Elastic property of a high-field ordered state observed in PrFe$_{4}$P$_{12}$

We present experimental results of elastic constants as a function of temperature and magnetic field for the Pr-based heavy fermion system PrFe$_{4}$P$_{12}$, especially in a high-field (HF) ordered phase discovered. Since the HF phase exists in a narrow temperature range below 0.7 K and for high fields above 7 T in a highly limited angular range around the [111] directions, the elastic constants C$_{L}$ = (C$_{11}$+2C$_{12}$+4C$_{44})$/3 and C$_{T}$ = (C$_{11}$-C$_{12}$+C$_{44})$/3 were measured by the longitudinal (L) one propagating along the [111] direction and by the transverse (T) one along the [111] direction polarized to the [1-11] one, respectively. A clear upturn was observed in both of the elastic constants below the HF ordered phase transition temperature. Furthermore, a remarkable elastic softening toward the transition temperature was observed in the temperature dependence of C$_{L}$, whereas no softening was observed in C$_{T}$. These results indicate that the softening is most likely to be due to the bulk modulus (C$_{11}$+2C$_{12})$/3. Thus, it is expected that the HF ordered phase seems to be accompanied by a strain fluctuation with $\Gamma _{1}$ spatial symmetry, namely a scalar phase transition with a multi-polar moment is a candidate for the HF ordered phase.