Unidirectional light propagation in multiferroics and multi-antiferroics

Transcription

1 Unidirectional light propagation in multiferroics and multi-antiferroics István Kézsmárki Department of Physics, Budapest University of Technology and Economics Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg TRR 80 Colleagues: Prof. S. Bordács, Dr. D. Szaller, Dr. V. Kocsis, D. Farkas, J. Vit Collaborators: Prof. Y. Tokura, RIKEN Center for Emergent Matter Science, Japan Prof. S-W. Cheong, Rutgers Universty, USA Prof. K. Ohgushi, Tohoku University, Japan Dr. T. Rõõm, Dr. U. Nagel, NICPB, Estonia Prof. J. Hemberger, Prof. M. Grüninger, University of Cologne, Germany Dr. K. Penc, Dr. J. Romhányi, Wigner Res. Inst. for Physics, Hungary Dr. R. Fishman, Oak Ridge National Lab, USA

2 Quadrochroism

3 Outline Static & optical magnetoelectric effects in multiferroics D B ˆ ˆ me em ˆ E ˆ H Quadrochroism & one-way trasparency via the optical magnetoelectric effect +k -k Target compounds: Ba 2 CoGe 2 O 7, LiCoPO 4

4 Multiferroics & magnetoelectric effect Ferroelectricity P +q -q -P -q +q Ferromagnetism M j -M -j r -r t -t Holy Grail of the field: Magnetoelectric memory devices 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)

5 Multiferroics & magnetoelectric effect ε χ me, χ em Generalized constituve relations D B ˆ ˆ me ˆ em ˆ E H Spaldin and Fiebig, Science (2005) me ij μ 2 no i j ( ) 2 2 NV n ij () ij () 0 M n n P 0 i 0 M n n P 0 no 2i i j ij () inversion (I) odd time reversal (T) odd static magnetoelectric effect directional anisotropy ij () inversion (I) odd time reversal (T) even vanishes in the static limit natural optical activity L.D. Barron, Molecular light scattering and optical activity (Cambridge, 2004)

6 Outline Static & optical magnetoelectric effects in multiferroics D B ˆ ˆ me em ˆ E ˆ H Quadrochroism & one-way trasparency via the optical magnetoelectric effect +k -k Target compounds: Ba 2 CoGe 2 O 7, LiCoPO 4

7 Optical magnetoelectric effect: Four-coloured optics P ω E ω +k M ω H ω Pω E ω H ω M ω -k different refractive indices for ±k propagation and two polarizations, termed as quadrochroism directional (±k) optical anisotropy is generally weak, N/N~ Rikken, Nature (1997) BUT can be strong in multiferroics!

8 Optical magnetoelectric effect: Four-coloured optics P ω E ω +k M ω H ω Pω E ω H ω M ω -k different refractive indices for ±k propagation and two polarizations, termed as quadrochroism directional (±k) optical anisotropy is generally weak, N/N~ Rikken, Nature (1997) BUT can be strong in multiferroics!

9 Optical magnetoelectric effect: One-way transparency Condition for one-way transparency: M j P i 1 [CGS] Kézsmárki, NatCommun (2014) BiFeO 3 Ba 2 CoGe 2 O 7 LiCoPO 4 Sr 2 CoSi 2 O 7 Ca 2 CoSi 2 O 7 GaV 4 S 8 Gd 0.5 Tb 0.5 MnO 3 Ni 3 TeO 6 CuB 2 O 4 CuFe 1 x Ga x O 2 Eu 0.5 Y 0.5 MnO 3 CaBaCo 4 O 7 SmFe 3 (BO 3 ) 4 Ba 2 CoGe 2 O 7 Kézsmárki, PRL (2011) Bordács, NatPhys (2012) Eu 0.5 Y 0.5 MnO 3 Takahashi, NatPhys (2012) Gd 0.5 Tb 0.5 MnO 3 Takahashi, PRL (2013) Sr 2 CoSi 2 O 7 & Ca 2 CoSi 2 O 7 Szaller, PRB (2014) Kézsmárki, NatCommun (2014) CuFe 1 x Ga x O 2 Kibayashi, NatCommun (2014) SmFe 3 (BO 3 ) 4 Pimenov, PRB (2015) CuB 2 O 4 Arima, PRL (2015) CaBaCo 4 O 7 Bordács, PRB (2015) BiFeO 3 Kézsmárki, PRL (2015) SmFe 3 (BO 3 ) 4 Kuzmenko, PRL (2018)

