Spatially modulated orbital-selective ferromagnetism in La 5 Co 2 Ge 3

We present density functional theory calculations for the low-${T}_{c}$ metallic ferromagnet ${\mathrm{La}}_{5}{\mathrm{Co}}_{2}{\mathrm{Ge}}_{3}$ at ambient and applied pressures. Our investigations reveal that the system is a quasi-one-dimensional ferromagnet with a peculiar coexistence of two different orbital-selective magnetic moments at two crystallographically inequivalent cobalt atoms, Co1 and Co2. Namely, due to different crystal-field splitting, the magnetic moment of Co1 atoms predominantly derives from ${d}_{xz}$ orbital whereas of Co2 atoms from ${d}_{xy}$ orbital. Consequently, Co1 and Co2 atoms develop unequal net magnetic moments, a feature that gives rise to a periodic, spatial modulation of magnetization along the crystallographic $c$-direction. The amplitude of the spatial modulation, small at ambient pressure, drastically increases with applied pressure, until Co2 atoms become nonmagnetic. With a help of a toy model mimicking found orbital-selective ferromagnetic order, we demonstrate that the increasing amplitude of spatial modulation provides a consistent interpretation to the recently observed resistivity anomaly emerging at applied pressure identified as the appearance of the new state. Although the proposed here the structural origin of the spatial modulation of magnetic moments in ${\mathrm{La}}_{5}{\mathrm{Co}}_{2}{\mathrm{Ge}}_{3}$ is an alternative one to the advocated for this material ferromagnetic quantum criticality avoidance, the effects of quantum fluctuations can still play an important role at pressure larger than up-to-date measured 5 GPa.