Uranium ferromagnet with negligible magnetocrystalline anisotropy: ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$

Strong magnetocrystalline anisotropy (MA) is a well-known property of uranium compounds. The almost isotropic ferromagnetism in ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ reported in this paper represents a striking exception. We present results for magnetization, ac susceptibility, thermal expansion, specific heat, and electrical resistivity measurements performed on a ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ single crystal at various temperatures and magnetic fields; we discuss the results in relation to first-principles electronic structure calculations. ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ behaves as an itinerant $5f$-electron ferromagnet ($T_{\mathrm{C}}=10.7\mathrm{K}, {\mu }_{\mathrm{S}}=0.85{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ at $1.9\mathrm{K}$). The ground-state easy magnetization direction is along the [111] axis of the cubic lattice. The anisotropy field ${\mu }_0{H}_{\mathrm{a}}$ along the [001] direction is only about $0.3\mathrm{T}$, which is at least three orders of magnitude smaller than for other U ferromagnets. At $T_r=5.9\mathrm{K}$ the easy magnetization direction changes to [001], and remains [001] up to $T_{\mathrm{C}}$. This transition is due to a change in magnetic symmetry, and is quite apparent in the low-field magnetization, ac susceptibility, and thermal expansion data, whereas only weak anomalies are observed at $T_r$ in the temperature dependence of the specific heat and electrical resistivity. The magnetoelastic interaction induces a rhombohedral (tetragonal) distortion of the paramagnetic cubic crystal lattice in the case of the [111] ([001]) easy magnetization direction. The rhombohedral distortion is connected with two crystallographically inequivalent U sites. Our density functional theory calculations, including spin-orbit interaction (SOI) of the U $5f$ electrons, also produces two inequivalent U sites, because SOI leads to a reduction of the symmetry of the former cubic structure. The calculated ground state is in agreement with the experimentally observed [111] easy magnetization direction. The first excited state has moments along the [001] direction, which agrees with the moment orientation for $T>T_{\mathrm{r}}$. The energy of the first excited state is $0.9\mathrm{meV}$ above the ground state, which is comparable to the value of $0.51\mathrm{meV}$, corresponding to $k_{\mathrm{B}}{T}_{\mathrm{r}}$. We propose that weak MA of the ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ compound is due to the lack of direct overlap of the $5f$ orbitals of the nearest U ions, which is screened out by the closed Ru and Ge cuboctahedra coordinating each U ion.

Figure 1

Structure of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ together with magnetic moments from theoretical calculations. Arrows for magnetic moments are in proper relative scale but in arbitrary units. ${\mathrm{U}}_1$ ions are blue, ${\mathrm{U}}_2$ are green, ${\mathrm{Ru}}_1$ and ${\mathrm{Ru}}_2$ are gray, and $\mathrm{Ge}$ are yellow. The shortest distances ${\mathrm{U}}_{(1,2)}-{\mathrm{Ru}}_1$ are marked by gray cylinders.

Figure 2

X-ray powder-diffraction pattern of an as-cast pulverized ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ single crystal measured at room temperature.

Figure 3

Field dependence of magnetization isotherms of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ at $1.9\mathrm{K}$ for the applied magnetic field along the [111] and [001] directions. The inset shows a low-field detail.

Figure 4

Temperature dependence of the magnetization of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ measured in a magnetic field of $10\mathrm{mT}$ (in the ZFC regime) applied along the [111] or [001] direction (a) and temperature dependence of the ac susceptibility in the ac field applied along the [111] direction (b). The inset in the upper panel shows field dependence of magnetization at $9\mathrm{K}$.

Figure 5

Arrott plots for ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ in a magnetic field applied along the [001] direction.

Figure 6

Arrott-Noakes plots reflecting the equation of states (with $\beta =0.31\pm 0.03$ and $\gamma =0.81\pm 0.04$) for ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ in the magnetic field applied along the [001] direction.

Figure 7

Temperature dependence of the inverse susceptibility of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ in a magnetic field of $1\mathrm{T}$ applied along the [111] and [001] direction. The full curve represents the fit with a modified Curie-Weiss law.

Figure 8

Temperature dependence of the heat capacity ($C/T$ vs $T$ plot) of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$. Inset: The $C/T$ vs $T^2$ plot.

Figure 9

Linear thermal expansion of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ along the [001] and [111] directions.

Figure 10

Linear thermal expansion of ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ along the [001] and [100] (denoted as ${\lambda }_{\mathrm{S}\left[001\right]}$ and ${\lambda }_{\mathrm{S}\left[100\right]}$ on the left axis) direction in a magnetic field of $30\mathrm{mT}$ applied along [001], and the corresponding thermal volume expansion (denoted as ${\omega }_S$ on the right axis). Temperatures are from $6.2\mathrm{K}$ to $T_{\mathrm{C}}$. The data are considered as the best estimation of corresponding spontaneous magnetostriction (see text).

Figure 11

Temperature dependence of electrical resistivity of the ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ measured for current along [111] and [001] direction.