Magnetoelectric Multiferroics -...
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Magnetoelectric Multiferroics
Kathrin Dörr, IFW Dresden, Postfach 270116, 01171 Dresden, Germany
ESM 2007, Cluj-Napoca, 14 September 2007
Thanks to M. Fiebig
History and fundamentals
Single-phase multiferroics
Composite multiferroics
Experimental techniques
Summary, Literature
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What is a multiferroic ?
“Crystals can be defined as multiferroic when two or more of theprimary ferroic properties [...] are united in the same ph ase.”
Hans Schmid (University of Geneva, Switzerland) in: M. Fiebig et al. (ed.), Magnetoelectric Interaction Phenomena in Crystals, (Kluwer, Dordrecht, 2004)
Primary ferroic ↔ formation of switchable domains:
Ferromagnetism Ferroelectricity Ferroelasticity Ferrot oroidicityspontaneous spontaneous spontaneous spontaneousmagnetization polarization strain magnetic vortex
Excludes anti-ferroicforms of ordering
N S+ − + −+ − + −+ −+ − + −+ −+ −+ −
Extension to anti-ferroic forms of ordering:
Compounds consisting of multiferroic sublattices (one or more of)
whose primary ferroic properties cancel in the macroscopic crystal
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Idea of the magnetoelectric effect
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Idea of the magnetoelectric effect
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Idea of the magnetoelectric effect
magnetoelectriceffect
magnetic shapememory effect
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Quantification of the ME effect
Free energy of magnetoelectric materials with „mixed term s“ in E, H:
F(Ei , Hj ) = - α α α α i j Ei Hj - ½ββββijk EiHj Hk - ½ γγγγijk EiEj Hk
magnetization: M(E) = - dF / dH
electric polarization: P(H) = - dF / dE requires breaking of time-reversal and space-inversion symmetries
♦♦♦♦ Linear magnetoelectric effect: Pi = ααααij Hj ; Mj = ααααij Ei
“the“ magnetoelectric effect
♦♦♦♦ Higher order terms for ββββ ≠ 0, γγγγ ≠ 0
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History
"C'est la dissymmétriequi crée le phénomène"(P. Curie, 1894)1894 P. Curie: discussed correlation of
magnetic and electric properties in low-
symmetry crystals
1926 P. Debye: “magneto-elektrischer
Richteffekt“
1957 L. D. Landau, E. M. Lifshitz: “The
magnetoelectric effect is odd with respect to
time reversal and vanishes in materials
without magnetic structure.“
1959 I. E. Dzyaloshinskii: predicted the
magnetoelectric effect in Cr2O3
1960 D. N. Astrov: first observation in Cr2O3
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History
M ∝∝∝∝ ααααE P ∝∝∝∝ αααα∗∗∗∗H
Cr2O3
D. N. Astrov, JETP 11, 708 (1960) V. J. Folen, PRL 6 , 607 (1961)
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The revival
Since about the year 2000:
♦ New materials (“designed“
composites) with much larger
ME effect
♦ New theoretical approaches /
concepts
♦ New experimental techniques
(neutron scattering, non-linear
optics)
1985 1990 1995 2000 2005 20100
20
40
60
80
100
120
140
160
180
200
Pub
licat
ions
/ ye
ar
Year
Publications on
"magnetoelectric"
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Sources of the magnetoelectric effect Limitation of the magnetoelectric effect: ααααij2 < χχχχiie χχχχjjmχχχχii
