Combining ferroelectricity and magnetism: the Combining ferroelectricity and magnetism: the low energy electrodynamicslow energy electrodynamics
Diyar TalbayevDiyar TalbayevDiyar TalbayevDiyar TalbayevCenter for Integrated NanotechnologiesCenter for Integrated Nanotechnologies
Los Alamos National LaboratoryLos Alamos National Laboratory
Toni TaylorToni TaylorA.V. BalatskyA.V. BalatskyDarryl SmithDarryl SmithStuart TrugmanStuart TrugmanJohn O’HaraJohn O’Hara
Los Alamos National LaboratoryLos Alamos National Laboratory Osaka University, JapanOsaka University, Japan
Tsuyoshi KimuraTsuyoshi Kimura
AcknowledgementsAcknowledgements
Rick AverittRick Averitt
Boston UniversityBoston University
Inha University, KoreaInha University, Korea
Namjung HurNamjung Hur
Nanyang Technological Nanyang Technological University, SingaporeUniversity, Singapore
Andrew LaforgeAndrew LaforgeDmitri BasovDmitri Basov
UCSDUCSD
Funding provided by the Los Alamos National Laboratory Directed Research and Development Program
Rick AverittRick Averitt University, SingaporeUniversity, Singapore
Elbert ChiaElbert ChiaRutgers UniversityRutgers University
Seongsu LeeSeongsu LeeS.S.--W. CheongW. Cheong
Ferroic propertiesFerroic properties
FERROMAGNETISMFERROELECTRICITY
High-power current-driven write operation
Low-power voltage-driven write
But…
Issues of fatigue need to be overcome
… enter MULTIFERROICITY!!!
Magnetoelectric multiferroicsMagnetoelectric multiferroics
MULTIFERROICS – materials with coexisting
magnetism and ferroelectricity.
Magnetic order Electric polar ization
magnetoelectric interaction
Possible applications for magnetoelectric materials
Magnetoelectric memoryMagnetically switched electro-optic deviceElectric-field-modulated visible Faraday rotatorMagnetically (electrically)-modulated piezoelectric (piezomagnetic) devices, etc.
V. E. Wood, A. F. Austin, Int. J. Magnetism 5, 303-315 (1974)
Magnetoelectric effectMagnetoelectric effect
BiFeO 3 : ferroelectric antiferromagnet
Bi
Turn the magnetic moments!
Apply electric fieldE
Fe ions:
OFe
Y.-H. Chu et al.,
Nat. Materials 7 478 (2008)
moments!
Top view
easy axis for magnetization
Dynamic magnetoelectric effectDynamic magnetoelectric effect
BiFeO 3
Bi
OFe
Top view
PM
Rock the polarization
excite phonons
Magnetic
Y.-H. Chu et al.,
Nat. Materials 7 478 (2008)
Magnetic moments respond!
DYNAMIC MAGNETOELECTRIC EFFECTMixing of magnetic and lattice vibrations –
Magnetic and lattice motion interacts with lightMagnetic and lattice motion interacts with light
Electromagnetic wave incident on the crystal
??
