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

The nature of magnetism in the doubly-diluted spinel ZnTiCoO4 = (Zn2+)( A ) [Ti4+Co2+]( B )O-4 is reported here employing the temperature and magnetic field (H) dependence of dc susceptibility (chi), ac susceptibilities (chi ' and chi ''), and heat capacity (C (p)) measurements. Whereas antiferromagnetic (AFM) Neel temperature T (N) = 13.9 K is determined from the peak in the partial differential (chi T)/ partial differential T vs T plot, the fit of the relaxation time tau (determined from the peak in the chi '' vs T data at different frequencies) to the Power law: tau = tau (0) [(T - T (SG))/T (SG)](-z nu ) yields the spin glass freezing temperature T (SG) = 12.9 K, z nu similar to 11.75, and tau (0) similar to 10(-12) s. Since the magnitudes of tau (0) and z nu 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: tau = tau (0) exp[E (a)/k (B)(T - T (0))] yielding E (a)/k (B) = 95 K, and tau (0) = 1.6 x 10(-13) s. It is argued that the comparatively large magnitude of the Mydosh parameter omega = 0.026 and k (B) T (0)/E (a) = 0.115 (MUCH LESS-THAN1) suggests cluster spin-glass state in ZnTiCoO4 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 lambda-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 (phi similar to 4.0) from the non-mean-field Almeida-Thouless line T (SG)(H) = T (SG)(0) (1 - AH (2/phi )). 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 chi vs T are fit to the modified Curie-Weiss law, chi = chi (0) + C/(T + theta), with chi (0) = 3.2 x 10(-4) emu mol(-1) Oe(-1) yielding theta = 4 K and C = 2.70 emu K mol(-1) Oe(-1). This magnitude of C yields effective magnetic moment = 4.65 mu (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).

Automated summary

The nature of magnetism in the doubly-diluted spinel ZnTiCoO4 = (Zn2+)( A ) [Ti4+Co2+]( B )O-4 is reported here. The study reveals the spin-glass state in ZnTiCoO4 below the spin glass freezing temperature T (SG) = 12.9 K. The field dependence of T (SG) and the magnetic phase diagram in the H-T plane are established.