Spin-glass behaviour in \(K_xRu_{4-y}Ni_yO_8\) hollandite materials

We report the synthesis and comprehensive ac and dc susceptibility measurements of \(K_xRu_{4-y}Ni_yO_8\) hollandite. The value of the relative frequency shift, \(δT_f\), has been determined as 0.025 which is within the range expected for spin-glass systems (0.005–0.06). Additionally, the characteristic flipping time of a single spin flip, \(τ_0\), and the dynamical critical exponent, −zv, were determined to have values of 5.82 × 10\(^{−8}\)s and 6.1(3), respectively from the power law. While the value of \(τ_0\) is comparatively very large, −zv is consistent with what is expected for spin-glass systems. Field-cooled hysteresis behavior demonstrates a small increase in the remnant magnetization (at 2 K) on increasing the strength of the cooling field, suggesting that the degree of short-range correlations increases consistent with the formation of larger spin clusters. Thermoremnant magnetization data indicate an exponential-like decay of the magnetization as a function of time with the remnant magnetization remaining nonzero. However, it is clear from these data that multiple components contribute to the decay behavior. Collectively, these data confirm spin-glass character for \(K_{0.73(3)}Ni_{1.9(5)}Ru_{2.1(5)}O_8\) and clearly demonstrate that the magnetic behavior of this material is far from simplistic.