Evolution of exchange interaction constants across magnetic phase transitions in the chromium spinel oxide ${\mathrm{CdCr}}_2{\mathrm{O}}_4$

High field electron spin resonance (ESR) and magnetization measurements reveal the crucial role of the strong spin-lattice coupling to generate the peculiar phase transitions in the chromium spinel oxide ${\mathrm{CdCr}}_2{\mathrm{O}}_4$, which possesses a spin-driven Jahn-Teller transition and a field-induced 1/2-magnetization plateau state. From our analysis of the ESR modes and the spin wave dispersion, which was observed from the previous neutron scattering studies, these magnetic properties are shown to originate from the modifications of the exchange interactions due to the lattice distortions. The evaluated exchange constants are examined by the magnetoelastic theory proposed by Penc $\mathit{et}\mathit{al}$.

Figure 1

Magnetization curves of ${\mathrm{CdCr}}_2{\mathrm{O}}_4$ for $H\parallel \left[100\right]$ and $\left[111\right]$. The solid curves are the experimental results obtained at 1.3 K. The curve for $H\parallel \left[111\right]$ is shifted up by 1.0 ${\mu }_{\mathrm{B}}/{\mathrm{Cr}}^{3+}$ for clarity. The dashed curve is the result calculated using magnetoelastic theory.

Figure 2

(a) Frequency dependence of ESR spectra in ${\mathrm{CdCr}}_2{\mathrm{O}}_4$, obtained at 1.3 K, in the frequency region from 655.7 GHz to 1016.7 GHz. The inset shows the extended ESR spectra at 847.0 GHz. (b) The ESR spectra in the frequency region from 92 GHz to 220 GHz. The vertical dashed line marks the transition field $H_{\mathrm{c}1}$. These ESR spectra were observed when the field was increasing.

Figure 3

Frequency-field relation of the ESR resonance points in ${\mathrm{CdCr}}_2{\mathrm{O}}_4$. Closed circles are the ESR resonance points observed for the polycrystalline sample. Closed squares and open triangles are the data points acquired with a single crystal in magnetic fields applied along [100] and [111] axis, respectively. Solid and dashed lines designate the theoretical ESR modes. The two solid curves below $H_{\mathrm{c}1}$ are the theoretical antiferromagnetic resonance modes given from our previous analysis described in Ref. [28]. The vertical dashed lines mark the transition fields $H_{\mathrm{c}1}$ and $H_{\mathrm{c}2}$.

Figure 4

Assumed magnetic structure used for our analysis in zero magnetic field.

Figure 5

Spin wave dispersion for ${\mathrm{CdCr}}_2{\mathrm{O}}_4$ in zero magnetic field. Closed circles are the experimental results obtained from the previous neutron scattering measurement [32]. Dashed and solid curves are the theoretical results calculated for (1 $k$ 0) and (0 $k$ 1) directions, respectively.

Figure 6

Exchange constants of the nearest-neighbor interactions in ${\mathrm{CdCr}}_2{\mathrm{O}}_4$. Closed circles are those evaluated from the analysis of the experimental results. Dashed curves are the results of the calculation based on the magnetoelastic theory. Vertical dashed lines are $H_{\mathrm{c}1}, H_{\mathrm{c}2}, H_{\mathrm{c}3}$, and $H_{\mathrm{s}}$.