Effect of mixing the low-valence transition metal atoms Y = Co, Fe, Mn, Cr, V, Ti, or Sc on the properties of quaternary Heusler compounds Co2-xYx FeSi (0≤x≤1)

PHYSICAL REVIEW MATERIALS 6, 064413 (2022) E ec o mixing he low- alence ansi ion me al a oms Y=Co, Fe, Mn, C , V, Ti, o Sc on he p ope ies o qua e na y Heusle compounds Co2−xYxFeSi (0 ⩽x⩽1) R. Maha ,1,*U. Ka ki,1Shambhu KC,1J. Y. Law,2V. F anco,2I. Galanakis ,3,†A. Gup a ,4and P. LeClai 1,‡ 1Depa men o Physics and As onomy, The Uni e si y o Alabama, Tuscaloosa, Alabama 35487, USA 2Depa amen o de Física de la Ma e ia Condensada ICMSE-CSIC, Uni e sidad de Se illa, Se illa 41080, Spain 3Depa men o Ma e ials Science, School o Na u al Sciences, Uni e si y o Pa as, GR-26504 Pa as, G eece 4Depa men o Chemis y and Biochemis y, The Uni e si y o Alabama, Tuscaloosa, Alabama 35487, USA (Recei ed 4 Ap il 2022; accep ed 9 June 2022; published 29 June 2022) In his pape we epo an expe imen al s udy o s uc u al, magne ic, and mechanical p ope ies o qua e na y Heusle alloys Co2−xYxFeSi (Y=Co,Fe,Mn,C ,V,Ti,o Sc,0⩽x⩽1) and he expe imen al indings a e suppo ed by ab ini io elec onic s uc u e calcula ions. The alloys we e syn hesized using an a c-mel ing echnique. Single phase mic os uc u es a e obse ed o all alloys subs i u ed wi h low- alence ansi ion me als Yexcep Sc. X- ay powde di ac ion pa e ns a oom empe a u e show he p esence o Heusle -like ace-cen e ed cubic c ys al s uc u e in all single phase specimens. The low- empe a u e sa u a ion magne ic momen s, as de e mined om magne iza ion measu emen s, ag ee ai ly well wi h ou heo e ical esul s and also ollow he Sla e -Pauling ule o humb o hal -me als, a p e equisi e o hal -me allici y. The alloys a e p edic ed o exhibi hal -me allic e omagne ism by ab ini io elec onic s uc u e calcula ions using he GGA+U app oach. All s able compounds a e obse ed o ha e high Cu ie empe a u es wi h linea dependence wi h he alence elec ons concen a ion in he alloys. Rela i ely high ha dness alues a e also measu ed, app oaching 15.7 GPa o Ti-subs i u ed ma e ial, highes among he alues epo ed o Heusle s so a . All hese p ope ies s ongly sugges he alloys a e p omising o he spin onic applica ions a oom empe a u e and abo e. DOI: 10.1103/PhysRe Ma e ials.6.064413 I. INTRODUCTION Co2-based ull Heusle compounds belong o a p omising class o ma e ials o magne oelec onics applica ions because o hei po en ial o hal -me allic e omagne ism (and esul - ing 100% spin pola iza ion), high Cu ie empe a u es, la ice ma ching wi h con en ional semiconduc o s, and p ope ies easily uned h ough subs i u ion. Wi h s oichiome ic com- posi ion Co2YZ,Yis usually ano he ansi ion me al and Zis a main g oup elemen , and compounds ypically c ys allize in he cubic L21s uc u e (space g oup Fm¯ 3m[1,2]). The main ea u es o in e es he e— he po en ial o hal -me allici y—is an excep ional elec onic s uc u e, one wi h an ene gy band gap a he Fe mi le el (EF) only o mino i y spin elec ons [3–7], which would yield 100% spin pola iza ion a he Fe mi le el. Howe e , he expe imen ally obse ed spin pola iza ion is always much smalle han 100%. The disc epancy be ween heo y and expe imen is expec ed o be due o s uc u al and chemical diso de [8,9]. Imp o emen s in a ious p ope ies such as s uc u e, magne iza ion, anspo , c i ical empe a- u e Tc, magne o esis ance, as well as high spin pola iza ion can be ealized in somewha diso de ed Heusle alloys by he subs i u ion o a ou h elemen , wi h he qua e na y analogs obse ed o ha e educed s uc u al diso de . The elemen al *[email p o ec ed] †[email p o ec ed] ‡[email p o ec ed] subs i u ion also al e s he deg ee o hyb idiza ion be ween he 3do bi als o di e en elemen s, wi h consequen changes in he posi ion o he Fe mi le el wi h espec o he spin sub- bands [10–15]. Tha is, adding a ou h elemen may se e o no only u he s abilize he s uc u e and educe diso de , i may also help une he p ope ies o in e es o mo e desi able alues. In p e ious s udies, he doping o low- alen ansi ion me al a oms in e na y Heusle alloys has been epo ed o open he mino i y spin ene gy gap a ound Fe mi le el, gi - ing 100% spin pola iza ion and s abilizing a hal -me allic s a e [16,17]. Ou ea lie wo k included a numbe o se ies based on Co2FeGe [18–20], subs i u ing o bo h Co and Fe, and clea ly demons a ing bo h he abili y o s abilize single phase ma e ial and une elec onic and magne ic p op- e ies. The Co2FeSi (CFS) pa en is e en mo e a ac i e as a s a ing poin o applica ions due o i s la ge magne ic momen o 6 μB/ .u. and high Cu ie empe a u e o 1100 K [5]. Howe e , he hal -me allici y in he pa en compound is pe haps s ill an open ques ion, as bo h hal -me allic [21] and non-hal -me allic [4] p ope ies ha e been epo ed heo e i- cally. Kandpal e al. [21] epo ed hal -me allic band s uc u e calcula ions using local spin densi y app oxima ion and gen- e alized g adien app oxima ion, including op imum e ec i e Coulomb exchange in e ac ion (Ue ). On he o he hand, Galanakis e al. [4] epo ed a non-hal -me allic s a e using he ull-po en ial sc eened Ko inga-Kohn-Ros oke G een’s unc ion app oach. In ha case, he Fe mi le el ell on he edge o he mino i y conduc ion band, leading o uns able 2475-9953/2022/6(6)/064413(12) 064413-1 ©2022 Ame ican Physical Socie y R. MAHAT e al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) hal -me allici y. Na u ally, hal -me allic e omagne s wi