M. Liu (刘俊明

J.

–

M. Liu (刘俊明

)

Laboratory of Solid State Microstructures, Nanjing University Laboratory of Solid State Microstructures, Nanjing University International Center for Materials Physics, Institute of Materia

International Center for Materials Physics, Institute of Materials Researchls Research

Manipulation of quantum fluctuations and

ferroelectricity in quantum paraelectrics

Content

 Background and Motivation

 A-site disorder: symmetry scenario

 Enhancement of QFs

 Magnetoelectric effect in EuTiO

 Summary

Background & motivation

 Typical perovskite structure with lattice distortion

What is ferroelectricity?

Background & motivation

 Typical perovskite structure without much lattice distortion What is quantum paraelectricity (QPE)?

PRB 72, 121101(R); PRB 19, 3593; PRL 52, 2289

Background & motivation

Simple mechanism for quantum fluctuations (QFs)

APL 93, 132903; PRL 74, 2587

Soft mode No symmetry break

Background & motivation

Simple theory on QPE

Z

 Z>  z(0)

1 1 0

' ( / 2) coth( / 2 ) C

T T T T

 



3 0 2

1 2

2a B

C q (3b 2b )kD

  

 ¹

T h

k

 

3 2

0

0 2

1 2 0

2a Dq

T ( 1)

q (3b +2b )kD 2a

 



 

PRB 72, 121101(R); PRB 19, 3593; PRL 52, 2289

PR 86, 118; PRB 18, 2394; PRB 8, 1256

Background & motivation

 Not only STO but also other titanates show QPE: (Ln_1/2Na_1/2)TiO₃ (Ln=Dy, Ho, Er, Tm, Yb, Lu)

 High dielectric susceptibility & low loss: potential applications

Other quantum paraelectrics PRB 77,052106

Background & motivation

Manipulate the QFs?

Science 276, 392; JPSJ 72, 37

A-site disorder: symmetry scenario

Symmetry scenario: SrTiO₃

 Tolerance factor t=1.01 (STO, cubic), 1.07 (BTO, tetragonal), 0.97 (CTO, tetragonal). SrTiO₃: a marginal system

 Oxygen isotope effect (right)

 Strain effect (bottom)

PRB 69, 024103; Nature 430, 758

A-site disorder: symmetry scenario

A-site structural disorder, without symmetry breaking

Keep macroscopic symmetry but modulating local disorder degree of freedom

2 2 2

A

A

r

r 

 

A-site disorder: symmetry scenario

Pure A-site structural disorder

4 0.390421

47.82 0.16

Sr_0.84Ca_0.102224Ba_0.057776TiO₃

3 0.390461

41.58 0.14

Sr_0.86Ca_0.089446Ba_0.050554TiO₃

4 0.390256

35.97 0.12

Sr_0.88Ca_0.076668Ba_0.043332TiO₃

3 0.390269

29.89 0.10

Sr_0.90Ca_0.063890Ba_0.036110TiO₃

4 0.390467

23.91 0.08

Sr_0.92Ca_0.051112Ba_0.028888TiO₃

14 0.390624

14.95 0.05

Sr_0.95Ca_0.031945Ba_0.018055TiO₃

9 0.390421

8.967 0.03

Sr_0.97Ca_0.019167Ba_0.010833TiO₃

7 0.390289

5.978 0.02

Sr_0.98Ca_0.012778Ba_0.007222TiO₃

0.3905 0

0 SrTiO₃

error (x10^-5) lattice parameters (nm)

² (10^-6nm²) x

Sample (SrCaBaTiO₃)

2 2 2

A

A r

r 



A-site disorder: symmetry scenario

Structural identification

A-site disorder: symmetry scenario

Dielectric evidence of FE state

1. Clear deviation from QPE state into FE- like state

2. It is really a FE

state?

A-site disorder: symmetry scenario

FE state at high disorder degree

T_m(x)=A(x−x_c)^r A=67.7

r=0.2158 x_c

=0.02758

Clear deviation from the pure QPE system

A-site disorder: symmetry scenario

Dielectric dispersion at low and high degrees of disorder

Clear relaxor ferroelectric behavior given by

the dielectric dispersion

A-site disorder: symmetry scenario

ferroelectricity

Loop for FE

Loop for RFE

Background & motivation

Manipulate the QFs?

Science 276, 392; JPSJ 72, 37

Enhancement of QFs

Problem II: how to enhance local quantum fluctuation?

PRB 54, 3151 Sr_1-xBa_xTiO₃

SrRuO₃ FM metal with T_c=160 K

Enhancement of QFs

Problem II: how to enhance local quantum fluctuation?

Sr

Ba

TiO

(SBT)

Ru-doping enhances the quantum fluctuation & draws SBT back to QPE

1. e

(doublet), t

(triplet) low-spin (t

)

2. High conductivity results from the 

overlap between cation t

and anion p

orbitals

Enhancement of QFs

Ru-doping: no symmetry breaking

Sr

Ba

Ti

Ru

O

Enhancement of QFs

Suppression of FE state into QFE and QPE

1 1 0

' ( / 2) coth( / 2 ) C

T T T T

 



SBTR (x=0) T

=72K

SBTR (x=0.02) T

=45K

Enhancement of QFs

Suppression of FE state into QFE and QPE

1 1 0

' ( / 2) coth( / 2 ) C

T T T T

 



439.8 -172.9

94 1.9

x=0.10

79.6 10.7

101 1.24

x=0.05

-4.4 67.7

131 1.15

x=0.02

-37.6 89.3

141 1.0

x=0.0

19.4 35.3

92 0.8

STO

T

-2T

(K) T

(K)

T

(K)

C(10

)

Enhancement of QFs

Raman evidence

TO

=174cm

TO

=549cm

FE modes

SrTiO

Sr

Ba

TiO

Enhancement of QFs

Raman evidence

Sr

Ba

Ti

Ru

O

x=0

Enhancement of QFs

Raman evidence

Sr

Ca

Ti

Ru

O

T_C=397.6x(0.07-x)^1/2

Background & motivation

Effect of spin order?

Science 276, 392; JPSJ 72, 37

Magnetoelectric effect in EuTiO

Motivation

FE

QFs Spin

EuTiO

Pm3m, a=0.3905nm Quantum paraelectric T

=30K

QFs vs FE

Eu

(S=7/2), G-AFM

Soft mode 10meV

Magnetoelectric effect in EuTiO

Preparation

Magnetoelectric effect in EuTiO

Magnetic behaviors

T

=5K, G-AFM

High H, G-AFM to FM

Magnetoelectric effect in EuTiO

Magnetic field induced QPE

T_S~40K, quantum saturation temperature T_N~5K, sharp drop of dielectric constant

Magnetoelectric effect in EuTiO

Magnetic field induced QPE

H→Eu²⁺(S=7/2) rotation

 = 

[1+  (S

 S

)]

Spin (Eu²⁺) -phonn (T_1u) coupling

Magnetoelectric effect in EuTiO

Magnetic field induced QPE

Magnetic field enhances the quantum fluctuations, and thus induces the magnetoelectric response

Summary



A-site disorder and B-site Ru

substitution can obviously modulate the QFs.



QFs can be respectively suppressed by the A-site disorder and enhanced by the Ru

substitution.



Excellent magnetoelectric effects in quantum

paraelectric EuTiO

.

Thank you for your attentions!