Giant Directional Optical Anisotropies in the THz regime
Spinwave Excitations in Multiferroics
István Kézsmárki
Budapest University of Technology
Collegues
Dr. Sándor Bordács
Dr. László Demkó
Dávid Szaller, PhD student
Collaborations
• Dr. Karlo Penc
• Dr. Titusz Fehér
Wigner Research Center for Physics
Budapest University of Technology
• Prof. Yoshinori Tokura University of Tokyo
• Dr. Shin Miyahara
University of Tokyo
• Prof. Toomas Rõõm
Institute for Biophysics, Tallin
• Dr. Hans Engelkamp
High Field Laboratory, Nijmegen
Overview
• Symmetry aspects of multiferroic order and magnetoelectric effects
• ”Simple” multiferroic compounds (Ba2CoGe2O7, Ca2CoSi2O7, ...)
• Coupled spin & polarization dynamics in multiferroics: electromagnons
• Peculiar optical properties of multiferroics
• Nonlinear applications in THz...
Multiferroics & magnetoelectric effect
Ferroelectricity
Ferromagnetism
+q
-q
M
-M
-P
P
+q
-q
r → -r
j
-j
t → -t
• Simultaneous breaking of time reversal and spatioal inversion
• Plenty of multiferroics even room-temperature ones!
• In hand: Ba2CoGe2O7 , Ca2CoSi2O7 , NdFe3(BO3)4 , TbFe3(BO3)4 ,
CoCr2O4 , FeCr2O4 , MnCr2O4, NiV3O8
Multiferroics & magnetoelectric effect
Ferroelectricity
Ferromagnetism
+q
-q
M
-M
-P
P
+q
-q
j
r → -r
-j
t → -t
Crosscoupling between
polarization and magnetization
induced by the spin-orbit interaction.
„Materials should exist, which can be polarized by a magnetic field and magnetized via an electric field.”
P. Curie, Journal de Physique 3, 393 (1894)
Multiferroics & magnetoelectric effect
Ferroelectricity
Ferromagnetism
+q
M
-q
-M
-P
P
+q
-q
j
r → -r
-j
t → -t
Free energy:
d.c. ME ME
effect:
Optical
effect:
constitutive relations
”Elementary excitations”:
Mi
Pj
Mi
Pj
Overview
• Symmetry aspects of multiferroic order and magnetoelectric effects
• ”Simple” multiferroic compounds (Ba2CoGe2O7, Ca2CoSi2O7, ...)
• Coupled spin & polarization dynamics in multiferroics: electromagnons
• Peculiar optical properties of multiferroics
• Nonlinear applications in THz...
Multiferroic state of Ba2CoGe2O7
P421m
i×4 = 4
Ba
Co
Ge
O
m[110]
[001]
[010]
[010]
21

[001]
[100]
• Tetragonal noncentrosymmetric crystal structure
[100]
V. Hutanu et al., Phys. Rev. B 84, 212101 (2011)
• Magetic Co2+ ions with S=3/2 in tetrahedral oxygen cages
• Easy-plane Néel antiferromagnet
V. Hutanu ... and I. Kézsmárki, Phys. Rev. B 86, 104401 (2012)
Multiferroic state of Ba2CoGe2O7
H || [110]
H || [100]
H || [110]
Co2+:
S=3/2 •
- , 2’[001]
m[110], m’[110]
P
2[100], 2’[010], 2’[001]
P=0
- , m’[110], 2’[001]
m[110]
P
Spin-dependent hybridization:
T. Arima, J. Phys. Soc. Jpn. 76, 073702 (2007)
H. Murakawa et al., Phys. Rev. Lett. 105, 137202 (2010)
Overview
• Symmetry aspects of multiferroic order and magnetoelectric effects
• ”Simple” multiferroic compounds (Ba2CoGe2O7, Ca2CoSi2O7, ...)
• Coupled spin & polarization dynamics in multiferroics: electromagnons
• Peculiar optical properties of multiferroics
• Nonlinear applications in THz...
Spinwave excitations in Ba2CoGe2O7
• Rule of thumb: 1 mode/sublattice, i.e. 2 modes for a Néel state
• Here: 6 modes excited by light absorption
• What are these ”extra modes”?
K. Penc, ..., and I. Kézsmárki, Phys. Rev. Lett. 108, 257203 (2012)
Spinwave excitations in Ba2CoGe2O7
Modes
in zero field
Magnetic susc.
~
Λ
Electric susc.
~
β
Inversion Ø
S=3/2 spin:
J, Jz exchange interaction
K. Penc, ..., and I. Kézsmárki, Phys. Rev. Lett. 108, 257203 (2012)
Λ single-ion anisotropy
Spinwave excitations in Ba2CoGe2O7
b- mode
[001]
b+ mode
[001]
• b- mode is the Goldstone mode (ω=0)
↔
dc magnetoelectric effect
• b+ would be the other Goldstone mode in the lack of magnetic anisotropy
Spinwave excitations in Ba2CoGe2O7
c+ mode
c- mode
S = 3/2 :
c-, c+ stretching (breathing) modes!
Spinwave excitations in Ba2CoGe2O7
d- mode
d+ mode
S = 3/2 :
d-, d+ : in the Λ/J → 0 limit spin is frozen only polarization can move!
Overview
• Symmetry aspects of multiferroic order and magnetoelectric effects
• ”Simple” multiferroic compounds (Ba2CoGe2O7, Ca2CoSi2O7, ...)
• Coupled spin & polarization dynamics in multiferroics: electromagnons
• Peculiar optical properties of multiferroics
• Nonlinear applications in THz...
Directional dichroism/birefringence in multiferroics
Magnetic excitations:
spinwaves (magnons)
Charge excitations:
phonons, electrons
”usual” matter
λ
multiferroics
i
i : r → -r
n+(+k)
T
T : t → -t
n-(+k)
+
+
Directional anisotropy
n-(-k)
• n(±ky ) =
4π
• Weak in ”usual matter”, ∆N/N ~10-4-10-6
n+(-k)
• Can be strong in multiferroics?
Directional dichroism/birefringence in multiferroics
Ba2CoGe2O7
T=P×M
k T
-k T
I. Kézsmárki et al., Phys. Rev. Lett. 106, 057403 (2011)
S. Bordács PhD Thesis
Directional dichroism/birefringence in multiferroics
Ba2CoGe2O7
M
k M
-k M
S. Bordács I. Kézsmárki et al., Nature Physics 8, 734 (2012)
S. Bordács PhD Thesis, D. Szaller MSc Thesis
chirality → natural optical activity
Other peculiar optical properties of multiferroics
• Directional anisotropies
• Negative index of refraction: n(±ky ) =
4π
• Large natural optical activity (circular birefringence/dichroism)
• Magnetic and/or electric control over optical properties
• Non-linearity of electromagnon excitations
Thank you for your attention!