first-principles study of large magnetoelectric coupling in triangular lattices

(1)kdelaney@mrl.ucsb.edu | MRL, UCSB | APS March Meeting 2008

1. Materials Research Laboratory, University of California, Santa Barbara, USA2. Zernike Institute for Advanced Materials, University of Groningen, The

Netherlands3. Materials Department, University of California, Santa Barbara, USA

kdelaney@mrl.ucsb.edu

First-Principles Study of Large Magnetoelectric Coupling in

Triangular Lattices

Supported by NSF MRSEC Award No. DMR05-20415

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

03.13.2008

(2)kdelaney@mrl.ucsb.edu | MRL, UCSB | APS March Meeting 2008

Magnetoelectrics

Linear Magnetoelectric tensor:

Non-zero a requires T,I symmetry breaking Size limit (in bulk):

iijj

jiji

EM

HP

jjiiij 2

M. Fiebig, J. Phys. D: Appl. Phys. 38, R123 (2005)

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Magnetoelectric Symmetry Requirements

ferroelectricferromagnets

MULTIFERROICS

certain anti-ferromagnets

OR

+ Many materials- Weak - relies on S.O.

+ Large ε, μ potentially large α- Few materials at room T NA Hill, JPCB 104, 6694 (2000)

Our route: superexchange-driven magnetoelectric coupling

Which materials break time-reversal AND space-inversion symmetry?

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θ

Superexchange

S1 S2

21 SSJH ex

Anderson-Kanamori-Goodenough rules:J(θ=90º)<0 (FM)

J(θ=180º)>0 (AFM)

E=0 E E

Mn-O-Mn Superexchange

Superexchange magnetoelectricity:

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Superexchange-driven Magnetoelectricity

Can occurs in geometrically frustrated AFMo Route to bulk materials

Mechanism:

Anderson-Kanamori-Goodenough rules:J(θ=90º)<0 (FM)

J(θ=180º)>0 (AFM)

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Kagomé Lattices

E=0Example Spin Structure

E M=0

“Antimagnetoelectric”

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Triangular Lattices in Real Materials YMnO3 Structure:

BAS B. VAN AKEN et al, Nature Materials 3, 164 (2004)

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Break self compensation: One triangle sense per layer

Breaking Self Compensation: No Vertex Sharing

CaAlMn3O7

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Calculation Details Vienna Ab initio Simulation Package (VASP) [1]

o Density functional theory (DFT)o Plane-wave basis; periodic boundary conditionso Local spin density approximation (LSDA)o Hubbard U for Mn d electrons (U=5.5 eV, J=0.5 eV)

[3]o PAW Potentials [2]o Non-collinear Magnetism

No spin-orbit interaction

Finite electric fieldo Ionic response onlyo Forces = Z*E

Z* from Berry Phase [4]o Invert force matrix to deduce R[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).

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DFT-LDA Electronic Structure; E=0

Ground-state magnetic structure from LSDA+U

Net magnetization = 0 μB

Crystal-field splitting and occupations for high-spin Mn3+

Local moment = 4μB/Mn

3d

dxz dyz

dx2-y2 dxy

dz2

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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

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Conclusions

Superexchange-driven Magnetoelectricity:o Proposed new structureo Triangular lattice:

uniform orientation in each plane No vertex sharing with triangles of opposite sense

o Key: avoid self-compensation in periodic systems

New materials under investigation

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Electric Field Application (Ionic Response)

Force on ion in applied electric field:

where

Force-constant Matrix

Equilibrium under applied field (assume linear):

i

iijj ZF *

j

iij R

PZ

*

j

iij R

FC

i

iijj FCR 1