Proximate Tomonaga-Luttinger liquid in a spin-1/2 ferromagnetic XXZ chain compound

The spin-1/2 ferromagnetic XXZ chain is a prototypical many-body quantum model, exactly solvable via the integrable Bethe ansatz method, hosting a Tomonaga-Luttinger spin liquid. However, its clear experimental realizations remain absent. Here, we present a thorough investigation of the magnetism of the structurally disorder-free compound LuCu(OH)$_3$SO$_4$. By conducting magnetization and electron-spin-resonance measurements on the single-crystal sample, we establish that the title compound approximates the spin-1/2 ferromagnetic XXZ chain model with a nearest-neighbor exchange strength of $J_1$ $\sim$ 65 K and an easy-plane anisotropy of $\sim$ 0.994. The specific heat demonstrates a distinctive power-law behavior at low magnetic fields (with energy scales $\leq$ 0.02$J_1$) and low temperatures ($T$ $\leq$ 0.03$J_1$). This behavior is consistent with the expectations of the ideal spin-1/2 ferromagnetic XXZ chain model, thereby supporting the formation of a gapless Tomonaga-Luttinger spin liquid in LuCu(OH)$_3$SO$_4$.