Crystal-field-induced magnetostrictions in the spin reorientation   process of Nd$_2$Fe$_{14}$B-type compounds
  Volume expansion $\Delta V / V$ 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, $\Delta V / V$ is shown to be a direct measure of second order CEF energy. Calculated anomalies in $\Delta V / V$ associated with the first-order magnetization process of Nd$_2$Fe$_{14}$B are presented, which well reproduced the observations. 
H. Kato, M. Yamada and T. Miyazaki