Up-up-down-down magnetic chain structure of the spin-$\frac{1}{2}$ tetragonally distorted spinel $\mathrm{GeC}{\mathrm{u}}_2{\mathrm{O}}_4$

$\mathrm{GeC}{\mathrm{u}}_2{\mathrm{O}}_4$ spinel exhibits a tetragonal structure due to the strong Jahn-Teller distortion associated with $\mathrm{C}{\mathrm{u}}^{2+}$ ions. We show that its magnetic structure can be described as slabs composed of a pair of layers with orthogonally oriented spin-$\frac{1}{2}$ Cu chains in the basal $ab$ plane. The spins between the two layers within a slab are collinearly aligned while the spin directions of neighboring slabs are perpendicular to each other. Interestingly, we find that spins along each chain form an unusual up-up-down-down (UUDD) pattern, suggesting a non-negligible nearest-neighbor biquadratic exchange interaction in the effective classical spin Hamiltonian. We hypothesize that spin-orbit coupling and orbital mixing of $\mathrm{C}{\mathrm{u}}^{2+}$ ions in this system are non-negligible, which calls for future calculations using perturbation theory with extended Hilbert (spin and orbital) space and calculations based on density functional theory including spin-orbit coupling and looking at the global stability of the UUDD state.

Figure 1

(a) Schematics of the crystal structure of $\mathrm{GeC}{\mathrm{u}}_2{\mathrm{O}}_4$. (b) Expanded view of $\mathrm{Cu}{\mathrm{O}}_6$ octahedra showing the bond length and bond angle. (c) Schematic of Cu tetrahedra with two different Cu-Cu bond lengths of each tetrahedron.

Figure 2

(a) Temperature dependence of magnetic susceptibility measured with various magnetic fields; inset shows an expanded view of low-temperature regime. (b) Temperature dependence of specific heat measured at zero and 9 T magnetic field. Inset shows an expanded view of magnetic susceptibility measured with 5000 Oe magnetic field.

Figure 3

(a) Neutron powder diffraction pattern (black dot) and Rietveld refinement (red curve) of $\mathrm{GeC}{\mathrm{u}}_2{\mathrm{O}}_4$ measured at 50 K. The Bragg peaks of the aluminum sample holder are also refined as indicated by the second row of Bragg positions (olive vertical lines). (b) The low-$Q$ region magnetic diffraction pattern obtained from the difference $I_{\mathrm{diff}}=I_{2\mathrm{K}}–I_{50\mathrm{K}}$ and its Rietveld refinement. The peak width of both nuclear and magnetic Bragg peaks is determined by the instrumental resolution.

Figure 4

Peak intensity of $\mathit{Q}=\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)$ magnetic Bragg peak as a function of temperature and the fitting to a power law. The large background above $T_{\mathrm{N}}$ is due to the fully open slit settings to get high neutron flux.

Figure 5

(a) Refined magnetic structure of $\mathrm{GeC}{\mathrm{u}}_2{\mathrm{O}}_4$ within one magnetic unit cell. (b) $ab$ plane projection of the spin structure showing the up-up-down-down configuration along the chain. (c) Closeup view of the spin structure of three corner-sharing Cu tetrahedra.