ain, mo e han wen y imes la ge compa ed o ha o gian magne os ic i e ma e ials [ 2 – 4 ]. C ucial o all e ec s is he p esence o MT, which is due o a peculia elec onic s uc u e in he icini y o he Fe mi le el [ 5 ]. The main examples o magne ic shape memo y (MSM) ma e ial a e Ni-Mn-Ga Heusle compounds. Howe e , hese compounds su e om se e al sho comings such as agili y [ 6 ] and ela i ely low ma ensi ic and e omagne ic ansi ion empe a u es [7–9]. Ma e ials 2020,13, 703; doi:10.3390/ma13030703 www.mdpi.com/jou nal/ma e ials Ma e ials 2020,13, 703 2 o 12 Heusle Fe-Mn-Ga compounds ha e been p oposed as good candida es o new MSM ma e ial [ 10 ] as hey ha e a much highe Cu ie poin han Ni-Mn-Ga. Howe e , i was ound e y soon ha ma ensi ic ans o ma ion is no a uni e sal ea u e, and i occu s only in some pa icula composi ions [ 11 – 14 ]. Apa om he mally induced ans o ma ion [ 15 ], e en he ield-induced ans o ma ion was obse ed o Fe2MnGa by Zhu e al. [16]. I was ound ha e na y compounds close o Fe 2 MnGa composi ion c ys allize in a ious cubic s uc u es de ined by a di e en a omic o de [ 12 ]. The o de ing is e y sensi i e o composi ional a ia ion and e en a e y small de ia ion om s oichiome y, o en negligible o e en unde ec able by usual EDS, can p oduce ei he bcc-like (diso de ed B2, o de ed L2 1 Heusle s uc u e) o cc-like (L1 2 s uc u e) phases o hei mix u e [ 12 , 17 ]. Appa en ly, he mal his o y can also play a ole in es ablishing a ious phases [18]. Unlike Ni-Mn-Ga, Fe-Mn-Ga compounds con ain wo kinds o a oms wi h di e en magne ic momen localiza ion bu wi h compa able magni ude. Thei in e ac ion can p o ide a ious magne ic a angemen s om an i e omagne ic o e i- o e omagne ic s a es. The close coexis ence o he phases in a single compound is indica ed by he exchange bias [ 19 ]. Such coexis ence, in connec ion wi h a complex in e play o bcc- and cc-like phases, esul s in complica ed magne ic beha io . O e all, he magne ic s a e is no well unde s ood e en o s oichiome ic Fe 2 MnGa. Despi e he mixed s uc u al o de o cc- and bcc-like phases in nea s oichiome ic Fe 2 MnGa, Kud ya se e al. we e able o de e mine i s elec onic and op ical p ope ies and compa e i wi h ab ini io calcula ions [ 13 , 20 ]. Howe e , he published esul s a e incomple e as he mos s udied composi ions a e close o he s oichiome ic Fe2MnGa compound. He e we p esen a comp ehensi e s udy encompassing p e ious expe imen al epo s and heo e ical p edic ions. We in es iga ed expe imen ally Fe 75-x Mn 25 Ga x compounds de i ed om Heusle compounds in a wide ange o composi ions wi h a ied Fe/Ga a ios while keeping he Mn con en cons an and equal 25 a %. The magne ic and MO measu emen s a e complemen ed wi h ab ini io calcula ions o s oichiome ic Fe 2 MnGa wi h di e en la ice s uc u es and magne ic o de ing in an a emp o cla i y he obse ed complex beha io and di e ences be ween ou expe imen al esul s and p e ious calcula ions. 2. Ma e ials and Me hods Polyc ys alline bulk samples we e p epa ed by a c-mel ing om pu e elemen s in A a mosphe e using a Buhle u nace. A e he homogeniza ion hea ea men a 1073 K/24 h, he samples we e cu and polished mechanically and elec oly ically o ob ain high-quali y su aces o scanning elec on mic oscopy (SEM) and op ical and magne o-op ical measu emen s. SEM was used o e eal he mic os uc u e, phase composi ion, and g ain size. We used SEM Tescan Fe a 3 equipped wi h elec on dispe sion spec oscopy (EDS) analyse and elec on backsca e ed di ac ion (EBSD) de ice. The c ys al s uc u e was e alua ed om EBSD. Composi ion o