Dynamic scaling analysis of the long-range RKKY Ising spin glass DyxY1−xRu2Si2

Abstract

Dynamic scaling analyses of linear and nonlinear ac susceptibilities in a model magnet of the long-rang Ruderman-Kittel-Kasuya-Yosida (RKKY) Ising spin glass (SG) ${\mathrm{Dy}}_{0.103}{\mathrm{Y}}_{0.897}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ were examined. The obtained set of critical exponents, $\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 1, $\ensuremath{\beta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 1, $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 2, and $z\ensuremath{\nu}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 3.4, indicates the SG phase transition belongs to a universality class different from that of either the canonical (Heisenberg) or short-range Ising SGs. The analyses also reveal a finite-temperature SG transition with the same critical exponents under a magnetic field and the phase-transition line ${T}_{\text{g}}(H)$ described by ${T}_{\text{g}}(H)\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}{T}_{\text{g}}(0)(1\ensuremath{-}A{H}^{2/\ensuremath{\phi}})$, with $\ensuremath{\phi}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 2. The crossover exponent $\ensuremath{\phi}$ obeys the scaling relation $\ensuremath{\phi}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}+\ensuremath{\beta}$ within the margin of errors. These results strongly suggest spontaneous replica-symmetry breaking (RSB) with a non- or marginal-mean-field universality class in the long-range RKKY Ising SG.