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

We report on the reentrant canonical semi spin-glass characteristics and controllable field-induced transitions in distorted Kagomé symmetry of (GeMn)Co 2 O 4 . This B -site spinel exhibits complicated, yet interesting magnetic behaviour in which the longitudinal ferrimagnetic (FiM) order sets in below the Néel temperature T FN ∼ 77 K due to uneven moments of divalent Co (↑ 5.33 μ B ) and tetravalent Mn (↓ 3.87 μ 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 and J 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 exponent zυ = (6.7 ± 0.07), spin relaxation time τ 0 = (2.33 ± 0.1) × 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 χ 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 0.8 Mn 0.2 )Co 2 O 4 . 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 χ p − 1 χ p = χ − χ 0 after subtracting the temperature independent diamagnetic term χ 0 (=−3 × 10 −3 emu mol −1 Oe −1 ) results in the effective magnetic moment μ eff = 7.654 μ B / f.u . This agrees well with the theoretically obtained μ eff = 7.58 μ B / f.u . resulting the cation distribution Mn 0.2 4 + ↓ A [ Co 2 2 + ↑ ] B <mml:mtext