Anisotropic magnetic phase diagram of PrB6 dominated by the O-xy antiferro-quadrupolar interaction

We have studied the specific heat, magnetoresistance and magnetization of P rB6 which shows two successive phase ransitions at T-IC from the commensura te (C) to incommensurate (IC) magnetic phase and at TN from the IC to param agnetic phase and obtained the magnetic phase diagram. The suppression of T N by the magnetic field shows the following anisotropy. Below similar to 12 T, T-N(< 111 >) < T-N(< 110 >) < T-N(< 001 >) and above similar to 12T, T-N (< 110 >) < T-N(< 111 >) < T-N(< 001 >). T-IC is suppressed by the magnetic field for H // < 001 > and < 110 > but T-IC(< 111 >) is enhanced largely w ith increasing magnetic field up to similar to 10T. It was found that the I C phase is divided into two phases below and above similar to 7T for the ma gnetic field around the H // < 111 > direction. The anisotropy of T-N is ex plained by the different magnitude of tile parallel alld perpendicular magn etic susceptibility whose weights depend on the magnetic field direction. T he anisotropic field dependence of T-IC at low magnetic field is explained by the different magnitude of the in-plane (H // < 110 >) and out-of-plane (H // z) perpendicular magnetic susceptibility in the C phase which origina tes from tile coexistence with the O-xy, quadrupole order. The small ordere d moment and twofold easy axis in the C phase are explained by tile coexist ence alld competition between the O-xy quadrupolar and antiferromagnetic ex change interactions in the Gamma (5) triplet ground state.