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!