$5f$ states in $\mathrm{U}{\mathrm{Ga}}_2$ probed by x-ray spectroscopies

The $5f$-based ferromagnet $\mathrm{U}{\mathrm{Ga}}_2$ with the Curie temperature $T_{\mathrm{C}}=125\mathrm{K}$ was investigated by x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) experiments at the $\mathrm{U}–M_{4,5}$ and Ga–K edges. The position of the $\mathrm{U}–M_4$ white line, determined in the high-energy resolution fluorescence detection XAS, suggests that $\mathrm{U}{\mathrm{Ga}}_2$ is neither a localized $5f^2$ nor an itinerant system with $5f$ occupancy close to $n_{5f}=3$. The analysis of the acquired $M_{4,5}$ XANES and XMCD spectra indicates the $5f$ occupancy close to 2.5 and a large orbital magnetic moment of the uranium $5f$ states (3.18 ${\mu }_{\mathrm{B}}$) that is partly compensated by the antiparallel spin moment (1.31 ${\mu }_{\mathrm{B}}$). Thus, the total $5f$ magnetic moment of 1.87 ${\mu }_{\mathrm{B}}$ is obtained, which is smaller than the known bulk magnetization of 3.0 ${\mu }_{\mathrm{B}}$ per formula unit, while the magnetic moments of the Ga atoms are negligible. Several methods based on density-functional theory were applied and the obtained results were compared with XAS spectral features, the Sommerfeld coefficient of the electronic specific heat, and the size of the U moments and $5f$ occupancies. A clear correlation is revealed between the $\mathrm{U}–M_4$ white-line position of three metallic uranium compounds and the calculated uranium ionicity. It is demonstrated that only electronic structure methods taking appropriate care of orbital magnetism and related atomic multiplet effects can successfully describe all considered properties.

Figure 1

$\mathrm{U}–M_4$ edge of $\mathrm{U}{\mathrm{Ga}}_2$ (black line) compared with spectra of $\mathrm{U}{\mathrm{Pd}}_3$, ${\mathrm{UO}}_2$, and $\mathrm{U}{\mathrm{Sn}}_3$, all from Ref. [36].

Figure 2

X-ray absorption at the $\mathrm{U}–M_5$ and $M_4$ edges for two different helicities (black and red) and the difference of the two helicities (blue).

Figure 3

X-ray absorption at the Ga–K edge for two different helicities (black and red) and their difference (blue).

Figure 4

$\mathrm{U}–M_{4,5}$ absorption edges of $\mathrm{U}{\mathrm{Ga}}_2$ measured in DAC with increasing hydrostatic pressure.

Figure 5

Variation of the U $5f$ and $6d$ occupancy as a function of pressure (wien2k, LSDA+U method with $U=2\mathrm{eV}$). The absolute value of the $6d$ filling is underestimated since only the charge density inside the muffin-tin sphere $\left(R_{\mathrm{MT}}=2.65a_{\mathrm{B}}\right)$ is counted whereas the $6d$ states are delocalized and extend to the interstitial region. In the tight-binding model used for the LDA+DMFT calculations, there are approximately 2 electrons in the uranium-$6d$-like Wannier functions. For comparison, the related fplo occupation numbers at zero pressure are $n_{6d}=1.96\left(1.10\right)$ for gross (net) occupation, which can be compared with the wien2k values of $n_{6d}=2.0\left(0.86\right)$ for total (muffin-tin sphere).

Figure 6

Shift of the measured ascending edge inflection point vs computed ionicity of the uranium atom in three metallic compounds. The filled circles mark data points; the line is intended to guide the eye.

Figure 7

Calculated $M_4$ spectra (thick blue lines) obtained by broadening the $j$-resolved densities of states $\left(5f_{5/2}–\mathrm{red}\right)$ corresponding to ferromagnetic solutions from GGA (fplo, left), GGA+OPC (fplo, middle), and LDA+DMFT* (right). The black lines with dots represent the experimental data from HERFD XAS (the same as shown in Fig. 1). The experimental spectrum was aligned with the theoretical main peak.

Figure 8

Comparison of all calculated $M_4$ spectra (full lines) with the experimental HERFD XAS data (dots). All data are the same as in Fig. 5, but nonmagnetic GGA is added. The main peaks of all datasets are aligned.