Search for a nematic phase in the quasi-two-dimensional antiferromagnet ${\mathrm{CuCrO}}_2$ by NMR in an electric field

The magnetic phase diagram of ${\mathrm{CuCrO}}_2$ was studied with an alternative method of simultaneous Cu NMR and electric polarization techniques with the primary goal of demonstrating that, regardless of cooling history of the sample, the magnetic phase with specific helmet-shaped NMR spectra associated with interplanar disorder possesses electric polarization. Our result unequivocally confirms the assumption of Sakhratov et al. [Phys. Rev. B 94, 094410 (2016)] that the high-field low-temperature phase is in fact a three-dimensional (3D) polar phase characterized by a 3D magnetic order with tensor order parameter. In comparison with the results obtained in pulsed fields, a modified phase diagram is introduced defining the upper boundary of the first-order transition from the 3D spiral to the 3D polar phase.

Figure 1

Crystal structure of ${\mathrm{CuCrO}}_2$ projected onto the $ab$ plane. The three layers, $\alpha \beta \gamma$, are the positions of ${\mathrm{Cr}}^{3+}$ ions.

Figure 2

Field evolutions of ${}^{63}\mathrm{Cu}$ NMR spectra measured at temperature 13 K and $\mathbf{H}\parallel \mathbf{c}$ after zero magnetic field cooling. The electric field $E=0$ during cooling for the green spectra (A) and $E=430$ kV for the red spectra (B). The spectra are shifted by the values ${\mu }_0{H}_0$ indicated to the left of each line. Symbols $m$ and $s$ correspond to the main $\left(m_I=+1/2\leftrightarrow -1/2\right)$ and high-field satellite $\left(m_I=+3/2\leftrightarrow +1/2\right)$ transitions, respectively. The spectra are taken successively in increasing field.

Figure 3

H-T magnetic phase diagram of ${\mathrm{CuCrO}}_2$ for $\mathbf{H}\parallel \mathbf{c}$. The dashed lines are from Ref. [1]. The red diamonds are obtained in the present work and the rest are from Ref. [4]. The hysteresis area is shaded. Typical NMR spectral shapes associated with each phase are illustrated.

Figure 4

${}^{63}\mathrm{Cu}$ NMR spectra $(m_I=+3/2\leftrightarrow +1/2$ transition), $\mathbf{H}\parallel \mathbf{c},\nu =173$ MHz, $T=15$ K. The sample was cooled from $T=30$ K in the fields $\mathbf{H}\parallel \mathbf{c},\mathbf{E}\parallel \left[110\right]$ with the values given in the figure.

Figure 5

Temperature dependence of polarization along [110]. The sample was cooled from $T=30$ K in the fields $\mathbf{H}\parallel \mathbf{c},\mathbf{E}\parallel \left[110\right]$ with the values given in the figure.