h a s able ene gy gap in mino i y spin channel a e desi ed o echnical applica ions, pa icula ly when one conside s ini e empe a u e e ec s [22,23]. I he Fe mi ene gy is nea one o he band edges, he ene gy gap may easily be smea ed ou a ini e empe a u es o des oyed by quasipa icle exci a ions [22,23]. To achie e obus ness, compounds wi h Fe mi le el loca ed a he middle o he mino i y ene gy gap a e highly p e e ed [22,23]. As such, he e is g ea u ili y in being able o sligh ly shi he posi ion o he Fe mi le el in a sys em ha is nea ly hal -me allic o s abilize a obus hal -me allic s a e, o o imp o e he obus ness o a ma ginal hal -me al. This is whe e qua e na y subs i u ion can play a decisi e ole: i Co2FeSi is no qui e a s able hal -me al, can he gen le subs i u ion o a ou h elemen push i owa d a s able hal - me allic s a e? And, a he same ime, can his also imp o e o he use ul p ope ies ha ha e led people o his sys em, such as magne ic o he moelec ic cha ac e is ics? This is he basic s a ing poin o he p esen wo k: i oneo heCoa ominCo 2FeSi is subs i u ed by ano he lowe alence ansi ion me al a om Y=Fe, Mn, C , V, Ti, o Sc, a spec um o alloys wi h ich and use ul p ope ies can be gene a ed. In ac his idea is al eady well unde s ood in he Heusle alloys in gene al. The in e se Heusle alloy Fe2CoSi (which one could iew as Co2−xFe1+xSi wi h x=1) has been epo ed o be ze o-gap hal -me al wi h e y low Gilbe damping [24,25]. The qua e na y Heusle CoFeMnSi has been obse ed heo e ically and expe imen ally o be a spin-gapless semiconduc o [26–28], CoFeC Si has been e- po ed o be hal -me allic wi h some s uc u al diso de [29], while CoFeVSi and CoFeTiSi a e epo ed heo e ically o be nea ly hal -me allic and hal -me allic espec i ely, bu bo h ha e been obse ed expe imen ally o show mul iphase be- ha io in bulk o m [30,31]. In all hese qua e na y Heusle alloys, he Fe mi le el lies on he edge o he mino i y alence band. As we go om Co2FeSi o CoFeYSi, o a lowe alence subs i uen Y, he Fe mi le el is shi ed om he lowe edge o he conduc ion band o he uppe edge o he alence band in he mino i y spin channel, in acco dance wi h he calcula ions by Galanakis e al. [32]. They sugges ed ha an expansion o he la ice should shi he Fe mi le el lowe in ene gy, while a con ac ion o he la ice should shi i highe . Since one can expec obus hal -me allici y wi h Fe mi le el exac ly in he middle o he mino i y spin band gap, his gi es us a p esc ip ion o a po en ially ma ginal hal -me al Co2FeSi. Since acco ding o Galanakis e al. he Fe mi le el ell on he edge o he mino i y conduc ion band, we would like o mo e he Fe mi le el lowe in ene gy, and his means a la ice expansion. This in u n means ha i we subs i u e a lowe alence Yelemen wi h la ge a omic adius han Co [33]inCo 2−xYxFeSi, we should be able o mo e he Fe mi le el owa d midgap. The subs i u ion o a Ya om o Co in Co2FeSi may hen be also seen as d-elec on de iciency. The e ha e al eady been se e al de ailed s udies on Co2FeSi showing ha subs i u ion plays an impo an ole in ealizing use ul elec onic and magne ic p ope ies and uning he Fe mi le el owa ds he cen e o he mino i y band gap [10,22,34–36]. The band gap a he Fe mi le el can be a ied by subs i u ing a ou h elemen a any o he h ee X/Y/Z si es, i.e., Co2−xY∗ xYZ,Co 2Y1−xY∗ xZ,o Co 2YZ1−xZ∗ xwhe e Y,Y∗a e low- alence ansi ion elemen s and Z,Z∗a e main g oup elemen s [9,37–42]. Subs i u ion a X/Ysi e is pe haps mo e con incing as he X/Ysi e elemen s play he main ole in ailo ing he hal -me allici y and magne ic p ope ies com- pa ed o he Zsi e elemen [32]. Fo example: C subs i u ion o Fe in Co2FeSi has been obse ed o inc ease he spin pola iza ion [10]; low Gilbe damping has been obse ed in a hal -me allic Co2FexMn1−xSi subs i u ional se ies [35]; and he uning o Fe mi le el o hal -me allici y has been demons a ed in Heusle alloy Co2FeAl0.5Si0.5[34,36]. I is he aim o his wo k o syn hesize Co2FeSi and in es iga e he e ec o low- alence ansi ion me al (Y=Fe, Mn, C , V, Ti, o Sc) subs i u ion o Co on s uc u al, elec onic, magne ic, and mechanical p ope ies. II. METHODS A. Expe imen al me hods Polyc ys alline Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, Ti, o Sc, 0 ⩽x⩽1) o -s oichiome ic Heusle alloys we e p e- pa ed by con en ional a c mel ing o cons i uen s o 99.99% pu i y on a wa e -cooled Cu hea h unde a gon low, wi h a base p essu e o 10−4mba . The mix u e was lipped and mel ed a leas 6 imes o ensu e chemical homogenei y. Ti was mel ed inside he acuum chambe sepa a ely as an oxy- gen ge e be o e mel ing he compound o a oid oxygen con amina ion. The weigh loss du ing he p ocess was less han 1%. The esul ing ingo s we e cu in o pieces and ex- amined using an ene gy dispe si e x- ay spec oscopy (EDS) de ec o equipped in a JEOL 7000 ield emission scanning elec on mic oscope (FESEM) o ensu e he a ge compo- si ion a e he a c mel ing. These pieces we e annealed in e acua ed qua z ubes o di e en hea ea men s, and cooled slowly in he u nace o ge op imum c ys alliza ion o p omo e he o ma ion o L21s uc u e. To make he compa ison uni o m ac oss all composi ions, only he sam- ples annealed unde simila hea ea men s (i.e., 900 ◦C o 7 days) a e epo ed. The hea ea men s we e ollowed by me allog aphy (see de ails in he Supplemen al Ma e ial o ou p e ious publica ions [43,44]) o p oduce a me allic shiny su ace o mic os uc u e analysis by op ical and elec on mic