he polyc ys alline bu ons we e de e mined by EDS wi h e o up o 1 a % pa icula ly on Mn con en . The e o s in hese pa icula compounds we e es ima ed om ou analyses o Ni-Mn-Ga Heusle compounds, using compa ison wi h X- ay luo escence analysis wi h s anda ds. The magne ic p ope ies wi h ield and empe a u e we e measu ed in he in e al om 10 o 1000 K and ield up o 9 T using a PPMS ib a ing sample magne ome e in PPMS by Quan um Design. The spon aneous sa u a ion magne iza ion was de e mined by ex apola ing he high- ield magne iza ion o ze o ield. A magne o-op ical spec ome e based on he o a ing analyze [ 21 ] me hod was ob ained o acqui e complex magne o-op ical Ke e ec (MOKE) in pola con igu a ion wi h nea ly no mal ligh incidence in he pho on ene gy ange om 1.2 o 4.5 eV. Applied magne ic ield was 1.2 T o b ing he samples close o he magne ic sa u a ion. All magne o-op ical da a we e measu ed a oom empe a u e. The Vienna Ab ini io Simula ion Package (VASP, e . 5.4.4) was used o s uc u al elaxa ion and calcula ions o magne ic momen s, densi ies o s a es (DOS) as well as op ical p ope ies o s oichiome ic Ma e ials 2020,13, 703 3 o 12 Fe 2 MnGa [ 22 , 23 ]. In ou calcula ion, he elec on-ion in e ac ion was desc ibed by p ojec o augmen ed- wa e (PAW) po en ials [ 24 , 25 ]. We used he g adien -co ec ed exchange–co ela ion unc ional p oposed by Pe dew e al. [ 26 ]. To include expec ed diso de , he Special Quasi andom Supe cell (SQS) [ 27 , 28 ] wi h 32 a oms as a model o diso de ed sys em was gene a ed using a sepa a e so wa e ool [ 29 ]. This me hod is based on op imizing pai co ela ion coe icien s o ep esen a s a is ically andom solid solu ion. 3. Resul s and Discussion P epa ed ma e ials anged om he Fe 25 Mn 25 Ga 50 o Fe 65 Mn 25 Ga 10 keeping Mn con en a 25 a % as close as possible. The chemical composi ion de e mined o mos compounds by EDS is lis ed in Table 1 oge he wi h sa u a ion magne iza ion and Cu ie empe a u e. The EDS analysis indica ed ha he nominal composi ion does no di e signi ican ly om he measu ed one. Lis ed samples we e u he analyzed by magne o-op ical measu emen s. Table 1. Composi ion, spon aneous magne iza ion M s , and Cu ie empe a u es T c o selec ed compounds. The spon aneous magne iza ion in Boh magne ons ( µB ) pe o mula uni ( .u.) and he Cu ie empe a u e o he second phase a e lis ed in b acke s. The M s was ob ained by ex apola ion he magne iza ion om high magne ic ield o ze o ield. The e o in de e mina ion o composi ion is abou 1 a %; o magne iza ion measu emen , he e o is abou 5%. Name Nominal De e mined by EDS Msa 10 K (Am2/kg) (µBpe .u.) Tc (K) Fe40 Fe40Mn25Ga35 Fe39.5Mn26Ga34.5 87 (3.77) 532 (183) Fe50 Fe50Mn25Ga25 Fe49Mn26Ga25 100 (4.23) 762 (554) Fe52 Fe52Mn25Ga23 Fe51Mn26Ga23 57 (2.40) 736 Single Fe56 Fe56Mn25Ga19 Fe56Mn26Ga18 1 a 300 K (0.04) An i e omagne ic ( aces o e o.) Fe65 Fe65Mn25Ga10 - 0.05 (0.02) An i e omagne ic TN=300 K 3.1. S uc u al P ope ies All s udied ma e ials had a cubic s uc u e a oom empe a u e. None o he s udied ma e ials exhibi ed ans o ma ion o he lowe symme y phase, ha is, ma ensi ic ans o ma ion (as de e mined om magne ic measu emen shown below) upon cooling. SEM obse a ion using backsca e ed elec ons e ealed ha wo compounds, Fe65 and Fe52, we e single cubic phase. The example o single-phase mic os uc u e is shown in Figu e 1( igh ). SEM indica ed a non-homogenei y o Fe50; howe e , di e en phases could no be esol ed. A no able excep ion was he Fe40 compound, in which wo di e en phases could be clea ly iden i ied, as shown in Figu e 1(le ). The EBSD measu emen indica ed wo cubic phases. These phases had e y simila composi ions as de e mined by EDS. Magne o-op ical Ke E ec (MOKE) mic oscopy indica ed ha only one phase was e omagne ic a oom empe a u e as he magne ic domains could be obse ed. The phase o med e omagne ic islands imme sed in a non-magne ic ma ix. The wo-phase cha ac e o he compound was con i med by magne iza ion measu emen (see below). Ma e ials 2020,13, 703 4 o 12 Figu e 1. Mic os uc u e o wo-phase Fe40 ( le ) and single-phase Fe52 ( igh ) samples obse ed by backsca e ed elec ons in SEM. I clea ly shows he wo-phase cha ac e o he Fe40 sample showing i egula lowe -like islands in a ma ix. Sample Fe52 is single phase wi h ela i ely la ge g ains. Composi ion de e mined by EDS is indica ed in he igu e. 3.2. Magne ic P ope ies Figu e 2summa izes he magne iza ion loops and empe a u e dependence o low- ield and high- ield magne iza ion o all magne ically o de ed samples. The low- ield magne iza ion con i med expec ed high Cu ie empe a u es in all compounds close o s oichiome y. The high Cu ie empe a u e phase can be iden i ied om he li e a u e as cc phase [ 12 , 13 ]. The highes empe a u e, abou 760 K, was measu ed o he sample (Fe50) closes o s oichiome y. The empe a u es a e lis ed in Table 1. The low- ield magne iza ion measu emen also con i med he single phase in Fe52 and he wo-phase cha ac e o Fe40 in ag eemen wi h SEM (Figu e 1), indica ing low Cu ie empe a u e (183 K) o he second phase. This ag eed wi h MOKE obse a ion a oom empe a u e. Acco ding o Kud ya se , he ma ix phase wi h a low Cu ie poin is he diso de ed bcc phase [12,13]. Mo eo e , he low- ield measu emen e ealed wo di e en high Cu ie empe a u es in Fe50 (as shown in he second panel o Figu e 2), indica ing, in acco dance wi h inhomogenei ies obse ed by SEM, ha he sample con ained wo di e en phases. Acco ding o Kud ya se [ 12 ], i should con ain cc and bcc phases. Al hough he cc phase exhibi ed a high Cu ie poin in acco dance wi h he li e a u e, he expec ed bcc phase had qui e a high Cu ie empe a u e compa ed o ha o Fe40. I seems o exclude he p esence o he bcc phase, bu i may be also asc ibed o di e en composi ion close o s oichiome y. On he o he hand, he Cu ie empe a u e o he assumed cc-phase is compa able wi h sample Fe52 in line wi h he li e a u e [ 13 ]. High- ield he momagne ic cu es suppo he desc ibed beha io ; howe e , he sepa a ion be ween phases canno be de e mined in any case. Magne iza ion loops o selec ed samples a oom empe a u e and close o 0 K, shown in Figu e 2, indica e ha he ma e ials close o s oichiome y we e all e omagne ic o e imagne ic in ag eemen wi h [ 12 ]. Wi h dec easing empe a u e, he sa u a ion magne iza ion was o en educed below oom empe a u e magne iza ion. The dec ease o sa u a ion magne iza ion wi h dec easing empe a u e is well illus a ed by high- ield he momagne ic cu es. This dec ease indica ed he onse o an i e omagne ic in e ac ion below oom empe a u e. In e es ingly, he Fe52 sample, which om SEM obse a ion and low- ield magne ic measu emen seems o be single-phase ma e ial, exhibi ed a sha ply inc easing coe ci i y and a s ong dec ease o low- ield magne iza ion wi h dec easing empe a u e. This beha io is no obse ed o any o he composi ions. The lowe ing suscep ibili y and inc eased coe ci i y can indica e enhanced magne ic domain pinning. I may be asc ibed o an i e omagne ism in dis u bed egions [ 12 ] as g ain bounda ies and e en wi hin an iphase bounda ies [30–32] on which he magne ic domain walls can be pinned. Ma e ials 