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 $\mathrm{LuCu}{\left(\mathrm{OH}\right)}_3{\mathrm{SO}}_4$. 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 $J_1\sim 65\mathrm{K}$ 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 $\le 0.02J_1$) and low temperatures $(T\le 0.03J_1)$. 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 $\mathrm{LuCu}{\left(\mathrm{OH}\right)}_3{\mathrm{SO}}_4$.