  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.
