Hu, Z.; Jha, A.; Siewierska, K.; Lenne, S.; le Berre, P.; Dempsey, N. M.; Stamenov, P.; Rode, K.; Coey, J. M. D.: Magnetism of sperimagnetic amorphous RCo3 thin films with R = Dy, Tb, and Tm. Physical Review B 112 (2025), p. 014441/1-13
10.1103/yzfd-jqvx
Open Access Version
Abstract:
The magnetization of amorphous sputtered films of a-119877;𝑥Co1−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-𝑥Co1−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⟩/𝐽are ∼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-Dy25Co75extrapolates 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.