Theory of Ferromagnetism in Double Perosvkites. Luis Brey CSIC-Madrid F. Guinea CSIC-Madrid S.Das Sarma Univ.Maryland
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1 Theory of Ferromagnetsm n Double Perosvktes. Lus Brey CSIC-Madrd F. Gunea CSIC-Madrd S.Das Sarma Unv.Maryland 1
2 OUTLINE Introduton to Fe based double perovsktes. Chemstry Band struture Ferromagnetsm ndued by arrers. Paramagnet Phase of Doubles Perovsktes. Mean Feld Theory. Hesenberg lke Hamltonan. Effet of the Eletron-Eletron nteraton. Summary
3 Sr FeMoO 6 Two nterpenetratng FCC sublattes (Fe and Mo) Sr 5s (4) Fe 3d 6 4s 3d 5 3 Mo 4d 5 5s 1 4d 1 5 O s p 4 s p 6 - (1-) Magnet atve orbtals, Fe (5/) Dstane Fe-Fe s larger than 5.5Å no dret nteraton. Eletrons lve n Mo (1 eletron per Fe) Ideal double perovskte struture. Sr Sr 1-x La x 1x eletrons per Fe (trvalent) Sr Sr 1-x K x 1-x eletrons per Fe (monovalent) Mo Re eletrons per Fe (Re: 5d 5 6s ).5<x<1.5
4 Interest of Fe-based Double Perovsktes. Hgh Ferromagnet T (more than 45K) Half metall ferromagnet. Eletral urrent s 1% spn polarzed. The T an be rased by eletron dopng. No lear the orgn of the ferromagnetsm. Attratve both n terms of bas nvestgatons and tehnologal applatons. 4
5 Some names (not all). Theory: Experments: T dereases wth eletron dopng!! D.D.Sarma et al. Band struture. Y.Tokura et al. Mar Garía et al. Y.Tokura et al. Band struture. D.D.Sarma et al. Fontuberta et al. I.V.Solovyev. Band struture. Ogale et al. Ibarra et al. F. Gunea et al. Monte Carlo. A.Mlls et al. DMFT (CPA) T s lower than observed. Make a mean feld theory and ompute T. Compare wth DMFT and MC. Try to mprove the model. (what other ngredents are needed.) Are the expermental fndngs ntrns or extrns propertes? 5
6 Ferromagnet Band struture t g orbtals t g Mo t g Fe-Mo x z - - y x z z y x - y e g Fe t g Fe E F d xy d xz d yz The symmetry of the t g orbtals mples that a gven orbtal an mx only orbtals of the same symmetry and only wth orbtals n the orrespondng plane. d αβ n the plane αβ The band struture s the sum of three two dmensonal tght bndng systems. =, ferromagnet DOS. t Mo-Fe, t Mo-Mo,, 6
7 Ferromagnet GS sheme. t Fe-Mo Energy t Mo-Mo - -- Mo - Fe - Mo - Fe - Mo - Fe -Mo - Fe The moton of the eletrons s through Fe ( ) and for mnmzng KE the arrers beome polarzed. The effetve AF ouplng between the arrers and the ore Fe ( ) produes ferromagnet order. 7
8 FERROMAGNETIC ORDER INDUCED BY THE CARRIERS Double Exhange (LaCaMnO 3 ) t osθ / T C ~ t<c C 1 > Inreases wth arrers dopng. de Gennes 6 8
9 FERROMAGNETIC ORDER INDUCED BY THE CARRIERS Double Exhange (LaCaMnO 3 ) T C ~ t<c C 1 > Dluted Magnet Semondutors (GaMnAs) t T C ~ N(E F ) Perturbaton theory Inreases wth eletron dopng Vonsovky ( 46) Zener ( 51) 9