oscopes. A e hea ea men and me allog aphy, he composi ion and homogenei y o he samples we e again con- i medbyEDS. The c ys al s uc u e was in es iga ed by means o x- ay di ac ion (XRD) using a B uke D8 Disco e x- ay di ac ome e equipped wi h monoch oma ic Co-Kα(λ= 0.179 nm) adia ion a oom empe a u e. The specimens we e c ushed by hand using a mo a and pes le, and he XRD mea- su emen s we e ca ied ou on he c ushed powde samples by o a ing a ound he φaxis o minimize su ace e ec s. I should be no ed ha ball milling can esul in a dis o ion o he c ys alline s uc u e due o mechanical obus ness o ou alloys (discussed in a subsequen sec ion). CaRIne c ys allog- aphy 4.0 so wa e [45] as well as in-house PYTHON code [46] including he dispe si e co ec ions o he a omic sca e ing ac o s we e used o simula e he XRD pa e ns o compa e wi h he expe imen al XRD pa e ns. Rie eld e inemen s o he XRD da a we e pe o med using MATCH! so wa e based 064413-2 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) on he FullP o algo i hm [47]. Magne iza ion iso he ms a 5 and 300 K we e s udied by means o Quan um Design Physical P ope ies Measu emen Sys em (PPMS) using small sphe ical sample pieces o ∼20–30 mg, while he high em- pe a u e magne iza ion was measu ed using LakeSho e VSM 7407. The mechanical p ope ies in e ms o Vicke s ha dness we e measu ed by using Buehle model 1600–6100 mic o- ha dness es e . B. Compu a ional me hods Ab ini io calcula ions a e pe o med using densi y- unc ional heo y (DFT) employing he p ojec o augmen ed wa e (PAW) pseudopo en ials by Blöchl [48], implemen ed by K esse and Fu hmülle in he Vienna ab ini io simula ion package (VASP)[49]. We ha e adop ed he gene alized- g adien app oxima ion (GGA) as o mula ed by Pe dew, Bueke, and E nze ho (PBE) o he elec onic exchange- co ela ion po en ial [50]. A 16-a om supe cell, i.e., 4 o mula uni s o he unde lying L21s uc u e adop ed by he pe ec ull-Heusle compounds like Co2MnGe is used in all o ou calcula ions. The in eg als in he ecip ocal space o cubic sys ems was done conside ing a 20 ×20 ×20 -cen e ed Monkho s -Pack g id [51] using he linea e ahed on me hod wi h Blöchl co ec ions. To al ene gies we e con e ged up o 10−7eV/cell wi h a cu o o he kine ic ene gy o he plane wa es o 520 eV. Full elaxa ion o cell (ini ially cubic) olume, shape, and a omic posi ions we e pe o med un il he o ces on each a om become less han 10−2meV/cell using he conjuga e-g adien me hod. Spin-o bi in e ac ion is igno ed in ou calcula ions as i is no c ucial o he hal - me allic p ope ies o Heusle compounds [52]. Ab ini io elec onic s uc u e calcula ions using GGA ap- p oach in he case o pa en compound CFS wi h 30 alence elec ons pe o mula uni has been epo ed o p edic a signi ican ly educed magne ic momen wi h espec o ex- pe imen and he Sla e -Pauling alue, due o he well-known on-si e elec onic co ela ions o he delec ons and ela ed ac ional s a e occupa ion [21]. The obse ed hal -me allic p ope ies o CFS is epo ed o be eco e ed by in oducing an app op ia e Hubba d U e m in o he elec onic Hamil- onian [21]. In ou s udy we ha e also p esen ed GGA+U calcula ions on Co2−xYxFeSi sys em and explo e how he CFS elec onic p ope ies a e a ec ed by low- alence a omic sub- s i u ions. The Hubba d Upa ame e canno be calcula ed simul a- neously wi h he minimiza ion o he o al ene gy because o al ene gy emains cons an wi h espec o he U e m. Bo h expe imen al and compu a ional de e mina ion o he U alues a e e y di icul and edious asks. In 2013 Sasioglu and collabo a o s employed he cons ained andom-phase app oxima ion (CRPA) scheme o calcula e he U alues o se e al hal -me als [53]. Fo he calcula ions p esen ed in he es o his wo k, we ha e used he semiempi ical alues men- ioned in Re . [54], whe e Kandpal e al. ha e employed he LDA+Uscheme o s udy he elec onic s uc u e o se e al hal -me allic Heusle compounds. The U alues used o he do bi als o Co, Fe, Mn, C , V, Ti, and Sc a e 1.92, 1.80, 1.69, 1.59, 1.34, 1.36, and 1.30 eV, espec i ely. Finally, i should be no ed ha he inclusion o Ua i icially opens a FIG. 1. Op ical mic og aph o Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, x=0.50) annealed a 900 ◦C o 7 days ollowed by slow cooling showing he g anula mic os uc u e. The samples we e e ched o 60 s using he Adle e chan . band gap in he mino i y spin channel and only compa ison o expe imen al da a gua an ees ha he Upa ame e s used in he calcula ions a e adequa e o a pa icula ma e ial. III. RESULTS AND DISCUSSIONS A. Expe imen al esul s and discussions 1. Mic os uc u al and composi ional analysis Op ical mic oscopy and SEM o polished and e ched samples a e e y help ul o cha ac e ize he mic os uc u e specially when he impu i y phase con en s a e ei he below he de ec ion limi o XRD (less han oughly 5% o he o e all olume) o amo phous in na u e [18,19,55,56]. These me hods p o ide a mo phological image which can clea ly expose seconda y phases and g ain bounda y seg ega ion e en o mino cons i uen s. We can i s specula e he p esence o impu i y phases by obse ing a eas o di e en con as in op ical mic oscopy, and subsequen ly SEM wi h EDS can be u ilized o quan i y whe he egions o di e en con as s uly ha e di e en composi ions o a e, o ins ance, jus di e en c ys alli e o ien a ions. Figu e 1shows he mic os uc u es o all single phase spec- imens Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, x=0.50) annealed