2020,13, 703 5 o 12 Figu e 2. Magne iza ion cu es a oom and 10 K empe a u es ( igh ) and he momagne ic cu es measu ed upon hea ing ( le ) o selec ed samples ma ked in igu e. Black line and le y-scale indica e sa u a ion magne iza ion a 9 T. Red line and igh y-scale indica e low- ield magne iza ion (0.01 T). Ma e ials 2020,13, 703 6 o 12 Figu e 3. Spon aneous magne iza ion a 10 K ob ained by ex apola ion om high- ield magne iza ion (up o 9 T) o ze o ield is ep esen ed by ed iangles. S oichiome ic composi ion o Fe 2 MnGa is ma ked by he e ical b oken line. Room empe a u e magne iza ion a 1.4 T ela ed o MO measu emen s is ep esen ed by black squa es. The es ima ed e o s in composi ion and magne iza ion de e mina ion a e ma ked. The compounds wi h he composi ion s ongly de ia ed om s oichiome y we e ei he pa amagne ic o an i e omagne ic. Clea an i e omagne ic beha io was obse ed o Fe65 wi h N é el empe a u e T N abou 300 K, de e mined om he empe a u e dependence o sa u a ion magne iza ion. This is simila o empe a u e, whe e he dec ease o sa u a ion magne iza ion is obse ed o o he composi ions. I sugges s ha he an i e omagne ic in e ac ion becomes g adually s onge wi h inc easing Fe con en (i.e., om Fe40 o Fe65 samples). The dependence o he spon aneous magne iza ion a 10 K on Fe con en shown in Figu e 3 summa izes p e ious obse a ions. Fo low Fe concen a ion he ma e ial is pa amagne ic, o highe Fe concen a ion, he e omagne ic in e ac ion is es ablished and sa u a ion magne iza ion inc eases. The maximum momen occu s a s oichiome y. Wi h inc easing Fe con en abo e s oichiome y, he magne iza ion sha ply d opped o almos ze o due o an i e omagne ic in e ac ion. The esidual magne ic momen o he compound wi h high con en o Fe can be due o no ully compensa ed an i e omagne ism o due o s uc u al inhomogenei y, ha is, he p esence o a small olume o e omagne ic phase o e en a minu e amoun o pu e Fe. Room empe a u e magne iza ion measu ed a 1.4 T ollows he ends obse ed o he spon aneous magne iza ion. I is also shown in Figu e 3as i is impo an o MO measu emen done a oom empe a u e. 3.3. Magne o-Op ical Spec oscopy Room empe a u e expe imen al spec a o pola Ke o a ion and ellip ici y a e shown in Figu e 4. The spec a o pola Ke o a ion exhibi mono onous beha io wi h an inc ease owa ds he low ene gy egion and an indica ion o a spec al s uc u e nea 2 eV. On he o he hand, he ellip ici y spec a ise wi h inc easing ene gy wi h a b oad maximum si ua ed nea 3.5 eV. This spec al dependence esembles al eady epo ed esul s on polyc ys alline Fe 48 Mn 24 Ga 28 [ 33 ] and Fe 50 Mn 25 Sn 25 [ 34 ] bulk samples. Howe e , he spec a we e comple ely di e en han hose p e iously epo ed on o he Heusle compounds con aining Mn, bu wi hou Fe a oms, such as Ni-Mn-Ga [ 35 , 36 ], Ni-Mn-Sn, Ni-Mn-Sb, o o he compounds con aining Mn a oms [ 37 ]. This esul indica es a majo di e ence in he elec onic band s uc u e be ween Fe-Mn-Ga and Ni-Mn-Ga compounds. Ma e ials 2020,13, 703 7 o 12 Figu e 4. Expe imen al spec a o pola Ke o a ion ( op ) and ellip ici y ( bo om ) measu ed a 1.2 T and oom empe a u e oge he wi h ab ini io heo e ical calcula ions. Figu e 4also shows s ong a ia ion o magne o-op ical e ec upon he composi ion o he sample. Al hough he spec al beha io is simila o all he samples, sample Fe50 exhibi s he highes MOKE ampli ude, whe eas sample Fe56 has almos negligible magne o-op ical esponse. This is consis en wi h magne ic measu emen s and is demons a ed in Figu e 5, whe e he ampli ude o MOKE a 1.5 eV is plo ed as a unc ion o Fe composi