multiferroics and magnetoelectrics: modelling and...

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

MULTIFERROICS AND

MAGNETOELECTRICS:

MODELLING AND UNDERSTANDING

Sponsored as a Starting Grant 2007 by the European Research Council - Eu FP7 IDEAS

Project “BISMUTH”:

Breaking Inversion-Symmetry in Magnets: Understand via THeory

Dr. Silvia PicozziConsiglio Nazionale delle Ricerche,

CNR-SPIN, UOS L’Aquila67100 L’Aquila, Italy

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

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FERROELECTRICITY: BASICS

“Order-disorder” vs “displacive”

•Ferroelectrics: polar materials, in which a spontaneous electric

polarization can be switched via an external electric field (P: primary

order parameter in the phase transition)

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

PROPER DISPLACIVE FERROELECTRICITY

•BaTiO3:

Up or down

displacement

of B-site cationPup

Pdw

Ba Ti

O

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

PROPER DISPLACIVE FERROELECTRICITY

•BaTiO3:

Up or down

displacement

of B-site cationPup

Pdw

Ba Ti

O

PE

FE

Hybridization:

Ti d (empty) -

O p states

“covalency-

driven”

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PROTON TRANFER: EFFICIENT SOURCE OF P

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MULTIFERROICS: BASICS

What are they?

Why are they useful?

Are they many or few?

Lone-pair MFs

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

MAGNETOELECTRICS MULTIFERROICS

Magnetoelectrics: Control

of P (M) via a magnetic

(electric) field

Magnetization vs

magnetic field in

FMs

M

H

Polarization vs

electric field in

FEs

P

E

Polarization vs

magnetic field in

MEs

P

H

M

E

Magnetization vs

electric field in

MEs

Ferroic: P, M or are spontaneously formed to produce

ferroelectricity, ferromagnetism or

ferroelasticity

Multiferroic: coexistence of at least

two kinds of long-range ordering

(MULTI-) FERROICS:

SYMMETRY PROPERTIES

W. Eerenstein, N. D. Mathur and J. F. Scott, N ature 442, 759 (2006)

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

CRITERIA FOR MAGNETISM AND FERROELECTRICITY

•Uncompensated spins form magnetic moments

• Exchange interaction results from virtual hopping of

electrons between ions

In order to stabilize ferro- or ferri- or antiferro-

magnetism one needs partially filled d-shells!

•Ferroelectricity requires “d0-ness”

•Ferromagnetism (or FiM- or AFM)

requires partially filled d-electrons

WAY OUT:

Put FE-active ion on A-site

Put magnetic ion on B-site

CHEMICAL

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The holy grail: BiFeO3

IMPROPER

FERROELECTRICITY IN MAGNETS

What do we mean by “improper ferroelectricity”?

Concepts:

how to break inversion symmetry

via spin- or charge-ordering

Materials and mechanisms

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

BREAKING INVERSION SYMMETRY IN MAGNETS

FERROELECTRICITY no Inversion Symmetry

Spin-order (some AFM

or “spiral”) Charge-order

•“Proper”

• Ionic displac. break

inversion symmetry (IS)

• “Covalency”-driven

Co

nv

en

tio

na

l

•“Improper”

• Electron degrees of freedom break IS

• “Correlation”-driven

No

n-C

on

ve

ntio

na

l

Orbital-order

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

Left handed

Left handed Right handed

HOW MAGNETIC ORDERING CAN BREAK INV. SYM.?

Spinspiral

TN

Ortho-TbMnO3

T.Kimura et al., Nature 425, 55 (03); S.W.Cheong and M.Mostovoy, Nature Mater. 6, 13 (07)

q

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

DZYALOSHINSKII-MORIYA VS HEISENBERG

p r ij x (S1 x S2)

p = (S1· S2)

Vector coupling: Requires non-collinear spins

Scalar coupling: Works with collinear spins

Superexchange striction

FM

AFM < FM

p

p’

?

Direct exchange striction

d’ > d

d

p

p’

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

DZYALOSHINSKII-MORIYA VS HEISENBERG

p r ij x (S1 x S2)

p = (S1· S2)

Vector coupling: Requires non-collinear spins

Scalar coupling: Works with collinear spins

Superexchange striction

FM

AFM < FM

p

p’

?

Through center of symmetry:

cancellation ==>> P = 0 !

Absence of inversion center:

P finite!

p

p

p’

p

1)

2)

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

E-TYPE

MANGANITES:

ELECTRONIC

AND IONIC

FERROELECTRICITY

•In collaboration with:

K. Yamauchi (CNR-INFM)I. A. Sergienko, E. Dagotto

(Oak Ridge Natl. Lab, Univ. Tennessee, TN)

Mn↑Mn↓O

Op

OapTw

o d

iffe

ren

t O

P

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

ORTHO-HoMnO3 AS A MAGNETICALLY

DRIVEN FERROELECTRIC

E1 E2

•First ab-initio calculation

of P driven by AFM*

• P is ~few C/cm2 (highest among magnetic

improper ferroelectrics)

• FE switching path via

spin-rotations

• Dual nature of P in real compounds:

ionic displacements and

electronic/magnetic

effects are both important

* S. Picozzi, K. Yamauchi, B. Sanyal,

I. Sergienko, E. Dagotto, PRL 99,

227201 (2007)

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

“Pure” charge-ordering

HOW CHARGE ORDERING CAN BREAK INV. SYM.?

