Reentrant canonical spin-glass dynamics and tunable field-induced transitions in (GeMn)Co₂O₄ Kagom lattice

We report on the reentrant canonical semi spin-glass characteristics and controllable field-induced transitions in distorted Kagom & eacute; symmetry of (GeMn)Co2O4. This B-site spinel exhibits complicated, yet interesting magnetic behaviour in which the longitudinal ferrimagnetic (FiM) order sets in below the N & eacute;el temperature T-FN similar to 77 K due to uneven moments of divalent Co (up arrow 5.33 mu(B)) and tetravalent Mn (down arrow 3.87 mu(B)) which coexists with transverse spin-glass state below 72.85 K. Such complicated magnetic behaviour is suggested to result from the competing anisotropic superexchange interactions (J(AB)/k(B) similar to 4.3 K, J(AA)/k(B) similar to -6.2 K and J(BB)/k(B) similar to -3.3 K) between the cations, which is extracted following the N & eacute;el's expression for the two-sublattice model of FiM. Dynamical susceptibility (chi(ac) (f, T)) and relaxation of thermoremanent magnetization, M-TRM (t) data have been analysed by means of the empirical scaling-laws such as Vogel-Fulcher law and Power law of critical slowing down. Both of which reveal the reentrant spin-glass like character which evolves through a number of intermediate metastable states. The magnitude of Mydosh parameter (Omega similar to 0.002), critical exponent z upsilon = (6.7 +/- 0.07), spin relaxation time tau(0) = (2.33 +/- 0.1) x 10(-18) s, activation energy E-a/k(B) = (69.8 +/- 0.95) K and interparticle interaction strength (T-0 = 71.6 K) provide the experimental evidences for canonical spin-glass state below the spin freezing temperature T-F = 72.85 K. The field dependence of T-F obtained from chi(ac) (T) follows the irreversibility in terms of de Almeida-Thouless mean-field instability in which the magnitude of crossover scaling exponent Phi turns out to be similar to 2.9 for the (Ge0.8Mn0.2)Co2O4. Isothermal magnetization plots reveal two field-induced transitions across 9.52 kOe (H-SF1) and 45.6 kOe (H-SF2) associated with the FiM domains and spin-flip transition, respectively. Analysis of the inverse paramagnetic susceptibility after subtracting the temperature independent diamagnetic term (=-3 x 10(-3) emu mol(-1) Oe(-1)) results in the effective magnetic moment = 7.654 mu(B)/f.u. This agrees well with the theoretically obtained = 7.58 mu(B)/f.u. resulting the cation distribution in support of the Hund's ground state spin configuration and of Mn4+ and Co2+, respectively. The H-T phase diagram has been established by analysing all the parameters (T-F(H), T-FN(H), H-SF1(T) and H-SF2(T)) extracted from various magnetization measurements. This diagram enables clear differentiation among the different phases of the (GeMn)Co2O4 and also illustrates the demarcation between short-range and long-range ordered regions.