Phonons ~ oscillating electric dipole
���� Coupling to the electric field of the light wave
Phonons in BiFeO 3
Lobo et al.,
Phys. Rev. B 76
172105 (2007)
33 cm -1 ~ 1 THz ~ 4 meV ���� Resonance in the dielectric function, a.k.a. optical conductivity:
ε(ω)ε(ω)ε(ω)ε(ω) σ(ω)σ(ω)σ(ω)σ(ω)
Magnetic and lattice motion interacts with lightMagnetic and lattice motion interacts with light
Electromagnetic wave incident on the crystal
Magnetic excitations in BiFeO 3
0.8
33 cm -1 ~ 1 THz ~ 4 meV
Magnons ~ oscillating magnetic dipole
���� Coupling to the magnetic field of the light wave
10 15 20 25 30 350.0
0.2
0.4
0.6
Tra
nsm
issi
on
Frequency (cm -1)
T=30 K
33 cm -1 ~ 1 THz ~ 4 meV
D. Talbayev et al.,
unpublished
light wave
���� Resonance in the magnetic susceptibility:
χ(ω)χ(ω)χ(ω)χ(ω) µ(ω)µ(ω)µ(ω)µ(ω)
Mix it up: electromagnonsMix it up: electromagnons
TbMn2O5 : antiferromagnet and ferroelectric
Sushkov et al, Phys. Rev. Lett. 98 27202 (2007)
electric dipole active magnon : electro magnon
Similar observations : multiferroics TbMnO 3, Eu0.75Y0.25MnO3
Pimenov et al., Nature Phys. 2 97 (2006)
Valdes Aguilar et al., Phys. Rev. B 76 060404R (2007)
Pimenov et al., Phys. Rev. B 77 014438 (2008)
Electromagnons determine magnetoelectric functionalityElectromagnons determine magnetoelectric functionality
Sushkov et al, Phys. Rev. Lett. 98 27202 (2007)
TbMn2O5 : antiferromagnet and ferroelectric
antiferromagnet, ferroelectric
paramagnet
onset of electromagnon response
i)i) Properties of electromagnons Properties of electromagnons depend on the microscopic ME depend on the microscopic ME
ferroelectric
∫∞
+=0
21
1 810 ωω
ωσε d)(
)(Electromagnon contributes to static dielectric constant:
(i)
Electromagnon properties depend on the microscopic magnetoelectric coupling
(ii)
Dynamic magnetoelectric effect in hexagonal BaDynamic magnetoelectric effect in hexagonal Ba0.60.6SrSr1.41.4ZnZn22FeFe1212OO2222
Layered magnetic structure Several magnetic phases
N. Momozawa and Y. Yamaguchi,
J. Phys. Soc. Jpn. 62 12992 (1993)T. Kimura, G. Lawes, and A.P. Ramirez, PRL 94 137201 (2005)
Dynamic magnetoelectric effect in hexagonal BaDynamic magnetoelectric effect in hexagonal Ba0.60.6SrSr1.41.4ZnZn22FeFe1212OO2222
Control of electric polarization by magnetic field:
T. Kimura, G. Lawes, and A.P. Ramirez, PRL 94 137201 (2005)
Electrons, phonons, magnons
visible optical pulse excitation, a.k.a. pump
TimeTime--domain studies of elementary excitationsdomain studies of elementary excitations
Pump and probe wavelength: 800 nm (~1.5 eV)
optical pulse interrogation (probe) of material’s response
Dynamics of photo-excited quasiparticles often expo ses properties not detected by conventional probes – transport, magneti zation, or optical
conductivity
TimeTime--domain detection of magnetic motiondomain detection of magnetic motionMagneto-optical Kerr effect (MOKE) – rotation of pol arization of light
upon reflection by a magnetized medium
reflected probe beam
MO
KE
inte
nsity
ferromagnet
La2/3Ca1/3MnO3
M
D. Talbayev et al, Phys. Rev. B 73 14417 (2006); Appl. Phys. Lett. 86 182501 (2005)
0 500 1000
MO
KE
inte
nsity
Time (ps)arrival of pump
effHMM ×−= γ&demaganisotropyeff HHHH ++= 0
20
40
60
80
1.5 T
1.0 T
0.5 T
0.1 T
R/R
(x1
0-6)
0 Tpump
probe
c axis
TimeTime--resolved reflectance : coherent responseresolved reflectance : coherent response
BaBa0.60.6SrSr 1.41.4ZnZn22FeFe1212OO2222 : photoinduced change in : photoinduced change in reflectancereflectance
Coherent excitation of Coherent excitation of magnetic or lattice motionmagnetic or lattice motion
0 50 100 150 200 250-20
0
20
2.5 T
2.0 T∆R
/R (
x10
Time (ps)
T=10 K400-nm pump and probe
B
D. Talbayev et al., Phys. Rev. Lett. 101 097603 (2008)
magnetic or lattice motionmagnetic or lattice motion
20
30
40
50
60
field normal to the c axis field along the c axis
10
20
30
40
50
Osc
illat
ion
freq
uenc
y (G
Hz)
ocsillation frequency ω
Magnetic or lattice?Magnetic or lattice?
