Distinct Magnetic Phase Transition at the Surface of an Antiferromagnet

In the majority of magnetic systems the surface is required to order at the same temperature as the bulk. In the present Letter, we report a distinct and unexpected surface magnetic phase transition at a lower temperature than the Néel temperature. Employing grazing incidence x-ray resonant magnetic scattering, we have observed the near-surface behavior of uranium dioxide. ${\mathrm{UO}}_2$ is a noncollinear, triple-$\mathbf{q}$, antiferromagnet with the U ions on a face-centered cubic lattice. Theoretical investigations establish that at the surface the energy increase—due to the lost bonds—is reduced when the spins near the surface rotate, gradually losing their component normal to the surface. At the surface the lowest-energy spin configuration has a double-$\mathbf{q}$ (planar) structure. With increasing temperature, thermal fluctuations saturate the in-plane crystal field anisotropy at the surface, leading to soft excitations that have ferromagnetic $XY$ character and are decoupled from the bulk. The structure factor of a finite two-dimensional $XY$ model fits the experimental data well for several orders of magnitude of the scattered intensity. Our results support a distinct magnetic transition at the surface in the Kosterlitz-Thouless universality class.

Figure 1

fcc allowed structural Bragg reflections in the $(001)\times (010)$ plane: $H$, $K$, $L$ are all even or all odd. The structural or charge bulk Bragg spots are solid red. The magnetic Bragg spots are open. The red solid lines show TRs that are both structural and magnetic. The blue dotted lines are pure MTRs. The inset schematically depicts the grazing incidence scattering geometry employed in the experiment. ${\alpha }_{i(f)}$, ${\mathbf{k}}_{i(f)}$ are the incident (final) angle and wave vector, respectively. $\mathbf{Q}$ is the wave-vector transfer, which is mainly contained within the surface.

Figure 2

Upper curves: The observed normalized intensity (closed symbols) at the magnetic truncation rod (0 $Q_K$ 0.97) for two temperatures below the bulk Néel temperature. Lower curves: The equivalent data (open symbols) for the bulk magnetic Bragg peak (011). The respective data are normalized and offset for clarity. The solid lines are best fits to the model described in the text.

Figure 3

Intensities vs wave vector as a function of temperature. One can observe that for temperatures above 22.8 K the reduction in intensity as a function of $Q_K$ is much more gradual (linear) than for lower temperatures, as shown explicitly for two temperatures in Fig. 2. This is a key signature of magnetic roughening. The data are offset for clarity.

Figure 4

(a) Open circles show the integrated intensity of the (011) magnetic Bragg reflection as a function of temperature. The transition is first order (discontinuous). The line connecting the points is a fit to the expression $I_0(1-(T/T_{\mathrm{N}}){)}^{2\beta }$ with $\beta =0.3$. The blue squares show the integrated intensity at the MTR (0 1 0.97) near the (011) Bragg spot. The transition at the surface appears continuous. (b) The variation of $\eta$ as a function of temperature. A discontinuity is identified at a temperature, $T_{\mathrm{KT}}$.