${\mathrm{CdEr}}_2{\mathrm{Se}}_4$: A New Erbium Spin Ice System in a Spinel Structure

Here we present a detailed study of the spinel ${\mathrm{CdEr}}_2{\mathrm{Se}}_4$ and show it to be a new instance of spin ice, the first one in an erbium material and the first one in a spinel. Definitive experimental evidence comes from the temperature dependence of the magnetic entropy, which shows an excellent agreement with the predicted behavior for a spin ice state. Crystal field calculations demonstrate that the change in the local environment from that of the titanates completely alters the rare-earth anisotropy giving rise, in the case of ${\mathrm{Er}}^{3+}$, to the required Ising anisotropy, when ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ behaves as an $XY$ antiferromagnet. This finding opens up the possibility of new exotic ground states within the ${\mathrm{CdR}}_2{\mathrm{Se}}_4$ and ${\mathrm{CdR}}_2{\mathrm{Se}}_4$ families.

Figure 1

Magnetic specific heat and corresponding integrated entropy (per mole of Er) for ${\mathrm{CdEr}}_2{\mathrm{Se}}_4$, showing a reasonable agreement with the predicted $S$ value for the degenerate 2 in 2 out spin ice state, $R\ln 2\mathrm{\text{−}}(R/2)\ln (3/2)$. The error in $S(T)$ has been estimated from the error bars of the parameters fitted in the calculation of $C_{\mathrm{MAG}}$. Inset: phonon, CEF, and magnetic contributions to $C(T)$.

Figure 2

Experimental (symbols) and calculated (solid lines) field dependence of the magnetization of a polycrystalline sample of ${\mathrm{CdEr}}_2{\mathrm{Se}}_4$.

Figure 3

Temperature dependence of the real and imaginary parts of the ac susceptibility at different frequencies. Inset: frequency dependence of the freezing temperature $T_p$. The line is a fit to a thermally activated behavior yielding an energy barrier of approximately 10 K.