Thermal conductivity of triangular-lattice antiferromagnet Na2BaCo(PO4)2: Absence of itinerant fermionic excitations

We present the ultralow-temperature specific heat and thermal conductivity measurements on single crystals of triangular-lattice antiferromagnet Na$_2$BaCo(PO$_4$)$_2$, which was recently argued to host itinerant fermionic excitations, like a quantum spin liquid, above its antiferromagnetic phase transition temperature $T_{\rm N}$ = 0.148 K. In specific heat measurements, we confirm the peaks due to antiferromagnetic ordering when magnetic field $\mu_0 H \leq$ 1 T, roughly consistent with previous work [N. Li $et$ $al.$, Nat. Commun. 11, 4216 (2020)]. However, in thermal conductivity measurements, we observe negligible residual linear term in zero and finite magnetic fields, in sharp contrast to previous report [N. Li $et$ $al.$, Nat. Commun. 11, 4216 (2020)]. At 0.35 K, the thermal conductivity increases with field up to 3 T then saturates, similar to that of another triangular-lattice compound YbMgGaO$_4$, which further shows that the heat is conducted only by phonons with scattering from spins and boundary. Our results clearly demonstrate the absence of itinerant fermionic excitations in the disordered state above $T_{\rm N}$ in this frustrated antiferromagnet Na$_2$BaCo(PO$_4$)$_2$, thus such a state is not as exotic as previously reported.