a 900 ◦C o 7 days, obse ed using an op ical mic oscope. Wi h he subs i u ion o 50% Ycon en (Co, Fe, Mn,C ,V,Ti,o Sc) o CoinCo 2FeSi, we obse ed single phase mic os uc u es excep o 50% Sc. Ou esul s a e in acco dance wi h p e ious epo s o 50% Co and Fe o Co in Co2FeSi. I is ound ha he g ain size o he alloys dec eased 064413-3 R. MAHAT e al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) FIG. 2. SEM mic og aph o Co2−xYxFeSi (Y=Co,Fe,Mn,C , V, o Ti, x=0.50) alloys annealed a 900 ◦C o 7 days ollowed by slow cooling, showing he g anula mic os uc u e. g ea ly wi h he subs i u ion o less alence Ycon en . The con as de eloped in mic og aph (see Figs. 1–5 in he Sup- plemen al Ma e ial [57]) sugges s signi ican composi ional di e ences be ween phases in he case o 50% Sc o Co. The composi ion was measu ed o di e om he a ge composi- ion by mo e han 5% wi h he seconda y phase mainly loca ed in g ain bounda ies. The s oichiome y wi hin he g ains o all he single-phase specimens was con i med as he a ge composi ion wi hin an ins umen al unce ain y o ∼5% using EDS (see Table I in he Supplemen al Ma e ial [57]). Figu e 2shows he ypical elec on images displaying he mic os uc u e o single phase alloys. The op ical and elec- on mic og aphs o all he emaining alloys in he se ies a e p esen ed in he Supplemen al Ma e ial [57]. 2. C ys al s uc u e and a omic o de analysis The s uc u al and chemical o de o he alloys is impo an o hei po en ial use in any kind o spin onics applica ions, and o his end s uc u al analysis has been pe o med wi h XRD. Figu e 3shows he powde XRD spec a o he s udied alloys wi h x=0.50, measu ed a oom empe a u e, using aCo-Kα adia ion sou ce (see Fig. 6 in he Supplemen al Ma e ial [57]). All he alloys showed single phase beha io excep o Sc, consis en wi h mic os uc u es obse ed in p e ious sec ion. Fo he Sc sample, as e isks deno e possible Heusle cubic peaks while o he peaks a e om seconda y phases/unknown impu i y phases. All he XRD peaks in single-phase alloys can be indexed o a ace-cen e ed cubic ( cc) s uc u e, wi h h,k,lall odd o e en. As expec ed only h ee dis inc ypes o peaks a e obse ed: undamen al FIG. 3. Expe imen al XRD pa e ns o Co2−xYxFeSi (Y=Co, Fe,Mn,C ,V,Tio Sc,x=0.50) alloy se ies annealed a 900 ◦C o 7 days in es iga ed a oom empe a u e, he e ∗co esponds o Heusle cubic peaks in Sc-based alloy while o he s a e om sec- onda y phase/unknown impu i y phase. The i s om he bo om is he simula ed XRD pa e n o o de ed L21s uc u e o Co2FeSi. The ela i e in ensi y (yaxis) is plo ed in log scale so ha all he peaks can be seen clea ly. peaks wi h h+k+l=4n, e en supe la ice peaks wi h h+ k+l=4n+2, and odd supe la ice peaks wi h h+k+l= 2n+1. Heusle alloys in he o de ed L21s uc u e a e cha ac- e ized by he p esence o supe la ice e lec ion (SR) peaks; he p esence o (111) peak indica es he chemical o de ing o a oms in oc ahed al posi ions, and (200) peak indica es he o de o a oms in e ahed al posi ions, while he (220) peak is a p incipal e lec ion which is independen o he s a e o he o de [58]. In ull Heusle alloys (FHA) o he ype X2YZ in he L21s uc u e, Zis he main g oup elemen wi h highes elec onega i i y which occupies 4a (0,0,0) Wycko si es in he Fm¯ 3mspace g oup, Yis he lowe alence ansi- ion me al a om wi h smalles elec onega i i y and occupies he 4b(1 2,1 2,1 2) Wycko si es, and he ansi ion me al X a oms a e o in e media e elec onega i i y and occupy he 8c(1 4,1 4,1 4) Wycko si es [co esponding o he 4c(1 4,1 4,1 4), and 4d(3 4,3 4,3 4) Wycko posi ions in he “hal Heusle ” C1b s uc u e o space g oup F¯ 43m][8,59]. He ea e , we e e o he 4a and 4b si es as he A subla ice and 4c and 4d oge he as he B subla ice, as shown in Fig. 4. The in en- si ies o supe s uc u e peaks a e a ec ed by a ious ypes o 064413-4 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) FIG. 4. C ys al s uc u e in a uni cell o (a) CFS and (b) Co1.50Y0.50FeSi (Y=Fe, Mn, C , V, Ti, o Sc) (I) con igu a ion men ioned in Table Iassuming L21s uc u e. The s uc u es a e shown in hei ideal, un elaxed o ms. a omic diso de s, e.g., (i) A2 (bcc) diso de due o andom dis ibu ion o a oms o e la ice si es 4a, 4b, 4c, and 4d which esul s in anishing supe s uc u e peaks, (ii) B2 (CsCl) diso de due o andom dis ibu ion be ween a oms in 4a and 4b si es which esul s only he (200) supe s uc u e peak and anishing (111) peak, and (iii) DO3(BiF3) diso de when diso de is be ween a oms in 4b, 4c, and 4d si es only [60]. This diso de ed s uc u e DO3 esul s in a (111) peak wi h much highe in ensi y han he (200) peak. All hese ypes o diso de would des oy he hal -me allic p ope y o he ma e ial by in oducing densi y o s a es (DOS) a Fe mi le el in he mino i y spin channel [41], e en hough he magne ic momen o he ma e ials may s ill ollow a Sla e -Pauling ule. AsshowninFig.3(see also Fig. 8 in he Supplemen al Ma e ial [57]), he supe la ice e lec ion peaks (111) and (200) a e clea ly isible as expec ed o he de ec - ee o - de ed Heusle s uc u e ( he deg ee o chemical o de ing has been ob ained using he Webs e ’s model [61]asdiscussedin Sec. I B o he Supplemen al Ma e ials [57]), indica ing he p esence o a long ange o de ing in all single phase spec- imens. The measu ed and expec ed alues o I111/I220 and I200/I220 a e obse ed o ag ee wi h each o he quali a i ely (see Fig. 8 in he Supplemen al Ma e ial [57]). In o de o gain mo e insigh on chemical o de ing, we pe o med