THz and infrared spectroscopy in magnetoelectric materials

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1 Sándor Bordács Budapest University of Technology, Budapest, Hungary THz and infrared spectroscopy in magnetoelectric materials Outline: Dynamical magnetoelectric coupling Multiferroic properties of melilites (Ba 2 CoGe 2 O 7 ) Electric dipole activity for spin-waves Unusual magneto-optical effects (optical magnetoelectric effect, magnetochiral effect) Optical magnetoelectric effect at room temperature (BiFeO 3 )

2 Magnetoelectrics magnetoelectric coupling D o me B c em c E H o N. A. Spaldin and M. Fiebig, Science (2005). FE flash memory piezoelectric actuators/transducers IR detectors 1 0 1

3 Magnetoelectrics magnetoelectric coupling D o me B c em c E H o N. A. Spaldin and M. Fiebig, Science (2005).

4 Symmetries in Magnetoelectrics Symmetry of a magnetic material: ρ(r), m(r) P inversion -P M T-reversal -M Material has: inversion symmetry P H P em H T-reversal symmetry P H or M E me 0 Both inversion and time-reversal symmetry must be broken in a material with linear ME effect! e.g.: chiral magnets, multiferroics

5 Symmetries in Magnetoelectrics Symmetry of a magnetic material: ρ(r), m(r) P inversion -P T-reversal HW: Cr 2 O 3 Material has: inversion symmetry P H P em H T-reversal symmetry P H or M E me 0 Both inversion and time-reversal symmetry must be broken in a material with linear ME effect! e.g.: chiral magnets, multiferroics Symmetry of the AF ground state in Cr 2 O 3 : D 3d (D 3 )=D 3 x(it)={c 3,C 2,iT} solution: χ xx = χ yy, χ zz

6 Magnetoelectric response in optics magnetoelectric coupling D o me B c em c E H o N. A. Spaldin and M. Fiebig, Science (2005). ij () ij () me ij 2 NV o o n no 0 M n n P 0 i 0 M n n P 0 i j 2 no 2 2i i j ij () Inversion (I) odd Time reversal (T) odd Dc magnetoelectric effect ij () Inversion (I) odd Time reversal (T) even Vanishes in the dc limit L.D. Barron, Molecular light scattering and optical activity (Cambridge, 2004).

7 Magnetoelectric response in optics Natural optical rotation me ij I T (M=0) em ji ij 0 ij High rotational symmetry δm ω =-χ E ω θ H ω δp ω =χ H ω E ω N i Directional dichroism/birefringence z y x Torroidal dichroism G.L.J.A. Rikken et al., Phys. Rev. Lett (2002). k P k M P M Symmetry: mm 2 N( k) xx zz I T (M 0) zx ij 0 δm ω =χ E ω H ω E ω δp ω =χ H ω E ω H ω δp ω δm ω Magnetochiral effect G.L.J.A. Rikken et al., Nature (1997). M k k M

8 Symmetries and optical phenomena i: r -r T: t -t i n + (+k) T n - (-k) n - (+k) n + (-k)

9 Faraday effect: Symmetries and optical phenomena i n + (+k) n - (+k) n - (-k) n + (-k) Natural optical activity: n + (+k) T n - (-k) n - (+k) n + (-k)

10 Magnetochiral effect derived from Maxwell eq.

11 Unidirectional absorption and dc ME effect I T ij 0 2 no 0 M o i n n Pj 0 ' ij 2 2 NV 2i M j P i o n Condition for unidirectional absorption: no Linear ME effect in a single domain compound: I. Kézsmárki, et al., Nat. Commun (2014). D. Szaller, et al., PRB (2014).

12 Crystal structure and magnetic order in Ba 2 CoGe 2 O 7 P42 1 m Ba Co m Ge O [001] [010] [010] [100] [100] [001] without magnetism tetragonal structure, apolar, achiral V. Hutanu et al., Phys. Rev. B (2011). Magnetic ion: Co 2+ (S=3/2) in tetrahedral environment Square lattice easy-plane antiferromagnet A. Zheludev et al., Phys. Rev. B (2003). V. Hutanu et al., Phys. Rev. B (2012).

13 Magnetic field induced ferroelectricity in Ba 2 CoGe 2 O 7 P H // [110] P = 0 H // [100] P H // [110] m [110], m [110] -, 2 [001] 2 [100], 2 [010], 2 [001] m [110] -, m [110], 2 [001] P C 0 P =0 P C 0 Spin dependent Co-O hybridization: Co T. Arima, J. Phys. Soc. Jpn (2007). H. Murakawa et al., Phys. Rev. Lett (2010).

