Functional transition metal oxides: effects,

J. J. – – M. Liu (刘俊明 M. Liu ( 刘俊明 ) ) Nanjing University Nanjing University Email:

Email: liujm@nju.edu.cn liujm@nju.edu.cn Group page

Group page http: http: //pld.nju.edu.cn/ //pld.nju.edu.cn/

Functional transition metal oxides: effects,

challenges, and opportunities

非线性光学 光记录

巨磁电 铁电、铁磁 巨磁电阻

磁记录等

高温超导电性 强电、弱电

巨介电 存贮、压电

巨功能

氧化物材料

量子新效应 新材料

X. G. Li, private commun.

N. A. Spaldin et al., Science 309 (2005) 391

Transports

Structure

Content

1. What we learn from chemists 2. CMR manganites

3. 4d/5d multifunctional oxides 4. Multiferroic oxides

5. Spin liquids and spin ices

6. Perspectives and challenges

What we learn from chemists

From Wikipeda & GC, Kentucky

Transition metal oxides embedded in the periodical chart of elements

3d, 4d, & 5d transition metals

What we learn from chemists

自旋 电荷

晶格

轨道

• Structure determines the interactions

• The interactions determine the orders

• Quantum theory on charges, spins, orbitals, and phonons

• Goodenough-Kanamori rules

• Tolerance factor

What we learn from chemists: Goodenough-Kanamori rules

 Semi-empirical rules applied to predict magnetic and electronic interactions in transition metal oxides.

 Extended rules to more complex transition metal oxides.

M-O-M bond angle~180^o M-O-M bond angle <180^o

What we learn from chemists: Tolerance factor

 A structural factor to measure the mismatch between AO layer and BO

layer in ABO

-type oxides.

 It has been extended to other transition metal oxides.

) 2

/(

) (

2 )

( r

r

r

r

d

d

f    

• f=1.0  ideal cubic

• f=0.96~1.0  rhombohedral & tetragonal

• f=0.75~0.96  orthorhombic

• f >1.0  hexagonal

What we learn from chemists: strong correlation

Kotliar, Phys. Today 2004 & GC, private comm.

What we learn from chemists: multifold landscape in energy

FM CO

AFM OO

OD

CD IN

ME SM

SG FIM

SL QP

What we learn from chemists: delicate balance

What we learn from chemists: effects & properties

 Always exhibit physical complexity and tunability

 Hard materials act like soft matter

 On the edge of multi-fold competitions

 Tend to show giant responses and dynamics in response to small perturbations

Four classes of typical and emergent materials

CMR manganites

R

A

MnO

CMR manganites: structure, charges, & orders

Y. Tokura, RPP69, 797 (2006)

CMR manganites: transport behaviors

Y. Tokura et al, JPSJ 63, 3931 (1994) A. Asamitsu et al. Nature 388, 50(1997)

CMR manganites: phase diagram

Cheong et al., 1999

S. Moreo et al, Science 283, 2034 (1999)

Synthesis issues

CMR manganites: electronic phase separation

M. Fäth et al., Science 285(1999) 1540

J. C. Loudon et al. Nature 420 (2002) 797

Quantum metal-insulator transitions (MIT) and electronic phase

separation

J. Burgy et al, PRL 87, 277202 (2001)

CMR manganites: focused issues

1. Low MR response to low magnetic field

2. Low temperature for applications

3. Synthesis of electron-type manganites

Tomioka and Tokura (1999)

CMR manganites: effects of disorder

S. Murakami et al, PRL 90, 197201 (2003)

Ground state competition at bi-critical points

Y. Tokura, Rep. Prog. Phys. 69, 797 (2006)

CMR manganites: effects of disorder

Ca La

Mn O

La Mn

Ca

Ca La

R_1-xA_xMnO₃

CMR manganites: effects of disorder

La_0.55Ca_0.45MnO₃: <r_A>=0.120nm Pr_0.55Ca_0.45MnO₃: <r_A>=0.118nm

Disorder  EPS but lower T and lower MR

Disorder  EPS but higher T and larger MR

CMR manganites: electroresistance

Electroresistance in manganites

A. Asamitsu et al. Nature 388, 50 (1997) J. Stankiewicz et al. PRB 61, 11236 (2000)

CMR manganites: electroresistance

La_5/8-yPr_yCa_3/8MnO₃ (y~0.4)

