Transcript presentation

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!