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analysis of the spectra in the relevant frequency range as presented below. 

Figure 2 shows the field dependent spectra for two dif- ferent geometries of the experiment. The thicknesses of the samples are similar for both orientations: 1.24 mm (upper panel) and 1.33 mm (lower panel), respectively. The spectra in the lower panel with ˜ e ‖ c and ˜ h ‖ a cor- respond well to the known results [26, 32] and show a mode at about 21 cm − 1 which appears after the field in- duced reorientation of spin cycloid to the ab -plane. Based on the weakness of this mode, both in Ref. [26] and in Ref. [32] it has been concluded that the mode around 21 cm − 1 is of purely magnetic origin and represent an antiferromagnetic resonance of the magnetic cycloid for ˜ h ‖ a -axis. Indeed, the strength of this mode (Δ ε ∼ 0 . 05, assuming electric origin) is extremely weak compared to electromagnon observed for ˜ e ‖ a (Δ ε ∼ 2) [9, 11]. The mode in Fig. 2 is observed for the ab -plane cycloid and within ˜ h ‖ a excitation conditions. Tracing this mode back into the bc -oriented cycloid in zero external fields, it can be expected to originate from the excitation conditions ˜ h ‖ c . (This corresponds to the interchanging of the a -axis and c -axis). Indeed, an AFMR mode excited for ˜ h ‖ c of the similar strength has been observed around 21 cm − 1 in the phase with the bc -plane cycloid [32]. 

A careful comparison of both panels in Fig. 2 reveals interesting difference between two excitation conditions. The strength of the mode in the geometry where ˜ e ‖ b is roughly the half of that where ˜ e ‖ c . This strongly suggests that for geometry in which ˜ e ‖ c the electric dipole contri- bution is indeed measurable and represent the previously unobserved ˜ e ‖ c counterpart of the electromagnon. These 

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results agree well with the original explanation of the electromagnons as electrically active eigenmodes of the cycloidal structure [9, 23]. 

In order to make the discussion quantitative, the ex- perimental spectra in the upper panel of Fig. 2 were fitted with magnetic Lorentz oscillator. If we now take the pa- rameters of the mode from the geometry with ˜ e ‖ b and plot the expected transmittance spectra for the geome- try ˜ e ‖ c we obtain the absorption value which is too weak compared to the experiment (the “ µ only” curve in the lower panel of Fig. 2). The only possible explanation is that this mode has distinct non-zero electric contribution along the c -axis. The actual fit for this geometry was obtained by taking parameters of the magnetic oscillator from ˜ e ‖ b , ˜ h ‖ a geometry and adding an electric oscillator with the same resonance frequency ν 0 = 20.7 cm − 1 and line width γ = 4.9 cm − 1 as the magnetic one. The rea- soning behind this assumption is that both contributions are electric and magnetic parts of the same eigenmode of the spin cycloid. The strengths of both components is given by Δ µ = 0 . 0038 and Δ ε = 0 . 05, respectively. 

Figure 3 shows the linear absorption coefficients α = 4 πκλ − 1 which allow direct comparison of different ex- perimental geometries. Symbols were calculated from transmittance spectra T using the expression T = (1 − R ) $^{2}$exp( − αd ), where R = | ( √ εµ − 1) / ( √ εµ + 1) | 2 is the reflectance on the boundary between the air and the sam- ple, and d is the sample thickness. Solid lines are model calculations using the same parameters as in Fig. 2. One can see again that the mode at 21 cm − 1 is stronger in the case of ˜ e ‖ c and ˜ h ‖ a excitation. (A weak narrow mode seen close to 22 cm − 1 for ˜ e ‖ b , ˜ h ‖ a geometry is possibly due to impurities in the sample. The strength of this mode is at least an order of magnitude smaller than the strength of the broad mode and doesn’t change the over- all picture.) 

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