Second-order effect of strain in singlet ground state compound PrNi5

The rare earth compound PrNi5 has a nonmagnetic singlet ground state. The ground state of PrNi5 crosses the first excited state when a magnetic field is applicated along the a-axis. This level crossing occurs at 20 T and causes anomalies in some substances. In particular, the elastic constant C-66 exhibits a large elastic softening at this level crossing point. The purpose of this paper is to analyze the behavior of C-66 when a magnetic field is applied to a system. The behavior of the temperature dependence of C-66 has been explained already. However the method of calculating the temperature dependence Of C66 cannot explain the field dependence of C-66. Hence the elastic softening and behavior above the level crossing point in C-66 are analyzed applying the higher order effect of strain to elastic constants. The higher order effect of strain is much smaller than the first-order effect of strains and is usually neglected. Not only a first-order strain but a second-order one is taken into account in our works.