14 Electromagnon excitation in Ba 2 CoGe 2 O 7 Inelastic neutron scattering: f=0.5 THz Optical magnon insensitive to E ω f=1 THz Electromagon excited by both E ω &H ω I. Kézsmárki, et al., Phys. Rev. Lett (2011). A. Zheludev et al., Phys. Rev. B (2003)

15 Electromagnon excitation in Ba 2 CoGe 2 O 7 k M P f=0.5 THz Optical magnon insensitive to E ω f=1 THz Electromagon excited by both E ω &H ω I. Kézsmárki, et al., Phys. Rev. Lett (2011).

16 Magnetic field induced chirality in Ba 2 CoGe 2 O 7 Magnetic field even polarization rotation indicates a chiral structure Magnetic switching of chirality + Magnetic order S. Bordács et al., Nature Physics 8, 734 (2012).

17 Magnetochiral effect α-niso 4 6H 2 O Δα/α~10-4 [N(CH 3 )(n-c 3 H 7 ) 2 ((R)-s-C 4 H 9 )][(Δ)-Mn(Λ)-Cr(ox) 3 ] ΔT/T~10-3 Ba 2 CoGe 2 O 7 Ca 2 CoSi 2 O 7 B (T) Frequency (THz) Frequency (THz) S. Bordács, et al., Nature Physics 8, 734 (2012). I. Kézsmárki, et al., Nat. Commun (2014).

18 Magnetoelectric sum rule D. Szaller, et al., PRB (2014).

19 High-magnetic field study of magnon modes Easy-plane antiferromagnet 2 magnon modes (Goldstone, optical branch)? K. Penc et al., Phys. Rev. Lett. 108, (2012).

20 Spin-waves in a non-centrosymmetric magnet S. Miyahara, N. Furukawa (exact diagonalization) J. Romhanyi, K. Penc (multi-boson spin-waves) J, J z exchange interaction Λ single-ion anisotropy non-centrosymmetric structure: P~S α S β Goldstone mode: Gaped AF resonance: Spin stretching modes: S. Miyahara, N. Furukawa, J. Phys. Soc. Jpn (2011). K. Penc et al., Phys. Rev. Lett. 108, (2012).

21 Directional dichroism in many other compounds D. Szaller et al., Phys. Rev. B 87, (2013).

22 A room-temperature multiferroic compound: BiFeO 3 Magnetically ordered P&M Ferroelectric, rhombohedral 640 K P 1100 K Cubic T [001] P 0 q 1 q 2 [100] [010] q 3

23 A room-temperature multiferroic compound: BiFeO 3 Magnetically ordered P&M Ferroelectric, rhombohedral 640 K P 1100 K Cubic T [001] P 0 q 1 q 2 [100] [010] q 3

24 Spin-wave spectrum of BiFeO 3 U. Nagel et al., Phys. Rev. Lett. 110, (2013).

25 Directional dichroism in BiFeO 3 H dc [1-10] H dc [110] U. Nagel et al., arxiv

26 Directional dichroism at room-temperature U. Nagel et al., arxiv

27 Theoretical model of DD in BiFeO 3 U. Nagel et al., arxiv

28 Conclusions Spin excitations in magnetoelectric multiferroics possess intriguing optical effects: Ba 2 CoGe 2 O 7, Ca 2 CoSi 2 O 7, Sr 2 CoSi 2 O 7, CaBaCo 4 O 7, (Eu,Y)MnO 3, (Tb,Gd)MnO 3, Cu(Fe,Ga)O 2, SmFe 3 (BO 3 ) 4 BiFeO 3 (at room temperature!) I. Kézsmárki et al., Phys. Rev. Lett. 106, (2011). S. Bordács et al., Nature Physics 8, 734 (2012). I. Kézsmárki, et al., Nat. Commun (2014). U. Nagel, et al., arxiv Theory: S. Miyahara, N. Furukawa, J. Phys. Soc. Jpn. 80, (2011). K. Penc et al., Phys. Rev. Lett. 108, (2012). Thank you for your attention!

29 BME, Fizika Tanszék MTA-BME Magneto-optikai Spektroszkópia Lendület Kutatócsoport Prof. Penc Karlo MTA Wigner Dr. Bordács Sándor Adjunktus Dr. Kézsmárki István Docens Orbán Ágnes Ph.D hallgató Butykai Ádám Ph.D hallgató Kocsis Vilmos Ph.D hallgató Szaller Dávid Ph.D hallgató Farkas Dániel Msc hallgató Molnár Petra Msc hallgató Molnár András Gépész, külsős