e: electric susceptibility χχχχjjm: magnetic susceptibility Large in ferroelectric and ferromagnetic samples → multiferroics
W. F. Brown et al., Phys. Rev. 168, 574 (1968)
+ − + −+ − + −+ −+ − + −+ −+ −+ −
“Likes“ 3dn with n=0
N S
“Likes“ 3dn with n≠≠≠≠0
N.A. Hill, J. Phys. Chem. B 104, 6694 (2000)
There are very few magnetic ferroelectrics. (N. Hill alias Nicola Spaldin)
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Magnetoelectric Multiferroics
History and fundamentals
Single-phase multiferroics
Composite multiferroics
Experimental techniques
Summary, Literature
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Single-phase multiferroics: overview
Most are ant i-ferroic in one of
the orders (magnetic / electric)
→→→→ small magnitude of M or P
Multiferroics “unusual“
because they circumvent thed0 / dn problem [1]
[1] C. Ederer and N. A. Spaldin, Curr. Opin. Sol. S tat. Mat. Sci. 9, 128 (05)
• Perovskite type:ABO 3, A2B`B``O 6 (e. g., BiFeO 3, TbMnO 3)
• Hexagonal structure:RMnO3 with R = Sc, Y, Ho-Lu
• Boracites:M3B7O13X with M = Cr, Mn, Fe ...; X = Cl, Br, I
• Orthorhombic BaMF 4 compoundsM = Mg, Mn, Fe, Co, Ni, Zn
and further ones (about 100)
• Non-multiferroic magnetoelectrics:
GdFeO3, LuFe 2O4
Very rare: RT multiferroics
(BiFeO3: ferroelectric + antif.mag)
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Magnetic control of ferroelectricity: TbMnO 3
ferroelectric
P changes direction in large magnetic fieldT. Kimura et al., Nature 426, 55 (2003)
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Spin spirals as source of polarization
In TbMnO3, a spiral spin structure and ferroelectricity appear at T ≤ Tlock. Spin spirals break time and space inversion symmetry
(promising for ME effect)
Polarization P ∝∝∝∝ eij x (S i x S j ) proposed (H. Katsura)
H. Katsura et al., PRL 95, 057205 (2005)
Si, Sj: magnetic moments
eij : unit vector connectingsites i, j
P: polarization
js: “spin current“
eij
Si Sj
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Spin spirals as source of polarization
A spin spiral can be characte-
rized by the propagationvector k, the rotation plane (jS)
and the cone angle β.
Note: not all spirals cause polarization !
Neutron diffraction: determinespin spiral structure
H. Katsura et al., PRL 95, 057205 (2005)
kP
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Charge-ordered compounds
D. V. Efremov et al., Nature Mat. 3, 853 (04)
(a) Mn4+ order or
(b) electron hole
at the O ? Intermediate
case (c) with
broken space
inversion
symmetry
a) “site-centered“
b) “bond-centered“
c) intermediate
Transition metal oxides (e. g. Pr1-xCaxMnO3):
eg electrons order in insulating phases
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HoMnO3
hexagonal structure
ferroelectric at ~870 K
Mn( ): antiferromagnetic, TN = 76 K, TSR = 34 – 40 K
Ho ( ): antiferromagnetic,
order sets in at TSR,
full order at THo = 6 K
P63cm
E = 0
a
2a
4b
P63cm
E = 0
a
2a
4b
Ho3+
Mn3+
O2-
T < TN: P63cm
T < TSR: P63cm
T. Lottermoser, M. Fiebig et al., Nature 430, 541 (2 004)
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HoMnO3: magnetic phase control by electric field
E
P63cmb
E
P63cmb
E ~ 100 kV cm -1
T. Lottermoser, M. Fiebig et al., Nature 430, 541 (2004)
Mn and Ho magnetic structures are coupled. In electric field, Mn reorients and Ho becomes ferromagnetic.
