{
  "id": "2310.13706",
  "version": "v1",
  "published": "2023-10-05T12:43:51.000Z",
  "updated": "2023-10-05T12:43:51.000Z",
  "title": "Optimized Analysis of the AC Magnetic Susceptibility Data in Several Spin-Glass Systems using the Vogel-Fulcher and Power Laws",
  "authors": [
    "Mouli Roy-Chowdhury",
    "Mohindar S. Seehra",
    "Subhash Thota"
  ],
  "comment": "33 pages, 4 main figures, 15 figures in the supplementary document. The following article has been submitted to AIP Advances",
  "categories": [
    "cond-mat.dis-nn",
    "physics.gen-ph"
  ],
  "abstract": "In spin-glasses (SG), the relaxation time $\\tau$ ($= 1/2{\\pi}f$) vs. $T_f$ data at the peak position $T_f$ in the temperature variation of the ac magnetic susceptibilities at different frequencies f is often fit to the Vogel-Fulcher Law (VFL): $\\tau=\\tau_0\\exp[E_a/k_b(T_f-T_0)]$ and to the Power Law (PL): $\\tau = \\tau_0^*[(T_f-T_{SG}/T_{SG}]^{-z\\nu}$. Both these laws have three fitting parameters each, leaving a degree of uncertainty since the magnitudes of the evaluated parameters $\\tau_0$, $E_a/k_B$, $\\tau_{0^*}$ and $z\\nu$ depend strongly on the choice of $T_0$ and $T_{SG}$. Here we report an optimized procedure for the analysis of $\\tau$ vs. $T_f$ data on several SG systems for which we could extract such data from published sources. In this optimized method, the data of $\\tau$ vs. $T_f$ are fit by varying $T_0$ in the linear plots of $\\ln \\tau$ vs $1/ (T_f - T_0)$ for the VFL and by varying $T_{SG}$ in the linear plot of $\\ln \\tau$ vs. $\\ln (T_f - T_{SG})/ T_{SG}$ for the PL till optimum fits are obtained. The analysis of the associated magnitudes of $\\tau_0$, $E_a/k_B$, $\\tau_{0^*}$ and $z\\nu$ for these optimum values of $T_0$ and $T_{SG}$ shows that magnitudes of $\\tau_{0^*}$, $\\tau_0$ and $z\\nu$ fail to provide a clear distinction between canonical and cluster SG. However, new results emerge showing $E_a/(k_BT_0) < 1$ in canonical SG whereas $E_a/(k_BT_0) >1$ for cluster SG systems and the optimized $T_0 <$ optimized $T_{SG}$ in all cases. Although some interpretation of these new results is presented, a more rigorous theoretical justification of the boundary near $E_a/(k_BT_0) \\sim 1$ is desired along with testing of these criteria in other SG systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T12:43:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ac magnetic susceptibility data",
      "power law",
      "spin-glass systems",
      "optimized analysis",
      "sg systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}