Two-state Weiss model for the anomalous thermal expansion in EuNi${}_{2}$P${}_{2}$

It has recently been found that the single crystalline EuNi${}_{2}$P${}_{2}$ shows an anormalous thermal expansion and its scaling relation to the average 4$f$ electron number. We point out that a phenomenological 2-state Weiss model can explain these behaviors. We also show that the model leads to the observed effective Bohr magneton number per atom (7.4 $\mu_{\rm B}$) in the high-temperature limit, and is consistent with the temperature dependence of experimental susceptibility. Moreover the model predicts that the 4$f$ contribution to the thermal expansion coefficient is in proportional to that of the specific heat. The results suggest that the strong temperature dependence found in these experimental data originates in the excitations from the heavy-fermion ground state to the independent 4$f^{7}$ atomic states.