István KézsmárkiBudapest University of Technology
Giant Directional Optical Anisotropies in the THz regime
Spinwave Excitations in Multiferroics
Collegues
Dr. Sándor Bordács Dr. László Demkó Dávid Szaller, PhD student
Collaborations
• Dr. Karlo Penc Wigner Research Center for Physics • Dr. Titusz Fehér 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
FerromagnetismFerroelectricity
M
j
P-q
+q-P
+q
-q
r → -r
-M
-jt → -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
FerromagnetismFerroelectricity
M
j
P-q
+q-P
+q
-q
r → -r
-M
-jt → -t
Multiferroics & magnetoelectric effect
P. Curie, Journal de Physique 3, 393 (1894)
„Materials should exist, which can be polarized by a magnetic field and magnetized via an electric field.”
Crosscoupling betweenpolarization and magnetization
induced by the spin-orbit interaction.
d.c. ME effect:
FerromagnetismFerroelectricity
M
j
P-q
+q-P
+q
-q
r → -r
-M
-jt → -t
”Elementary excitations”:
Mi Mi Pj Pj
Free energy:
Multiferroics & magnetoelectric effect
Optical ME effect:constitutive relations
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...
[010]
[001][100]
21
m[110]
[001]
[010]
[100]
4
BaCoGeO
P421m
• Tetragonal noncentrosymmetric crystal structure 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)
i×4 =
Multiferroic state of Ba2CoGe2O7
P = 0
H || [100]
P
H || [110]
P
H || [110]
H. Murakawa et al., Phys. Rev. Lett. 105, 137202 (2010)
Spin-dependent hybridization:
m[110], m’[110], 2’[001]- m[110], m’[110], 2’[001]-2[100], 2’[010], 2’[001]
T. Arima, J. Phys. Soc. Jpn. 76, 073702 (2007)
Multiferroic state of Ba2CoGe2O7
Co2+:S=3/2 •
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)
J, Jz exchange interaction Λ single-ion anisotropy
S=3/2 spin:
Magnetic susc.
~
Λ
Electric susc.β~
Inversion Ø
Modesin zero field
K. Penc, ..., and I. Kézsmárki, Phys. Rev. Lett. 108, 257203 (2012)
Spinwave excitations in Ba2CoGe2O7
b- mode b+ mode
• b- mode is the Goldstone mode (ω=0) ↔ dc magnetoelectric effect
• b+ would be the other Goldstone mode in the lack of magnetic anisotropy
[001][001]
Spinwave excitations in Ba2CoGe2O7
c- mode c+ mode
c-, c+ stretching (breathing) modes!
S = 3/2 :
Spinwave excitations in Ba2CoGe2O7
d- mode d+ mode
d-, d+ : in the Λ/J → 0 limit spin is frozen only polarization can move!
S = 3/2 :
Spinwave excitations in Ba2CoGe2O7
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...
n+(+k)
n+(-k)n-(+k)
n-(-k)T
i
multiferroics
”usual” matter
λ
Magnetic excitations:spinwaves (magnons)
Directional dichroism/birefringence in multiferroics
Charge excitations:phonons, electrons
++
Directional anisotropy
•
• Weak in ”usual matter”, ∆N/N ~10-4-10-6
• Can be strong in multiferroics?
n(±ky ) = 4π i : r → -r
T : t → -t
I. Kézsmárki et al., Phys. Rev. Lett. 106, 057403 (2011)
S. Bordács PhD Thesis
Directional dichroism/birefringence in multiferroics
T = P × M
k -kT T
Ba2CoGe2O7
chirality → natural optical activity
S. Bordács I. Kézsmárki et al., Nature Physics 8, 734 (2012)
S. Bordács PhD Thesis, D. Szaller MSc Thesis
Directional dichroism/birefringence in multiferroics
k -kM M
M
Ba2CoGe2O7
Other peculiar optical properties of multiferroics
• Directional anisotropies
• Negative index of refraction:
• Large natural optical activity (circular birefringence/dichroism)
• Magnetic and/or electric control over optical properties
• Non-linearity of electromagnon excitations
n(±ky ) = 4π
Thank you for your attention!