1
Multifunctional materials: the case of multiferroics. Can they revolutionize
some modern electronic components?
Michel Viret, Dorothée Colson, Delphine LebeugleDSM/IRAMIS/SPEC, CEA Saclay, France
Alexandra MouginLPS, University of Orsay, France
Delphine Lebeugle Séminaire ICMAB, 26 Octobre 2007
NNNNSSSS_+
Magnetization and electric polarization
Magnetic dipole → Magnetization Electric dipole → Polarization
MMMM PPPP
Magnetic fields and electric fields in nature :
3Ferroelectric and ferromagnetic materials
Ferroelectricity (T<TCE):Ps can be switched by Eappl
P
EcE
++
++
+Ps
-Ps
Ferromagnetism (T<TCM) :
MS can be reversed by Happ
M
+MS
HcH
- MS
M
+MS
HcH
- MS
+ _EEEE
---- PPPP
+P+P+P+P
_ +
NNNNSSSSBBBB
+M+M+M+M
----MMMM NNNN SSSS
4
Ferroelectric
Magnetic :
Ferro and ferrimagnetic (rare) AF spiral structures (the most common)
Magnetoelectric coupling
Introduction to multiferroic materials
Daniel Khomskii, Physics 2, 20 (2009)
Multiferroics:at the same time FE and FM
Rare materials
5
Review : First compounds ~1950
Few multiferroic materials (~60)
Perovskite-type structures ex : YMnO 3, BiFeO 3 …
Interests : Studying coupling between the ≠ variables
ex : coupling between ferroelectric and magnetic order parameters H influences PS
E influences M
Fundamental physics:
- understanding the origin of the coupling
- studying physics of magnetic oxides + electric fields
Technological applications:
- bifunctional materials : spintronics + ferroelectric technology
Possibility of switching P S by H (several examples) or M by E (rare)
Introduction to multiferroic materials
6
_+
_ +
BBBB
+ P+ P+ P+ P
---- PPPP
NNNNSSSS
N S
EEEE
+ M+ M+ M+ M
---- MMMM
Magneto-electric coupling
E →→→→ M, H →→→→ P
Magneto-electric coupling
7
Maxwell’s equations in vacuum linking E and B:
Magneto-electric coupling
cjeB→
→
mjmq E
→→
spinjmq
mq−
ES
→ A spin current generates an electric field
8
In the solid state
Electric fields generated by:
1) Spin currents associated with charge currents
‘Anomalous Hall Effect’ in ferromagnetic metals
2) Spin currents without charge currents
Can occur in insulators!
Magneto-electric coupling
9
V
d-orbitals d-orbitals
p-orbitals
P
sj
1e2e
12er
js = spin current
Katsura-Balatsky-Nagaosa PRL07
PS due to the magnetic structure
sjeP→→→
∝ 12 x
Magneto-electric coupling
→ In non-colinear magnetic structures, a polarisation can exist
Problem: P is normally tiny!But: P and M are linked!
In a solid with non-colinear magnetism (generalised Dzyaloshinski-Moriya interactions):
Typically oxydes with distorted crystallographic cells : EDM = Dij . (Si x Sj)O2-
Fe3+Fe3+
Pi→
10
Ferroelectricity in spiral magnets
PS α q ij ×××× (Si x Sj) qij : unit vector connecting 2 sitesSi,j : local spins
→ Analogous to Dzialoshinskii-Moriya (DM) interaction
EDM = 0 if PS Q and PS e Q : propagation vectore : spin rotation axis
Spiral magnetic structure : (cycloidal or helicoidal)
P≠0 → Improper ferroelectricity
Mostovoy, PRL, 96, 067601 (2006)
Sergienko et al., PRB, 73, 094434 (2006)
Sinusoidal magnetic structure :
P=0 → No ferroelectricity
Magneto-electric coupling
Technological point of view
Spintronics
Giant MagnetoResistance (GMR) →→→→ 2008 Nobel Prize : Albert Fert (Thalès)
http://www.research.ibm.com/research/demos/gmr/cybe rdemo1.htm
Bit 0
Bit 1
Discharged capacitor ↔ Bit 0Charge capacitor ↔ Bit 1
RAM (Random Access Memory) + Volatile
= SDRAM (Synchronous Dynamic Random Access Memory)
Technological point of view
Volatile capacitive memory :
0
0
0 0
1 1
1
1
0
0 0
1 0 10
1 0
10
10
0
0
10↔
working memory : volatile memory + perpetual discharge
RAM (Random Access Memory) + Non-volatile
= MRAM (Magnetic Random Access Memory)
Technological point of view : the future !!