10 FERROMAGNETIC ORDER INDUCED BY THE CARRIERS Double Exhange (LaCaMnO 3 ) T C ~ t<c C 1 > Dluted Magnet Semondutors (GaMnAs) T C ~ N(E F ) x Double Perovsktes SrFeMoO 6 t No dluted. very large Paramagnet atom T C ~? 1
11 STRATEGY: Mean Feld Approxmaton F[m]= E KE [m] F ons [m] m, magnetzaton order paramater m m F = Carrers at T=, E F >>kt 3 E KE TC = ( m ) We need to know the paramagnet phase (Ab nto band struture alulaton are done for ordered ferromagnet phase) 11
12 PARAMAGNETIC PHASE os(θ /) t os(θ k /) t os(θ /) Spn hannel. t sn(θ /) -t sn(θ k /) -t sn(θ /) Spn hannel. k 1
13 PARAMAGNETIC PHASE, VCA /3 t <os(θ /)>=<sn(θ /)>= /3 -/3 t Unt ell Fe Mo 13
14 PARAMAGNETIC PHASE, VCA /3 t os(θ /)>=<sn(θ /)>= /3 -/3 t Unt ell Fe Mo 14
15 PARAMAGNETIC PHASE (3) /3 t t os(θ /) -t sn(θ /) 15
16 PARAMAGNETIC PHASE /3 t t os(θ /) /3 t -t sn(θ /) 16
17 PARAMAGNETIC PHASE We refer the spns of the Mo, to the Fe spn n the same unt ell. t os(θ /) t Channel -t sn(θ /) Channel ant- Vrtual Crystal Approx. t t < os(θ /)> -t <sn(θ /)> Fe Mo 17
18 VCA HAMILTONIAN H = ( t t t ) Mo Mo <, > Fe Mo Fe Mo d d θ < os > (, p θ d, p < os > θ d < sn > y -x -y x, p θ ) < sn ( ) ( ) x, ap x, p, ap, ap x y, p x y, ap y, p y, ap > (, ap, p, p 18, ap ),p(ap) destroys an eletron n Mo at ste, wth spn parallel (antparallel) to the spn of the Fe spn. d destroys an eletron n Fe at ste., wth th spn parallel to the ore spns.
19 PARAMAGNETIC PHASE m= Densty of states - =.3eV tmo-mo=.15ev tmo-fe=.3ev Mo Re x=1 x= Energy (ev) <os θ />=<sn θ />= /3 DOS at the Ferm Energy nreases wth dopng and s rather smooth between x= and x=. T smooth between these denstes?. 19
20 Cure Temperature. m=<osθ > <os θ / > /3/5 m <sn θ / > /3-/5 m Usng the expetaton values of < d> obtaned n the paramagnet phase, we obtan E KE (m ) and T C = 3 E ( m KE ) Perturbaton Theory
21 Cure Temperature as funton of x 5 Cure Temperature Mo - =.3eV tmo-mo=.15ev tmo-fe=.3ev Re Low T C x (eletron onentraton) Maxmum x ~1. T C = for x ~. Agreement wth MC and DMFT Dsagreement wth experments! 1
22 Expermental varaton of Cure Temperature wth eletron densty 1 Navarro et al. PRB 64, 9411 (1)
23 Cure Temperature as funton of x t Fe-Mo =.5 (ev) - =.3eV. tμο Μο=.15 (ev) - =.3eV t Μο Μο eletron densty Low T C. t Fe-Mo (ev) Eletron densty Maxmum x ~1. Inreases wth t Fe-Mo T C = for x ~. Independent of t Fe-Mo and t Mo-Mo 3
24 Cure Temperature as funton of x tfe-mo=.5 ev tmo-mo=.15ev (- ) (ev) Low T C. Maxmum x ~1. T an be ftted T C = for x ~. Always. Agreement wth MC and DMFT Dsagreement wth experments! eletron densty 4
25 5 Why ths behavor? Let us rewrte the nternal energy of the system n other way. ( ) ( ) > < > < > < > < = > < ap y ap y x ap x Mo Fe p y p y x p x p Mo Fe ap p p ap ap ap p p Mo Mo d t d t t d d H,,,,,,,,,,,,,,,, sn os ) ( sn ) ( os ) ( θ θ θ θ We wrte the energy as a funton of the orentaton of the Fe spns, {S }. E(osθ /, snθ /). We use the expetaton values of the paramagnet phase.