G. Garbarino et al. PRB 74, 100401(R) (2006)

Dielectrophoresis mechanism

electrophoresis dielectrophoresis

CMR manganites: electroresistance

Dielectrophoresis scenario consistent with experiments

S. Dong et al. PRB 76, 32409 (2007)

CMR manganites: spintronics & RRAM

• High spin-polarized ratio

• Low T and high H

CMR manganites: spintronics & RRAM

Application of dielectrophoress to resistance RAMS

Z. Yan et al. APL 95, 143502 (2009)

Z. Yan et al. APL 96, 012103 (2010)

CMR manganites: spintronics & RRAM

4d/5d multifunctional oxides (Ba,Sr,Ca)

T

O

, n=1, 2, 3, 

T=Ru, Ir, Rh etc

4d/5d oxides: extended charge density

From Wikipeda

GC, private commun

4d/5d oxides: Ruddlesden-Popper series

Ruddlesden-Popper oxide series:

(Ba,Sr,Ca)

T

O

n=1, 2, 3, 

T=Ru, Ir, Rh etc

Tough to synthesize

4d/5d oxides: T=Ru as an example from GC, MPLB (2008)

• Simplified phase diagram for (Ca,Sr)_n+1Ru_nO_3n+1

• Rich phases competing to each other, depening on n

G. Cao et al. MPLB22, 19 (2008)

4d/5d oxides: T=Ru as an example

Very different behaviors between Sr- & Ca-based systems

4d/5d oxides: phenomena & possible physics in n=2

 Crystal fields

 Hund’s rule interactions

 p-d electron hybridization

 Electron-lattice coupling

 Spin-orbital coupling (~0.4 eV (5d), 0.1 eV (4d), 0.02 eV (3d))

A set of balances between different degrees of freedom

A wide range of novel physical phenomena surprisingly in one material

 Highly anisotropic behaviors

 Mott-like transition

 Antiferromagnetic metallic state

 Metamagnetism

 Colossal magnetoresistance

 Bulk spin-valve effect

 Quantum oscillations & H-oscillation

 Nonlinear conduction

4d/5d oxides: phenomena & possible physics in n=2

 b-axis is the easy axis

 For B//b, _c drops at M-switching due to the spin-polarized transition. Then

_c increases due to the spin-orbit ordering

 For B//a, a rapid drop at B~15T

 For B//c, the Shubnikov-de Haas (SdH) oscillations

 The fully spin-polarized state may not be the most favored state for

conduction.

Ca

Ru

O

4d/5d oxides: phenomena & possible physics in n=2

 Very soft orbital order (OO) and spin order (SO)

 Delicate inter-coupling between these orders allow very different ground states and transport

behaviors

 Effect of orbital ordering here seems extremely remarkable

4d/5d oxides: phenomena & possible physics in n=2

 Cr-doping induces the extends the AFM-M state

 Cr-doping allows the spin cant at low B

 Bulk spin valve effect

4d/5d oxides: phenomena & possible physics in n=2

 Quantum oscillation (SdH effect)

 Fine Landau level in response to external magnetic field

Multiferroic oxides

Multiferroics: motivation

Multiferroics: spin/polarization exclusion

+ +

-

+ +

Partially filled d shells break Time reversal symmetry

N. A. Hill, Why are there so few magnetic ferroelectrics? J. Phys. Chem. B 104: 6694 (2000).

Empty d shells break Space reversal symmetry

Magnetism Ferroelectricity

Multiferroics: new symmetry argument

If spin order is spatially inhomogeneous, symmetry allows for the 3

-order coupling P∂M and then P may appear.

=

+P

/2 

Mostovoy, PRL 96, 067601 (06)

Multiferroics: frustration induced spiral spin order

 AFM triangular-lattice favors FSO.