: non-volatile memory + working memory : energy loss + writing defaults
Conclusion : we have to address the bits really individually and without any dissipation→→→→ Addressing with an electric field
14
Technological applications
Technological advances : - transducers, sensors
- spintronics (spin-filter, spin-transistor)
- information storage technology (FeRAM and MRAM)
→ encoding information in a single multiferroic bit : 4 states memory :
1 (+P,+ M)
2 (+P,- M)
3 (-P,+ M)
4 (-P,- M)
Introduction to multiferroic materials
Gajek et al., Nature Materials, 6, 296 (2007)
→ data written electrically (low energy) and read magnetically
V
MNMMF
Au
→→→→ Low R→→→→ High RE
15
Switching PS with magnetic field in spiral magnets
P(H) in TbMn2O5 at 3K and 28K
Hur et al., Nature, 429, 392 (2004)
Low temperature
Weak effect
Existing materials
Switching P with H demonstrated
What about switching M with E?
16
(010)
[111]
The case of BiFeO3 : ferroelectric, ferroelelastic and magnetic at 300K
Ferroelectric properties (TC ~ 1090 K )
Cubic perovskite structure → pseudo-cubic : rhombohedral distortion PS due to Bi3+ and Fe3+ displacements along [111]
α = 89.47°
PS [111]
54 pm (Bi 3+)
13 pm (Fe3+)
Large atomic displacements →→→→ large P S
Kubel et al., Acta Cryst. B, 46 , 698 (1990)
17
λ = 64 nm
[10-1]
[111]
PS
e
q
Magnetic properties (TN ~ 640K)
Modulated antiferromagnetic structure
Cycloidal arrangement of the Fe3+ magnetic moments
PS ~ (e ×××× q) q : propagation vectore : spin rotation axis
The case of BiFeO3 : ferroelectric, ferroelelastic and magnetic at 300K
Sosnowska et al., J. of Phys. C, 15 , 4835 (1982)
18
Peritectic melting point → flux method
Composition : 0.8Bi2O3/0.2Fe2O3
2 impurities : Bi2Fe4O9 and Bi25FeO39
Importantly : Tcryst. < TCurie
Single crystal of BiFeO31.4 x 1.6 x 0.04 mm3 (SEM)
500 µm500 µm
Synthesis
600
40 60 80Fe2O3 Bi2O3
700
800
900
1000
20
Liquide (L)
Bi 2
Fe 4
O9
α α α α B
iFeO
3
Bi 4
0Fe 2
O63
L + Bi 2Fe4O9
L + αααα BiFeO 3
αααα BiFeO 3+
Bi 40Fe2O63
L + ββββ BiFeO 3
β β β β B
iFeO
3
% molaire
Tem
péra
ture
(°C
)
1 ferroelectric domain crystal
c
d
2 ferroelectric domains crystal
Polarized light optical microscopy
Ferroelectric studies
_ +---- PPPP
_++ P+ P+ P+ P
_++ P+ P+ P+ P
20
Polarization loop on BiFeO3 single crystals
-200
-100
0
100
200
-200 -100 0 100 200
Tension (V)
Cou
rant
(nA
)PS [111]
Eapp
54°
PS [111]Eapp
54°
Lebeugle et al., PRB, 76, 024116 (2007)
* Neaton, PRB, 71, 014113 (2005)
Charge current versus applied voltage :
High resistivity ρ(300K,100V) ~ 6.1010 Ω.cm
Very large PS~ 100 µC/cm² (BaTiO3 Ps ~ 25 µC/cm²) as theoretically predicted*
