Magnetic transition in K₄Cu₄OCl₁₀: A model system of three-dimensional spin-12 tetrahedra

Isolated spin tetrahedral systems with weak intertetrahedral couplings, as have been reported for Cu₂Te₂O₅X₂ (X = Cl, Br) and the related compound Cu₄Te₅O ₁₂Cl₄, have received much attention recently because they represent an interesting class of magnets that consist of weakly coupled magnetic clusters and, in particular, they can directly demonstrate the interplay of intertetrahedral couplings with built-in tetrahedral frustration. However, there is much debate about the structural low dimensionality of the Cu-Te-O-Cl(Br) compounds and its effect on the magnetism of the material. Here, we present a model spin tetrahedral system K₄Cu₄OCl ₁₀, with almost isotropic magnetic coupling within the tetrahedron and three-dimensional connection of the tetrahedra. The system enters a spin-singlet state with a susceptibility maximum at T_max = 11 K, and then enters an antiferromagnetic order at T_N = 4.4 K. The ratio T_N/T_max = 0.40 is close to the T_N/T _max = 0.38 for Cu₂Te₂O₅Br ₂, which is viewed as an indicator of closeness to quantum criticality. Evidence in muon-spin rotation or relaxation suggests an incommensurate ordering. This work shows that the previously revealed ground state in anisotropically structured Cu₂Te₂O ₅X₂ compounds also exists in an isotropic spin tetrahedral system.