Magnetostriction of hexagonal HoMnO$_{3}$ and YMnO$_{3}$ single crystals

We report on the magnetostriction of hexagonal HoMnO$_{3}$ and YMnO$_{3}$ single crystals in a wide range of applied magnetic fields (up to $H$ = 14 T) at all possible combinations of the mutual orientations of magnetic field $H$ and magnetostriction $\Delta L/L$. The measured $\Delta L/L(H,T)$ data agree well with the magnetic phase diagram of the HoMnO$_3$ single crystal reported previously by other authors. It is shown that the nonmonotonic behavior of magnetostriction of the HoMnO$_3$ crystal is caused by the Ho$^{3+}$ ion; the magnetic moment of the Mn$^{3+}$ ion parallel to the hexagonal crystal axis. The anomalies established from the magnetostriction measurements of HoMnO$_3$ are consistent with the phase diagram of these compounds. For the isostructural YMnO$_3$ single crystal with a nonmagnetic rare-earth ion, the $\Delta L/L(H,T)$ dependences are described well by a conventional quadratic law in a wide temperature range (4–100 K). In addition, the magnetostriction effect is qualitatively estimated with regard to the effect of the crystal electric field on the holmium ion.