Observation of an extraordinary antiferromagnetic transition on the NiO(100) surface by metastable helium atom diffraction

Abstract

We report on the temperature dependence of magnetic diffraction peaks obtained by scattering of coherent metastable $2{}^{3}S$ helium atomic beams from the (100) surfaces of antiferromagnetic NiO crystals. The data obtained are related to the surface sublattice magnetization using a formalism developed within the framework of the eikonal approximation. The results reveal a surface antiferromagnetic transition that belongs to the universality class of the anisotropic extraordinary surface transition of the three-dimensional Heisenberg model (3D HM) with surface anisotropy $(d=3,$ $n=3,$ ${m}_{e}=1):$ A 2D surface spin-ordering transition takes place at 529 K, followed by a crossover to a multicritical regime at the bulk Ne\'el temperature ${T}_{N}^{b}=523.6\mathrm{K}.$ We obtain the crossover function by plotting the sublattice magnetization ${m}_{1},$ against the crossover scaling variable $|{(J}_{s}{/J}_{s}^{c})\ensuremath{-}1|/[{(T/T}_{c}^{b})\ensuremath{-}1{]}^{\ensuremath{\varphi}},$ where ${J}_{s}$ is an effective surface exchange coupling, ${J}_{s}^{c}$ is its critical value, ${T}_{c}^{b}$ is the bulk critical temperature, and using the crossover exponent $\ensuremath{\varphi}=0.57,$ derived by Diehl and Eisenriegler for the 3D anisotropic HM (AHM). This function is very similar to that reported by Binder and Landau for the 3D Ising model with $\ensuremath{\varphi}=0.56,$ and we may ascertain that the critical behavior of the 3D extraordinary transition for both models is quite similar. The critical behavior of the NiO(001) surface reported here is attributed to the presence of single-site spin anisotropy in an otherwise Heisenberg-like surface layer, absent in the bulk because of its higher symmetry. We obtain an estimate of the anisotropy energy of $D=\ensuremath{-}2.5\mathrm{meV},$ by electronic-structure cluster calculations employing Hartree-Fock states with configuration interactions. The fact that the presence of surface single-site anisotropy leads to enhancement of the surface Ne\'el temperature is supported by recent mean-field theoretical studies based on the Schwinger-boson formalism, which indicate that for $D/Jg0.1$ the surface Ne\'el temperature is consistently higher than that of the bulk even when the surface superexchange energy is suppressed to 75% of the bulk value.