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)₃SO₄. 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 J₁ ~ 65 K and an easy-plane anisotropy of ~ 0.994. The specific heat demonstrates a distinctive power-law behavior at low magnetic fields (with energy scales ≤ 0.02J₁) and low temperatures (T ≤ 0.03J₁). 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)₃SO₄.