10 Optical magnetoelectric effect: One-way transparency matter light T = P M k = E H ferrotoroidicity induced directional anisotropy k T -k T Kézsmárki, PRL (2011)

11 Optical magnetoelectric effect: One-way transparency matter light M k charility induced directional anisotropy k M -k M Bordács, NatPhys (2012)

12 Outline Static & optical magnetoelectric effects in multiferroics D B ˆ ˆ me em ˆ E ˆ H Quadrochroism & one-way trasparency via the optical magnetoelectric effect +k -k Target compounds: Ba 2 CoGe 2 O 7, LiCoPO 4

13 Multiferroic Ba 2 CoGe 2 O 7 P42 1 m (D 2d ) Ba Co Ge O [001] i 4 = 4 [010] m [110] [010] [100] [001] 2 1 [100] Tetragonal noncentrosymmetric crystal structure Hutanu, PRB (2011) Magetic Co 2+ ions with S=3/2 in tetrahedral oxygen cages Easy-plane Néel antiferromagnet Hutanu, PRB (2012)

14 Multiferroic Ba 2 CoGe 2 O 7 H [110] H [010] H [110] H [100] m [110], m [110] -, 2 [001] - 2 [100], 2 [010], 2 [001] P 2 [100], 2 [010], 2 [001] m [110], m [110], 2 [001] P=0, left-handed P=0, right-handed P Spin-dependent hybridization: Co Arima, JPSJ (2007) Murakawa, PRL (2010)

15 Multiferroic Ba 2 CoGe 2 O 7 mm 2 T = P M k T k -T T-type DA Kézsmárki, PRL (2011)

16 Multiferroic Ba 2 CoGe 2 O M k M k -M MC-type DA Bordács, NatPhys (2012)

17 Multiferroic Ba 2 CoGe 2 O 7 Ca 2 CoSi 2 O 7 Ba 2 CoGe 2 O 7 Four different values of the refractive index for a given axis of propagation: forward and backward (±k) propagation and two orthogonal polarizations, Magnons with nearly optimal magnetoelectric ratio,, Connection with dc ME effect: ij Kézsmárki, NatCommun (2014)

18 Multiferroic Ba 2 CoGe 2 O 7 S=3/2 spin: J, J z exchange interaction Λ single-ion anisotropy [001] b- mode 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 Penc, PRL (2012)

19 Outline Static & optical magnetoelectric effects in multiferroics D B ˆ ˆ me em ˆ E ˆ H Quadrochroism & one-way trasparency via the optical magnetoelectric effect +k -k Target compounds: Ba 2 CoGe 2 O 7, LiCoPO 4

20 Li CoO 6 Multi-antiferroic LiCoPO 4 orthorhombic Pmna (point group: mmm) distorted chessboard layers of CoO 6 octahedra highly distorted CoO 6 octahedra Þ z P antiferroelectricity (along x) x y P M magnetic order develops below T N =21K antiferromagnetism (along y) orthorhombic Pmna (point group: mmm ) y me antiferroelectricity x antiferromagnetism y Þ ± xy x

21 Multi-antiferroic LiCoPO 4 me xy 0 Magnetoelectric poling: E 0 y H 0 x E 0 =2 kv/cm μ 0 H 0 =1 T me xy 0 Sign of me xy depends on the sign of the poling E 0 H 0 field

22 Multi-antiferroic LiCoPO 4 E y w H x w Sign of me () xy depends on the sign of the poling E 0 H 0 field Remnant directional anisotropy in an antiferromagnet Contrast between AFM domains via simple absorption Kocsis, arxiv:

23 Multi-antiferroic LiCoPO 4 where where Kocsis, arxiv:

24 Thank you for your attention! PhD and postdoc positions open in Department of Experimental Physics V, Center for Electronic Correlations and Magnetism of University of Augsburg