Spin-orbit coupling inactivity of Co$^{2+}$ ion in geometrically frustrated magnet GeCo$_2$O$_4$

We report single-crystal neutron diffraction studies on a spinel antiferromagnet GeCo$_2$O$_4$, which exhibits magnetic order with a trigonal propagation vector and tetragonal lattice expansion ($c/asimeq1.001$) below $T_{rm N}=21$ K. For this inconsistency between spin and lattice in symmetry, magnetic Bragg reflections with a tetragonal propagation vector were discovered below $T_{rm N}$. We discuss spin and orbital states of Co$^{2+}$ ion underlying the new magnetic component.