Rie eld e inemen o expe imen al XRD pa - e n o Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, x= 0.50) conside ing h ee nondegene a e con igu a ions as p e- sen ed in Table I. De ails o he e inemen s o he bes i con igu a ion (I) a e p o ided in Table II. The obse ed, calcula ed and di e ence p o iles o he bes i con igu a- ion (I) a e pe o ming he Rie eld e inemen a e p o ided in he Supplemen al Ma e ial [57]. The c ys al s uc u e o TABLE I. Possible si e assignmen s o cubic Co2−xYxFeSi (Y= Co,Fe,Mn,C ,V,Ti,o Sc,x=0.50) Heusle sys em. 4a 4b 4c 4d Type (0,0,0) (1 2,1 2,1 2)( 1 4,1 4,1 4)( 3 4,3 4,3 4) ISiFe 0.50Y0.50 Co0.50Fe0.50 Co II Si Co0.50Y0.50 Fe Co III Si Fe Co0.50Y0.50 Co TABLE II. Goodness o i pa ame e s (χ2and RB agg ac o ) ob ained om Rie eld e inemen o Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, x=0.50) alloys. Yelemen χ2RB agg Co 1.1 5.3 Fe 1.3 6.9 Mn 1.5 11.2 C 1.9 9.1 V 1.6 8.3 Ti 1.5 7.7 his con igu a ion is shown in Fig. 4(b) (see Fig. 9 in he Supplemen al Ma e ial [57] o o he possible con igu a ions). In his con igu a ion, we p esumed ha low- alence Ysub- s i uen a oms will displace Fe a oms om 4b si es owa ds aca ed Co si es, and Ya oms will subsequen ly ill he si es p e iously occupied by Fe. This esul s in Ya oms o ming an ionic- ype subla ice wi h Si, which has a la ge elec onega- i i y, a he han wi h Co and Fe and he sys em becomes s able by Ydona ing i s elec ons o o he elemen s in he alloy. The Co and displaced Fe a oms ha e in e media e elec- onega i i ies and occupy e ahed al si es [8,59]. In o he wo ds, Co and Fe a oms a e assumed o be on he e ahed al subla ice B (4c and 4d) and Fe, Y, and Si on he oc ahed al subla ice A (4a and 4b). This Hume-Ro he y condi ion o phase s abili y o subs i u ional solid solu ion also suppo s his a omic con igu a ion. Acco ding o his ule, he a omic size di e ence be ween wo elemen s should be no la ge han 15% and elec on nega i i y di e ence no highe han 0.4 in o de o o m he s able solid solu ion [62–64]. How- e e , complemen a y measu emen s like neu on di ac ion, synch o on x- ay di ac ion echniques which a e capable o di e en ia ing elemen s ha a e close o Fe/Co a e equi ed o be e unde s and he chemical o de ing in he c ys al la ice. We used Cohen’s me hod wi h a Nelson-Riley ex apola ion o accu a ely de e mine he la ice pa ame e s om XRD da a [66]. The dependence o he la ice pa ame e aon he Y con en o Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, 0⩽x⩽1) is shown in Fig. 5(a) while Fig. 5(b) shows he a ia ion o la ice pa ame e wi h a omic numbe o Yele- ( a ) ( b ) FIG. 5. Va ia ion o la ice pa ame e wi h (a) Ycon en in Co2−xYxFeSi (Y=Co,Fe,Mn,C ,V,o Ti,0⩽x⩽1), and (b) a omic numbe o low- alence ansi ion me al elemen Yin Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, x=0.50) showing linea beha io . The pink da a poin s ep esen li e a u e alues [5,65]. 064413-5 R. MAHAT e al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) ( a ) ( b ) FIG. 6. (a) Iso he mal magne iza ion cu es o Co2−xYxFeSi (Y =Co,Fe,Mn,C ,V,o Ti,x=0.50) a 5 K. (b) The sa u a ion magne ic momen e sus alence elec on coun s pe o mula uni s wi h elemen Y, bo h expe imen al (a 5 and 300 K) and expec ed om he Sla e -Pauling ule o hal -me als. The pink da a poin s ep esen epo ed li e a u e alues [5,65]. men in Co1.50Y0.50FeSi (Y=Co, Fe, Mn, C , V, o Ti). I is no iced ha he la ice pa ame e inc eases linea ly wi h he subs i u ion o less alence Ycon en , consis en wi h Vega d’s law [67] as a omic adii dec ease in he o de Ti >V >C >Mn >Fe >Co [33]. 3. Magne ic cha ac e iza ion Mos o he Co-based hal -me allic Heusle alloys show a Sla e -Pauling-like beha io o he magne iza ion when c ys- allized in a ully o de ed s a e [68]. The Sla e -Pauling (SP) ule ela es he dependence o he magne ic momen wi h he alence elec on concen a ion (Z ) ollowing a simple elec- on coun ing scheme o o de ed, hal -me allic e omagne ic Heusle compounds. I he alue o he sa u a ion magne iza- ion changes wi h Yelemen acco ding o he Sla e -Pauling ule o humb o hal -me als, hen we expec he o al magne- iza ion o be [4,8] M =[(2 −x)ZCo +xZY+ZFe +ZSi]−24,(1) whe e M is he o al spin magne ic momen pe .u. in μBand Ziis he numbe o alence elec ons o each indi idual a om. In Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, 0 ⩽x⩽1) sys em, he o al numbe o alence elec ons change om 30 in CFS o 25 in CoFeTiSi. The e o e, he SP beha io p edic s ha he sa u a ion magne ic momen should dec ease wi h he subs i u ion o Yelemen o Co. Speci ically, a sa u a ion magne ic momen o M(Y)=6−x(ZCo −ZY)(2) is hus expec ed o Co2−xYxFeSi. Fo magne ic p ope ies, we p ima ily used he VSM op- ion o a Quan um Design PPMS Dynacool wo king in he empe a u e ange o T=5 o 400 K and wi h maximum magne ic ield o 9 T o obse e low empe a u e magne- iza ions o all single-phase alloys. Figu e 6(a) shows he iso he mal magne iza ion cu es measu ed a 5 K o x=0.50 (see Figs. 11–13 in he Supplemen al Ma e ial [57] o mag- ne iza ion cu es o all o he alloys in he se ies), as expec ed o e omagne s. All he alloys a e sa u a ed in a magne ic ield o abou 4 kOe which indica es small magne oc ys alline aniso opy in he specimens. The A o plo me hod [69] (a) (b) FIG. 7. (a) Tempe a u e dependence o magne iza ion a 100 Oe, and (b) a ia ion o Cu ie empe a u e as a unc ion o alence elec on coun s pe o mula uni s wi h elemen Y(x=0.50). The inse