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Magnetism of sperimagnetic amorphous RCo3 thin films with R = Dy, Tb, and Tm

Zexiang Hu1, Ajay Jha1, Katarzyna Siewierska2, Simon Lenne1, Pierre le Berre3, Nora M. Dempsey3, Plamen Stamenov1, Karsten Rode1, and J. M. D. Coey1,*

  • *Contact author: jcoey@tcd.ie
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Phys. Rev. B 112, 014441 – Published 22 July, 2025

DOI: https://doi.org/10.1103/yzfd-jqvx

Abstract

The magnetization of amorphous sputtered films of a-RxCo1−x, with x≈0.25 and R = Dy, Tb, or Tm, is investigated by magnetometry, anomalous Hall effect, and magneto-optic Kerr effect to understand how the magnetic structure of the films is influenced by temperature and the quadrupole and higher multipole moments of the rare-earth charge distribution. Square magnetic hysteresis loops with perpendicular magnetic anisotropy and divergent coercivity that reaches 3.5 T in the vicinity of the compensation temperature Tcomp are observed at 175 and 200 K for Dy and Tb films, respectively, but the coercivity in Tm films never exceeds 0.5 T and shows no divergence near the compensation at 50 K. The temperature dependence of the net rare-earth moment is inferred from the cobalt moment of soft ferromagnetic a-YxCo1−x. The magnitude of the second-order random anisotropy energy exceeds the antiparallel R-Co exchange coupling for all three rare earths. The negative quadrupole moments of Dy and Tb lead to random easy-axis anisotropy with large coercivity. The positive quadrupole moment of Tm favors random hard-axis anisotropy where each Tm has an easy plane. The resulting sperimagnetic ground states are modeled by a distribution of rare-earth moments within a cone of half-angle θ0 whose axis is antiparallel to the ferromagnetic axis of cobalt. The reduced moment 〈Jz〉/J at T = 0 is calculated from a one-atom Hamiltonian as a function of α, the ratio of uniaxial anisotropy to exchange energy per rare-earth atom for different angles θ between the local anisotropy axis, and the ferromagnetic Co axis. Extrapolated values of 〈Jz〉/J are ∼0.75 at low temperature for both Dy and Tb, with a sharp increase <10 K attributed to higher-order multipole moments. The hard-axis random anisotropy resulting from the positive quadrupole moment of Tm leads to a larger low-temperature value of 〈Jz〉/J = 0.84. On increasing temperature, the magnitude of the rare-earth moment and the local random anisotropy that creates the sperimagnetism are reduced; the cone angle narrows, but the noncollinear structure persists well above room temperature for Dy but not for Tb, a difference related to the opposite signs of their hexadecapole moments. A temperature-dependent spin-flop field observed near compensation in a-Dy25Co75 extrapolates to 2.0 T at Tcomp, a remarkably low value that is associated with the nonrigid character and high transverse susceptibility of the frustrated Dy subnetwork. An x-ray photoemission electron microscopy investigation of partial single-pulse all-optical switching in a 10 nm a-Dy25Co75 film as a function of temperature establishes that the process is stochastic, and unrelated to inhomogeneities in the films. The size of the sperimagnetic domains in the unmagnetized state is ∼200 nm, <300 K.

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Phys. Rev. B 112, 014441– Published 22 July, 2025
  • Received 5 January 2024
  • Accepted 11 June 2025
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