Crystal-field-induced magnetostrictions in the spin reorientation process of Nd${}_2$Fe${}_{14}$B-type compounds

Volume expansion $\mathrm{\Delta }V\mathrm{/}V$ associated with the spin reorientation process of Nd${}_2$Fe${}_{14}$B-type compounds has been investigated in terms of simple crystalline-electric-field (CEF) model. In this system, $\mathrm{\Delta }V\mathrm{/}V$ is shown to be a direct measure of second order CEF energy. Calculated anomalies in $\mathrm{\Delta }V\mathrm{/}V$ associated with the first-order magnetization process of Nd${}_2$Fe${}_{14}$B are presented, which well reproduced the observations.