MULTIFERROICS AND MAGNETOELECTRICS: MODELLING AND ...static.sif.it/SIF/resources/public/files/congr11/mc/picozzi.pdf · MULTIFERROICS AND MAGNETOELECTRICS: MODELLING AND UNDERSTANDING

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


QuickTime™ and aTIFF (Uncompressed) decompressor

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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)


PROPER DISPLACIVE FERROELECTRICITY

•BaTiO3:

Up or down

displacement

of B-site cationPup

Pdw

Ba Ti

O


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”



PROTON TRANFER: EFFICIENT SOURCE OF P













MULTIFERROICS: BASICS

What are they?

Why are they useful?

Are they many or few?

Lone-pair MFs


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)


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

INCOMPATIBILITY!QuickTime™ and a

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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


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


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


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’


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)


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


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)


“Pure” charge-ordering

HOW CHARGE ORDERING CAN BREAK INV. SYM.?

Neutral chain

+ - + +- -

Inversion center: no P


Site

centered

CO

Bond

centered

CO

Structural dimerization



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.?


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


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?


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


MAGNETOELECTRICITY IN Ba2CoGe2O7

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

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

Antiferromagnetism, TN=6.7K

= 24°

sin(2)


H-dependence of P

MAGNETOELECTRICITY IN Ba2CoGe2O7

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

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

= 24°


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


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)


(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


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!

Documents

MULTIFERROICS AND MAGNETOELECTRICS: MODELLING AND ...static.sif.it/SIF/resources/public/files/congr11/mc/picozzi.pdf · MULTIFERROICS AND MAGNETOELECTRICS: MODELLING AND UNDERSTANDING