Antiferromagnetic short-range order and cluster spin-glass state in diluted spinel ZnTiCoO4

Abstract

The nature of magnetism in the doubly-diluted spinel ZnTiCoO4 = (Zn2+) A [Ti4+Co2+] B O4 is reported here employing the temperature and magnetic field (H) dependence of dc susceptibility (χ), ac susceptibilities (χ′ and χ″), and heat capacity (C p) measurements. Whereas antiferromagnetic (AFM) Néel temperature T N = 13.9 K is determined from the peak in the ∂(χT)/∂T vs T plot, the fit of the relaxation time τ (determined from the peak in the χ″ vs T data at different frequencies) to the Power law: τ = τ 0 [(T − T SG)/T SG]−zν yields the spin glass freezing temperature T SG = 12.9 K, z ν ∼ 11.75, and τ 0 ∼ 10−12 s. Since the magnitudes of τ 0 and z ν depend on the magnitude of T SG, a procedure is developed to find the optimum value of T SG = 12.9 K. A similar procedure is used to determine the optimum T 0 = 10.9 K in the Vogel–Fulcher law: τ = τ 0 exp[E a/k B(T − T 0)] yielding E a/k B = 95 K, and τ 0 = 1.6 × 10−13 s. It is argued that the comparatively large magnitude of the Mydosh parameter Ω = 0.026 and k B T 0/E a = 0.115 (≪1) suggests cluster spin-glass state in ZnTiCoO4 below TSG. In the C p vs T data from 1.9 K to 50 K, only a broad peak near 20 K is observed. This and absence of λ-type anomaly near T N or T SG combined with the reduced value of change in magnetic entropy from 50 K to 1.9 K suggests only short-range AFM ordering in the system, consistent with spin-glass state. The field dependence of T SG shows slight departure (ϕ ∼ 4.0) from the non-mean-field Almeida–Thouless line T SG(H) = T SG(0) (1 − AH 2/ϕ ). Strong temperature dependence of magnetic viscosity S and coercivity H C without exchange bias, both tending to zero on approach to T SG from below, further support the spin-glass state which results from magnetic dilution driven by diamagnetic Zn2+ and Ti4+ ions leading to magnetic frustration. Magnetic phase diagram in the H–T plane is established using the high-field magnetization data M(H, T) for T < T N which reveals rapid decrease of T SG with increase in H whereas decrease in T N with increase in H is weaker, typical of AFM systems. For T > T N, the data of χ vs T are fit to the modified Curie–Weiss law, χ = χ 0 + C/(T + θ), with χ 0 = 3.2 × 10−4 emu mol−1 Oe−1 yielding θ = 4 K and C = 2.70 emu K mol−1 Oe−1. This magnitude of C yields effective magnetic moment = 4.65 μ B for Co2+, characteristic of Co2+ ions with some contribution from spin–orbit coupling. Molecular field theory with effective spin S = 3/2 of Co2+ is used to determine the nearest-neighbor exchange constant J 1/k B = 2.39 K AFM and next-nearest-neighbor exchange constant J 2/k B = −0.66 K (ferromagnetic).