Ec ~ 12 kV/cm, Emax ~ 40 kV/cm
First P(E) at 300K on BiFeO3 single crystals
-75
-50
-25
0
25
50
75
-50 -40 -30 -20 -10 0 10 20 30 40 50
E (kV/cm)
P[0
10] (
µµ µµC/c
m²)∫∝ I.dtP
T = 300K
Ferroelectric properties
21
22
In neutron diffraction : 1 magnetic spiral = 2 satellites in reciprocal space
The crystals have become FE bi-domain and the magnetic structure has changed
Neutron diffraction and magnetoelectric study
λ = 64 nm
[10-1]
[111]
PS
e
q
λ = 64 nm
[10-1]
[111]
PS
e
q
4-circles neutron diffraction Super 6-T2 diffractometer / ORPHEE reactor / LLB, France
0.988
0.994
1
1.006
1.012
-0.012 -0.006 0 0.006 0.012
(ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
q1 = [δδδδ 0- δδδδ]
q2 = [0δδδδ- δδδδ]
a*c*
b*
q3 = [- δδδδ δδδδ 0]
0.988
0.994
1
1.006
1.012
-0.012 -0.006 0 0.006 0.012
(ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
0.988
0.994
1
1.006
1.012
-0.012 -0.006 0 0.006 0.012
(ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
q1 = [δδδδ 0- δδδδ]
q2 = [0δδδδ- δδδδ]
a*c*
b*
q3 = [- δδδδ δδδδ 0]
Pic magnétique : (1/2, -1/2, 1/2) Pic magnétique : (1/2, -1/2, 1/2)
0.988
0.994
1
1.006
1.012
-0.012 -0.006 0 0.006 0.012
(ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
71°
q1 = [δδδδ 0- δδδδ]
q2 = [0 δδδδ- δδδδ]
a*c*
b*
q3 = [- δδδδ δδδδ 0]
q1 = [δδδδ 0- δδδδ]
0°
0.988
0.994
1
1.006
1.012
-0.012 -0.006 0 0.006 0.012
(ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)ξ,0,−ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
(ξ,0
,ξ)
71°
q1 = [δδδδ 0- δδδδ]
q2 = [0 δδδδ- δδδδ]
a*c*
b*
q3 = [- δδδδ δδδδ 0]
q1 = [δδδδ 0- δδδδ]
0°
EEEE
2 satellites in reciprocal spacein the virgin state
4 satellites in reciprocal spaceAfter application of E
23
Domain I
P [111]q1
Rotation plane : (-12-1) = P[111] × q1
Neutron diffraction and magnetoelectric study
24
Domain II
P [1-11]
q1
Rotation plane : (121) = P’[1-11] × q1
Neutron diffraction and magnetoelectric study
25
P [111]
P [1-11]
q1
E
Lebeugle et al., PRL100, 227602 (2008).
Neutron diffraction and magnetoelectric study
Evidence for the coupling between M and P at 300K by neutron diffraction on BiFeO3 single crystals.
26
In order to address a net M moment : FM layer on BFO crystal
BFO (AFM and FE at 300K ) + FM layer →→→→ compensated system
BFO// NiFe layer (10nm) // Protection layer of Au (4 nm)
[101]
[10-1]
(010)
[101]
[10-1]
(010)
Crystal of BFO 1x1x0.04 mm3
BiFeO crystal
Au (4nm)
3
NiFe (10nm)
Au (4nm)
Exchange coupling
27
Noguès et al., JMMM, 192, 203 (1999)
FM and AFM layers in contact :
• Enhancement of Hc
→→→→ Exchange coupling at interface.
