Spin-liquid behavior in the spinel-type Cu(Cr1−xZrx)2S4

Abstract A spinel mixed crystal CuCrZrS 4 has an asymptotic Curie temperature θ ≈62 K with an effective number of Bohr magnetons p eff =3.70/Cr-atom. The most striking feature is the absence of peak or step in the heat capacity at temperatures close to 62 K. The geometrical spin frustration is introduced through antiferromagnetic interaction due to the substitution of nonmagnetic Zr for Cr atom, on the B sites forming a network of linked tetrahedra. The magnetizations in field-cooled (FC) and zero-field-cooled (ZFC) are observed with irreversibility in T ⩽ T g (≈10 K). This paper will present the magnetic properties of mixed crystals Cu(Cr 1− x Zr x ) 2 S 4 focused on the specimen for x =0.45 which has θ =164 K and p eff =2.37/Cr-atom. Experimental results lead to a physical picture for Cu(Cr 1− x Zr x ) 2 S 4 that a spin-glass state for T ⩽ T g , a spin-liquid state which remains unordered in a cooperative paramagnetic state termed a spin-liquid state for T g ⩽ T ⩽ θ , and a spin-gas state for θ ⩽ T with a Curie–Weiss law. The spins for T g ⩽ T ⩽ θ will exhibit subtle correlations in the absence of long-range order and may form into clusters of frustrated system. In comparison with a typical ferromagnet for T ⩽ θ , the fairly slender magnetization as a function of temperature is observed in a constant field. The difference of hysteresis curves between the spin-glass state for T ⩽ T g and the spin-liquid state for T g ⩽ T ⩽ θ is clearly detected in low magnetic field.