1. István Kézsmárki Budapest 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

2. Overview Symmetry aspects of multiferroic order and magnetoelectric effects ”Simple” multiferroic compounds (Ba 2 CoGe 2 O 7, Ca 2 CoSi 2 O 7,...) Coupled spin & polarization dynamics in multiferroics: electromagnons Peculiar optical properties of multiferroics Nonlinear applications in THz...

3. Multiferroics & magnetoelectric effect FerromagnetismFerroelectricity M j P -q +q -P +q -q r → -r -M -j t → -t Simultaneous breaking of time reversal and spatioal inversion Plenty of multiferroics even room-temperature ones! In hand: Ba 2 CoGe 2 O 7, Ca 2 CoSi 2 O 7, NdFe 3 (BO 3 ) 4, TbFe 3 (BO 3 ) 4, CoCr 2 O 4, FeCr 2 O 4, MnCr 2 O 4, NiV 3 O 8

4. FerromagnetismFerroelectricity M j P -q +q -P +q -q r → -r -M -j t → -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 between polarization and magnetization induced by the spin-orbit interaction.

5. d.c. ME effect: FerromagnetismFerroelectricity M j P -q +q -P +q -q r → -r -M -j t → -t ”Elementary excitations”: M i P j Free energy: Multiferroics & magnetoelectric effect Optical ME effect: constitutive relations

6. Overview Symmetry aspects of multiferroic order and magnetoelectric effects ”Simple” multiferroic compounds (Ba 2 CoGe 2 O 7, Ca 2 CoSi 2 O 7,...) Coupled spin & polarization dynamics in multiferroics: electromagnons Peculiar optical properties of multiferroics Nonlinear applications in THz...

7. [010] [001] [100] 2121 m [110] [001] [010] [100] 4 Ba Co Ge O P42 1 m  Tetragonal noncentrosymmetric crystal structure V. Hutanu et al., Phys. Rev. B 84, 212101 (2011) Magetic Co 2+ 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 Ba 2 CoGe 2 O 7

8.  P = 0 H || [100] P  H || [110] P H. Murakawa et al., Phys. Rev. Lett. 105, 137202 (2010) Spin-dependent hybridization: m [110], m’ [110], 2’ [001] - - 2 [100], 2’ [010], 2’ [001] T. Arima, J. Phys. Soc. Jpn. 76, 073702 (2007) Multiferroic state of Ba 2 CoGe 2 O 7 Co 2+ : S=3/2

9. Overview Symmetry aspects of multiferroic order and magnetoelectric effects ”Simple” multiferroic compounds (Ba 2 CoGe 2 O 7, Ca 2 CoSi 2 O 7,...) Coupled spin & polarization dynamics in multiferroics: electromagnons Peculiar optical properties of multiferroics Nonlinear applications in THz...

10. Spinwave excitations in Ba 2 CoGe 2 O 7 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)

11. J, J z exchange interaction Λ single-ion anisotropy S=3/2 spin: Magnetic susc. ~ Λ Electric susc. β ~ Inversion Ø Modes in zero field K. Penc,..., and I. Kézsmárki, Phys. Rev. Lett. 108, 257203 (2012) Spinwave excitations in Ba 2 CoGe 2 O 7

12. b- modeb+ 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] Spinwave excitations in Ba 2 CoGe 2 O 7

13. c- mode c+ mode c-, c+ stretching (breathing) modes! S = 3/2 : Spinwave excitations in Ba 2 CoGe 2 O 7

14. d- moded+ mode d-, d+ : in the Λ/J → 0 limit spin is frozen only polarization can move! S = 3/2 : Spinwave excitations in Ba 2 CoGe 2 O 7

15. Overview Symmetry aspects of multiferroic order and magnetoelectric effects ”Simple” multiferroic compounds (Ba 2 CoGe 2 O 7, Ca 2 CoSi 2 O 7,...) Coupled spin & polarization dynamics in multiferroics: electromagnons Peculiar optical properties of multiferroics Nonlinear applications in THz...

16. 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(±k y ) = 4π i : r → -r T : t → -t

17. I. Kézsmárki et al., Phys. Rev. Lett. 106, 057403 (2011) S. Bordács PhD Thesis Directional dichroism/birefringence in multiferroics T = P × M k -k TT Ba 2 CoGe 2 O 7

18. 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 -k MM M Ba 2 CoGe 2 O 7

19. 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(±k y ) = 4π

20. Thank you for your attention!