{
  "id": "2401.05722",
  "version": "v1",
  "published": "2024-01-11T07:57:14.000Z",
  "updated": "2024-01-11T07:57:14.000Z",
  "title": "Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers",
  "authors": [
    "Clémentine Courtès",
    "Matthieu Boileau",
    "Raphaël Côte",
    "Paul-Antoine Hervieux",
    "Giovanni Manfredi"
  ],
  "comment": "28 pages",
  "categories": [
    "cond-mat.mes-hall",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature regime, where thermal fluctuations are modeled by a random magnetic field whose variance is proportional to the temperature. By rescaling the temperature proportionally to the computational cell size $\\Delta x$ ($T \\to T\\,\\Delta x/a_{\\text{eff}}$, where $a_{\\text{eff}}$ is the lattice constant) [M. B. Hahn, J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures $T_{\\text{C}}$ that are in line with the experimental values for cobalt, iron and nickel. For finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie temperature varies with the smallest size $d$ of the system. We show that the difference between the computed finite-size $T_{\\text{C}}$ and the bulk $T_{\\text{C}}$ follows a power-law of the type: $(\\xi_0/d)^\\lambda$, where $\\xi_0$ is the correlation length at zero temperature, and $\\lambda$ is a critical exponent. We obtain values of $\\xi_0$ in the nanometer range, also in accordance with other simulations and experiments. The computed critical exponent is close to $\\lambda=2$ for all considered materials and geometries. This is the expected result for a mean-field approach, but slightly larger than the values observed experimentally.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-11T07:57:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ferromagnetic nanowires",
      "micromagnetic simulations",
      "size dependence",
      "nanolayers",
      "random magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}