 1D chain magnet with the competition between NN FM coupling

(J) and NNN AFM coupling (J  ) favors FSO if |J  /J|>1/4. (JPCM

7, 8605 (1995))

Multiferroics: frustration induced spiral spin order

T. Goto et al.

PRL 92,257201 (2004)

RMnO ₃ phases

RMnO ₃ phases

Multiferroics: take TbMnO₃ as an example

T. Arima et al.

PRL 96, 097202(2006)

TbMnO

Multiferroics: take TbMnO₃ as an example

Kimura, Annu. Rev. Mater. Res.37, 387 (2007)

Multiferroics: take CoCr₂O₄ as an example

 CoCr

O

system with conical spin order:

Yamasaki et al, PRL 96, 207204 (06)

Multiferroics: take Ba₂Mg₂Fe₁₂O₂₂ as an example

Ishiwata et al, Science 319, 1643 (08)

 Ba

Mg

Fe

O

helimagnet:

Multiferroics: take spin ice as an example

P =0

P >0

<111>

<111>

Ho

Ti

O

^{P S}

Multiferroics: take spin ice as an example

Multiferroics: take spin ice as an example

Multiferroics: take spin ice as an example

Multiferroics: charge-order induces polarization

PRL 100, 047601 (2008).

Ca

CoMnO

Multiferroics: charge-order induces polarization

Ca

Co

Mn

O

Multiferroics: charge-order induces polarization

LuFe

O

– charge order below ~350K creates alternating layers with Fe

/Fe

ratios of 2/1 and 1/2, inducing net polarization.

Ikeda et al, Nature 436, 1136 (05)

Multiferroics: charge-order induces polarization

 Pr

Ca

MnO

– possible

polarization due to the site-center (a) and bond-center (b) charge order.

Efremov et al, Nature Mat. 3, 853 (04)

Multiferroics: charge-order induces polarization

 Pr

Ca

MnO

– Indirect evidence for local ferroelectric domains by HRTEM+electron optics.

PCMO x=0.32, T=300K PCMO x=0.32, T=300K P~1.2mC/m

P~1.2mC/m

Jooss et al, PNAS 104-13597 (07)

Multiferroics: charge-order & orbital order

 Unknown region in X-W-T phase diagram

Multiferroics: charge-order & orbital order

 For doped manganites: R

A

MnO

, x=1/4.

 DE+NN-SE+JT, without DMI and NNN-SE

 New phase: spin- orthogonal stripe (SOS) phase.

 Large J

& small JT ().

 C

E

phase: xC- AFM+(1-x)E-AFM.

Dong et al. PRL

Multiferroics: charge-order & orbital order

Charge order, orbital order, & ferroelectricity

Multiferroics: charge-order & orbital order

 Large J

(narrow bandwidth) and small JT distortion

 quadruple (AA

)B

O

family, e.g. (A

B

)(B

B

)O

.

 B-O-B angle less than 140

and the JT Q

mode can be weak.

Multiferroics: possible electronic phase separation

Spiral:

TbMnO

E-AFM:

HoMnO

T _PM

IC

Reduced bandwidth Tc

T

Bicritical point of

dual multiferroic phases?

Phase separation by disorder?

Multiferroics: possible electronic phase separation

Spiral spin order

E-AFM

Perspectives & challenges

 A variety of materials to be explored

 A comprehensive understanding of the strongly correlated properties

 Rich physics but soft electronic & magnetic structure/property

 Enhancement of these effects up to room temperature: physically accessible?

Thank you for your attentions!!!

Thank you for your attentions!!!

Spin liquid and spin ice

Spin liquid & spin ice: spin frustration

Spin liquid & spin ice: spin ice

J. Snyder et al, Nature 413, 48 (2001)

Spin liquid & spin ice: zero-point entropy

A. P. Ramirez et al, Nature 399, 333 (1999)

 Highly frustrated configurations

 A variety of energy equivalent states with remarkable zero-point enttropy

 Classical spin ice frozen into disorder state at T0

 Quantum spin ice with strong quantum fluctuations at T=0

 Magnetic monopole and anti-

monopole ^Dy2Ti2O7

Spin liquid & spin ice: magnetic monopole & antimonopole

L. Balents, Nature 464, 199 (2010)

Magnetic monopole & anti-monopole (pair) Magnetic flux loop & chiralty A topological defect without breaking the lattice symmetry

Spin liquid & spin ice: Dirac string

T. Fennel et al, Science 326, 415 (2009)

A pair of monopoles apart from each other by a trail flipped spins

Dirac string

C. Castelnovo et al, Nature 451, 42 (2008)

Spin liquid & spin ice: magnetic monopole & antimonopole

L. Balents, Nature 464, 199 (2010)

A simple Hamiltonian to spin systems with localized electrons:

Classical or quantum spin interaction

For non-localized electrons, consult to Hubbard model & Mott transition

Crystal field effect, inducing Magnetocrystalline anisitropy