0.0 0.5 1.0 1.5 2.0
10
Magnetic field (T)
T=10 K0
10 Osc
illat
ion
freq
uenc
y (G
Hz)
N. Momozawa and Y. Yamaguchi, J. Phys. Soc. Jpn. 62 12992 (1993)
D. Talbayev et al., Phys. Rev. Lett. 101 097603 (2008)
Strong evidence in support of magnetic origin of th e excitation – electron spin resonance, i.e., k=0 magnon
λ/nfPHONONS ∝
Oscillation frequency:
More evidence against the latticeMore evidence against the lattice
∆R/R
(ar
b. u
nits
)
T=15 KH=0.2 T
400 nm
800 nm
LuMnO3
D. Lim et al., Appl. Phys. Lett. 83 4800 (2003)
0 50 100 150 200
(∆R/R(800)-decay) x 10
∆
Time (ps)
D. Talbayev et al., Phys. Rev. Lett. 101 097603 (2008)
Identical oscillation frequency at different probe wavelengths
Calculation of magnon frequenciesCalculation of magnon frequencies
N. Momozawa and Y. Yamaguchi,J. Phys. Soc. Jpn. 62 12992 (1993)
B
∑ ++⋅⋅⋅= )();;( 222121 SizLizSSLLLjSiex MMDMMMMMMHH
D – the only free parameter
T. Kimura, G. Lawes, and A.P. Ramirez, PRL 94 137201 (2005)
Calculation of magnon frequenciesCalculation of magnon frequencies
D. Talbayev et al., Phys. Rev. Lett. 101 097603 (2008)
40
60
80
1.5 T
0.5 T
R
/R (
x10-6
)
0 T
Dynamic magnetoelectric effectDynamic magnetoelectric effect
BaBa0.60.6SrSr 1.41.4ZnZn22FeFe1212OO2222
2
1
1
+−=
n
nR
ε=n
Modulation of reflectance
Modulation of n and εεεε
0 50 100 150 200 2500
201.5 T∆R
/R (
x10
Time (ps)
T=10 K400-nm pump and probe
Modulation of n and εεεεby magnon motion: dynamic magnetoelectric effect
Optical detection of magnetic state using reflectio n –implications for data storage and spintronics.
Tc=875 K
PFE
Magnetoelectricity in hexagonal HoMnOMagnetoelectricity in hexagonal HoMnO33
Ferroelectric
z=0z=c/2
40 K < T < 72 KTR TN
Mn ions:
Triangular antiferromagnet, TN=72 K
Litvinchuk et al., JPCM 16 809 (2004)
z=0
z=c/2
Vajk et al., PRL 94 87601 (2005)
5 K < T < 40 K
T < 5 K
THo
TRTHo
Two sites: Ho(1) C3v
Ho(2) C3 – ordered for T<THo=5 K
z
Magnetoelectricity in hexagonal HoMnOMagnetoelectricity in hexagonal HoMnO33
Magnetism of Ho 3+
(S=2, L=6, J=8) ions:
T<TN E=0
Mag
netiz
atio
n
Applied electric field induces magnetization of Ho ions:
Hint=ΣSHoΑSMn
Lottermoser et al., Nature 430 541 (2004)
Mag
netiz
atio
n
(110)
c (001)
||h||H
static field
FarFar--infrared study of magnetic excitationsinfrared study of magnetic excitations
HoMnO3
⊥h⊥H
lightwave
3 6 9 12 15
-0.5
0.0
0.5
1.0
E fi
eld
ampl
itude
Time (ps)
SAMPLE REFERENCE
1 THz � 300 µm � 0.004 eV �33cm-1 � 47 K
FarFar--infrared study of magnetic excitationsinfrared study of magnetic excitations
gating pulse
excitation pulse
Time (ps)
0.0 0.5 1.0 1.5 2.0 2.5 3.00
5
10
15
20
25
E fi
eld
ampl
itude
Frequency (THz)
SAMPLE REFERENCE
gating pulse
• Broadband• Measurement of electric field E
(1) Photoconductive antennas
(2) Electro-optic crystals
||h
⊥h
Magnetic excitations in HoMnOMagnetic excitations in HoMnO33
0.10
0.15
0.20
0.25
0.30
Tra
nsm
issi
on h || c
T=10 K
20 30 40 50 60 70 80 90 1000.00