26 Hesenberg-lke desrpton of Double Perovsktes.(1) E = <, > Fe Mo C θ, os Fe Mo S θ, sn Mo Mo C θ, os Mo Mo S θ, sn KE due to the moton of the arrers wth spn loally parallel to the Fe ons. KE due to the moton of the arrers wth spn loally ant-parallel to the Fe ons 6
27 Hesenberg-lke desrpton of Double Perovsktes(). E = <, > Fe Mo C θ, os Fe Mo S θ, sn Mo Mo C θ, os Mo Mo S θ, sn Couplngs (K) =.3eV tmo-mo=.15ev tmo-fe=.3ev Fe Mo C Fe Mo S Mo Mo C Mo Mo S Eletron Densty 7
28 Hesenberg-lke desrpton of Double Perovsktes(3). E = E Hes. <, > Fe Mo C 1 = θ, os Fe Mo S θ, sn Mo Mo C θ, os Mo Mo S θ, sn ( Fe Mo Fe Mo Mo Mo Mo Mo ) C S C S osθ, <, > m t Mo-Fe t Mo-Mo T C 1 = ( Fe Mo Fe Mo Mo Mo Mo Mo ) C S C S Ferromagnet ouplng Ant-Ferromagnet ouplng 8
29 For x>1., T C dereases wth dopng beause the loose of KE n the antparallel hannel s bgger than the gan of KE n the parallel hannel Couplngs (K) =.3eV tmo-mo=.15ev tmo-fe=.3ev Eletron Densty Fe Mo C Fe Mo S Mo Mo C Mo Mo S Hesemberg Couplng(K) Phase separaton? Eletron Densty What ngredent n the problem wll prvlege a hannel aganst the other? 9
30 What ngredent n the problem wll prvlege a hannel aganst the other? Coulomb Interaton. Intraband Hubbard term, U, penalzes the oupaton of two spn orentatons at the same ste. U n n Interband Coulomb nteratons, U, are weaker than ntreband. (Kanamor, Castellan, Tang ) No orbtal orderng. 3
31 EFFECT OF THE ON-SITE COULOMB REPULSION ON T C 35 Cure Temperature (K) =.3eV tmo-mo=.15ev tmo-fe=.3ev U/t Fe-Mo U, both n Fe and Mo. Mean feld approx. U<<W 8 t Fe-Mo Densty of Eletrons 31
32 EFFECT OF THE ON-SITE COULOMB REPULSION ON T C U, both n Fe and Mo =.3eV tmo-mo=.15ev tmo-fe=.3ev U<<W 8 t Fe-Mo. 3 T nreases at x=1 T fnte at x=. U / t Fe-Mo Eletron Densty 3
33 SUMMARY We have presented a Mean Feld Theory for ferromagnetsm n Fe-based Double Perovsktes. Agreement wth MC and DMFT. Low T at x=1 No Ferromagnetsm at x= Dsagreement wth Experments. T nreases wth dopng. Inluson of eletron-eletron nteraton (moderate values of U) nreases T and makes the x= ase ferromagnet. 33
34 Densty of States T= Ferromagnet Phase Densty of States t Mo-Mo =.15eV t Mo-Fe =.5eV t Fe-Fe =.3eV =1.1eV =1.4eV Phllps et al. x=1 (Mo) x= Fe Mo Mo Fe Energy (ev) Densty of States t Mo-Mo =.35/4eV t Mo-Fe =.35eV t Fe-Fe =. =4eV =4eV x=1 (Mo) x= Fe Mo Fe Mo Energy (ev) 34
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