Synchrotron x-ray scattering of magnetic and electronic structure of UN and ${\mathrm{U}}_2{\mathrm{N}}_3$ epitaxial films

We examine the magnetic ordering of UN and of a closely related nitride, ${\mathrm{U}}_2{\mathrm{N}}_3$, by preparing thin epitaxial films and using synchrotron x-ray techniques. The magnetic configuration and subsequent coupling to the lattice are key features of the electronic structure. The well-known antiferromagnetic (AF) ordering of UN is confirmed, but the expected accompanying distortion at ${\mathrm{T}}_N$ is not observed. Instead, we propose that the strong magnetoelastic interaction below ${\mathrm{T}}_N$ causes substantial changes in the strain in the sample being measured. These strains vary as a function of the sample form. As a consequence, the accepted AF configuration of UN may be incorrect. In the case of cubic $\alpha -{\mathrm{U}}_2{\mathrm{N}}_3$, no single crystals have been previously prepared, and we have determined the AF ordering wave vector. The AF ${\mathrm{T}}_N$ is close to that previously reported. In addition, resonant diffraction methods have identified an aspherical quadrupolar charge contribution in ${\mathrm{U}}_2{\mathrm{N}}_3$ involving the $5f$ electrons.

Figure 1

Lattice parameters as measured from different reflections for the UN film. The values reported by Marples 1970 [18] are given by inverted triangles. $c$ is defined as the lattice parameter in the growth direction of the film. The UN film thickness is 200 nm and the film is deposited on a Nb (001) buffer on a sapphire $\left(1\overline{1}02\right)$ sub- strate [5].

Figure 2

Relative variation of the lattice parameters in UN below ${\mathrm{T}}_N$ as measured in our work and previously reported in Refs. [18, 19, 20, 21].

Figure 3

The relationship between the tetragonal distortion, $\left|c/a-1\right|$, versus the relative change of the FWHM ($\mathrm{\Delta }d/d$) obtained in a simulation for UN. The proportionality factor is 417. The inset shows the profiles that would have been measured by Marples et al. (1975) [19] if $(c/a-1)=6.5\times {10}^{-4}$. Our data shows that any distortion is smaller, $\le 2.3\times {10}^{-4}$ for $\left|c/a-1\right|$.

Figure 4

The relative strain below ${\mathrm{T}}_N$ for the UN film sample in two different directions. The growth direction is given by the (0 0 10) reflection, showing a tensile (expanding) strain as the temperature is lowered below ${\mathrm{T}}_N$. The in-plane strain (which is compressive in nature) is deduced from combining the results from the (0 0 10) and (555) reflections, and is reduced below ${\mathrm{T}}_N$. The error bars are $\pm 5\times {10}^6$ units.

Figure 5

Plot of the square root of the integrated intensity of the (001) for UN and (003) for ${\mathrm{U}}_2{\mathrm{N}}_3$ as a function of reduced temperature $t=({\mathrm{T}}_N-\mathrm{T})/{\mathrm{T}}_N$ on a log-log plot to determine ${\mathrm{T}}_N$ and $\beta$. The dotted black line gives $\beta =0.31$ as determined for bulk UN Ref. [29].

Figure 6

The lattice parameter $c$ and the FWHM ($\mathrm{\Delta }d/d$) observed for the various specular peaks as a function of temperature. The large differences in measured $c$ lattice parameter, when the energy is shifted from 15 keV to the resonant energy of 3.72 keV, is caused by refraction. The expected values of the (001) and (002) at 3.72 keV, assuming the values at 15 keV are correct, are given as dashed lines using $\delta =2.0\times {10}^{-4}$, see text.

Figure 7

Polarization dependence of the specular peaks (00L) in ${\mathrm{U}}_2{\mathrm{N}}_3$ at 10 K measured at the U $M_4$ resonance energy. The data shows a complete separation between the charge peaks from the bcc structure and the magnetic peaks arising from the ordered moments below ${\mathrm{T}}_N=73$ K. The (002) is a weak reflection; its presence signifies that the positional parameter for the ${\mathrm{U}}_2$ atom is different from zero. The (003) reflection is magnetic and disappears at ${\mathrm{T}}_N$.

Figure 8

Energy dependence of the diffraction peaks in both UN and ${\mathrm{U}}_2{\mathrm{N}}_3$. (a) and (b) show that there is no signal at the (001) of UN at $T=80$ K ($T>{\mathrm{T}}_N$) and that the energy dependence of the charge (002) does not change with temperature. The bottom panel (c) shows how charge peaks from ${\mathrm{U}}_2{\mathrm{N}}_3$ vary in energy according to the groups listed in Table 1. Groups B, C, and E in ${\mathrm{U}}_2{\mathrm{N}}_3$ sense the $f^{\prime \prime }$ term of the scattering factor, the same term observed in magnetic scattering. Reflections in Groups A (not shown) and D have a standard charge profile in energy through the resonance. These profiles are independent of temperature.