shows he i s -o de de i a i e o magne iza ion as a unc ion o empe a u e, he minima o which is used o ex ac Tc. The pink da a poin s ep esen s epo ed li e a u e alues [5,65]. (i.e., by linea ex apola ion o H/M=0o M2 e sus H/M cu es) was u ilized o de e mine he spon aneous magne- iza ions [see inse o Fig. 6(a)]. To al sa u a ion magne ic momen s (Ms) ob ained om he spon aneous magne iza ion a 5 K a e obse ed o ollow he Sla e -Pauling ule o humb o hal -me als (see ed da a poin s) and dec ease wi h he dec ease o alence elec ons in Ya oms [see Fig. 6(b)]. The dec ease o Msis expec ed due o he dec ease in he numbe o Co a oms. The magne ic momen pe o mula uni o x=0, i.e., CFS, is measu ed o be 5.92 μB, which is also in good ag eemen wi h epo ed esul s [5,65]. The sys em- a ic a ia ion o sa u a ion magne ic momen s wi h Ya om concen a ion (0 ⩽x⩽1) in he se ies is p o ided in Fig. 14 in he Supplemen al Ma e ial [57]. The sligh de ia ion o magne ic momen s om expec ed Sla e -Pauling alues could be due o he sligh a ia ion in he s oichiome y o he alloys, weighing and measu emen e o s, pa ial su ace oxida ion, and he measu emen empe a u e o 5 K. The expe imen ally de e mined magne ic momen s a e also in good ag eemen wi h hose ob ained om i s -p inciple calcula ions (see Ta- ble IV), as discussed in a o hcoming sec ion. Figu e 7(a) shows he empe a u e dependen speci ic mag- ne iza ion o he alloys o x=0.50 (see Fig. 14 in he Supplemen al Ma e ial [57] o all o he alloys in he se- ies), measu ed by means o a ib a ing sample magne ome e (LakeSho e VSM 7407) equipped wi h a high empe a u e s age. We p esen he esul s abo e 300 K so ha he beha io close o he Cu ie empe a u e Tcis no masked by he apid dec ease o he magne iza ion a lowe empe a u es. Mo e- o e , he measu emen s we e no pe o med a sa u a ion bu in a cons an magne ic ield o 100 Oe. This leads o a mo e d as ic d op o he magne iza ion a he Tcbu i allows he mo e p ecise de e mina ion o Tcwhich is ou goal. The Cu ie empe a u es Tcwe e ex ac ed om he in- lec ion poin , i.e., by aking he minima o he i s -o de de i a i e o M(T) cu es [see inse in Fig. 7(b)]. The Cu ie empe a u e is obse ed o dec ease wi h he subs i u ion o low- alence ansi ion me al elemen Ydue o he weakening o he exchange in e ac ion caused by a small magne ic mo- men o subs i u ed elemen Ycompa ed o Co. The dec ease in Tccan also be a ibu ed o he inc ease in la ice pa ame e 064413-6 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) TABLE III. Expe imen al la ice pa ame e s and sa u a ion magne ic momen s a T=5 K along wi h he Sla e -Pauling (SP) alues, and he measu ed Cu ie empe a u e (Tc)o Co 2−xYxFeSi (Y=Co,Fe,Mn,C ,V,o Ti,0⩽x⩽1) alloy se ies. The numbe s in pa en heses a e he unce ain y in he las digi , e.g., 5.92(3) =5.92 ±0.03. Values in squa e b acke s a e aken om he li e a u e. Exp . la ice Exp . MsSP TcVicke s ha dness Se ies Concen a ion pa ame e (Å) (μB/ .u.) (μB/ .u.) (K) (GPa) Co2FeSi x=0a=5.641(2)[5.636] 5.92(3)[6.00] 6.00 1094(10)[1100][5,70] 7.33(4) Co2−xFexFeSi x=0.25 a=[5.641] [5.75] 5.60 [1058][65,70]– x=0.50 a=5.646(2)[5.642] 5.58(2)[5.62] 5.50 1040(10)[1069][65,70] 7.55(6) x=0.75 a=[5.647] [5.60] 5.20 [1052][65,70]– x=1a=[5.655] [5.20] 5.00 [1036][65,70]– Co2−xMnxFeSi x=0.25 a=5.646(2) 5.57(4) 5.50 – 7.51(4) x=0.50 a=5.651(2) 5.06(3) 5.00 947(10) 7.94(3) x=0.75 a=5.658(3) 4.49(2) 4.50 869(10) 8.51(5) x=1a=5.661(2) 4.03(3) [3.99] 4.00 761(10)[763] 9.69(7) Co2−xC xFeSi x=0.25 a=5.650(2) 5.20(4) 5.25 969(10) 7.82(6) x=0.50 a=5.662(1) 4.46(3) 4.50 873(10) 8.61(8) x=0.75 a=5.673(2) 3.72(2) 3.75 790(10) 9.78(9) x=1a=5.687(3) 2.91(2)[2.82] 3.00 710(10) 11.33(9) Co2−xVxFeSi x=0.25 a=5.656(1) 4.89(4) 5.00 924(10) 8.52(5) x=0.50 a=5.671(1) 3.90(3) 4.00 791(10) 9.85(7) x=0.75 a=5.683(3) 2.89(4) 3.00 553(10) 11.37(8) x=1†a=5.694(6) 1.45(5) 2.00 345(10) 11.79(10) Co2−xTixFeSi x=0.25 a=5.665(4) 4.75(5) 4.75 902(10) 10.75(7) x=0.50 a=5.681(2) 3.45(2) 3.50 720(10) 12.58(3) x=0.75 a=5.707(3) 2.23(5) 2.25 487(10) 13.81(9) x=1aa=5.716(6) 0.88(9) 1.00 331(10) 15.72(14) aMul iphase specimen. wi h he subs i u ion o Ychanging he dis ance be ween magne ic ions leading o a weak exchange in e ac ion. A linea dependence is ob ained when plo ing Tcas a unc ion o numbe o alence elec on concen a ion, and hence Ms [see Fig. 7(b)], which is expec ed in hal -me allic Co-based Heusle alloys [38]. Acco ding o his plo , Tcis he highes o hose ha exhibi a la ge magne ic momen , o equi a- len ly o hose wi h a high alence elec on concen a ion as de i ed om he Sla e -Pauling ule. The high alues o Tcusually imply s able magne ism and hal -me allici y o e wide empe a u e ange, necessa y in p ac ical applica ions. The sys ema ic a ia ion o Cu ie empe a u es wi h Ya om concen a ion (0 ⩽x⩽1) in he se ies is p o ided in Fig. 14 in he Supplemen al Ma e ial [57]. The expe imen al alues o la ice pa ame e s, sa u a ion magne ic momen s a 5 K, Cu ie empe a u es, and co - esponding mechanical ha dness alues o all single phase specimens in Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti, 0⩽x⩽1) alloy se ies a e summa ized in Table III. 4. Vicke s mic oha dness Fo indus ial applica ions, ma e ials equi e mechanical obus ness o unde go epe i i e he mal cycling and esis c acking om ib a ions. He e we ha e measu ed he me- chanical p ope ies in e ms o Vicke s ha dness. Figu e 8(a) displays he a ia ion o Vicke s mic oha dness wi h an- si