Multiferroicity of ${\mathrm{CuCrO}}_2$ tested by electron spin resonance

We have carried out the electron spin resonance (ESR) study of the multiferroic triangular antiferromagnet ${\mathrm{CuCrO}}_2$ in the presence of an electric field. The shift of ESR spectra by the electric field was observed; the value of the shift exceeds that in materials with linear magnetoelectric coupling. It was shown that the low-frequency dynamics of magnetically ordered ${\mathrm{CuCrO}}_2$ is defined by joint oscillations of the spin plane and electric polarization. The results demonstrate an agreement with theoretical expectations of a phenomenological model [V. I. Marchenko, J. Exp. Theor. Phys. 119, 1084 (2014)].

Figure 1

(a) Crystal structure of ${\mathrm{CuCrO}}_2$ projected on the $ab$ plane. The three layers, $\alpha ,\beta ,\gamma$, are the positions of ${\mathrm{Cr}}^{3+}$ ions. (b) Scheme of the spin structure at zero magnetic field for ${\mathbf{k}}_{ic}\parallel \left[110\right]$ [the spins with the same numbers in (a) are codirected].

Figure 2

Lines show frequency–resonance-field diagrams $\left[{\nu }_3\left(H_R\right)\right]$ computed for different angles $\alpha$ between $\mathbf{H}$ and [110]. Symbols show $\nu \left(H_R\right)$ measured at the field perpendicular to one side of the triangular structure. Solid symbols correspond to absorption lines from domain “A” $\left(\alpha ={90}^{\circ }\right)$ and open symbols from domains “B” and “C” $\left(\alpha =\pm {30}^{\circ }\right)$. $T=4.2$ K.

Figure 3

Left panel: Scheme of the experimental cell: a rectangular resonator with holes of coupling with the ultrahigh-frequency transmission line, the sample of a plate form with a silver paste electrode. Right panel: Three possible magnetic domains in the sample, shown schematically as “A”, “B”, “C”, and the mutual orientation of the applied electric and magnetic fields and crystallographic axes of the sample. The bold lines on the scheme aligned along heights of the triangles indicate the projection of spin planes at $H=0$. The bold side of the triangle marks the direction of the wave vector of the magnetic structure in each domain. The developed plane of the sample is perpendicular to one side of the triangular crystal structure. For domain “A”, $\mathbf{H}\parallel \left[1\overline{1}0\right]$ and $\mathbf{E}\parallel \left[110\right]$; for “B”, $\mathbf{H}\parallel \left[210\right]$ and $\mathbf{E}\parallel \left[0\overline{1}0\right]$; and for “C”, $\mathbf{H}\parallel \left[\overline{1}\overline{2}0\right]$ and $\mathbf{E}\parallel \left[\overline{1}00\right]$. Red and black arrows indicate the two possible directions of electric polarization for domains “A”, “B”, and “C”.

Figure 4

Top panel: Field scan of the transmitted power. Middle panel: Field scans of oscillation amplitude of the transmitted high-frequency power $P_{tr}^{\sim }$ at the frequency of the applied alternating electric field $E^{\sim }$ measured with the phase detection technique. $E_{\_}=+500$ kV/m and $E^{\sim }=250$ kV/m. Red and black scans correspond to different polarities of the superconducting solenoid. The arrows at the abscissa axes show the field of spin-flop reorientation $H_c$ in domain “A”. Bottom panel: $|P_{tr}^{\sim }\left(E^{\sim }\right)|$ dependencies measured at $H=1.02,1.66$ T shown in the middle panel with arrows. $\nu =42.2$ GHz and $T=4.2$ K.

Figure 5

Top panel: Field scan of $P_{tr}$. Bottom panel: four consequent field scans of $P_{tr}^{\sim }$ measured at $E^{\sim }=250$ kV/m. Scans I and IV were measured at $E_{\_}=+500$ kV/m (red lines) and II and III were measured at $E_{\_}=-500$ kV/m (blue lines). Directions of field scans are shown with arrows. The scoped scans of $P_{tr}^{\sim }\left(H\right)$ in the range of the absorption line from domain “A” are shown in the inset. $\nu =45.6$ GHz and $T=4.2$ K.

Figure 6

Top panel: $P_{tr}^{\sim }\left(H\right)$ measured at $\nu =42.2$ GHz, $T=4.2$ K and different values of the permanent electric field $E_{\_}$. $E^{\sim }=250$ kV/m. Bottom panel: $P_{tr}^{\sim }\left(E_{\_}\right)$ measured at $H=1.01$, 1.07 T.

Figure 7

Top panel: Field scan of $P_{tr}\left(H\right)$. Middle panel: $P_{tr}^{\sim }\left(H\right)$ measured at the permanent electric fields $E_{\_}=0$ and $E_{\_}=\pm 500$ kV/m. $E^{\sim }=250$ kV/m. Bottom panel: field scans of the algebraic half-sum and half-difference of $P_{tr}^{\sim }\left(H\right)$ measured at $E_{\_}=+500$ kV/m and $E_{\_}=-500$ kV/m (blue and red dotted lines). The algebraic sum is close to $P_{tr}^{\sim }\left(H\right)$ measured at $E_{\_}=0$ (green solid line). The black solid line shows a scaled field derivative of the transmitted power. $\nu =42.2$ GHz and $T=4.2$ K.

Figure 8

Top panel: Field scan of $P_{tr}$. Middle panel: $P_{tr}^{\sim }\left(H\right)$ measured at $E^{\sim }=125$ kV/m and $E_{\_}=+500$ kV/m, $E_{\_}=-500$ kV/m (red and black lines, respectively). Bottom panel: field scan of the half-difference of $P_{tr}^{\sim }\left(H\right)$. The blue solid line shows a scaled field derivative of the transmitted power. Two different coefficients were used for scaling: one for $H<1.1$ T and the other for higher fields. $\nu =38.6$ GHz and $T=4.2$ K.

Figure 9

The angular dependence of the resonance field $H_R\left(\alpha \right)$ for field $\mathbf{H}$ applied in the (110) and $\left(1\overline{1}0\right)$ planes. Symbols: red circles correspond to the absorption lines from domain “A”, and black squares from domains “B” and “C”. Lines: expected dependencies: $H_R\left(\alpha \right)=H_R(\alpha =0)/\text{cos}\left(\alpha \right)$. $\nu =42.25$ GHz and $T=4.2$ K.

Figure 10

Angular evolution of the field dependence records of the transmitted power at $\nu =117.5$ GHz and $T=1.3$ K. $\mathbf{H}$ rotates in the triangular plane. $\alpha =0$ corresponds to the direction $\mathbf{H}\parallel \left[110\right]$ for one of the domains. The maximal intensity of the transmitted power is normalized to 1. Lines are shifted along the ordinate around the line at $\alpha ={90}^{\circ }$ for clarity.

Figure 11

Angular dependencies of the resonance fields measured at $\nu =79.3$ GHz, $T=1.3$ K (symbols in the top panel) and at $\nu =36.1$ GHz and $T=4.2$ K measured in Ref. [15] (symbols in the bottom panel). $\mathbf{H}$ rotates in the $ab$ plane. Computed dependencies of $H_R\left(\alpha \right)$ for three domains are given by solid lines of different colors.