Kris T. Delaney1, Maxim Mostovoy2, Nicola A. Spaldin3 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

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)

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

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

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)

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

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

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

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).

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

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

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

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