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First Principles Study of Electronic Structure and Magnetism in Novel Spin Chain Oxides Indra Dasgupta Department of Phy

First Principles Study of Electronic Structure and Magnetism in Novel Spin Chain Oxides Indra Dasgupta Department of Physics, IIT Bombay E-mail: dasgupta@phy.iitb.ac.in. Collaboration: B. R. K. Nanda, University of Missouri, Columbia Acknowledgement:

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First Principles Study of Electronic Structure and Magnetism in Novel Spin Chain Oxides Indra Dasgupta Department of Phy

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  1. First Principles Study of Electronic Structure and Magnetism in Novel Spin Chain Oxides Indra Dasgupta Department of Physics, IIT Bombay E-mail: dasgupta@phy.iitb.ac.in Collaboration: B. R. K. Nanda, University of Missouri, Columbia Acknowledgement: S. Satpathy, University of Missouri, Columbia

  2. Crystal Structure of Ca3ABO6 B A O Octahedra Trigonal-Prism Hexagonal arrangement of Chains • Different geometric environment of metallic ions  various spin and charge configuration • Metal-Metal, d(inter-chain) > d(intra-chain)  quasi one-dimensionality • Triangular lattice  topological magnetic frustration

  3. Magnetic Properties of Ca3Co2O6 • TC1=24K  Intra-chain ferromagnetic order is reached. • TC2(12K)<T< TC1)  Antiferromagnetic inter-chain interaction (Partially Disorde- red Antiferromagnetic State(PDA)) • T< TC2 Ferrimagnetic order, Spin Freezing ……………. • Neutron: Local magnetic moment at Cooct = 0.08B Cotrig= 3.00B A. Maignan et.al. Eur. Phys. J. B. 15 657 (2000) Magnetization: Magnetic moment 4.00B PDA Ferri

  4. Novel Magnetic properties of some other members of the family Ca3ABO6 Ca3Co2O6 and Ca3CoRhO6Two magnetic transition temperatures TC1 and TC2 with partially disordered antiferromagnetic state in the intermediate temperature range. Ca3CoIrO6Only one magnetic transition at 30K of a spin-glass like frustrated type. Ca3FeRhO6 Antiferromagnetic intra chain coupling Ca3Co1+xMn1-xO6(x=0.0,0.25)Long range magnetic ordering of antiferro type. (No spin-glass freezing inspite of Co-Mn disorder). Ca3ZnCoO6Ferromagnetic below 25K. Ca3ZnMnO6Antiferromagnetic with TN = 25.5K A systematic understanding of magnetic properties is lacking.

  5. Some Issues to be addressed by First Principles Calculations Spin and Charge state of these systems Nature of Magnetism Exchange Paths and Origin of Magnetism Role of electron-electron correlation

  6. First Principles Calculations: Foundations • Kohn-ShamDensity functional theory • Reduction to an effective non-interacting system. • Self-consistent solution to an one electron Schrödinger equation. Basis Set: Linear methods  LMTO (Andersen, 1975) →Total Energy, Magnetic Moment …. Third Gen LMTO/NMTO + Downfolding : Extraction of hopping parameters, Exchange paths, Wannier functions…. Electron Correlations: LDA+U, Exact diagonalization studies

  7. eg (x2-y2, 3z2-1) yz,xz Octahedra 3z2-1 B-d A-d t2g (xy,yz,xz) xy,x2-y2 Trigonal prism Structure and Crystal Field Splitting

  8. yz,xz 3z2-1 xy,x2-y2 t2g (xy,yz,xz) Paramagnetic DOS of Ca3Co2O6 (Charge States) eg (x2-y2, 3z2-1) Cotrig3+(d6) Cooct3+(d6)

  9. Paramagnetic DOS of Ca3FeRhO6 (Charge States) Rh d6  Rh 3+ Fe d5  Fe 3+

  10. Paramagnetic DOS of Ca3ZnMnO6 & Ca3ZnCoO6 (Charge States) Zn 2+  Co 4+ (d5) & Mn 4+ (d3)

  11. Spin-polarized calculations and spin states

  12. yz,xz Co1(oct)-d 3z2-1 Co2(trig)-d t2g xy,x2-y2 Ferromagnetic DOS of Ca3Co2O6 (Spin-States) • Co1 low spin and Co2 high spin consistent with neutron data. • Mag. Mom. at Co1(0.27µB), Co2(2.76µB), O(0.15µB) and total(4.0 µB) consistent with magnetization data.