Neutral chain

+ - + +- -

Inversion center: no P

Inversion center: no P

Site

centered

CO

Bond

centered

CO

Structural dimerization

Inversion center: no P

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

Structural dimerization“Pure” charge-ordering

+ - + +- -

+ + +- - -

Combination

Intermediate

Bond- and site-

centered

CO

Absence of

inversion

center:

it can be polar !!

Neutral chain Inversion center: no P

HOW CHARGE ORDERING CAN BREAK INV. SYM.?

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

CLASSIFICATION OF

IMPROPER MULTIFERROICS

Improper

Multiferroics

Spin-ordering

driven

“DM”-driven

(spin-orbit related)

“Heisenberg”-driven

(mostly collinear)

Charge-ordering

driven

TbMnO3

RMn2O5

(R=Tb,Dy,Ho)

LiCu2O2, LiCuVO4

LuFe2O4

Fe3O4

La0.5Ca0.5MnO3

RNiO3 (R = Pr, …, Lu)

RMnO3

(R=Ho,..,Lu)

Ca3CoMnO6

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

Crystalline hybrid materials like

Metal Organic Frameworks (MOFs)

attractive materials for gas storage,

drug delivery, catalysis, ….

Pls attend talk

by Dr. Alessan-

dro Stroppa

MAGNETOELECTRICITY

in Ba2CoGe2O7

New mechanism:

spin-dependent p-d hybridization

What can DFT say?

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

MICROSCOPIC ORIGIN OF ME EFFECT

p r ij x (S1 x S2)

i) Inverse

Dzyaloshinskii-Moriya

Vectorial coupling:

e.g. spin spiral in TbMnO3

pi J12 (S1· S2)ii) Heisenberg-type exchange

striction

Scalar coupling:

e.g. AFM-E HoMnO3

i) and ii) Inter-site

spin interaction

iii) Spin-dependent p-d hybridizatione.g. CuFeO2

T. Arima, JPSJ 76, 073702 (2007).

e

p (S · e)2eSingle-site

spin-orbit coupling

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

MAGNETOELECTRICITY IN Ba2CoGe2O7

H. Murakawa, Y. Onose, S. Miyahara, N. Furukawa

and Y. Tokura, PRL105, 137202(2010).

Antiferromagnetism, TN=6.7K

= 24°

sin(2)

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

H-dependence of P

MAGNETOELECTRICITY IN Ba2CoGe2O7

H. Murakawa, Y. Onose, S. Miyahara, N. Furukawa

and Y. Tokura, PRL105, 137202(2010).

= 24°

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

CALCULATED ME EFFECT IN

Ba2CoGe2O7

Co1

(0, 0, 0)

Co(1/2, 1/2, 0)

a

b

Ba

Ge

O

P

Energy (meV/Co) (μB) (μC/m2)

MAE S 100 S 110

Co2+: eg2 t2g

3 eg2 t2g

0 small MAE

Spins in ab plane: OK with expts

Induced P by keeping AFM config and rotating spins

(under SOC)

Pc µsin2f

Pc sin (2) :

OK with expts

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

CALCULATED ME EFFECT IN

Ba2CoGe2O7

Co1

(0, 0, 0)

Co(1/2, 1/2, 0)

a

b

Ba

Ge

O

Expts:

Pcmax =

120μC/m2

cant AFM spinsM//110

H110

'

P

Induced P by canting spins w.r.t [1-10] AFM config

0 30 60 90

Spin-canting angle f’ (°)

-20

-10

0

10

20

Pc

(mC

/m2)

0 5 10 15H(T)

-20

-10

0

10

20

Pc (

mC

/m2)

F110

A1-10

H110

NB: Assume = M/H110

= 0.25 B/Co (expt)

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

(LOCAL) MICROSCOPIC ORIGIN OF P: SOC

non-bonding occupied state

yz-zx /√2

P

asymmetric-bonding non-occupied states

xy

z

x2-y2

x2-y2: -0.05

3z2-r2: -0.4

yz, zx: +0.9

xy: +1.2

EF

E (eV)

1

2

3

yz+zx /√2

P

0

SOC mixing

DFT-obtained Co d-orbital occupation

(% for spin sum) under enhanced SOC

θ spin polar angle, Φ spin azimuth angle

Most occupied orbital to the spin

Maximum P when Co spin parallel to upper or lower Oxygen bonds

Silvia Picozzi Congresso SIF - L’AQUILA Sept 29th 2011

Diana IusanPaolo Barone

Alessandro Stroppa Johan Hellsvik

THANKS TO THE “BISMUTH” GROUP !!

FORMER MEMBERS(but still actively

collaborating)

Kunihiko Yamauchi

Tetsuya

Fukushima

THANKS FOR YOUR ATTENTION!