Valence instability across the magnetostructural transition in ${\mathrm{USb}}_2$

We have performed pressure-dependent x-ray diffraction and resonant x-ray emission spectroscopy experiments on ${\mathrm{USb}}_2$ to further characterize the antiferromagnetic-ferromagnetic transition occurring near 8 GPa. We have found the magnetic transition coincides with a tetragonal to orthorhombic transition resulting in a 17% volume collapse as well as a transient $f$-occupation enhancement. Compared to ${\mathrm{UAs}}_2$ and UAsS, ${\mathrm{USb}}_2$ shows a reduced bulk modulus and transition pressure and an increased volume collapse at the structural transition. Except for an enhancement across the transition region, the $f$ occupancy decreases steadily from 1.96 to 1.75.

Figure 1

(a) Representative background-subtracted PXRD patterns (markers) and fit (solid lines). The $P=8.2$ and 9 GPa data show the coexistence of each phase, and the bumps just below ${10}^{\circ }$ and at ${15}^{\circ }$ in the 10.6-GPa data correspond to the last remaining peaks of the low-pressure phase. (b) Distinct PXRD measurement at $P=10.5$ GPa used to determine the high-pressure phase. The solid black line shows the resulting Le Bail fit and accounts for each peak in the pattern, and the blue ticks correspond to the reflections for the $Pmm2$ structure; the small bump below ${10}^{\circ }$ is due to the low-pressure phase, and the bump near ${15}^{\circ }$ is an artifact of the measurement that showed up at all pressures for this measurement. The solid blue line shows the difference curve and is offset by $-5$.

Figure 2

Calculated lattice parameters and volume for ${\mathrm{USb}}_2$. The gray rectangle corresponds to the transition width found from the structural data, and the dashed black line is the transition width measured from transport measurements [9]. The solid line in (b) represents a fit to the Birch-Murnaghan equation of state up to 8 GPa and yields values of $B=68.7$ GPa and $B^{\prime }=4.7$. Error bars are smaller than the markers and have been omitted for clarity.

Figure 3

RXES spectra at select pressures. There exists an overall trend of intensity shifting to higher incident and transferred energies with pressure, although from 9.5 to 11 GPa an unusual enhancement of the low-energy intensity occurs. The vertical gray line is a guide to the eye for easier comparisons between pressures. Each spectrum is normalized to a peak intensity of 1.0.

Figure 4

X-ray absorption spectra in partial fluorescence yield mode at select pressures. The peak location shifts to higher incident energies $E_i$ with increasing pressure, indicating a decrease in $f$ occupation. The abrupt enhancement from 9.5 to 11 GPa is particularly obvious in these scans. Each scan is offset by 0.1 and is normalized to an edge jump of unity. Error bars are smaller than the markers and have been omitted.

Figure 5

(a)–(d) Example fits at $P=1.4$ GPa to the emission scans at incident energies used to determine the line shapes. (e) Lorentzian amplitudes as a function of pressure for $P=1.4$ GPa. Error bars from the fitting procedure are included in (e), although they are discernible only from the data points near $E_i=17.160$ keV.

Figure 6

$n_f$ determined via the method proposed by Dallera et al. [20]. There is a gradual decrease in $n_f$, although a temporary enhancement occurs across the magnetostructural transition. The gray rectangle corresponds to the transition width found from the structural data, and the dashed black lines show the transition width measured from transport measurements [9]. An offset of around 1 GPa between the pressure measured in the structure and x-ray absorption would be plausible.

Figure 7

Fit of the high-pressure structure using the $Pbnm$ structure with $a=7.819$ Å, $b=6.926$ Å, and $c=4.395$ Å at 10.5 GPa. The reflections are indicated by the blue ticks. Several peaks cannot be indexed using this space group and are indicated with an asterisk (*).

Figure 8

Acquired images for the two distinct measurements of ${\mathrm{USb}}_2$. Left: Image collected at $P=10.6$ GPa. Right: Image collected at $P=10.5$ GPa. Both patterns suffer from single-crystal peaks, which make it challenging to extract the atomic positions. The solid black lines correspond to space between individual image plates and the diode, which blocks a section of the emitted x-ray beam.

Figure 9

$n_f$ determined via the full spectrum Kramers-Heisenberg analysis. Uncertainty of one standard deviation at fixed peak positions is smaller than the markers.

Figure 10

(a) and (b) RXES spectra and (c) and (d) fit for $P=1.4$ GPa and $P=16$ GPa. The vertical gray line is centered at 17 160 eV and is a guide to the eye.