1. Nonlinear Optical Spectroscopy in Multiferroics Speaker: Zuanming Jin

2. Outline Multiferroics RMnO 3 Linear Optical Property X (1) Nonlinear Optical Property X (2) --SHG Time-resolved nonlinear Optical Spectroscopy (TR- NLOS) X (3) BiFeO 3 Linear Optical Property X (1) Nonlinear Optical Property X (2) --SHG Third Nonlinear response Our results

3. Materials with strongly coupled magnetic and electronic degrees of freedom provide challenges for both fundamental many-body physics and advanced functional materials. Recently, multiferroics, where both electric and magnetic orders coexist in the same phase, have attracted great interest. However, such systems are rare in nature.

4. Multiferroic materials with both polar and magnetic order parameters usually show a relatively low-symmetry crystal structure due to the absence of both time and space inversion symmetries; hence, a strong interaction between the low-lying magnetic and lattice excitations can occur, leading to rich new physics phenomena.

5. These material systems have two kinds of crystal structure. Depending on the rare-earth ionic radius, they form either an orthorhombic phase R =La–Dy or a hexagonal phase R=Ho– Lu (or Sc, Y). RMnO 3

6. These material systems have two kinds of crystal structure. Depending on the rare-earth ionic radius, they form either an orthorhombic phase R =La–Dy or a hexagonal phase R=Ho– Lu (or Sc, Y).

7. Rare-earth manganites (R =Sc, Y, Ho, Er, Tm, Yb, Lu, In) which crystallize in a hexagonal structure. Along with the crystal structure, the local environment of the Mn 3+ ions in the orthorhombic and hexagonal manganites is also different. Therefore the electronic and magnetic properties in these two classes of materials are vastly different. Crystallographic unit cell of hexagonal RMnO3, space group P63cm RMnO 3

8. Schematic drawing of the crystal structure and the 3d orbitals in the MnO 5 polyhedron for hexagonal RMnO 3. PHYSICAL REVIEW B 74, 014422 (2006)

9. Electronic energy-level scheme

10. Linear Optical Property Optical spectroscopy has been a powerful tool for investigating systematic electronic band structure of the strongly correlated electron systems. Phys. Rev. B 78, 054440 (2008)

11. The inter-site transition peak shifted more rapidly when the temperature crossed the Neel temperature, suggesting that a change in the non-collinear spin correlation can influence the electronic properties of multiferroic hexagonal manganites.

12. SHG One of which is caused by the noncentrosymmetric ferroelectric ordering of charges, whereas the other is due to the centrosymmetric antiferromagnetic ordering of spins.

13. Time-resolved nonlinear optical spectroscopy All-optical studies in a two-beam configuration, in which an intense (pump) light beam excites the medium and a less intense (probe) beam monitors the pump-induced nonlinear changes of its properties. In such a configuration, the nonlinearity can be expressed through the third-order nonlinear polarization vector P 3 (w) arising from the interaction of the pump E(w) and probe e(w) electric fields:

14. Time-resolved nonlinear optical spectroscopy Equation can be rewritten as a relation between the pump- induced perturbation of the dielectric permittivity tensor Ɛ (w) and the nonlinear susceptibility tensor X (3) : The product E k (w)E l *(w) can be conveniently decomposed into a symmetric and an antisymmetric part with respect to permutations of the indices k and l. The symmetric part is real and nonzero when the pump is linearly polarized, while the antisymmetric part is imaginary and nonzero when the pump beam is circularly polarized.

15. Time-resolved nonlinear optical spectroscopy The tensor itself comprises a symmetric and an antisymmetric part with respect to permutations of the indices i and j. The nonlinearities resulting in and can be shown to be determined by the real and imaginary parts of E k (w)E l *(w), respectively. Within the studied spectral range, the observed nonlinear optical properties are determined by the d –d transition in Mn 3+ ions.

16. Time-resolved nonlinear optical spectroscopy Spectral dependences of the photo-induced magneto-optical Kerr rotation (full circles) and ellipticity (open circles) in (a) ErMnO 3, (b) ScMnO 3, and (c) YMnO 3.

17. The dependence of the Kerr ellipticity upon Δt d is shown for ErMnO 3. From the maximum value reached by the amplitude B of the fast component within the experimental spectral range, we could estimate the maximum of the relevant third-order susceptibility x (3) of ErMnO 3 to be of the order of 2*10 -9 esu. Photo-induced “birefringence” Photo-induced “MOKE”

18. Time-resolved nonlinear optical spectroscopy Spectral dependences of B and C, amplitudes of the relaxing contributions to the photo-induced differential refractive index of ErMnO 3. The amplitude B of the fast relaxing contribution shows a maximum at the energy of the transition in Mn 3+ ions, whereas the amplitude C of the slowly relaxing part changes sign at approximately the same energy.

19. Time-resolved nonlinear optical spectroscopy The complex refraction index should be sensitive to this nonequilibrium state. Thus the temporal behavior of the photo-induced ‘‘birefringence’’ is driven by the dynamical phenomena involving phonons. The spectral dependence of the refraction index within a given energy range comprising only one electronic transition can be presented as the sum of an energy-independent contribution resulting from all electronic transitions outside the considered spectral range and of a contribution resulting from the transition within this range.

