### Abstract

We first present a scaling argument for the relaxation times in spin glasses, as suggested by Binder and Young. We emphasize the relevance of our dynamic measurements near the magnetic field-temperature transition line to equilibrium properties such as the nonlinear susceptibility. We show how, in the insulating system Eu_{0.4}Sr_{0.6}S, the phase lag of the ac susceptibility with respect to the modulated field relates the measuring frequency ω to a characteristic response time τ. We are thus able to define the zero field freezing temperature, T_{f}(ω). Two scaling models are tested, appropriate to a finite critical temperature, T_{c}, and to a zero temperature transition. Respectively, this leads to two critical slowing down regimes: τ/τ_{0} ∼ (T - T_{c})^{-zv} and ln(τ/τ_{0}) ∼ T^{ -zv}. Both are shown to be consistent with the data, and to lead to T_{c} = 1.50 K, zv = 8, τ_{0} = 3x10^{-12} s; or T_{c} = 0, zv = 9 and τ _{0} = 10^{-8} s. The set of parameters derived for the former (finite T_{c}) case appears to be more consistent with previous data on Eu_{0.4}Sr_{0.6}S, and with recent computer simulations. We then generate, in the magnetic field-temperature plane, lines T_{f} (ω, H) associated with the response time τ. We include remanent magnetization measurements which refer to well defined experimental time scales (≤1 s or ≤25 s). The entire set of scaled data, for the case when T_{c} = 1.50 K, strongly suggests that the response time diverges for H^{ 1 2} ∼ T - T_{c}. This is of the form of a de Almeida-Thouless transition line with, however, a non-mean-field exponent.

Original language | English (US) |
---|---|

Pages (from-to) | 1-5 |

Number of pages | 5 |

Journal | Journal of Magnetism and Magnetic Materials |

Volume | 54-57 |

Issue number | PART 1 |

DOIs | |

State | Published - 1986 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

_{0.4}Sr

_{0.6}S: A dynamic scaling analysis.

*Journal of Magnetism and Magnetic Materials*,

*54-57*(PART 1), 1-5. https://doi.org/10.1016/0304-8853(86)90464-6

**Experimental search for the spin-glass transition in Eu _{0.4}Sr_{0.6}S : A dynamic scaling analysis.** / Bontemps, N.; Rajchenbach, J.; Chamberlin, Ralph; Orbach, R.

Research output: Contribution to journal › Article

_{0.4}Sr

_{0.6}S: A dynamic scaling analysis',

*Journal of Magnetism and Magnetic Materials*, vol. 54-57, no. PART 1, pp. 1-5. https://doi.org/10.1016/0304-8853(86)90464-6

_{0.4}Sr

_{0.6}S: A dynamic scaling analysis. Journal of Magnetism and Magnetic Materials. 1986;54-57(PART 1):1-5. https://doi.org/10.1016/0304-8853(86)90464-6

}

TY - JOUR

T1 - Experimental search for the spin-glass transition in Eu0.4Sr0.6S

T2 - A dynamic scaling analysis

AU - Bontemps, N.

AU - Rajchenbach, J.

AU - Chamberlin, Ralph

AU - Orbach, R.

PY - 1986

Y1 - 1986

N2 - We first present a scaling argument for the relaxation times in spin glasses, as suggested by Binder and Young. We emphasize the relevance of our dynamic measurements near the magnetic field-temperature transition line to equilibrium properties such as the nonlinear susceptibility. We show how, in the insulating system Eu0.4Sr0.6S, the phase lag of the ac susceptibility with respect to the modulated field relates the measuring frequency ω to a characteristic response time τ. We are thus able to define the zero field freezing temperature, Tf(ω). Two scaling models are tested, appropriate to a finite critical temperature, Tc, and to a zero temperature transition. Respectively, this leads to two critical slowing down regimes: τ/τ0 ∼ (T - Tc)-zv and ln(τ/τ0) ∼ T -zv. Both are shown to be consistent with the data, and to lead to Tc = 1.50 K, zv = 8, τ0 = 3x10-12 s; or Tc = 0, zv = 9 and τ 0 = 10-8 s. The set of parameters derived for the former (finite Tc) case appears to be more consistent with previous data on Eu0.4Sr0.6S, and with recent computer simulations. We then generate, in the magnetic field-temperature plane, lines Tf (ω, H) associated with the response time τ. We include remanent magnetization measurements which refer to well defined experimental time scales (≤1 s or ≤25 s). The entire set of scaled data, for the case when Tc = 1.50 K, strongly suggests that the response time diverges for H 1 2 ∼ T - Tc. This is of the form of a de Almeida-Thouless transition line with, however, a non-mean-field exponent.

AB - We first present a scaling argument for the relaxation times in spin glasses, as suggested by Binder and Young. We emphasize the relevance of our dynamic measurements near the magnetic field-temperature transition line to equilibrium properties such as the nonlinear susceptibility. We show how, in the insulating system Eu0.4Sr0.6S, the phase lag of the ac susceptibility with respect to the modulated field relates the measuring frequency ω to a characteristic response time τ. We are thus able to define the zero field freezing temperature, Tf(ω). Two scaling models are tested, appropriate to a finite critical temperature, Tc, and to a zero temperature transition. Respectively, this leads to two critical slowing down regimes: τ/τ0 ∼ (T - Tc)-zv and ln(τ/τ0) ∼ T -zv. Both are shown to be consistent with the data, and to lead to Tc = 1.50 K, zv = 8, τ0 = 3x10-12 s; or Tc = 0, zv = 9 and τ 0 = 10-8 s. The set of parameters derived for the former (finite Tc) case appears to be more consistent with previous data on Eu0.4Sr0.6S, and with recent computer simulations. We then generate, in the magnetic field-temperature plane, lines Tf (ω, H) associated with the response time τ. We include remanent magnetization measurements which refer to well defined experimental time scales (≤1 s or ≤25 s). The entire set of scaled data, for the case when Tc = 1.50 K, strongly suggests that the response time diverges for H 1 2 ∼ T - Tc. This is of the form of a de Almeida-Thouless transition line with, however, a non-mean-field exponent.

UR - http://www.scopus.com/inward/record.url?scp=0022008481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022008481&partnerID=8YFLogxK

U2 - 10.1016/0304-8853(86)90464-6

DO - 10.1016/0304-8853(86)90464-6

M3 - Article

AN - SCOPUS:0022008481

VL - 54-57

SP - 1

EP - 5

JO - Journal of Magnetism and Magnetic Materials

JF - Journal of Magnetism and Magnetic Materials

SN - 0304-8853

IS - PART 1

ER -