ion. As one can see om his igu e, he magne iza ion oge he wi h MOKE has a maximum o nea ly s oichiome ic composi ion. Figu e 5. Composi ion-dependen pola Ke e ec o Fe-Mn-Ga compounds a he pho on ene gy o 1.5 eV. Ma e ials 2020,13, 703 8 o 12 3.4. Theo e ical Calcula ions To explain ou expe imen al da a and o compa e wi h p e iously published esul s, we pe o med new ab ini io calcula ions wi h s oichiome ic composi ion. Kud ya se e al. [ 13 ] show ha he L2 1 o de ed s uc u e has sligh ly highe o al ene gy and hus i does no appea in he s oichiome ic compound. This calcula ion seems o sugges ha he e is no Heusle compound wi h p ope o de ing. We nex conside ed he L12( cc) o de ed s uc u e. P e ious ab ini io calcula ions pe o med o he s oichiome ic compound wi h he L1 2 ( cc) o de indica ed he e omagne ic o de ing as he mos s able wi h a magne ic momen o 6.13 µB / .u. This is signi ican ly highe han measu ed alues o sa u a ion magne iza ion o 4.23 µB / .u. In con as , he e imagne ic o de ing wi h opposi e o ien a ion o magne ic momen s a Fe and Mn a oms exhibi s much smalle magne ic momen s o 0.48 µB/ .u. [13]. In ou calcula ion, we used he L1 2 ( cc) s uc u e desc ibed p e iously [ 13 ] bu we conside ed opposi e o ien a ion o magne ic momen a neighbo ing Fe a oms wi hin he same plane. This esul ed in a magne ic momen o 1.90 µB / .u. An e en highe magne ic momen o 2.75 µB / .u. was ound o an i e omagne ic in e ac ion be ween Fe planes, whe eas in-plane in e ac ion be ween Fe a oms was e omagne ic. The magne ic momen is, howe e , s ill lowe han expe imen ally obse ed alues o nea ly s oichiome ic compounds. Fu he inc easing o magne ic momen s can be achie ed by conside ing he chemical diso de be ween Ga and Fe a oms in he L1 2 la ice. We used he Special Quasi andom Supe cell (SQS) [ 27 , 28 ] wi h 32 a oms as a model o diso de ed sys em. Such a supe cell exhibi s a magne ic momen o 4.31 µB / .u. due o he opposi e o ien a ion o magne ic momen s a pa icula Fe a oms. An i e omagne ic in e ac ion appea s i he Fe a om is su ounded a leas by six o he Fe a oms. In an o de ed L1 2 s uc u e, each Fe a om is su ounded by only ou o he Fe a oms. Mo eo e , we also ound ha his e imagne ic s a e o diso de ed s uc u e was ene ge ically mo e a o able han e omagne ic o de ing abou 0.017 eV/a om. This clea ly indica es ha he compound Fe50 is diso de ed L12, which esul s in he highes magne ic momen o all e imagne ic s a es. Fo sligh ly non-s oichiome ic compounds wi h excess Fe con en (i.e., he Fe52 sample), a sha p dec ease o magne ic momen down o 2.4 µB / .u. was obse ed in he expe imen . Based on he heo e ical calcula ion o s oichiome ic compound, his sha p dec ease o magne ic momen can be explained by he disappea ance o he diso de and he appea ance o L1 2 o de ing. The heo e ical p edic ion o o de ed compounds is 2.75 µB / .u o 1.9 µB / .u., depending on he mode o an i e omagne ic in e ac ion as desc ibed abo e. The u he sha p decline o magne ic momen obse ed in he expe imen in he compounds wi h highe Fe con en can be asc ibed o ully es ablished an i e omagne ic in e ac ion. The ab ini io calcula ion showed ha u he dec ease o magne ic momen is due o inc easing chance o o m Fe clus e s wi h opposi ely o ien ed magne ic momen s a Fe a oms. The p edic ed end was obse ed in he expe imen ; howe e , he expe imen ally obse ed magne iza ion dec ease is much sha pe han p edic ed. To explain he missing MT in he in es iga ed samples, he ab ini io calcula ions o MOKE spec a o L2 1 and diso de ed L1 2 s uc u es we e pe o med