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First-Principles Study of Large Magnetoelectric Coupling in Triangular Lattices

First-Principles Study of Large Magnetoelectric Coupling in Triangular Lattices. Kris T. Delaney 1 , Maxim Mostovoy 2 , Nicola A. Spaldin 3. Materials Research Laboratory, University of California, Santa Barbara, USA

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First-Principles Study of Large Magnetoelectric Coupling in Triangular Lattices

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  1. First-Principles Study of Large Magnetoelectric Coupling in Triangular Lattices Kris T. Delaney1, Maxim Mostovoy2, Nicola A. Spaldin3 • Materials Research Laboratory, University of California, Santa Barbara, USA • Zernike Institute for Advanced Materials, University of Groningen, The Netherlands • Materials Department, University of California, Santa Barbara, USA • kdelaney@mrl.ucsb.edu 03.13.2008 Supported by NSF MRSEC Award No. DMR05-20415

  2. Magnetoelectrics • Linear Magnetoelectric tensor: • Non-zero a requires T,I symmetry breaking • Size limit (in bulk): M. Fiebig, J. Phys. D: Appl. Phys. 38, R123 (2005)

  3. Magnetoelectric Symmetry Requirements Which materials break time-reversal AND space-inversion symmetry? ferroelectric ferromagnets MULTIFERROICS certain anti-ferromagnets OR + Large ε, μ potentially large α - Few materials at room T NA Hill, JPCB 104, 6694 (2000) + Many materials - Weak - relies on S.O. Our route: superexchange-driven magnetoelectric coupling

  4. E=0 E E Superexchange • Mn-O-Mn Superexchange • Superexchange magnetoelectricity: θ Anderson-Kanamori-Goodenough rules: J(θ=90º)<0 (FM) J(θ=180º)>0 (AFM) S1 S2

  5. Superexchange-driven Magnetoelectricity • Can occurs in geometrically frustrated AFM • Route to bulk materials • Mechanism: Anderson-Kanamori-Goodenough rules: J(θ=90º)<0 (FM) J(θ=180º)>0 (AFM)

  6. E M=0 “Antimagnetoelectric” Kagomé Lattices E=0 Example Spin Structure

  7. Triangular Lattices in Real Materials • YMnO3 Structure: BAS B. VAN AKEN et al, Nature Materials 3, 164 (2004)

  8. Breaking Self Compensation: No Vertex Sharing • Break self compensation: One triangle sense per layer CaAlMn3O7

  9. Calculation Details • Vienna Ab initio Simulation Package (VASP) [1] • Density functional theory (DFT) • Plane-wave basis; periodic boundary conditions • Local spin density approximation (LSDA) • Hubbard U for Mn d electrons (U=5.5 eV, J=0.5 eV) [3] • PAW Potentials [2] • Non-collinear Magnetism • No spin-orbit interaction • Finite electric field • Ionic response only • Forces = Z*E • Z* from Berry Phase [4] • Invert force matrix to deduce DR [1] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996). [2] G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). [3] Z. Yang et al, Phys. Rev. B 60, 15674 (1999). [4] R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993).

  10. DFT-LDA Electronic Structure; E=0 Crystal-field splitting and occupations for high-spin Mn3+ • Ground-state magnetic structure from LSDA+U dz2 3d dx2-y2 dxy dxz dyz Local moment = 4μB/Mn Net magnetization = 0 μB

  11. E m Magnetoelectric Coupling • Magnetoelectric Response: • Compare: Cr2O3 • small effect: • E field of 106 V/cm produces M equivalent to reversing 5 out of 106 spins in the AFM lattice

  12. Conclusions • Superexchange-driven Magnetoelectricity: • Proposed new structure • Triangular lattice: • uniform orientation in each plane • No vertex sharing with triangles of opposite sense • Key: avoid self-compensation in periodic systems • New materials under investigation

  13. Electric Field Application (Ionic Response) • Force on ion in applied electric field: where • Force-constant Matrix • Equilibrium under applied field (assume linear):

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