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We present density functional theory calculations for low-$T_c$ metallicferromagnet La$_5$Co$_2$Ge$_3$ at ambient and applied pressures. Ourinvestigations reveal that the system is a quasi-one-dimensional ferromagnetwith a peculiar coexistence of two different orbital-selective magnetic momentsat two crystallographically inequivalent cobalt atoms, Co1 and Co2. Namely, dueto different crystal-field splitting, the magnetic moment of Co1 atomspredominantly 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 magnetizationalong crystallographic $c$-direction. The amplitude of the spatial modulation,small at ambient pressure, drastically increases with applied pressure, untilCo2 atoms become nonmagnetic. With the help of a toy model mimicking foundorbital-selective ferromagnetic order, we demonstrate that the increasingamplitude of spatial modulation provides a consistent interpretation to therecently observed resistivity anomaly emerging at applied pressure identifiedas the appearance of the {\it new state}. Although, proposed here structuralorigin of the spatial modulation of magnetic moments in La$_5$Co$_2$Ge$_3$ isan alternative one to the advocated for this material ferromagnetic quantumcriticality avoidance, the effects of quantum fluctuations can still play animportant role at pressure larger than up-to-date measured 5GPa.

Spatially modulated, orbital selective ferromagnetism in La$_5$Co$_2$Ge$_3$