First-principles prediction of phase transition of YCo$_5$ from self-consistent phonon calculations

Recent theoretical study has shown that the hexagonal YCo$_5$ is dynamically unstable and distorts into a stable orthorhombic structure. In this study, we show theoretically that the orthorhombic phase is energetically more stable than the hexagonal phase in the low-temperature region, while the phonon entropy stabilizes the hexagonal phase thermodynamically in the high-temperature region. The orthorhombic-to-hexagonal phase transition temperature is $\sim$165 K, which is determined using the self-consistent phonon calculations. We investigate the magnetocrystalline anisotropy energy (MAE) using the self-consistent and non-self-consistent (force theorem) calculations with the spin-orbit interaction (SOI) along with the Hubbard $U$ correction. Then, we find that the orthorhombic phase has similar MAE, orbital moment, and its anisotropy to the hexagonal phase when the self-consistent calculation with the SOI is performed. Since the orthorhombic phase still gives magnetic properties comparable to the experiments, the orthorhombic distortion is potentially realized in the low-temperature region, which awaits experimental exploration.