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

We report on the reentrant canonical semi spin-glass characteristics and controllable field-induced transitions in distorted Kagomé symmetry of (GeMn)CoO. This-site spinel exhibits complicated, yet interesting magnetic behaviour in which the longitudinal ferrimagnetic (FiM) order sets in below the Néel temperature∼ 77 K due to uneven moments of divalent Co (↑ 5.33) and tetravalent Mn (↓ 3.87) 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 (/∼ 4.3 K,/∼ -6.2 K and/∼ -3.3 K) between the cations, which is extracted following the Néel's expression for the two-sublattice model of FiM. Dynamical susceptibility (()) and relaxation of thermoremanent magnetization,() 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= (6.7 ± 0.07), spin relaxation time= (2.33 ± 0.1) × 10s, activation energy/= (69.8 ± 0.95) K and interparticle interaction strength (= 71.6 K) provide the experimental evidences for canonical spin-glass state below the spin freezing temperature= 72.85 K. The field dependence ofobtained from() 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 (GeMn)CoO. Isothermal magnetization plots reveal two field-induced transitions across 9.52 kOe () and 45.6 kOe () 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 × 10emu molOe) results in the effective magnetic momentμeff= 7.654/. This agrees well with the theoretically obtainedμeff= 7.58/. resulting the cation distributionMn0.24+↓A[Co22+↑]BO4in support of the Hund's ground state spin configurationS=3/2andS= 1/2of Mnand Co, respectively. Thephase diagram has been established by analysing all the parameters ((),(),() and()) extracted from various magnetization measurements. This diagram enables clear differentiation among the different phases of the (GeMn)CoOand also illustrates the demarcation between short-range and long-range ordered regions.