arXiv:1001.1148v1 [cond-mat.str-el] 7 Jan 2010 Evidence of electro-active excitation of the spin cycloid in TbMnO 3 A. M. Shuvaev, 1 V. D. Travkin, 2 V. Yu. Ivanov, 2 A. A. Mukhin, 2 and A. Pimenov 1 $^{1}$Experimentelle Physik 4, Universit¨ at W¨ urzburg, D-97074 W¨ urzburg, Germany $^{2}$General Physics Institute, Russian Academy of Science, 119991 Moscow, Russia (Dated: October 4, 2018) Terahertz electromagnetic excitations in the multiferroic TbMnO 3 at the field-induced magnetic transition are investigated for different orientations of the magnetic cycloid. In addition to the elec- tromagnon along the a -axis, the detailed polarization analysis of the experimental spectra suggests the existence of an electro-active excitation for ac electric fields along the crystallographic c -axis. This excitation is possibly the electro-active eigenmode of the spin cycloid in TbMnO 3 , which has been predicted within the inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling. Ferroelectric polarization in spiral magnets has been successfully explained on the basis of the inverse Dzyaloshinskii-Moriya (DM) coupling between the mag- netic moments [20–22]. Within this model a spiral spin structure lowers the symmetry of the system leading to an effective magnetoelectric coupling term and an elec- trical polarization P in the form Multiferroics represent an intriguing class of materials in which magnetism and electricity are strongly coupled. This magnetoelectric coupling leads to a mutual influ- ence of magnetic and electric ordering, which results in a rich new physics and in various possible applications [1– 4]. Recently, a new class of multiferroics has attracted enormous interest because the ferroelectric polarization in these systems is induced by a cycloidal ordering of the magnetic moments [5–7]. The magnetic and electric or- der in these materials are accompanied by coupled spin- lattice vibrations [8] showing strong electric dipole activ- ity and termed electromagnons [9, 10]. Initially detected in GdMnO 3 and TbMnO 3 [11], the electromagnons ap- pear to exist in cycloidal magnetic phases of many differ- ent multiferroics [12–19]. In most cases, distinct struc- ture of these excitations is seen including two or more separate modes. For example, in TbMnO 3 one can ob- serve at least 3 excitations: two with the energy around ≃ 2 meV (10-20 cm − $^{1}$) and the third one at ≃ 8 meV (60 cm − $^{1}$). tion must be parallel to the c-axis ( P ‖ c ) and the electro- magnons should be excited for ac electric fields parallel to the a-axis (˜ e ‖ a ). Accordingly, for the ab-plane oriented cycloid the polarization P ‖ a and electromagnons for ˜ e ‖ c should be observed. This basically corresponds to the in- terchange of the a and c -axes in the excitation conditions. Although the orientation of the static electric polariza- tion has been confirmed in many experiments [5, 24, 25], the excitation conditions for the electromagnon contra- dicted the predictions of the model: the selection rules for the excitations remained the same (i.e. ˜ e ‖ a ) inde- pendently of the orientation of the cycloid [11–19]. In order to account for this contradiction, a model based on Heisenberg exchange coupling between spins has been proposed recently [18, 26, 27]. According to this model, the structural peculiarities of orthorhombic multiferroic manganites lead to the selection rules ˜ e ‖ a regardless of the orientation of the spin cycloid. Here S$_{i}$ and S$_{j}$ are the neighboring spins and e$_{ij}$ is the lattice vector connecting them. Consequently, it was rea- sonable to assume the same mechanism to explain the existence of the electromagnons [23]. In this model the electromagnons are the eigenmodes of the spin cycloid which can be excited by electric component of the elec- tromagnetic wave [9]. However, after initial success of this explanation a number of experimental results con- tradicted the predictions of the model. The basic exam- ple can be given by TbMnO 3 at low temperatures: the DM model predicts that the excitation conditions for the electromagnon should be tied to the magnetic cycloid, i.e. for the bc-plane oriented cycloid the electric polariza- The Heisenberg exchange model assigns the high en- ergy electromagnons observed between 60 cm − 1 and 80 cm − 1 to the zone edge magnons [18, 26–28], but the nature of the lower energy elecromagnons close to 20 cm − 1 remains uncertain. It seems reasonable to re- call the statements of the DM model and to assume that the low-frequency electromagnons are somehow related to the excitations of the spin cycloid observed by inelastic neutron scattering (INS) [29–31] because the characteris- tic frequencies coincide closely [29, 32]. This assumption is supported by a recent observation of the magnetic exci- tation channel for electromagnons [32] which can be also seen as antiferromagnetic resonances (AFMR) within cer- tain excitation conditions. However, in order to prove this assumption, the predicted excitation conditions for the eigenmodes of the cycloid should be found experi- mentally. Most specifically, one should expect the ex- citation conditions along the c -axis if the spin cycloid is oriented in the ab -plane. Such excitation conditions were not observed up to now [26, 32]. A possible reason for this fact is the weakness of the dielectric contribution of the spin modes within the DM mechanism. In order to resolve this experimental difficulty, TbMnO 3 seems to be an ideal candidate, because the magnetic cycloid can be P ∼ e$_{ij}$ × S$_{i}$ × S$_{j}$ . (1)