The nature of magnetism in the doubly-diluted spinel ZnTiCoO4 is reported here employing the temperature and magnetic field dependence of dc- and ac-susceptibilities, and heat capacity (CP) measurements. The antiferromagnetic Néel temperature (TN~13.8 K) is determined from the peak in the ∂(χT)/∂T vs. T plot and the Power law yields the spin-glass freezing temperature Tg ~ 12.9 K with critical exponent zν ~ 11.75. Since the magnitudes of t o and zν depend on the magnitude of Tg, a procedure is developed to find the optimum value of Tg = 12.9 K. A similar procedure is used to determine the optimum T0 = 10.9 K in the Vogel-Fulcher law yielding Ea/kB = 95 K, and t 0 = 1.6 ×10-13 sec. It is argued that the comparatively large magnitude of the Mydosh parameter Ω = 0.024 and Ea/(kBT0)=8.7(>>1) suggests cluster-spin-glass state in ZnTiCoO4 below Tg. In the CP vs T data from 1.9K to 50K, the observation of only a broad peak near 20K and absence of λ-type anomaly near TN or Tg combined with the reduced value of change in magnetic entropy from 50K to 1.9K suggests the presence of only short-range ordering in the system, consistent with spin-glass state. The field dependence of Tg shows slight departure from the non-mean-field Almeida-Thouless line. Strong temperature dependence of magnetic viscosity S and coercivity HC without exchange bias, both tending to zero on approach to Tg from below, further support the spin-glass state which results from magnetic dilution driven by 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 < TN which reveals rapid decrease of Tg with increase in H whereas decrease in TN with increase in H is weaker, typical of antiferromagnetic systems.

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We report the slow spin dynamics of cluster spin-glass spinel Zn(Fe1-xRux)2O4 by means of detailed dc-magnetization and ac-susceptibility studies combined with the heat capacity analysis. Two specific compositions (x = 0.5, 0.75) have been investigated in detail along with the substitution of Jahn-Teller (JT) active spin-1/2 Cu2+ ions at B-sites. Measurements based on the frequency and temperature dependence of ac-susceptibility (χac (f,T)) and the subsequent analysis using the empirical scaling laws such as: (i) Vogel-Fulcher law and (ii) Power-law reveal the presence of cluster spin-glass state below the characteristic freezing temperature TSG (17.77 K (x = 0.5) and 14 K (x=0.75)). Relaxation dynamics of both the compositions follows the non-mean field AT-line approach (TSG (H)=TSG (0)(1-AH2/ϕ), with ideal value of ϕ = 3. Nevertheless, the analysis of temperature dependent high field dc-susceptibility, χhf (2 kOe ≤ HDC ≤ 20 kOe, T) provides evidence for Gabay‒Toulouse type mixed-phase (coexistence of spin-glass and ferrimagnetic) behavior. Further, in case of Cu0.2Zn0.8FeRuO4 system, slowly fluctuating magnetic clusters persist even above the short-range ferrimagnetic ordering temperature (TFiM) and their volume fraction vanishes completely across ~ 6TFiM. This particular feature of the dynamics has been very well supported by the time decay of thermoremanent magnetization and heat-capacity studies. We employed the high temperature series expansion technique to determine the symmetric exchange coupling (JS) between the spins which yields JS = ‒3.02×10‒5 eV for Cu0.2Zn0.8FeRuO4 representing the dominant intra-sublattice FM interactions due to the dilute incorporation of the JT active Cu2+ ions. However, the AFM coupling is predominant in ZnFeRuO4 and Cu0.2Zn0.8Fe0.5Ru1.5O4 systems. Finally, we deduced the magnetic phase diagram in the HDC–T plane using the characteristic parameters obtained from the field variations of both ac- and dc-magnetization measurements.

This work presents the magnetic field-temperature (H-T) phase diagram, exchange constants, specific heat (C P ) exponents and magnetic ground state of the antiferromagnetic MnNb 2 O 6 polycrystals. Temperature dependence of the magnetic susceptibility χ (= M/H) yields the Néel temperature T N = 4.33 K determined from the peak in the computed ∂(χT)/∂T vs T plot in agreement with the transition in the C P vs T data at T N = 4.36 K. The experimental data of C P vs T near T N is fitted to C P = A|T − T N | −α yielding the critical exponent α = 0.12(0.15) for T > T N (T < T N ). The best fit of χ vs T data for T > 50 K to χ = χ 0 + C/(T − θ) with χ 0 = −1.85 × 10 −4 emu mol −1 Oe −1 yields θ = −17 K, and C = 4.385 emu K mol −1 Oe −1 , the latter giving magnetic moment μ = 5.920μ B per Mn 2+ ion. This confirms the effective spin S = 5/2 and g = 2.001 for Mn 2+ and the dominant exchange interaction being antiferromagnetic in nature. Using the magnitudes of θ and T N and molecular field theory (MFT), the exchange constants J 0 /k B = −1.08 K for Mn 2+ ions along the chain c-axis and J ⊥ /k B = −0.61 K as the interchain coupling perpendicular to c-axis are determined. These exchange constants are consistent with the expected χ vs T variation for the Heisenberg linear chain. The H-T phase diagram, mapped using the M-H isotherms and M-T data at different H combined with the reported data of Nielsen et al, yields a triple-point T TP (H, T) = (18 kOe, 4.06 K). The spin-flopped state above T TP and the forced ferromagnetism for H > 192 kOe are used to estimate the anisotropy energy H A ≈ 0.8 kOe.