1. 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
Supported by NSF MRSEC Award No. DMR

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. 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

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. “Antimagnetoelectric”
Kagomé Lattices E
M=0
“Antimagnetoelectric”
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, (1996).
[2] G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
[3] Z. Yang et al, Phys. Rev. B 60, (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. 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

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):