Unkown Gapless Excitation in Antiferromagnetic State of Yb Zigzag Chain System YbCuS2

Frustrated systems formed by rare-earth elements have attracted much attention. The strong spin-orbit coupling and the crystalline electric field effect associated with 4$f$ electrons of rare-earth ions lead to highly anisotropic exchange interactions, providing a novel platform for the quantum spin systems.
YbCuS$_2$ is a magnetic semiconductor with Yb zigzag chains along the a-axis. YbCuS$_2$ has an orthorhombic structure with the space group $P2_1 2_1 2_1$. At zero magnetic field, the magnetic specific heat divided by the temperature $C_{\mathrm m}/T$ shows a sharp peak at $T_{\mathrm O} \sim$ 0.95 K, indicating a first-order phase transition. The magnetic field $H$ dependence of $T_{\mathrm O}$ shows peculiar structure and the $H$-$T$ phase diagram cannot be explained by a conventional magnetic transition, suggesting a nontrivial ground state arising from the magnetic frustration in the Yb zigzag chain. However, the order parameter of the magnetic state below $T_{\mathrm O}$ has not been decided yet.
To investigate the magnetic properties at low temperatures from a microscopic point of view, we performed $^{63/65}$Cu nuclear quadrupole resonance (NQR) measurements on polycrystalline YbCuS$_2$. Since the sharp NQR peaks were observed above $T_{\mathrm O}$, quality of the YbCuS$_2$ sample can be good without any impurity phases or site mixing. Below $T_{\mathrm O}$, the paramagnetic peaks split into the multi peaks due to the internal magnetic fields, evidencing an antiferromagnetic phase transition. The magnetic order signals coexist with the paramagnetic signals for 0.85 K $ < T \leq T_{\mathrm O}$, indicating a first-order phase transition, which is consistent with the sharp peak in the specific heat. Although YbCuS$_2$ is a semiconductor, the nuclear spin-lattice relaxation rate $1/T_1$ exhibits the $T$-linear behavior below 0.5 K, which can be generally observed in metals. Surprisingly, $1/T_1T$ in YbCuS$_2$ at 0.1 K is by more than one order of magnitude larger than $1/T_1T$ in a Cu metal. This behavior suggests the presence of the novel gapless spin excitation at low temperatures in YbCuS$_2$.