ion me als o inc easing a omic numbe in Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, o Ti) se ies wi h 0 ⩽x⩽1 and Fig. 8(b) shows he a ia ion o allows wi h x=0.50, all measu ed a oom empe a u e. The co esponding ha ness alues a e gi en in Table III. The da a we e aken om a leas 12 di e en egions o each sample wi h 0.2 kg load and 10 s loading ime and a e age alues a e epo ed he e. The Vicke s ha dness is calcula ed om HV =1.8544F/D2[kg/mm2],(3) whe e Dis he diagonal leng h o he imp ession o he di- amond p obe. Rela i ely high ha dness alues a e measu ed, app oaching 15.72 GPa o CoFeTiSi, highes among he al- ues epo ed o Heusle s so a [18–20,43,44,71–73]. The ha dness is obse ed o inc ease wi h he subs i u ion o Y ( a ) ( b ) FIG. 8. Vicke s ha dness e sus Ycon en in Co2−xYxFeSi (Y= Co, Fe, Mn, C , V, Ti, o Sc), all annealed a 900 ◦C o 7days (a) o all he alloys 0 ⩽x⩽1, and (b) o alloys wi h x=0.50. The imp in s o he inden e wi h adial c acks o Ti =1 [bo om igh o (a)] and Ti =0.50 [ op igh o (b)] a e shown. 064413-7 R. MAHAT e al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) TABLE IV. Pa ame e s ex ac ed om DFT calcula ions (bo h GGA and GGA+Uapp oach) o ype I con igu a ion. In he able M,MSP, a,and ep esen calcula ed magne ic momen , Sla e -Pauling momen , op imized la ice pa ame e , and ene gy gap a Fe mi le el. The las column shows he e agonali y in he s uc u e a/c−1. The alues in he pa en heses ep esen he calcula ed alues using GGA app oach. YMM SP aTe .  elemen Con igu a ions 4d 4c 4b 4a (μB/ .u.) (μB/ .u.) (Å) (a/c−1) (eV) Co Co8-Fe4Si44Co 4Co 4Fe 4Si 6.000(5.484) 6.000 5.636 0.012 0.791 Fe Co6Fe2-Fe4Si44Co 2Fe,2Co 4Fe 4Si 5.502(5.369) 5.500 5.640 0.012 0.387 Mn Co6Fe2-Fe2Mn2Si44Co 2Fe,2Co 2Mn,2Fe 4Si 5.000(4.999) 5.000 5.645 0.012 0.575(0.138) C Co6Fe2-Fe2C 2Si44Co 2Fe,2Co 2C ,2Fe 4Si 4.500(4.480) 4.500 5.657 0.012 0.626 VCo 6Fe2-Fe2V2Si44Co 2Fe,2Co 2V,2Fe 4Si 3.999(3.856) 4.000 5.678 0.012 0.176 Ti Co6Fe2-Fe2Ti2Si44Co 2Fe,2Co 2Ti,2Fe 4Si 3.500(3.463) 3.500 5.690 0.012 0.597 Sc Co6Fe2-Fe2Sc2Si44Co 2Fe,2Co 2Sc,2Fe 4Si 3.000(2.994) 3.000 5.717 0.012 0.719 elemen o inc easing a omic adius and depends on phases p esen as epo ed in he li e a u e [74]. B. Theo e ical esul s and discussions The pa en compound Co2FeSi o he se ies Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, Ti, o Sc, x=0.50) has al eady been epo ed in he li e a u e o o m he L21s uc u e wi h a low deg ee o chemical diso de [22] and ou expe imen al in es iga ions con i med he low- alence ansi ion me als Y subs i u ion o Co in Co2FeSi also gi e s able single phases wi h XRD pa e ns consis en wi h he o de ed L21s uc u e (excep o scandium subs i u ed alloy). These expe imen al ac s allow us accu a e compa ison be ween expe imen and heo y. We no e ha DFT using he GGA app oach p edic s a signi ican ly educed magne ic momen wi h espec o ex- pe imen and Sla e -Pauling alues, bu ha he in oduc ion o Hubba d U e ms in he GGA app oach, i.e., GGA+U, e- sol es he disc epancy in Co2FeSi [21,22]. In o de o p edic he size and na u e o band gaps and magne ic momen s, we ha e he e o e pe o med he elec onic-s uc u e calcula ions using bo h GGA and GGA+Uapp oaches. Fo heo e ical calcula ions, bulk Co1.50Y0.50FeSi (Y=Co, Fe, Mn, C , V, Ti, o Sc) cubic supe cell s uc u es consis ing o 16 a oms we e cons uc ed using he Mon e Ca lo spe- cial quasi andom s uc u e (MCSQS) me hod [75] which is a pa o he open sou ce ATAT oolki [76] accessible om [77]. The MCSQS me hod can handle double-si e subs i u- ions as desc ibed in he expe imen al sec ion abo e aking ca e o nea es neighbo in e ac ion and p edic s a special quasi andom s uc u e by gene a ing a se o clus e s wi h speci ic co ela ions ela i e o a a ge andom s uc u e. The bes MCSQS s uc u es we e con i med a e wai ing o a long enough ime un il a co ela ion di e ence ela i e o he a ge andom s uc u e app oaches ze o. The p edic ed MCSQS s uc u es a e in good ag eemen wi h con igu a ion I p edic ed in Table I[see also Fig. 4(b)]. The p edic ed MC- SQS s uc u es we e hen op imized using GGA me hod. The expe imen al la ice cons an s ex ac ed in ou expe imen al wo k we e employed as s a ing alues o he calcula ions. The op imized la ice pa ame e s a e in good ag eemen wi h expe imen al alues, inc easing wi h he subs i u ion o a oms wi h low alency. All he calcula ed pa ame e s a e p esen ed in Table IV. Figu e 9shows he calcula ed spin pola ized densi y o s a es (DOS) plo s o majo i y and mino i y spin channels using bo h GGA (blue) and GGA+U( ed) whe e he Fe mi le el is ep esen ed by he ze o ene gy. Ou calcula ions show he sys ema ic shi ing o Fe mi le el om conduc ion band edge in he pa en compound Co2FeSi owa ds he ene gy gap in mino i y spin channel a e subs i u ing low- alence an- si ion me als (see Fig. 15 in he Supplemen al Ma e ial [57] FIG. 9. Spin pola ized o al densi y o s a es (TDOS) o Co1.50Y0.50FeSi (Y=Co, Fe, Mn, C , V, Ti, o Sc) alloys using bo h GGA (blue) and GGA+U( ed) me hods. Numbe o s a es in each plo is scaled wi h espec o 1 .u. 064413-8 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) o he a om- esol ed DOS). In he GGA app oach, only he Co1.50Mn0.50FeSi alloy is obse ed o be a pe ec hal -me al wi h he Fe mi le el wi hin he ene gy gap in he mino i y spin channel. Mo eo e , in he case o he Co1.50C 0.50FeSi alloy, he p esence o he C a om leads o a peak in he majo i y spin ds a