spintronics with ferroelectrics - 東京大学 · evgeny tsymbal department of physics and...
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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)
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: