Complex magnetic structures of a Shastry-Sutherland lattice TmB ₄ studied by powder neutron diffraction analysis

Powder neutron diffraction analysis was performed on Tm ¹¹B ₄, which undergoes successive transitions at T _N1 = 11.7 K, T* = 11 K, and T _N2 = 10 K. An incommensurate structure with two propagation vectors, k ₂ = [1 ± k′ ± k″, ±k″; 0] and k ₂′ = [1 ± k′ ± 3k″, ±k″; 0] (k′ = 0.1226 and k″ ≃ 0.012), is suggested for phase II (T* ≤ T ≤ T _N1). Phase III (T _N2 ≤ T ≤ T*) is described by one propagation vector, k ₃ = [1 ± k′, 0, 0]. The propagation vector for phase IV (T ≤ T _N2) further changes to a commensurate one characterized by k ₄ = [100]. Four Tm moments in the c-plane order in a (+-+--) type, where + and -- mean the directions of the moments parallel and antiparallel to the c-direction, respectively. The diffuse scattering intensity around the (100) magnetic reflection remains above T _N2 up to 20 K.