20. Time-resolved nonlinear optical spectroscopy The latter depends on photon energy and is characterized by an s-like spectrum. In the frame of this model, the fast relaxing component arises from photo-induced changes of the energy-independent part of the signal, i.e., it is mostly due to spectral changes outside the considered energy range. A spectral maximum of the fast relaxing contribution within this range shows that the initial optical excitation of the system consists of transitions in Mn 3+ ions. The fast relaxation can therefore be attributed to phonon thermalization through the anharmonic decay of optical phonons. On the other hand, the slowly relaxing component shows a distinctive dispersion mostly conditioned by effective changes of the spectral weight of the resonant transition.

21. summary The decay of the nonlinearity resulting in an antisymmetric perturbation of the dielectric permittivity tensor was shown to be conditioned by the relaxation of the excited electrons. The nonlinear symmetric perturbation of the tensor extends over a longer time span, and experiences a drastic change of its spectral dependence within the first 1.5 ps, the analysis of which led us to attribute its decay to both phonon thermalization and lattice cooling.

22. BiFeO 3 Bismuth ferrite, BiFeO 3, the focus of this study, has a robust ferroelectric polarization (~100 uC/cm -2 ) at room temperature, that is the largest among known ferroelectrics. At RT, BiFeO 3 is a rhombohedrally distorted ferroelectric perovskite with space group R3c and a Curie temperature, T C ~1100 K. It also shows a G-type canted antiferromagnetic order below Néel temperature, T N ~640 K, and, in the bulk, an incommensurately space- modulated spin structure along (110) h.

23. Linear optical spectroscopy electronic energy-level scheme for the Fe 3+ ion Vol. 17, No. 13 / OPTICS EXPRESS 10971 PHYSICAL REVIEW B 79, 224106 (2009)

24. Linear optical spectroscopy PHYSICAL REVIEW B 79, 224106 (2009)

25. Linear optical spectroscopy Appl. Phys. Lett. 97, 121102 (2010)

26. The 1965 discovery and identification of magnon side bands in the linear optical-absorption spectrum of simple antiferromagnetic insulators contributed to a comprehensive understanding of the static and dynamical optical properties of ordered magnetic systems. These studies were based on the resonant enhancement of the susceptibility,, that appears in the linear interaction. One can generally express as R. L. Greene, D. D. Sell, W. M. Yen, A. L. Schawlow, and R. M. White, Phys. Rev. Lett. 15, 656 (1965) Linear optical spectroscopy

27. When electric-dipole-active magnetic excitations couple to electronic excitations, magnon sidebands are located at where is a single-magnon energy, n is the number of magnons assisting the transition, and Ee corresponds to the electronic crystal-field transitions. Linear optical spectroscopy

28. Magnon sidebands have been extensively studied by linear spectroscopy at low temperatures. magnon sidebands were recently observed in the linear magneto-optical absorption spectrum of BiFeO 3 under high magnetic fields and low temperatures. Phys. Rev. B 79, 134425 (2009) Linear optical spectroscopy

29. With the rapid development of modern lasers, second- harmonic generation (SHG), as the lowest-order non- linear optical process, has emerged as a powerful tool to study light-matter interactions. In a magnetically ordered system, spin waves can also effectively couple to the nonlinear susceptibility tensor.

30. With the rapid development of modern lasers, second- harmonic generation (SHG), as the lowest-order non- linear optical process, has emerged as a powerful tool to study light-matter interactions. In a magnetically ordered system, spin waves can also effectively couple to the nonlinear susceptibility tensor. Appl. Phys. Lett. 92, 121915 (2008)

31. Raman scattering Recent works on low-energy Raman-scattering experiments in BiFeO 3 have shown a strong interaction between optical phonons and magnons manifested as several sharp resonances (up to 12 peaks in the 5–60 cm −1 energy range) corresponding to two species of electromagnon excitations with distinctive dispersive energy curves depending on their coupling to the electrical polarization.

32. Third-order nonlinear response Filled and open circles are the OA and CA Z-scans, respectively. Intensity independence of (a) 2PA coefficient α 2 and (b) nonlinear refraction index n 2 for the BFO film. Vol. 17, No. 13 / OPTICS EXPRESS 10971

33. Dual-Color Femtosecond Spectroscopy J Supercond Nov Magn (2011) 24: 731–734

34. Ultrafast dynamics in multiferroic BiFeO3 We report the ultrafast time-resolved optical measurements of multiferroic BiFeO 3, which exhibits both magnetic and ferroelectric ordering at room temperature. The coupling between these two orders makes it an attractive material for potential data-storage devices. However, a detailed understanding of this coupling is still under debate. Ultrafast optical spectroscopy can potentially shed light on magnetoelectric coupling in BiFeO 3 by unraveling the different contributions in the time domain. Here, we use degenerate 400 nm pump-probe spectroscopy to excite and probe a BiFeO3 thin film above its bandgap. The measured relaxation consists of a fast decay (˜1 ps) followed by a slow recovery (˜150 ps). We attribute the fast component to the recovery of photoexcited carriers. The slow recovery may be due to spin-lattice relaxation. Yu-Miin Sheu, Rohit Prasankumar, Antoinette Taylor (Los Alamos National Laboratory)