Uranium ferromagnet with negligible magnetocrystalline anisotropy - $\mathrm{U_{4}Ru_{7}Ge_{6}}$

Strong magnetocrystalline anisotropy is a well-known property of uranium compounds. The almost isotropic ferromagnetism in $\mathrm{U_{4}Ru_{7}Ge_{6}}$ reported in this paper represents a striking exception. We present results of magnetization, AC susceptibility, thermal expansion, specific heat and electrical resistivity measurements performed on a $\mathrm{U_{4}Ru_{7}Ge_{6}}$ single crystal at various temperatures and magnetic fields and discuss them in conjunction with results of first-principles electronic-structure calculations. $\mathrm{U_{4}Ru_{7}Ge_{6}}$ behaves as an itinerant 5$f$-electron ferromagnet ($T_{\mathrm{C}}= 10.7 K$, $\mu_{\mathrm{S}}= 0.85 \mu_{\mathrm{B}}/f.u.$ at 1.9 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 of $\sim0.3 T$, which is at least 3 orders of magnitude smaller value than in other U ferromagnets. At $T_{r}=5.9 K$ the easy magnetization direction changes for [001] which holds at temperatures up to $T_{\mathrm{C}}$. The magnetoelastic interaction induces a rhombohedral (tetragonal) distortion of the paramagnetic cubic crystal lattice in case of the [111]([001]) easy-magnetization direction. The rhombohedral distortion is connected with two crystallographically inequivalent U sites. The ab initio calculated ground-state magnetic moment of $1.01 \mu_{\mathrm{B}}/f.u.$ is oriented along [111]. The two crystallographically inequivalent U sites are a consequence of spin-orbit coupling of the U 5$f$-electrons. In the excited state which is only 0.9 meV above the ground state the moment points to the [001] direction in agreement with experiment.