Antiferromagnetic short-range order and cluster spin-glass state in diluted spinel ZnTiCoO 4 .

The nature of magnetism in the doubly-diluted spinel ZnTiCoO 4 = (Zn 2+ ) A [Ti 4+ Co 2+ ] B O 4 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 ZnTiCoO 4 below T SG . 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 Zn 2+ and Ti 4+ 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 Co 2+ , characteristic of Co 2+ ions with some contribution from spin-orbit coupling. Molecular field theory with effective spin S = 3/2 of Co 2+ 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).