using he complex pe mi i i y enso ob ained wi hin he linea esponse heo y as implemen ed in he VASP 5.4 code. The esul s a e shown in Figu e 4 oge he wi h expe imen al da a. Theo e ical spec a o L2 1 s uc u e do no ollow expe imen al da a, as hey exhibi se e al maxima and minima and change sign o MOKE se e al imes ac oss he in es iga ed ene gy ange. This indica es he absence o L2 1 o de in he in es iga ed samples. On he o he hand, he spec a o he diso de ed L1 2 s uc u e p o ide be e ag eemen wi h he expe imen . They exhibi simila mono onous inc ease and dec ease o pola Ke o a ion and ellip ici y, espec i ely. Admi edly, he ampli ude o he e ec is lowe han he expe imen al da a o he Fe50 sample. Howe e , his can be explained by he ela i ely small uni cell (32 a oms) used in he calcula ion due o p ohibi i ely high memo y equi emen s. Such a small cell migh desc ibe Ma e ials 2020,13, 703 9 o 12 he mo e se e e de ia ion om he ully o de ed s uc u e han he diso de p esen in ou sample. This de ia ion hen changes he elec onic s uc u e excessi ely as mani es ed by he smoo h DOS below, which can esul in a supp ession o he p obabili y o elec onic ansi ions esponsible o magne o-op ical esponse. To explain he di e ence in he MOKE o s oichiome ic Ni-Mn-Ga and in es iga ed Fe-Mn-Ga samples, spin- esol ed o al DOS we e calcula ed and a e displayed in Figu e 6. Figu e 6. Calcula ed spin- esol ed o al DOS o L2 1 and diso de ed L1 2 s uc u es compa ed o hose o s oichiome ic Ni2MnGa. Compa ing he o al DOS o L2 1 and diso de ed L1 2 s uc u es wi h hose epo ed o Ni 2 MnGa [ 5 ], one can see a majo di e ence in he majo i y spin channel jus abo e he Fe mi le el. While he L2 1 and diso de ed L1 2 s uc u es o Fe 2 MnGa ha e a clea ly isible band app oxima ely 0.2–0.3 eV abo e he Fe mi le el ( isible as a sha p peak indica ed by a ows), his band is comple ely missing in he case o Ni 2 MnGa. I indica es ha a subs i u ion o Ni by Fe esul s in he p esence o emp y s a es abo e he Fe mi le el in he majo i y spin channel, which can ac as exci ed s a es o pa icula elec onic ansi ions. Figu e 6also shows ha he diso de ed L1 2 s uc u e exhibi s highe DOS a Fe mi ene gy compa ed o he L21s uc u e. On he o he hand, he mino i y spin channel looks simila o he case o Ni 2 MnGa [ 5 ] as well as o bo h Fe-Mn-Ga s uc u es. The e o e, one should expec ce ain simila i ies in he MOKE spec a o hese wo compounds. Indeed, besides s ong mono onous inc ease/dec ease owa ds he low ene gy egion, one can see ce ain indica ions o spec al s uc u es in expe imen al MOKE spec a a ound 2 eV in o a ion and 3 eV in ellip ici y. These may o igina e, simila ly o Ni 2 MnGa [ 35 , 36 ], om ansi ions be ween s a es in he mino i y spin channel. Howe e , hei ansi ion p obabili y is much lowe compa ed o he low ene gy ansi ions. This is he case o he diso de ed L1 2 s uc u e whe e he ene gy gap in he mino i y spin channel a ound he Fe mi le el is no obse ed con a y o he L2 1 s uc u e and Ni 2 MnGa (see Figu e 6). High DOS a ound he Fe mi ene gy aise he op ical abso p ion a lowe ene gies [ 20 ] and enhance he magne o-op ical esponse as was expe imen ally obse ed in he spec a o pola Ke o a ion. The huge di e ence in DOS in he icini y o he Fe mi le el mos likely supp esses he MT. Since he ene gy gap in he mino i y spin channel makes he ma ensi e phase mo e ene ge ically a o able o e aus eni e [ 5 ] (i is shi ed om below he Fe mi le el o he Fe mi le el du ing he MT), he s abiliza ion o he diso de ed L1 2 s uc u e in he in es iga ed compound is he eason o he missing MT.