Magneto-optical THz study in multiferroic Ni$_3$V$_2$O$_8$*

We present results of absorption measurements in THz region, from 3 to 220\,cm$^{-1}$, in multiferroic Ni$_3$V$_2$O$_8$ in magnetic fields up to 12\,T and temperatures above 2\,K. Ni$_3$V$_2$O$_8$ is a magnetic insulator with Ni$^{2+}$ spin-1 ions arranged in a kagom\'{e} staircase lattice. The phase diagram of Ni$_3$V$_2$O$_8$ is complicated - ground state changes from paramagnetic (PM) to high temperature incommensurate (HTI) helical state, at 9.1\,K in zero field. In low temperature incommensurate (LTI) phase below 6.3\,K spontaneous electric polarization $\mathbf{P}$ appears along the $b$ axis. $\mathbf{P_b}$ can be suppressed by further cooling below 3.9\,K or by application of external magnetic field. Low energy optical excitations are discussed for all low-$T$ phases of Ni$_3$V$_2$O$_8$. Polarization sensitive absorption measurements are performed to distinguish between magnetoand electroactive spin excitations i.e. magnons and electromagnons. Different optical selection rules for magnon and electromagnon excitations enable us to search for evidence of the spin helix plane orientation and its changes at critical magnetic fields and temperatures.