Evgeny Tsymbal Department of Physics and Astronomy

Nebraska Center for Materials and Nanoscience University of Nebraska-Lincoln

Spintronics with Ferroelectrics

Ferroelectrics: Field Effect

FE

FM − − − − − − − − − − + + + + + + + + + +

Ba2+

Ti4+ O2-

Ba2+

Ti4+

O2-

P P

Ferroelectric BaTiO3

• Large polarization charge: 10 ‒ 100 μC/cm2 (~ 0.1 ‒ 1 e/a2)

• Polarization charge screening: “field effect”. Effective electric fields up to 10 V/Å (1 GV/cm)

• Non-volatile capability

• Controlled by fields of ~ 1 MV/cm Three order in magnitude smaller!

• Spontaneous electric polarization switchable by electric field

• Polar displacements ~ 0.1-0.2Å

• Perovskite structure

Control of spin-dependent properties relevant to spintronics

Ferroelectrics: Strain and Bonding

FE

FM

• Interface strain effects

Tensile Compressive

• Interface bonding effects

P P FE

FM

Ferroelectrically induced:

• High quality epitaxial structures with nearly atomic precision interface control: PLD, MBE

• Epitaxial strain to stabilize polarization • Stable and switchable polarization in sub nm thick films

BaTiO3

SrRuO3

SrRuO3

RHEED AFM HRTEM

Ferroelectrics: Epitaxial Thin Films

Ferroelectric

M

P

Magnetic (Ferromagnetic, Ferrimagnetic, Antiferromagnetic)

ε

Magnetoelectric Interfaces

• Strain mediated: Piezoelectricity & Magnetostriction or Piezomagnetism • Electronically driven: Spin-polarized screening or interface bonding

• Interface magnetization • Magnetocrystalline surface anisotropy • Interface magnetic order • Curie temperature • Electron and spin transmission across interfaces • Exchange bias • Spin waves

Effects of ferroelectric polarization on:

Surface Magnetoelectric Effect on Fe (001)

E

Electric field induces a surface magnetic moment Effect is small

sμ M α E0Δ =

αs ≈ 2.4×10-14 G cm2/V E = 1 V/nm -> Δm ≈ 2×10-3µB per Fe

Fe

-1 0 1

3.06

3.08

3.10 M || [100]

Mag

netic

mom

ent, µ B

Electric field, V/Å

Duan et al, PRL 101, 137201 (2008)

αs – surface magnetoelectric coefficient

• broken space inversion & time reversal symmetries

Fe(001) Surface DOS

0=σ ε E

Origin of Magnetoelectric Effect

Magnetoelectric coefficient:

;

↑ ↓

↑ ↓↑ ↓

↑ ↓ ↑ ↓

↑ ↓

↑ ↓

↑ ↓

+

= =

− −+

−+s

σ = σ σ

n nσ ε E σ ε En n

ε Eμσ σ n nM = μe e n n

μ μn nα Pec ecn n

0 0

0 BB

B B2 2

Δ =

= =

sμ M α E0Δ =

Fundamental limit for the linear ME effect

≈ ×sμα

ec-14 2B

2= 6.44 10 Gcm / V Universal constant for half-metals: Duan et al., PRB 79, R140403 (2009)

Ferroelectric Effect on Interface Magnetization

Spin density

OO

RuRuRu

0.0

0.4

OORuRu

B TiO

-0.0450

0.547

0.800

S R O

Ru

0.8

Niranjan et al, APL 95, 052501 (2009) BaO RuO2 P

BaTiO3 SrRuO3

SrRuO3

• Itinerant ferromagnet (~1 μB/f.u.)

• Curie temperature 160 K • Perovskite structure • Good lattice match to BaTiO3 • Epitaxial strain to stabilize

polarization (SrTiO3 substrate)

ΔmRu = 0.31 μB

Ec ~ 0.1 V/nm

Ferroelectric Effect on Interface Magnetization

Spin density

OO

RuRuRu

0.0

0.4

OORuRu

B TiO

-0.0450

0.547

0.800

S R O

Ru

0.8

Niranjan et al, APL 95, 052501 (2009) BaO RuO2 P

BaTiO3 SrRuO3

Spin resolved density of states

Change in the exchange splitting at the interface

2

1

0

1

2

Energy (eV)

minority

majority

left right

DOS

Δ = 0.71 eV Δ = 0.35 eV

Ferroelectric Effect on Interface Magnetization

Niranjan et al, APL 95, 052501 (2009)

Spin resolved density of states

Change in the exchange splitting at the interface

2

1

0

1

2

Energy (eV)

minority

majority

left right

DOS

Δ = 0.71 eV Δ = 0.35 eV

2 22 1F

F

II

ρρ

−∆ =

′

Explains calculated change in exchange splitting with FE polarization reversal

Im∆ =

I − Stoner exchange constant

Stoner model for itinerant magnetism:

Inducing Magnetism on a Non-Magnetic Surface

Can we induce a surface magnetism by electric field ?