0 20 40 60 80 100
0
1
2
3
-2 -1 0 1 2-1.0
-0.5
0.0
0.5
1.00
0 10 20 30 40 50 60 70 80
T Ho
TR
TN
a
× 1.5 I
SH(y)
ISH
(x)
ISH
(y)
ISH
(x)
Temperature (K)
SH
inte
nsity
IS
H
E = 0
E ≠ 0
E ≠ 0
c
µ0H
z = 0.5 T
∆Φ =
[Φ(+
E) −
Φ(−
E)]
/2 (
°)
Temperature (K)
E = 0
b
T = 1.4 K
Far
aday
rot
atio
n Φ
(°/
µm)
Magnetic field µ0H
z (T)
Mn
Ho
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BiFeO3
Switching of FE domains (PFM
tip) ⇒ switching of AFM domains
in BiFeO3 films at 300 K
T. Zhao et al., Nature Mat. 5 (06)
Magnetic(PEEM)
Electric (PFM)
• perovskite type structure
• multiferroic with the highest
ordering temperatures :
ferroelectric: TC = 1103 K
antiferromagnetic: TN = 643 K
(spin spiral)
Application: control the exchange bias by electric field
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“Electromagnons“
In magnetoelectrics, new excitations /
quasiparticles are possible:
Magnons (spin waves) associated with
dielectric polarization excited by GHz
electric field⇒ “electromagnons“
A. Pimenov et al., Nature Physics 2, 97 (06)
ε1
ν (cm-1)0 30Resonances in the dielectric
function, suppressed by
magnetic field
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“Electromagnons“
In magnetoelectrics, new excitations /
quasiparticles are possible:
Magnons (spin waves) associated with
dielectric polarization excited by GHz
electric field⇒ “electromagnons“
A. Pimenov et al., Nature Physics 2, 97 (06)
ε2
Resonances in the dielectric
function, suppressed by
magnetic field
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Magnetoelectric Multiferroics
History and fundamentals
Single-phase multiferroics
Composite multiferroics
Experimental techniques
Summary, Literature
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Composite multiferroics create large response M(E) or P(H) at ambient temperatures
ferromagnet: H →→→→ M
ferroelectric: E →→→→ P
+Couple them and
expect:
H →→→→ P, E →→→→ M
multiferroic
composites
Magnets
Tb1-xDyxFe2
La0.7Sr0.3MnO3
CoFe2O4
YIG (garnets)
Fe, Py, ..
Ferroelectrics
BaTiO 3
Pb(Zr,Ti)O 3
SrBi 2Ta2O9
PMN-PT
PVDF, …
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Magnetoelectric coupling
piezoelectricmagnetostrictive
σσσσ1. Mechanical strain
magnet
FEE + + +
E
P- - -
2. Interface charge / bonding effects
a) Field effect
b) Bond effect: change in bonding upon P reversal alter s interfacemagnetization C. G. Duan, E. Y. Tsymbal, PRL 95 (06)
S. X. Dong, D. Viehland et al., APL 85 (04)
H E
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Types of strain-coupled composites
• Mixed, sintered powders
• Free-standing laminar composites
• Layered thin film structures
• Nanostructured composite films
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Free-standing laminar composites
J. Ryu et al., Jap. J. Appl. Phys. 40, 4948 (2001)
Piezoelectric and magnetostrictive
components glued or hot-pressedtogether
Example: PZT/Terfenol-D trilayer
magnetoelectric voltage coefficient:
dE/dH = 4.7 V / (cm Oe)
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Free-standing laminar composites
Piezoelectric and magnetostrictive
components glued or hot-pressedtogether
Huge values at resonances in theAC magnetic field
Sensitive (low noise) magnetic fieldsensors (D. Viehland et al.)