  13. Antiferromagnetic Ca3FeRhO6 Fe3+ Rh3+ Antiferromagnetism is mediated by super-exchange

  14. eg-down d-down eg-up t2g-down d- up t2g-up yz,xz 3z2-1 d-up,down xy,x2-y2 Ferromagnetic DOS for Ca3ZnCoO6 Co-d5 Zn-d10

  15. eg-down yz,xz d-down eg-up 3z2-1 t2g-down d-up,down d-up t2g-up xy,x2-y2 Ca3ZnMnO6 Zn-2+ Mn-4+ Mn1-d3 Zn-d10 Mn2-d3 eg-up d-up eg-down t2g-up d-down t2g-down Half filled t2g states  Antiferromagnetism is mediated by superexchange

  16. Magnetic Structure of Ca3ABO6 AFM-II (e.g. Ca3ZnMnO6) AFM-I Ferromagnetic Ferrimagnetic

  17. Origin of magnetism

  18. Role of oxygens in magnetism Hybridization of TM’s with oxygen  large spin polarization of oxygens Formation of extended localized magnetic moments centered at the trigonal prismatic HS states Extended moments couple along the chain via the non-magnetic octahedral TM atoms.

  19. Co-oct 3z2 Co-trig 3z2 hoppings Interaction is AFM Cotrig 3z2 Cooct 3z2 Cotrig 3z2 Oxygens have more imp. role to play

  20. Ferromagnetic Interaction along chains: DFT downfolded bands and a generic model  Case study Ca3Co2O6 NN Orbital Hopping integrals in eV t3 t2 t4 t3 t3 t3 t1 t4 Oxygen is responsible for coupling between states. Interaction among the chains is negligible. Exchange Paths

  21. The Origin of Ferromagnetic Interaction: A Model Hamiltonian Cotrig Cooct Cotrig H = HKE + Hcorr + HHund Parameters: U=5-6eV, JH=0.6-1eV

  22. Exchange Interaction in Ca3Co2O6 Exact diagonalization study for 3-site model Hund Exchange is crucial to stabilize ferromagnetism

  23. Magnetism in Ca3ZnCoO6 and Ca3ZnMnO6 Both intra-chain and inter-chain hoppings are important. TM-TM interaction stabilize magnetism without role of the oxygens. Magnetism can be understood involing Goodenough-Kanamori rules. Small band-width suggests that Coulomb correlation is important.

  24. Role of electron-electron correlation

  25. eg yz,xz d-1 d1 d-2 3z2-1 t2g d0 2SOC xy,x2-y2 d2 Co1(oct)-d Co2(trig)-d Metal Insulator Transition LDA+U electronic structure of Ca3Co2O6 cond-mat 0504490 Either SO or JT required for Insulating properties

  26. LDA+U electronic structure of Ca3ZnCoO6 Ferromagnetic Insulator

  27. Conclusion: • LSDA electronic structure calculation leads to a half-metallic ferromagnetic state for Ca3Co2O6 and Ca3ZnCoO6, and anti- ferromagnetic insulating state for Ca3FeRhO6 • Hund-exchange is crucial for stabilizing Ca3Co2O6 in ferro- magnetic state with oxygens playing important role • In addition to U, spin-orbit coupling is required to obtain an insulating state for Ca3Co2O6 . • Inclusion of local Coulomb interaction parameter U makes Ca3ZnCoO6 insulating. • Ca3ZnMnO6 supports antiferromagnetism.

  28. The Origin of Ferromagnetic Interaction: A Model Hamiltonian • Cotrig-3z2-1 and Cooct-t2g states are only retained. Fresard et. al cond-mat 0309031 Co2 Co2 Co1 H = HKE + Hcorr + HHund Parameters: U=5-6eV, JH=0.6-1eV

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