Effects of high pressure on the structural, magnetic, and transport properties of the itinerant 5$f$ ferromagnet ${\text{U}}_2$${\text{Fe}}_3$Ge

Crystal structure, magnetic, and transport properties of the ${\text{U}}_2$${\text{Fe}}_3$Ge compound have been studied under hydrostatic pressure. ${\text{U}}_2$${\text{Fe}}_3$Ge crystallizes in the hexagonal crystal structure of the ${\text{Mg}}_2$${\text{Cu}}_3$Si type, an ordered variant of the ${\text{MgZn}}_2$ Laves structure (C14). The Laves phase has proven highly stable; the crystal structure is maintained up to 27 GPa, the highest applied pressure. X-ray diffraction data revealed that the $c$ direction, where the shortest U-U bonds lie, is softer than the $a$ direction. The bulk modulus $B_0$ is ∼100 GPa. ${\text{U}}_2$${\text{Fe}}_3$Ge is an itinerant ferromagnet with the Curie temperature $T_{\mathrm{C}}$ = 55 K and the spontaneous magnetic moment $M_{\mathrm{s}}=1{\mu }_{\mathrm{B}}$ per formula unit at ambient pressure. The two parameters decrease rapidly under pressure with the rates $\mathrm{d}\left(\ln M_s\right)/\mathrm{d}p=-0.33$ GPa${}^{-1}$ and $\mathrm{d}\left(\ln T_{\mathrm{C}}\right)/\mathrm{d}p=-0.27$ GPa${}^{-1}$. The extrapolation of $T_{\mathrm{C}}$ and $M_{\mathrm{s}}$ indicates that the magnetic order will be suppressed between 3 and 4 GPa. Electrical resistivity was found to decrease gradually with increasing pressure. The data in the ferromagnetic state points to the opening of a gap in the magnon spectrum at higher pressures. ${\text{U}}_2$${\text{Fe}}_3$Ge is relatively more sensitive to pressure than isostructural ${\text{UNi}}_2$.

Figure 1

Unit cell of the compound ${\text{U}}_2$${\text{Fe}}_3$Ge.

Figure 2

X-ray diffraction pattern of ${\text{U}}_2$${\text{Fe}}_3$Ge taken at 0.1 GPa (red open symbols) with the Le Bail fitting (black line) and the difference profile (bottom blue line). It shows the calculated Bragg positions of ${\text{U}}_2$${\text{Fe}}_3$Ge (green vertical bars) and of the Inconel gasket (red vertical bars), together with the Miller indexes for both.

Figure 3

Partial representation of the diffraction patterns taken at different pressures, reflecting the shifting and broadening of the diffraction peaks of ${\text{U}}_2$${\text{Fe}}_3$Ge with increasing applied pressure. The broadening is mostly due to imperfect hydrostaticity.

Figure 4

Pressure dependence of the lattice parameters $a$ and $c$, and relative volume $V/V_0$ for ${\text{U}}_2$${\text{Fe}}_3$Ge. The full line in the lattice parameters represents the fits according to Eq. (2), while for $V/V_0$, it corresponds to the fit to the Birch-Murnaghan equation of state according to Eq. (1).

Figure 5

Pressure changes of the relative lattice parameters Δ$a$/$a$ and Δ$c$/$c$ and volume $\Delta V/V$ for ${\text{U}}_2$${\text{Fe}}_3$Ge.

Figure 6

Temperature dependence of the magnetization along the $a$ axis of the ${\text{U}}_2$${\text{Fe}}_3$Ge single crystal in a field of (a) 0.01 T and (b) 2 T under different pressures. Note the different magnetization scales in the two panels.

Figure 7

Magnetization curves along the $a$ axis of the ${\text{U}}_2$${\text{Fe}}_3$Ge single crystal at (a) $T$ = 2 K and (b) $T=50$ K at various pressures.

Figure 8

Temperature evolution of the magnetization curve along the $a$ axis of the ${\text{U}}_2$${\text{Fe}}_3$Ge single crystal under $p$ = 0.74 GPa. The inset shows the temperature dependence of the spontaneous magnetic moment under this pressure.

Figure 9

(a) ${\text{U}}_2$${\text{Fe}}_3$Ge spontaneous magnetic moment and Curie temperature dependence as a function of pressure, and (b) relative change of the $c$ parameter.

Figure 10

(a) Temperature dependence of the normalized electrical resistivity ρ, and (b) several temperature derivatives for pressures in the range $p$ = 0.71–3.51 GPa for ${\text{U}}_2$${\text{Fe}}_3$Ge with current flowing along the $a$ axis. The inset in panel (a) presents the electrical resistivity in absolute values at $p$ = 2.55 GPa (bottom) and 3.51 GPa (top). The temperature derivatives showing the evolution of $T_{\mathrm{C}}$ and $T_{\max }$ with the pressure are plotted in the inset of panel (b). The arrows on the dρ/d$T$($T$) dependence show the position of $T_{\mathrm{C}}$ and $T_{\max }$.

Figure 11

Derivative of the logarithmic dependence of $T_{\mathrm{C}}$ against the volume plotted for ${\text{U}}_2$${\text{Fe}}_3$Ge and ${\text{UNi}}_2$, showing how the same range of pressure affects both compounds. The dashed lines are guides to the eye.