J. Zhai, D. Viehland et al., APL 89, 83507 (06)
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Layered thin film structures
Heteroepitaxial growth of multilayers on monocrystalline substrates⇒ good elastic coupling at the FE/FM interface⇒ field effect at interfaces⇒ further mechanisms: multiferroic tunnelbarriers depending on electric and magneticfield (see below)
Disadvantage:
Clamping to the substrate , weak strain
Substrate
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Layered thin film structures
-10 -5 0 5 10
75
80
85
90
95
mag
netiz
atio
n (e
mu
/ cm
3 )
electric field (kV / cm)
La0.7Sr0.3MnO3 (30 nm) / PMN-PT
T = 330 K
µµµµ0H = 10 mT
δεδεδεδεxx = - 0.1 %
-10 -5 0 5 10
-5
0
5
αα αα (
10-8 s
/ m
)
electric field (kV / cm)
magnetoelectric coupling factor
αααα = µµµµ0 dM / dE ≤ 5⋅⋅⋅⋅10-8 s / m
-10 -5 0 5 10
-0.10
-0.05
0.00
0.05
in-p
lane
str
ain
(%)
electric field (kV / cm)
T = 300 Kcompressionexpansionpiezo - crystal
magnetic film
Vpiezo
Films on piezoelectric substrate
PMN-PT(001)
C. Thiele, K. D., Phys. Rev. B 75, 054408 (07)
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Nanocolumnar composites
H. Zheng et al., Science 303, 661 (04)
Two-dimensional structures
(like columns) may show larger
strain on a rigid substrate.⇒ self-organized growth⇒ nanofabrication (templates)
CoFe2O4 - BaTiO3 nanocolumnar film
BTO
CFO
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Nanocolumnar composites
MFM images,
quadratic area
electrically
written @ -16 V
F. Zavaliche, R. Ramesh et al., Nano Lett. 7, 1586 (0 7)
Local magnetizationelectrically written
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Field effect experiments
T. Kanki et al., APL 83, 4860 (03) X. Hong et al., PRB 68, 134415 ( 03)
PZT – La0.8Sr0.2MnO3 (4 nm)PZT - La0.9Ba0.1MnO3 (6 nm)
ferroelectricchannel
Vgate
x- rays, light
substrate
PTC
♦ Hystereticmodulation of the
charge density in a
magnetic channel
♦ Low screeninglength⇒ study and control interface
magnetism
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Multiferroic tunnel barrier
La0.1Bi0.9MnO3 tunnel barriers
a) Ferromagnetic insulator: spin filtering
b) ferroelectric: barrier profile depends on P direction Magnetic and electric control of a tunnel current
M. Gajek et al., Nature Mat. 6, 296 (07)
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Applications
• Microwave applications:
transducer H(ω) → E(ω)
electromechanical: 100 kHz, magnetic resonances: 10 – 100 GHz
• Magnetic field sensors (free-standing laminar composites)
• Suggested: magnetoelectric electronics
(Electric control of magnetization in memories, logical circuits, ..)
16 Mbit MRAM (IBM, Infineon)
Si
MOS-FET SQUID
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Magnetoelectric Multiferroics
History and fundamentals
Single-phase multiferroics
Composite multiferroics
Experimental techniques
Summary, Literature
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Second harmonic generation (SHG)
Electric field in matter: E(w) = E0eiωt(Incident light wave: frequency, direction, amplitude, polarization)P(ω) = ε0 χ E(ω) ~ eiωtLinear approximation only for weak (light) fields
For strong electromagnetic fields (e.g. laser):P = ε0 ( χ(1) E + χ(2) E E + χ(3) E E E + ... )with leading-order nonlinear term:P(2ω) = ε0 χ(2) E(ω) E(ω) ~ ei2ωt→ Frequency doubling ("second harmonic generation", SHG)
∑ ω−−ω−−⟩⟩⟨⟩⟨⟨∝χ i gigf EEEE greiireffreg ))(2( ||||||)2( hh rrr
E(ω)
E(ω)
P (2ω)
E x c i t e d s t a t e
G r o u n d s t a t e
Intermedi-ate states
⟨ | f
⟨ | i
⟨ |g
Microscopically:second-order perturbationM. Fiebig, thesis (Universität Dortmund, 1996)
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Second harmonic generation (SHG)
SHG: Si(2ωωωω) ∝∝∝∝ χχχχijk Ej(ωωωω) Ek(ωωωω)Scr Smag
1.8 2.0 2.2 2.4 2.6 2.8 3.00
T = 10 K
crystallog.magnetic
SH
inte
nsity
SH energy (eV)
Cr2O3
χχχχijk ↔↔↔↔ symmetry ↔crystallographic and magneticstructure (Note: the higher the
symmetry the more χijk = 0) Spectroscopy : sublatticeselective excitation Spatial resolution: imagingof domain structures
M. Fiebig, thesis (Universität Dortmund, 1996)
Simultaneous access to magnetic
and ferroelectric order / domains!
