Single-crystal study of the honeycomb XXZ magnet BaCo${}_2$(PO${}_4$)${}_2$ in magnetic fields

We present a study of high-quality BaCo${}_2$(PO${}_4$)${}_2$ single crystals via magnetization, heat-capacity, thermal-expansion and magnetostriction measurements. Sharp anomalies in the thermodynamic properties at $T_N=3.4$K reveal a long-range antiferromagnetic order in these single-crystalline samples, which is absent in polycrystalline BaCo${}_2$(PO${}_4$)${}_2$. The temperature dependent magnetic susceptibilities for in-plane and out-of-plane magnetic fields are strongly anisotropic and reveal a pronounced easy-plane anisotropy. A Curie-Weiss analysis implies strong orbital magnetism, as it is known from the sister compound BaCo${}_2$(AsO${}_4$)${}_2$ that is discussed as a potential Kitaev spin-liquid material. When applying in-plane magnetic fields at low temperature, BaCo${}_2$(PO${}_4$)${}_2$ is driven to another ordered phase at a critical field $H_{C1}\approx 0.11$T and then undergoes a further field-induced transition to a highly polarized paramagnetic phase at $H_{C2}\approx 0.3$T, which is again similar to the case of BaCo${}_2$(AsO${}_4$)${}_2$. In addition, our lowest-temperature data reveal that the field-induced transitions in BaCo${}_2$(PO${}_4$)${}_2$ become dominated by thermally assisted domain-wall motion.