Observation of an intersublattice exchange magnon in CoCr${}_2$O${}_4$ and analysis of magnetic ordering

We report on an investigation of optical properties of multiferroic CoCr${}_2$O${}_4$ at terahertz frequencies in magnetic fields up to 30 T. Below the ferrimagnetic transition (94 K), the terahertz response of CoCr${}_2$O${}_4$ is dominated by a magnon mode, which shows a steep magnetic-field dependence. We ascribe this mode to an exchange resonance between two magnetic sublattices with different $g$ factors. In the framework of a simple two-sublattice model (the sublattices are formed by Co${}^{2+}$ and Cr${}^{3+}$ ions), we find the inter-sublattice coupling constant, $\lambda =-(18\pm 1)$ K, and trace the magnetization for each sublattice as a function of field. We show that the Curie temperature of the Cr${}^{3+}$ sublattice, ${\Theta }_2$ $=$ $(49\pm 2)$ K, coincides with the temperature range, where anomalies of the dielectric and magnetic properties of CoCr${}_2$O${}_4$ have been reported in literature.

Figure 1

Examples of raw far-infrared transmittance spectra of CoCr${}_2$O${}_4$ in Faraday geometry. The absorption line, marked as “Line 1,” is discussed in the course of the article. At the higher-frequency end of the spectra, there is an indication of another, very broad, line (“Line 2?”).

Figure 2

Field dependence of the magnon frequency for 4 and 30 K. Symbols are the experimental data, and lines represent the results of simultaneous fits of the optical data with Eq. (3) and of magnetization data from Ref. 3 with Eqs. (1) and (2). Note that the onset of the vertical scales is at 10 cm${}^{-1}$.

Figure 3

Example of a fit by use of Eqs. (1) and (2) to the magnetization data obtained at 0.1 T (simultaneously, the magnon-frequency data were fitted with the same set of free parameters; see Fig. 2). Contributions of the Co${}^{2+}$ and Cr${}^{3+}$ sublattices are shown with opposite signs. The contribution of the Cr${}^{3+}$ sublattice diminishes at $T_C$, rather than at ${\Theta }_2$ $=$ 49 K, because of the coupling between the sublattices.

Figure 4

Magnetization of the Co${}^{2+}$ and Cr${}^{3+}$ sublattices in CoCr${}_2$O${}_4$, as obtained from the model fits with Eqs. (1, 2, 3). The lowest-field points are at 0.1, 0.5, and 1 T.