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Second harmonic generation
Non-vanishing χyyy:
Mn excitation for this
particular triangular structure2.2 2.4 2.6 2.8 3.0 3.2
0
20 40 60 8005Γ1→5Γ2S
H in
tens
ity
SH energy (eV)
χyyy
T
N
2.46 eV
Temperature (K)
YMnO3
295 KPol. σ+
1 mm
Antiferromagnetic 180°domains
Cr2O3
Antiferromagnetic domains,
contrast depends on
(circular) light polarization
M. Fiebig, PRL 1996, and further references years 2000 -05
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Direct strain on piezoelectric substrates
J.-P. Locquet et al., Nature 394, 453 (1998)
Find strain-sensitive materials
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Direct strain on piezoelectric substrates
In-situ strain:
•••• biaxial, uniform
•••• reversible
C. Thiele, K. D. at el., APL 87, 262502 (05) M. Bieg alsky, H. M. Christen, K. D. (2007)
piezo - crystal
conducting film
Vpiezo
IVI > 0V = 0PMN-PT(001)
72Pb(Mg1/3Nb2/3)O3 – 28PbTiO 3
rhombohedral, a = 4.02 Å
αααα = 89.90o
cf. LaAlO 3: αααα = 89.93o
92 94 96 98 100 102
103
104
105
106 V = 300 V V = 0
Inte
nsity
(a.
u.)
2 Theta (degree)
MgO 004
PMN-PT 004
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33a
Direct strain on piezoelectric substrates
C. Thiele, K. D. at el., APL 87, 262502 (05)
piezo - crystal
conducting film
Vpiezo
IVI > 0V = 0PMN-PT(001)
72Pb(Mg1/3Nb2/3)O3 – 28PbTiO 3
rhombohedral, a = 4.02 Å
αααα = 89.90o
cf. LaAlO 3: αααα = 89.93o
In-situ strain:
•••• biaxial, uniform
•••• reversible
175 200 225 250 275 3000
2
4
6
0
100
200
300
400
resi
stan
ce
(kΩΩ ΩΩ
)
temperature (K)
δεδεδεδεxx = - 0.12 %
gaug
e fa
ctor
δεδεδεδεxx = 0
La0.8Ca0.2MnO3/PMN-PT(001)
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Summary
Magnetoelectric multiferroics:
♦ joined magnetic and electric polarizibility in one material
♦ Most single-phase compounds for basic research (low T -apart from BiFeO3, low magnitude of ME effect)
♦ Composites for application (large ME effect at RT, mostlystrain-coupled)
Outlook:
♦ Understanding spiral magnetoelectricity
♦ Toroidal domains
♦ Little work on dynamic properties
♦ Stable magnetoelectric switching at 300 K
♦ Superlattices for “unconventional optics“
♦ Charge effects (e. g., field effect) at interfaces
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Literature
Recent reviews :
M. Fiebig: Revival of the magnetoelectric effect, J. Phys. D 38, R123 (2005)
W. Prellier, M. P. Singh, P. Murugavel: The single-phasemultiferroic oxides – from bulk to thin film, J. Phys.: Cond. Matter 17, R803 (2005)
N. A. Spaldin, M. Fiebig: The renaissance of magnetoelectric multiferroics, Science 309, 391 (2005)
W. Eerenstein, N. D. Mathur, J. Scott: Multiferroic and magnetoelectric materials, Nature 442, 759 (2006)
D. I. Khomskii: Multiferroics – different ways to combinemagnetism and ferroelectricity, J. Magn. Magn. Mater. 306, 1 (2006)
*Proceedings of the MEIPIC conferences
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