Coexistence of localized and collective magnetism in the coupled-spin-tetrahedra system Cu₄Te₅O₁₂Cl₄

We report high-field magnetization, electron spin resonance (ESR), and Raman scattering measurements of the coupled spin-tetrahedra system Cu₄Te₅O₁₂Cl₄ with magnetic ordering at T_N = 13.6 K. We find thermodynamic and spectroscopic signatures for the concomitant occurrence of localized and collective magnetism. Magnetization measurements up to 60 T exhibit a spin-flop transition at μ₀H_SF = 16 T only for H∥c as well as periodic magnetization steps at μ₀H = 16.5, 24.8, 33.8, 42.3, and 49.7 T, which are independent of the crystallographic orientations. For T > T_N, the temperature dependence of ESR linewidth is described by a critical power law, ΔB_pp(T) ∝ (T−T_N)^{−0.56±0.02}. For T < T_N, an antiferromagnetic resonance mode is observed for H ∥ c, and its linewidth is given by ΔB_pp(T) ∝ T^3.13±0.04, being close to T⁴ expected for a classical magnet. Raman spectra show three one-magnon-like excitations superimposed on a broad two-magnon continuum. While the two higher frequency modes show an intensity variation in accordance to a three-dimensional Heisenberg antiferromagnet, the lower frequency mode clearly deviates. These results suggest that Cu₄Te₅O₁₂Cl₄ is a unique material which shows a dual character of zero-dimensional, localized and three-dimensional, collective magnetic behaviors.