Double exchange in double perovskites: Ferromagnetism and Antiferromagnetism

Transcription

1 Double exchange in double perovskites: Ferromagnetism and Antiferromagnetism Prabuddha Sanyal University of Hyderabad with H. Das, T. Saha Dasgupta, P. Majumdar, S. Ray, D.D. Sarma H. Das, P. Sanyal, D.D. Sarma, T. Saha Dasgupta, submitted to PRB P. Sanyal, H. Das & T. Saha Dasgupta: PRB, 80, (2009) P. Sanyal and P. Majumdar, Phys. Rev. B,80, (2009).

2 DOUBLE PEROVSKITES: INTRODUCTION General Formula: A2BB/O6. Examples: Sr2FeMoO6, Sr2FeWO6 B atoms (eg. Fe) and B/ atoms (eg. Mo) alternate on corners of the perovskite unit cell, surrounded by Oxygen octahedra, while the A atom (eg. Sr) occurs at the body centres. Different choices for B and B can give rise to different magnetic configurations and electronic properties. Sr2FeMoO6 is a half-metallic ferromagnet (TC~410K), while Sr2FeWO6 is an antiferromagnetic insulator (TN~20K)..

3 Sr2FeMoO6 : Induced moment on Mo due to hybridizing with Fe (DE-type) Sr2FeWO6 : No hopping via W since the levels are pushed out of exchange gap of Fe. => No DE, Superexchange driven antiferromagnet. Sarma et al., PRL 85, 2549 (2000).

4 Effective double exchange type model Hamiltonian Iron: 3d5: Hund s rule: Large (classical) spin S=5/2 : Site-localized. Mo: 4d1: S= -1/2: Mobile electron: gives rise to metallic behaviour. Ferrimagnet: Stotal= 2 t2g hopping t2g S=5/2 Fe 2-sublattice Kondo lattice hamiltonian : Mo Energy scales: tfe-mo, Δ=εMo-εFe, J Can one get AF phases from this model? Note: No superexchange!!!

5 DERIVING AN EFFECTIVE SPIN MODEL (analytical procedure) (2-sublattice Kondo Project out Fe fermion spin Integrate out Mo fermions lattice model) (J infinity limit) Effective model with Spinless Fe fermion only Fe core spins and core spin S The effective spin model obtained resembles the double exchange case in basic structure, but the exchange can be much more complex!! H= << ij >> Dij Dij= [ a k n F a k Δn F Δ ]e ± ±k ± 1 Si Sj 2 ik. r i r j ak = ± where, eg., Δ± Δ2 4ε k 2 2

6 Effective exchange vs. number of active Fermion degrees of freedom assuming ferromagnetic core spin background DNN (blue) and DNNN (red) vs Ntotal for Δ=0 Effective exchange changes sign for intermediate fillings! Instability of the ferromagnetic state at these fillings!

7 Phase diagram: presence of AF phases!! Effective Exchange calculation Fully numerical Exact Diagonaliza tion+monte Carlo calculation

8 THE THREE PHASES IN 2D 0-π 0-0 (Ferro) π-π

9 THE THREE PHASES IN 3D A-type AFM Ferro G-type AFM

10 Tc vs filling in ferromagnetic phase for different Δ DMFT result of Millis et. al. SCR result (1st step)

11 Validation in terms of first principles calculations Takes into account realistic chemical and structural parameters. Sr2-xLaxFeMoO6: Dope Sr2+ by La3+, which is an effective electron doping. Thus increase filling from 1 to 3. Supercell calculations to mimic the doping effect: x=0,1,1.5,2 LMTO (localized Muffin-tin basis set) as well as Projected Augmented Wave (PAW: VASP) calculations, with GGA, and PW91 exchange-correlation.

12 Ab-initio results: LMTO, VASP The energy difference ΔE between FM and AFM-A phases for a two unit supercell (20 atoms). ΔE goes from -ve to +ve as the filling increases.

13 Ab-initio results: (LDA+U) A Hubburd U on the Iron site (GGA+U) stabilizes the AFM phase further. More detailed investigations including Coulomb correlations are currently underway.

14 Structural changes and optimization Experimental reports of structural change from tetragonal I4/mmm to monoclinic P21n symmetry upon La-doping close to 1. [Phys. Rev. B, 64, (2001) Other works reported no changes in structure. [J. Appl. Phys., 104, (2008)]. To settle the issue, we carried out structural optimization using VASP for LFMO, and found the distorted P21n structure to be of lower energy, although the distortion was small. The AFM phases are lower in energy than the FM phase even for this symmetry.