Cooling under Hcool through TN :
→→→→ Exchange bias at interface :
• Shift or « bias » of hysteresis loop
• Unidirectional anisotropy
• Heb(θ) sinusoidal• Hc(θ) and Heb(θ) max along Hcool
I)
II)
III)
cool N
1
2
Hcool through TNcool N
1
2
Hcool through TN
Hc = f(θ)
Hc = f(θ)
Heb = f(θ)Heb
12
34
3 4
Unidirectional exchange coupling : exchange bias
28
• Roughness and formation of domain walls to the interface
• Requirement of uncompensated spins :
N = L² / a² L² : area of the AFM domain
a : cell parameter
Heb α - Jex/L
Small domain size : bias is higher (multidomain state is favorable)
In summary :
2 kinds of spins are involved :
1) Pinned uncompensated spins with strong anisotropy : Bias
2) Spins with weak anisotropy free to rotate : No bias but enhanced HC
Angular dependances of Hc and Heb evidence the nature of involved
spins and the strength of AFM anisotropy / EC.
Malozemoff model
Why Hebexp ≠ 0 in compensated systems ?
29
500 µm500 µm
Appearance of easy and hard axes at 90°from each ot her
Crystal in the virgin state
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
-15 -10 -5 0 5 10 15
H (mT)
M (a.u.)
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
-15 -10 -5 0 5 10 15
H (m T)
M (a.u.)
Hard axis
Easy axis
0
4
8
120
30
60
90
120
150180
210
240
270
300
330
0
4
8
121.2
0.8
0.4
0.0
0.4
0.8
1.2
Hsw
itch (
mT
)
Hswitch
Mrem
α (°)
Mre
m/M
s
30
H
H
++
++
++
++
++
++
--
--
--
--
- -- -
++
++
++
++
+ ++ +
(a) BFO
(b) Py
(c) Py
q
Uniaxial exchange due to a rippling pattern induced in the permalloy
31
E = 25 kV/cm
-30 -20 -10 0 10 20 30
-0.010
-0.005
0.000
0.005
0.010
Domains 1+2 Domain 1
α = 65°
Ker
r ro
tatio
n (°)
H (mT)
500 µm500 µm
Different regions where the ansotropy axes are at 9 0°between each other
After poling
0.0
0.4
0.8
1.20
30
60
90
120
150180
210
240
270
300
330
0.0
0.4
0.8
1.2
Mre
m/M
s
Domain 1 Domain 2
αααα (°)
0
5
10
15
030
60
90
120
150180
210
240
270
300
330
0
5
10
15
αααα (°)
Hsw
itch (
mT
)
Domain 1 Domain 2
32
Electric contrast
Magnetic contrast during H sweeps
The magnetic anisotropy is linked to the polarisati on domains
Exchange coupling
33
Mag2FE2
After several poling cycles, the exchange domains d o not correspond exactly to the polarisation domains
→→→→ Consistent with an exchange caused by the cycloids
34
Thin films:
Strain effects suppress the cycloid→ generates a global magnetic moment→ Can induce a linear Magneto-electic effect: αijMixPj→ Better for the magneto-electric coupling??
Perspectives
SrTiO3 (Substrate)BiFeO3 (AFM + FE)CoFeB (FM)Au (Protection)
SrTiO3 (Substrate)BiFeO3 (AFM + FE)CoFeB (FM)Au (Protection)
Laser
HFC
longitudinal magnetic hysteresis cycle (MOKE) of a CoFeB layer deposited on BFO/STO.
-150 -100 -50 0 50 100 150
-0.010
-0.005
0.000
0.005
0.010
Rot
atio
n K
err
(°)
H (Oe)
Hech
Magnetic exchange at the interface:
Exchange Bias
35Conclusion
Room-temperature multiferroics are a promising route to design magnetic/electric memories
Fully compensated crystals not ideal?Thin film?Substitution?
→ Make the AF a little magnetic…
→ Perspectives using Exchange Bias to make a device addressable by H and E fields.
36Addendum
Photovoltaic effect in BiFeO3T. Choi, S. Lee,* Y. J. Choi, V. Kiryukhin, S.-W. CheongSCIENCE VOL 324 3 APRIL 2009