1FIρ >

Stoner criterion for itinerant magnetism

Ag

Pd

E

I ≈ 0.65eV ; IρF ≈ 0.96

-6 -4 -2 0 20

1

2 EF

surface Pd

E (eV)

DO

S (e

V-1)

Sun et al., PRB 81, 064413 (2010)

Electric-Field Induced Magnetism on a Pd (001) Surface

Second-order phase transition

1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

m (µ

B)

E (V/Å)

model DFT, S layer DFT, (S-1) layer

( )F FE Eρ ρ α= +

( ) 2 2 Fc

F

m E E EIαρρ

= −′

Linearized Stoner model:

Sun et al., PRB 81, 064413 (2010)

-10-505

10

0 5 10 15 20 25 300

5

10

15

z (Å)

spin

den

sity

(10-3

µB/Å

3 )ch

arge

den

sity

(10-3

e/Å3 )

E=1.2 V/Å E=1.5 V/Å E=1.8 V/Å E=2.5 V/Å

VacuumPd AgVacuumE

Require very large electric fields which may be produced by an adjacent ferroelectric

Electric Field Effect on Magnetocrystalline Surface Anisotropy

Screening charge induced by electric field

sK β EΔ = βs – VCMA coefficient

→ Change in relative population of d-orbitals at the surface → Change in surface magnetocrystalline anisotropy (MCA)

Electric field control of magnetization orientation

E

FM metal - - - - - - - - -

+ + + + + + + + +

Magnetic Anisotropy

MCA energy determined by spin-orbit interaction: L SH ξ= ⋅

Bulk magnetocrystalline anisotropy (MCA) Surface (interface) MCA Shape anisotropy

2 2

,

z x

o u u o

o L u o L uK

ε ε

−∝

−∑

sensitive to orbital population

within 2nd order perturbation theory

Eshape ≈ µ0M2cos2θ - volume

Esurface ≈ - KScos2θ - surface

In thin films: θ

z

M

FM

Large perpendicular magnetic anisotropy (PMA): K ~ 2 erg/cm2

Increases with field away from interface Effect due to change in occupation of Fe-

3d orbitals (dxz,dyz → dxy)

X

Z

-0.0050

-0.0025

0

0.0025

0.0050

E

E

X

Y

-0.0050

-0.0025

0

0.0025

0.0050

Interface Fe atoms

dxz

dxy

Niranjan et al., APL 96, 222504 (2010)

Fe/MgO(100) Interface

0.0 0.5 1.02.06

2.08

2.10

2.12

MA

E (e

rg/c

m2 )

E (V/nm)

E Fe MgO

βs ≈ 0.05 pJ/Vm – consistent with experiment

Toggle Switching of Magnetization

Tsymbal, Nat. Mater. 11, 12 (2012)

Wang et al., Nat. Mater. 11, 64 (2012)

Shiota et al., Nat. Mater. 11, 39 (2012)

Significant interest from industry

Ferroelectric Control of Magnetic Interface Anisotropy

Induced charge density 0.002 e/Å3

-0.002 e/Å3

x-y plane

Fe

Fe

Fe Fe

0.004 e/Å3

0

Fe Fe

x-z plane y-z plane

Large perpendicular anisotropy Large change with polarization

switching Effect due to the relative change

in 3d orbitals occupation Consistent with Fe/MgO

Lukashev et al., JPCM 24, 226003 (2012)

Ec ~ 0.1 V/nm ⇒ βs ~ 3 pJ/Vm

P

Fe

BaTiO3

K ≈ 1.3 erg/cm2 K ≈ 1.0 erg/cm2

P

VCMA effect enhanced by two orders in magnitude!

Electrostatic Doping of Magnetic Perovskites: La1-xAxMnO3

Magnetic perovskites: La1-xAxMnO3 (A2+ = Ca, Sr, Ba)

La1-xSrxMnO3

Transition from FM to AFM order near x ~ 0.5

Mn

O

LaMnO3: Eg1

La1-xSrxMnO3: Eg1-x

SrMnO3: Eg0

3d orbitals

Eg

T2g

(1-x) electrons dz2, dx2‒y2

dxy, dxz, dyz

Hole doping of LaMnO3:

Electrostatic Doping of Magnetic Perovskites: La1-xAxMnO3

Magnetic perovskites: La1-xAxMnO3 (A2+ = Ca, Sr, Ba)

La1-xSrxMnO3

Transition from FM to AFM order near x ~ 0.5

Changing magnetic order by “electrostatic doping” at an interface with a ferroelectric?

