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rotated between ab -plane and bc -plane in external mag- netic fields. Thus the ultimate experiment must follow the c -axis response at the magnetically induced rotation of the cycloid. 

In this work we have carried out detailed polarization analysis of terahertz excitations in TbMnO 3 . Special at- tention has been payed to the selection rules of different excitations upon the rotation of the spin cycloid from bc - to ab -plane in external magnetic field B ‖ b -axis. It was found that a new excitation arises in the high-field phase with excitation conditions ˜ e ‖ c and ˜ h ‖ a . We argue that this excitation could not be explained by purely magnetic contribution but carries substantial electric component. 

The transmittance experiments at terahertz frequen- cies (3 cm − 1 < ν < 30 cm − $^{1}$) have been carried out in a Mach-Zehnder interferometer arrangement [33, 34] which allows measurements of amplitude and phase shift in a geometry with controlled polarization of radia- tion. The experiments in external magnetic fields up to 8 T have been performed in a superconducting split- coil magnet with polypropylene windows. Single crys- tals of TbMnO 3 have been grown using the floating-zone method with radiation heating. The samples were char- acterized using X-ray, magnetic, dielectric and optical measurements [9, 35]. The results of these experiments including the magnetic phase diagram are closely similar to the published results [24]. 

The paramagnetic phase in TbMnO 3 above 40 K is followed by a sinusoidally-modulated antiferromagnetic state which transforms below 28 K into the cycloidal spin structure oriented within the bc -plane [36, 37] (inset in Fig. 1). According to the symmetry analysis [6, 22] and Eq. (1), static electric polarization along the c -axis is allowed in the low-temperature phase. In external mag- netic fields the spin-cycloid rotates from bc -plane towards the ab -plane [25, 31]. Correspondingly, the electric polar- 

ization rotates from P ‖ c -axis to the P ‖ a -axis [5, 24, 25]. Dynamic experiments on TbMnO 3 in external mag- netic fields reveal that the c -axis properties are indeed sensitive to the orientation of the cycloid. The exam- ples of such changes are shown in Fig. 1 which represents the terahertz properties of TbMnO 3 in external magnetic field B ‖ b inducing the transition from bc -plane to ab - plane oriented cycloid. The magnetic field scans in these experiments were made in the geometry with ˜ e ‖ c and ˜ h ‖ a and at T = 10 K. The data are represented as re- fractive index n + iκ = √ εµ as both electric and magnetic contributions could be mixed in this experimental geom- etry. The transition from bc -plane to ab -plane cycloid in the high magnetic fields is clearly seen. Already at this point it is evident that the observed changes are strongly frequency dependent. Here the data at 4.7 cm − 1 is in- fluenced by a Tb-mode around 5 cm − 1 [32] which disap- pears in the high-field phase with the ab -plane cycloid. This leads to a substantial decrease of the absorption ( κ (4.7 cm − $^{1}$)) and reveals a bit complicated structure in 

<img src='content_image/404399.jpg'>

refractive index below 10 cm − $^{1}$. The changes observed at 4.7 cm − 1 can be well understood assuming a suppression of a Lorentzian mode situated between 5 and 6 cm − $^{1}$. 

Three higher frequency scans (15.8, 20, and 28 cm − $^{1}$) in Fig. 1 show more systematics, and can be reduced to a growth of the absorption mode around 20 cm − 1 in the phase with the ab -plane cycloid. This is a typical behavior for a Lorentz oscillator which appears close to 20 cm − 1 simultaneously with the ab -plane cycloid. In- deed, strong additional absorption arises near the fre- quency ≃ 20 cm − 1 and is substantially reduced above and below this frequency (lower panels, 28 cm − 1 and 16 cm − $^{1}$, respectively). In addition to a strongly in- creased absorption around the resonant frequency, the refractive index in Lorentzian model may in rough ap- proximation be simplified to the following statements: n ( ν ) ≈ n ∞ + Δ n for ν < ν 0 and n ( ν ) ≈ n ∞ − Δ n ( ν 0 /ν ) 2 for ν > ν 0 . Here n ∞ is the contribution from the high-frequency processes, Δ n reflects the strength of the Lorentzian mode, and ν 0 ≈ 20 cm − 1 is the resonance frequency. Therefore, after the growth of the Lorentzian (Δ n = 0 → Δ n ̸ = 0) at the magnetic transition we expect an increase of the refractive index below the resonance frequency and a decrease above it. This is roughly the behavior of the refractive index, observed at 15.8 cm − 1 ( ν < ν 0 ) and 28 cm − 1 ( ν > ν 0 ). The main changes, seen in Fig. 1, appears at the magnetic transition and are therefore related to the rotation of the magnetic cycloid. However, better understanding of the underlying processes can be obtained within a direct 