15 FM PHASE As doping increases, the filling increases, Fermi energy moves to right, and hits the singularity for x=2 (LFMO). => FM solution becomes unstable

16 AFM PHASE Note the 3peak structure for the AFM phases near the Fermi energy.

17 Comparison with results from model calculations DOS for the 3 phases (degenerate case: Δ=0). The Mo-peak for the opposite spin channel in the FM phase is at E=0. The 3-peaked structure in the AFM phases arise from Vanhove singularites due to reduced dimensionality.

18 'REAL' DOS for Fe t_{2g} in AFM1 phase by NMTO downfolding!!

19 MODEL-> ABINITIO-> MODEL BY NMTO DOWNFOLDING

20 EFM-EAFM for A-type (dashed) and G-type (solid) phases, from Exact Diagonalization of NMTO downfolded t2g - alone hamiltonian on 8x8x8 system

21 Tc (*) and TN(\) from model Hamiltonian obtained from NMTO downfolding into t2g orbitals, using Exact Diagonalization on 8x8x8 system

22 Variational phase diagram at T=0 using the 3 phases

23 Exp. M-H data (x=1:1.5) -> Ferro to antiferro

24 FC-ZFC plots: signature of frustration, phase coexistence?

25 M-H loops in presence and absence of ferromagnetic impurity

26 Conclusion Electron doping is capable of stabilizing the AFM phase over the FM phase. This is a kinetic energy driven stabilization rather than superexchange. This produces a 'metallic' AFM state rather than an insulating one as observed in Sr2FeWO6. This has been checked using an LDA+U calculation also: U=4eV. As the filling increases, in the half-metallic FM phase the Fermi energy hits the localized spin up Mo level. This makes FM state unstable. AFM phase is kinetic energy stabilized at high filling [Both spin channels can hop, lowering the total energy]..

27 THANK YOU!

28

29 3d-5d series: Sr2CrB/O6: TC increases monotonically from W to Os. Very high Tc~700K in Os compound! However, filling increases from 1(W) to 2(Re) and 3 (Os) Also, Δ increases from W to Os. Hence TC should have decreased!! B/=W,Re,Os

30 New Player: Oxygen!! Both B/ and O levels come down from W->Re->Os, and finally O level becomes almost degenerate with B/ level. Evidence for intrinsic moment in Re and Os *. Hence, Superexchange important. Maximum for Os due to level positions. * A. Winkler et. al., New J. Phys., 11, (2009)

31 Modified Hamiltonian for 3d-5d: Superexchange term Competition between kinetic energy driven antiferromagnetism (J) and superexchange (J2)!

32 Epara-EFM without(l) and with (R) J2 (superexchange) term The TC thus decreases with increasing filling as expected in the 1st case, due to dominance of kinetic energy driven antiferromagnetism. In the 2nd case, superexchange stabilizes a moment on the B/ site, ferromagnetism favoured.

33 Energy levels and effective Wannier functions from NMTO downfolding* La doping does not change the basic level diagram. La doping weakens the hybridiza tion. * Andersen & Saha-Dasgupta, PRB, 62, (2000)

34 FM PHASE As doping increases, the filling increases, Fermi energy moves to right, and hits the singularity for x=2 (LFMO). => FM solution becomes unstable

35 AFM PHASE Note the 3peak structure for the AFM phases near the Fermi energy.

36 B-B/ DISORDER: LATTICE GAS MODEL Non-monotonic dependence of antisite concentration on annealing temperature in Sr2FeMoO6. (Sarma et.al.: PRL (2007) H=V ij>ni n j Monte Carlo simulations: Heating run with memory starting from a random initial configuration: Non-monotonic behaviour of structure factor for small annealing time.

37 Sr2FeMo1-xWxO6: 3 species Blume-Emery Griffiths Model: H= 2 2 ij> [ JSi S +L S S +S +KS 2 S ] 2 S j i j i j j i Good ordering between B site Fe (black) and B/ site Mo/W (white/yellow), but no ordering between Mo and W observed on B/ site.

38 CONCLUSION: FUTURE DIRECTIONS We have obtained an effective model involving only the Fe core spins, and shown that it has a form which resembles in some respect the Anderson Hasegawa model. However, the effective exchange is more complicated, and appears to change sign at some fillings, indicating an instability of the ferromagnetic phase at those fillings. ED+MC, TCA calculations also indicate existence of antiferromagnetic phases. The effect of Mo-Mo hopping is currently being studied; offers an alternate pathway for the Mo spins to delocalize. The fact that there are competing phases even in the clean limit has been noticed earlier by F. Guinea et. al. We now want to solve the electronic problem in the disordered background with antisite defects using both SCR and ED+MC methods. The effect of Tungsten doping on electronic and magnetic properties : competition between ferro-metallic and antiferro-insulating phases.