Magnetism in the few-monolayers limit: A surface magneto-optic Kerr-effect study of the magnetic behavior of ultrathin films of Co, Ni, and Co-Ni alloys on Cu(100) and Cu(111)

The surface magneto-optic Kerr effect (SMOKE) was used to investigate the magnetic properties of epitaxial thin films of Co, Ni, and their alloys grown on Cu(100) and Cu(111). The Curie temperature ${\mathit{T}}_{\mathit{C}}$ is higher for the same films of a given thickness on Cu(111) than on Cu(100). All the films show a change in the power-law exponent \ensuremath{\beta} of the magnetization density M\ensuremath{\sim}(1-T/${\mathit{T}}_{\mathit{C}}$${)}^{\mathrm{\ensuremath{\beta}}}$ with reducing film thickness. Ni films on Cu(100) undergo a particularly abrupt crossover at \ensuremath{\sim}7 monolayers (ML) from three-dimensional Heisenberg (\ensuremath{\beta}=0.37) to finite-size two-dimensional XY (\ensuremath{\beta}=0.23) behavior as the film thickness is reduced. The characteristic power-law exponent \ensuremath{\beta}=0.23 of these films appears to be an experimental realization of Kosterlitz-Thouless behavior over a restricted temperature range. A similar, but more gradual crossover occurs for the Ni films on Cu(111) at 8 to 12 ML. The finite-size scaling behavior in the few-monolayers-thickness range is compared with that reported for Ising thin-film behavior. In all instances ${\mathit{T}}_{\mathit{C}}$ extrapolates with decreasing thickness to zero at one monolayer. The dimensionality crossover and finite-size scaling behavior is discussed in the light of our current understanding of spin-wave quantization, anisotropy, and film microstructure.