Reentrant canonical spin-glass dynamics and tunable field-induced transitions in (GeMn)Co₂O₄Kagomé lattice

We report on the reentrant canonical semi spin-glass characteristics and controllable field-induced transitions in distorted Kagomé symmetry of (GeMn)Co₂O₄. ThisB-site spinel exhibits complicated, yet interesting magnetic behaviour in which the longitudinal ferrimagnetic (FiM) order sets in below the Néel temperatureT_FN∼ 77 K due to uneven moments of divalent Co (↑ 5.33μ_B) and tetravalent Mn (↓ 3.87μ_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∼ 4.3 K,J_AA/k_B∼ -6.2 K andJ_BB/k_B∼ -3.3 K) between the cations, which is extracted following the Néel's expression for the two-sublattice model of FiM. Dynamical susceptibility (χ_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 (Ω ∼ 0.002), critical exponentzυ= (6.7 ± 0.07), spin relaxation timeτ₀= (2.33 ± 0.1) × 10^-18s, activation energyE_a/k_B= (69.8 ± 0.95) K and interparticle interaction strength (T₀= 71.6 K) provide the experimental evidences for canonical spin-glass state below the spin freezing temperatureT_F= 72.85 K. The field dependence ofT_Fobtained fromχ_ac(T) follows the irreversibility in terms of de Almeida-Thouless mean-field instability in which the magnitude of crossover scaling exponent Φ turns out to be ∼2.9 for the (Ge_0.8Mn_0.2)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 susceptibilityχp-1χp=χ-χ0after subtracting the temperature independent diamagnetic termχ0(=-3 × 10^-3emu mol^-1Oe^-1) results in the effective magnetic momentμeff= 7.654μ_B/f.u. This agrees well with the theoretically obtainedμeff= 7.58μ_B/f.u. resulting the cation distributionMn0.24+↓A[Co22+↑]BO4in support of the Hund's ground state spin configurationS=3/2andS= 1/2of Mn⁴⁺and Co²⁺, respectively. TheH-Tphase diagram has been established by analysing all the parameters (T_F(H),T_FN(H),H_SF1(T) andH_SF2(T)) extracted from various magnetization measurements. This diagram enables clear differentiation among the different phases of the (GeMn)Co₂O₄and also illustrates the demarcation between short-range and long-range ordered regions.