BaTiO3

P

La0.5Sr0.5MnO3

P

FM AFM - - - - - - - + + + + + + +

Interface Electronic Structure of La0.5Sr0.5MnO3

Accumulation or depletion of electronic charge controls majority-spin eg state population and thus magnetic order

Burton et al., PRB 80, 174406 (2009)

Interface Magnetic Reconstruction

Change in the local magnetic order from FM to AFM induced by ferroelectric polarization reversal

AFM

BaTiO3 La05Sr0.5MnO3 FM

Gain in energy: 29 meV

Burton et al., PRB 80, 174406 (2009)

Tunneling Electroresistance (TER) effect: resistive switching of FTJ at coercive electric field

Metal

Metal Ferroelectric 1 – 3 nm

Ferroelectric Tunnel Junction (FTJ)

Ba2+

Ti4+ O2-

Ba2+

Ti4+

O2-

P P

BaTiO3

P

Tsymbal et al., Science 313, 181 (2006); MRS Bulletin 37, 138 (2012)

Reliable FTJ Devices

FTJs with ON/OFF resistance ratio exceeding 103 at room temperature

Multiferroic Tunnel Junction (MFTJ)

MFTJ combines TMR with TER making a four-state resistive device Effect of ferroelectric polarization on transport spin polarization Multifunctional properties

Ferromagnet

Ferroelectric

M

M P

Ferromagnet

MFTJ = MTJ + FTJ

Magnetic tunnel junction with a ferroelectric barrier

Zhuravlev et al, APL 87, 222114 (2005); PRB 81, 104419 (2010)

-0.09

-0.06

-0.03

0.00

0.03

0.06

0.09

0.12

SrBaBaBaBaBaBa SrSr

M-O

Disp

lacem

ents

(Å)

Atomic LayerSrSr

TiTiTiTiTiTi RuRuRu RuRu

SrRuO3/BaTiO3/SrRuO3 Multiferroic Tunnel Junction (MFTJ)

BaO SrO

RuO2 TiO2

Higher P Lower E

Lower P Higher E

Velev et al., Nano Lett. 9, 427 (2009)

G (10-7e2/h) ↑↑ ↑↓ TMR (%) → 3.76 0.83 350 ← 11.82 1.69 590

TER (%) 210 100

Four conductance states in SrRuO3/BaTiO3/SrRuO3 MFTJ

Co-existence of TER and TMR

M

P

Velev et al., Nano Lett. 9, 427 (2009)

10-1

k y (π/

a)

>4x10-6

2x10-6

0.0

kx (π/a)

majority minority M

P

K||-resolved Transmission

TMR – selection rules for electronic transmission TER – attenuation constant in the barrier

Decay constant

Ferroelectric Control of Spin Polarization

Pantel et al., Nature Mater. 11, 289 (2010)

Coexistence of TMR and TER Change of TMR sign with ferroelectric polarization reversal

Magnetoelectrically Driven TER Effect

More than 20 fold change in resistance !

Burton et al., PRL 106, 157203 (2011)

LSMO (x = 0.3) BTO LSMO (x = 0.4) current

La0.7Sr0.3 Ba La0.6Sr0.4 Mn Ti O

Electrically-Controlled Atomic Spin Valve

BTO LSMO (x = 0.3)

Layer and spin resolved density of states

E

- EF (

eV)

2 0 -2 -4

Polarization driven magnetic moment reversal acts as a spin valve enhancing dramatically resistance for antiparallel state

2 0 -2 -4

LSMO (x = 0.4) Burton et al., PRL 106, 157203 (2011)

La0.5Ca0.5MnO3 ~1nm

Experiments

4 nm

LSM

O

BTO

LSM

O

LCM

O

HRTEM & EELS

LSMO

STO substrate

Au/Cr

I

V

Device structure

Yin et al., Nature Mater. 12, 397 (2013)

‒ ‒ ‒ ‒ ‒

La0.7Sr0.3MnO3 + + + + + P

BaTiO3 La0.7Sr0.3MnO3 ‒ ‒ ‒ ‒ ‒

+ + + + +

FM Metal AFM Insulator

Experimental Result: ~10,000% TER

with LCMO interlayer TER ~ 10,000%

without LCMO interlayer TER ~ 40%

-1

0

1

Time (s)

R (kΩ

)

