Dynamic scaling analysis of the long-range RKKY Ising spin glass ${\mathrm{Dy}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$

Dynamic scaling analysis of the long-range RKKY Ising spin glass ${Dy}_{x} Y_{1 - x} {Ru}_{2} {Si}_{2}$

Y. Tabata, T. Waki, and H. Nakamura

Phys. Rev. B 96, 184406 – Published 6 November 2017

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) ${Dy}_{0.103} Y_{0.897} {Ru}_{2} {Si}_{2}$ were examined. The obtained set of critical exponents, $γ \sim$ 1, $β \sim$ 1, $δ \sim$ 2, and $z ν \sim$ 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 $T_{g} (H)$ described by $T_{g} (H) = T_{g} (0) (1 - A H^{2 / ϕ})$ , with $ϕ \sim$ 2. The crossover exponent $ϕ$ obeys the scaling relation $ϕ = γ + β$ 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.

Received 30 May 2017
Revised 6 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.184406

Physics Subject Headings (PhySH)

Magnetism

Spin glasses

Magnetization measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Tabata^*, T. Waki, and H. Nakamura

Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan

^*tabata.yoshikazu.7e@kyoto-u.ac.jp

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Vol. 96, Iss. 18 — 1 November 2017

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Figure 1
(a) The real part of the ac susceptibility $χ_{ac}^{'}$ with $ω =$ 0.01 Hz at $T =$ 1.9 K. (b) The real part of the full nonlinear ac susceptibility $χ_{nl}^{'}$ with several representative frequencies at $T =$ 1.9 K. Solid lines in (a) and (b) represent the fitting results using Eq. (3) up to $n =$ 2. The dashed line in (a) represents a leading term in Eq. (3), $3 χ_{2}^{'} H^{2}$ . Temperature dependences of (c) the real part of the linear ac susceptibility $χ_{0}^{'}$ and (d) first nonlinear ac susceptibility coefficient $χ_{2}^{'}$ with several representative frequencies. Solid lines represent the corresponding dc susceptibilities, $χ_{0}^{dc}$ and $χ_{2}^{dc}$ .
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Figure 2
(a) Double-logarithmic plot of $χ_{2}^{'}$ with several representative frequencies against the reduced temperature $ɛ = T / T_{g} - 1$ assuming $T_{g} =$ 1.905 K. The dashed line represents a divergent behavior of $χ_{2}^{'} \propto ɛ^{- 1.05}$ . (b) Double-logarithmic plot of $χ_{2}^{'}$ at $T =$ 1.9 K against the frequency. The dashed line represents a divergent behavior of $χ_{2}^{'} \propto ω^{- 0.33}$ . (c) Dynamic scaling plot of $χ_{2}^{'}$ in the form of $- χ_{2}^{'} ɛ^{γ}$ vs $ω ɛ^{- z ν}$ , described in Eq. (A3). Dashed lines represent the asymptotes of the scaling function given in Eq. (A4). (d) Dynamics scaling plot of $χ_{nl}^{'}$ at $T =$ 1.9 K in the form of $- χ_{nl}^{'} H^{- 2 / δ}$ vs $ω H^{- 2 z ν / β δ}$ , described in Eq. (A9). The dashed line represents the asymptote of the scaling function given by Eq. (A10).
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Figure 3
(a) Temperature dependence of the imaginary part of the ac susceptibility $χ^{''}$ with several representative frequencies at a zero field. (b) Double-logarithmic plot of $χ^{''}$ at $T =$ 1.9 K and 4.0 K against the frequency. Solid lines represent nonanalytic and nearly analytic behaviors at 1.9 and 4.0 K, $ω^{0.35}$ and $ω^{0.95}$ , respectively. (c) Dynamic scaling plot of $χ^{''}$ in the form of $(χ^{''} / χ_{eq}) ɛ^{- β}$ vs $ω ɛ^{- z ν}$ , described in Eq. (B6). Dashed lines represent the asymptotes of the scaling function given in Eq. (B4).
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Figure 4
Dynamic scaling plots of $χ^{''}$ in the form of $(χ^{''} / χ_{eq}) ɛ {(H)}^{- β}$ vs $ω ɛ {(H)}^{- z ν}$ at $H =$ (a) 100, (b) 200, and (c) 300 Oe. Dashed lines represent the asymptotes of the scaling function given in Eq. (B4). (d) Scaling plot of $χ^{''}$ for all fields is simultaneously shown to see a field-independent feature of the scaling function $K (x)$ . Dashed lines in (d) are the asymptotes using the mean value $\bar{β} =$ 1.11 and $\bar{z ν} =$ 3.35 shown in Fig. 5.
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Figure 5
(a) $H T$ phase diagram of ${Dy}_{0.103} Y_{0.897} {Ru}_{2} {Si}_{2}$ derived from the dynamic scaling analyses of $χ^{''}$ . (b) Double-logarithmic plot of $T_{g} (H)$ in the form of $H$ vs $1 - T_{g} (H) / T_{g} (0)$ . Solid lines in (a) and (b) represent the fitting result using Eq. (4). (c) Field dependences of the critical exponents $β$ and $z ν$ . Dashed lines represent the mean value $\bar{β} =$ 1.11 and $\bar{z ν} =$ 3.35.
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Dynamic scaling analysis of the long-range RKKY Ising spin glass ${Dy}_{x} Y_{1 - x} {Ru}_{2} {Si}_{2}$

Y. Tabata, T. Waki, and H. Nakamura

Phys. Rev. B 96, 184406 – Published 6 November 2017

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

Y. Tabata, T. Waki, and H. Nakamura

Phys. Rev. B 96, 184406 – Published 6 November 2017

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Dynamic scaling analysis of the long-range RKKY Ising spin glass ${Dy}_{x} Y_{1 - x} {Ru}_{2} {Si}_{2}$