0.05
Frequency (cm-1)
h | c
���� Crystal field excitations of Ho ions
���� Antiferromagnetic resonance (AFMR) of Mn ions
Neutron scattering: Vajk et al., Phys. Rev. Lett. 94 87601 (2005)
Two Ho 3+ (S=2, L=6, J=8) cites with C3 and C3v point symmetries
Crystal field splitting of HoCrystal field splitting of Ho3+3+ ground stateground state
J=8
06 ,s
428 m,,±±
a6
06 ,s
7±
8±m = -8..+8
Abragam and Bleaney, Electron paramagnetic resonance of transition ions, Clarendon press, 1970
333 −+=s
517 m,,±±
333 −−=a
06 ,s
1±
0
The electrostatic environment of Ho ions determines the crystal field splitting
Magnetic resonance of Mn ionsMagnetic resonance of Mn ions
M3
M2
M1
z
∑2
λ
B
B
Classical treatment
ji MMF ⋅Σ= λ zi
zi MBMK Σ−+ ∑
2)(
Interaction parameters measured by neutron scatteri ng in zero field by Vajk et al., Phys. Rev. Lett. 94 8760 1 (2005)
Magnetic resonance of Mn ionsMagnetic resonance of Mn ions
40
50
60
70
80
90
40
50
60
70
80
90
40
50
60
70
80
90
T=10 K, B || c
Fre
quen
cy (
cm-1)
T=10 K, B | c
20
30
40
0 1 2 3 4 5 6 7 820
30
40
0 1 2 3 4 5 6 7 820
30
40
Magnetic field (T)
Fre
quen
cy (
cm
Magnetic field (T)
D. Talbayev et al., Phys. Rev. Lett. 101 247601 (2008)
Magnetic resonance of Mn ionsMagnetic resonance of Mn ions
0MH ex λ=0KMH d =
D. Talbayev et al., Phys. Rev. Lett. 101 247601 (2008)
0KMH d =Palme et al., Solid State Comm. 76 873 (1990)
Why the discrepancy?
Exchange coupling between Ho and Mn ionsExchange coupling between Ho and Mn ions
Penney et al., J. Appl. Phys. 40 1234 (1969)
YMnO3: similar material – hexagonal lattice, ferroelectri c, triangular antiferromagnet … but Y ions are not magn etic
…and the calculation works!!
Sato et al., Phys. Rev. B 68 014432 (2003)
Discrepancy in HoMnO 3 is due to Ho-Mn (HM) exchange interaction:
MnMnHoHM Bχ== ~
Effective magnetic field acting on Mn ions!
Mnz
Bzz
Mnjz
Hoizij
HMex S
g
BJSSJH
µχ== ~
1−=HMλ∑∑ == MnizHM
Mniz
Bz
zHM MBMB
gg
JF λ
µχ
2
6
D. Talbayev et al., Phys. Rev. Lett. 101 247601 (2008)
Magnetoelectricity in HoMnOMagnetoelectricity in HoMnO33
Ferromagnetic exchange between Ho and Mn:
Mnjz
Hoiz
zij
HMex SSJH
~= 0~ <z
ijJ
Same interaction responsible for the magnetoelectri city:T<TN E
Mag
netiz
atio
n
Lottermoser et al., Nature 430 541 (2004)
Mag
netiz
atio
nMagnons allow the determination of microscopic
details of magnetoelectric interaction.
In HoMnO 3, it is the Ho-Mn magnetic exchange coupling.
SummarySummary
Magnetic and lattice excitations (magnons and phono ns) play a fundamental role in the quest for understand ing and exploiting magnetoelectric materials
(i)
Detection of magnetic motion and magnetic state via the modulation of reflectance
(ii)
0.5 T
∆R/R
(x1
0-6)
BaBa0.60.6SrSr 1.41.4ZnZn22FeFe1212OO22
22
0 50 100 150 200Time (ps)
T=10 K400-nm pump and probe
Properties of magnons and phonons help reveal the microscopic details of magnetoelectric interaction
(iii)
Mnjz
Hoiz
zij
HMex SSJH
~=
HoMnO3