0 20 40 60 80 100101

102

103

V puls

e (V)

-2 -1 0 1 2

1.05

1.20

1.35

Vpulse (V)

J2R (kΩ

)

10

100

1000 J1

Effect is reversed when LCMO is deposited on bottom interface

Reproducible switching behavior

0 50 100 150 200 250 300

-2

-1

0

1

2

PFM TERV C (

V)

T (K)

PFM data

TER associated with FE polarization switching

Magnetoresistance

Consistent with the magnetic reconstruction mechanism

High field data

-1.0 -0.5 0.0 0.5 1.0100

150

200

250120016002000

P PR

(kΩ

)H (kOe)

0 30 60 900

50100400

600

800

1000

1200

1400

0 30 60 900

40600

900

1200

J1 J2∆R

(kΩ

)

H (kOe)

TER

(%)

H (kOe)

TMR

Yin et al., Nature Mater. 12, 397 (2013)

e

Metal/n-Ferroelectric Heterojunction

Normal Metal: Ferroelectric polarization dependent resistance

Ferromagnetic Metal: Ferroelectric polarization dependent spin-polarization

P n-FE

(n-BaTiO3)

FM Metal (SrRuO3)

Band Bending across n-BaTiO3

Shottky or Ohmic contact depending on polarization orientation

Schottky

Ohmic

Ohm

ic

Scho

ttky

P

n-BaTiO3 SrRuO3

SrRuO3

Liu et al., PRB 88, 165139 (2013)

Transmission

n-BTO

SRO

Fermi surfaces (view along z-direction)

105 change in the interface resistance by switching ferroelectric polarization

Liu et al., PRB 88, 165139 (2013)

Schottky Ohmic RA = 5.5×102 Ωµm2 RA = 3.78×107 Ωµm2

Tran

smis

sion

Fermi Surface of SrRuO3

• SrRuO3 is a ferromagnet below 160K • Spin-dependent electric band structure (1.2μB/f.u.)

Spin-dependent transmission is expected across SrRuO3/n-BaTiO3 interface

Majority spin Minority spin

dxy

dxz,yz dz 2

SP=(T↑-T↓)/(T↑+T↓) Spin Polarization

Significant change in the transport spin-polarization with ferroelectric polarization reversal

Transport Spin-Polarization O

hmic

Sc

hott

ky

Majority spin Minority spin

T↑ T↓

T↑ T↓

Transmission

SP=-98%

SP=-65%

Liu et al., PRL 114, 046601 (2015)

Origin of Spin-Polarization Change

Negative spin-polarization due to large minority-spin Fermi wave vector Change in the spin-polarization with ferroelectric polarization switching

due to change in the barrier height Change in sign of the spin polarization for small electron doping

Fermi surface of SrRuO3

0.079zk↑ ≈ Å-1 0.634zk↓ ≈ Å-1

Majority spin Minority spin

dz 2

dxz,yz

κ - attenuation constant

2 2

2 2z z z z

sz z z z

k k k kPk k k k

κ γκ γ

↑ ↓ ↑ ↓

↑ ↓ ↑ ↓

− −=

+ +

A simple model: Tunneling across a Schottky barrier

similar to Slonczewski, PRB 39, 6995 (1989)

Liu et al., PRL 114, 046601 (2015)

Conclusions

Ferroelectric polarization provides a new degree of freedom to control materials properties relevant to spintronics

• Interface magnetization • Interface magnetic order • Magnetocrystalline surface anisotropy • Electron and spin tunneling • Spin injection

Switchable ferroelectric polarization at the interface with a magnetic metal forms a non-volatile spin-dependent state interesting for device applications

U. Nebraska-Lincoln: J. D. Burton, Xiaohui Liu, Sitaram Jaswal

U. Puerto-Rico: Julian Velev

East China Normal U.: Chun-Gang Duan

Inst. Technology, India: Manish Niranjan

U. Northern Iowa: Pavel Lukashev

RAS, Moscow, Russia: Mikhail Zhuravlev

ICTP, Trieste, Italy: Alexander Smogunov Erio Tosatti

Adv. Sci. Res. Center, Japan: Sadamichi Maekawa

U. Nebraska: Alexei Gruverman Alexander Sinitskii U. Wisconsin: Chang-Beom Eom Penn State: YueWei Yin Qi Li U. Sci. & Tech. China, Hefei: Xiao-Guang Li Oak Ridge National Laboratory: Young-Min Kim Albina Borisevich Stephen Pennycook Seoul Nat. U.: Sang Mo Yang Tae Won Noh

Theory: Experiment:

Acknowledgements

Funding: