Anisotropic Magnetic Phase Diagram of PrB₆Dominated by the<i>O</i>_{<i>x</i><i>y</i>}Antiferro-Quadrupolar Interaction

Abstract

We have studied the specific heat, magnetoresistance and magnetization of PrB 6 which shows two successive phase ransitions at T IC from the commensurate (C) to incommensurate (IC) magnetic phase and at T N from the IC to paramagnetic phase and obtained the magnetic phase diagram. The suppression of T N by the magnetic field shows the following anisotropy. Below ∼12 T, T N <111> < T N <110> < T N <001> and above ∼12 T, 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 with increasing magnetic field up to ∼10 T. It was found that the IC phase is divided into two phases below and above ∼7 T for the magnetic field around the H ∥<111> direction. The anisotropy of T N is explained by the different magnitude of the parallel and perpendicular magnetic susceptibility whose weights depend on the magnetic field direction. The 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 originates from the coexistence with the O x y quadrupole order. The small ordered moment and twofold easy axis in the C phase are explained by the coexistence and competition between the O x y quadrupolar and antiferromagnetic exchange interactions in the Γ 5 triplet ground state.