es in he icini y o Fe mi le el consis en wi h p e ious obse a ions [18,78,79]. The nonze o con ibu ion o DOS om Fe(I) (which sha es he same subla ice A wi h Y a oms) a Fe mi le el in he mino i y spin channel is obse ed o play a majo ole in des oying he hal -me allici y in all o he alloys. The inclusion o elec on-elec on co ela ion in GGA+Uapp oach shi s he Fe mi le el wi hin he gap o all compounds esul ing in a hal -me allic beha io . We should no e ha he mino i y spin ene gy band gap dec eases as we subs i u e lowe - alence ansi ion me al a oms o Co in Co2FeSi. The ab ini io calcula ed ene gy gaps a e p o ided in Table IV. In Table III we p o ide he expe imen ally de e mined o al spin magne ic momen s in μB o all he samples which we ha e g own, and in Table IV we summa ize he o al spin magne ic momen s calcula ed using bo h he GGA unc ional and he GGA+Uapp oach o he x=0.5 case. The inclu- sion o elec on-elec on co ela ion in he GGA+Uapp oach opens he gap, as expec ed, in he mino i y spin channel, he Fe mi le el shi s wi hin he gap o all compounds esul ing in calcula ed o al spin magne ic momen s sligh ly la ge han GGA ones and in almos pe ec ag eemen wi h he ones p edic ed by he Sla e -Pauling ule. Al hough di e ences be ween bo h GGA and GGA+Ucalcula ed alues and he expe imen al ones a e qui e small, we expec ha GGA+U pe o ms sligh ly be e han GGA since (a) calcula ions a e done a 0 K and expe imen al magne ic momen s we e mea- su ed a 5 K and (b) samples ha e an in insic deg ee o diso de despi e hei e y high c ys allini y. Thus calcula ions should sligh ly o e es ima e he spin magne ic momen s wi h espec o he expe imen ally measu ed ones. IV. CONCLUSION In summa y, qua e na y Heusle alloys Co2−xYxFeSi (Y= Co, Fe, Mn, C , V, Ti, o Sc, 0 ⩽x⩽1) we e syn hesized and a combined expe imen al and heo e ical s udy o s uc u al, elec onic, magne ic, and mechanical p ope ies o qua e na y Heusle alloys Co2−xYxFeSi (Y=Co, Fe, Mn, C , V, Ti, o Sc, x=0.50) we e ca ied ou . The alloys we e iden i ied as po en ial hal -me allic e omagne s by ab ini io elec onic s uc u e calcula ions using he GGA+Uapp oach while only Co1.50Mn0.50FeSi is p edic ed o be po en ial hal -me al in GGA app oach. The s uc u al analysis e eals ha he alloys c ys allize in a cubic Heusle s uc u e. A ce ain amoun o diso de is obse ed in V and Ti subs i u ed alloys. The magne ic p ope ies we e analyzed a bo h 5 and 300 K. The sa u a ion magne ic momen s o he alloys measu ed a 5 K a e in ai ag eemen wi h hose expec ed om Sla e -Pauling ule. The esul s a e also in acco dance wi h he elec onic s uc u e calcula ions, indica ing he hal -me allici y and high spin pola iza ion equi ed o spin onics applica ions. The Cu ie empe a u es o all compounds a e highe han 700 K, allowing use a oom empe a u e and abo e. Robus me- chanical p ope ies wi h ha dness alues inc easing wi h he subs i u ion o Yelemen and wi h i s a omic adius a e also obse ed. This manne o subs i u ion o low- alence ansi ion me al a oms o design new qua e na y Heusle com- pounds gi es eno mous po en ial o many oom empe a u e applica ions such as in spin onics o he moelec ics and o he a eas o esea ch, and clea ly dese e u he explo a ion on hin ilms in he u u e. ACKNOWLEDGMENTS We would like o acknowledge D . Ma k Wea e o help- ul discussions on measu emen s o mechanical p ope ies and o p o iding he ins umen o ha dness measu emen s. This wo k u ilizes he acili ies o e ed by Cen al Analy ical Facili y (CAF) o Uni e si y o Alabama. We a e hus g a e ul o he membe s o CAF o helping us wi h measu emen s. The compu a ional esou ces we e p o ided by he UA High Pe o mance Compu ing Facili y (UAHPC). The inancial suppo o conduc his wo k was sou ced om NSF DMREF G an No. 1235396, and NSF DMR G an No. 1508680. The au ho s a e hank ul o NSF o p o iding he suppo o ca y ou his wo k. [1] T. Hahn, The 230 space g oups, in In e na ional Tables o C ys allog aphy Volume A: Space-G oup Symme y (Sp inge , Be lin, 2006), pp. 112–717. [2] M. J. Mehl, D. Hicks, C. Tohe , O. Le y, R. M. Hanson, G. Ha , and S. Cu a olo, The AFLOW lib a y o c ys al- log aphic p o o ypes: Pa 1, Compu . Ma e . Sci. 136,S1 (2017). [3] R. A. de G oo , F. M. Muelle , P. G. an Engen, and K. H. J. Buschow, New Class o Ma e ials: Hal -Me allic Fe omagne s, Phys. Re . Le . 50, 2024 (1983). [4] I. Galanakis, P. H. Dede ichs, and N. Papanikolaou, Sla e -Pauling beha io and o igin o he hal -me allici y o he ull-Heusle alloys, Phys.Re .B66, 174429 (2002). [5] S. Wu mehl, G. H. Feche , H. C. Kandpal, V. Kseno on o , C. Felse , and H.-J. Lin, In es iga ion o Co2FeSi: The Heusle compound wi h highes Cu ie empe a u e and magne ic mo- men , Appl. Phys. Le . 88, 032503 (2006). [6] P. B own, K.-U. Neumann, P. Webs e , and K. Ziebeck, The magne iza ion dis ibu ions in some Heusle alloys p oposed as hal -me allic e omagne s, J. Phys.: Condens. Ma e 12, 1827 (2000). [7] A. Yamasaki, S. Imada, R. A ai, H. U sunomiya, S. Suga, T. Mu o, Y. Sai oh, T. Kanoma a, and S. Ishida, O bi al angula momen um and in e p e a ion o co e-abso p ion magne ic ci - cula dich oism on he band pic u e in Co-based Heusle alloys Co2YSn(Y=Ti,Z ,and Nb), Phys. Re . B 65, 104410 (2002). [8] T. G a , C. Felse , and S. S. Pa kin, Simple ules o he unde - s anding o Heusle compounds, P og. Solid S a e Chem. 39,1 (2011). [9] C. Felse and A. Hi oha a, Heusle Alloys (Sp inge , Be lin, 2015). 064413-9