First-order ferroelastic transition in a magnetoelectric multiferroic: CuCrO${}_2$

We present the magnetic phase diagram of the multiferroic geometrically frustrated antiferromagnet CuCrO${}_2$ determined using dielectric constant and ultrasonic velocity measurements with the magnetic field parallel to the $\left[1\overline{1}0\right]$ direction. According to these measurements, at zero field the magnetoelectric phase induced by a proper screw magnetic ordering is observed below $T_{N1}=23.4$ K, while the velocity measurements reveal another transition at $T_{N2}=24.3$ K. As the dielectric and velocity measurements were performed simultaneously, our results confirm the presence of an intermediate nonferroelectric magnetic state between the magnetoelectric and paramagnetic phases. Moreover, our observations indicate that this intermediate phase persists up to 7 T for a field applied along the $\left[1\overline{1}0\right]$ direction. Based on similar observations obtained on the multiferric compounds CuO and MnWO${}_4$, this intermediate state is most likely a collinear antiferromagnetic phase. Apart from two phases observed at zero field, the ultrasonic velocity measured in the magnetoelectric phase as a function of the magnetic field reveals a spin-flop transition at $H_{\mathrm{flop}}=5$ T at 23 K, which is attributed to the flop of the spin spiral from the (110) plane to the $\left(1\overline{1}0\right)$ plane. In this paper, we also present a detailed analysis of the elastic properties of CuCrO${}_2$. The analysis of the data using a Landau-type free energy indicates that CuCrO${}_2$ undergoes a first-order pseudoproper ferroelastic transition leading to a $\overline{3}m\rightharpoonup 2/m$ structural transition at $T_{N2}$. According to the model, the order parameter of the ferroelastic-antiferromagnetic transition at $T_{N2}$ belongs to the $E_g$ irreducible representation of the trigonal $\overline{3}m$ point group, and the magnetic moments must act as a secondary order parameter.

Figure 1

The projection of a triangular lattice layer of magnetic (Cr) ions (large filled circles) and adjacent oxygen layers above (small filled circles) and below (small open circles) the Cr layer along the $c$ direction in CuCrO${}_2$ and the symmetry operations of the $\overline{3}m$ point group with respect to the hexagonal and Cartesian coordinate systems.

Figure 2

The relative velocity variations of (a) $T_x{P}_y$ in CuCrO${}_2$ (continuous lines) and CuFeO${}_2$ (dotted lines) and (b) $L_x$ in CuCrO${}_2$ and CuFeO${}_2$. The dashed blue line corresponds to the prediction of the Landau model for a second-order pseudoproper ferroelastic phase transition proposed for CuFeO${}_2$ (Ref. 29). The experimental and numerical data for CuFeO${}_2$ are reprinted with permission from G. Quirion, M. J. Tagore, M. L. Plumer, and O. A. Petrenko, Phys. Rev. B 77, 094111 (2008). Copyright (2008) by the American Physical Society.

Figure 3

Temperature dependence of the normalized acoustic-mode velocities (dotted lines) in CuCrO${}_2$ and the predictions of the Landau model for a first-order pseudoproper ferroelastic transition (continuous lines): (a) $T_x{P}_y$; (b) $T_y{P}_x$; (c) $L_x$; (d) $L_y$; (e) $T_y{P}_z$; (f) $T_x{P}_z$.

Figure 4

Temperature dependence of the dielectric constant ${\epsilon }_{\left[110\right]}$ measured simultaneously with the acoustic mode $T_y{P}_x$ ($T_{\left[1\overline{1}0\right]}{P}_{\left[110\right]}$ in the hexagonal setting) in CuCrO${}_2$ at fields parallel to the $\left[1\overline{1}0\right]$ direction. The label $T_y{P}_x$ indicates that a transverse acoustic mode propagates along the $y$ axis with a polarization parallel to the $x$ axis.

Figure 5

Relative velocity variation of the longitudinal mode $L_y$ ($L_{\left[1\overline{1}0\right]}$ in the hexagonal setting) in CuCrO${}_2$ as a function of magnetic field parallel to the [$1\overline{1}0$] direction.

Figure 6

Magnetic field vs temperature phase diagram of CuCrO${}_2$ for fields parallel to the $\left[1\overline{1}0\right]$ direction. Data were obtained with increasing magnetic field.