Up-up-down-down magnetic chain structure of the spin- 12 tetragonally distorted spinel GeCu2O4

Abstract

GeCu 2 O 4 exhibits a tetragonal spinel structure due to the strong Jahn-Teller distortion associated with Cu 2+ ions. We show that its magnetic structure can be described as slabs composed of a pair of layers with orthogonally oriented spin ½ 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 nearestneighbor biquadratic exchange interaction in the effective classical spin Hamiltonian. We hypothesize that spin-orbit coupling and orbital mixing of Cu 2+ ions in this system is nonnegligible, 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.

Origin of up-up-down-down magnetic order in Cu2GeO4

“…In contrast, case i) captures the full Cu-O hybridization, makes F (q) less symmetric, and causes a faster decay at higher q's. Similar effects were reported for other Cu 2+ oxides [60,61] and may be responsible for the reduced ordered moment of 0.89(5) µ B determined by neutron diffraction using the ionic form-factor for Cu 2+ [22].…”

“…IV A and from the direct relaxation of the magnetic structure within VASP, we estimate only a weak noncollinearity with the canted moment of about 0.005 µ B . Such a moment is clearly too small to be detected by powder neutron diffraction [22], but is allowed by symmetry and may be relevant to the development of electric polarization, as we further explain in Sec. V.…”

“…One puzzling case in this series is Cu 2 GeO 4 [21] that reveals an unanticipated antiferromagnetic up-up-downdown (UUDD) order [22] despite the prediction of FM J 1 * altsirlin@gmail.com and AFM J 2 , both of the same magnitude [23]. This parameter regime would normally lead to the incommensurate spiral order, similar to LiCuVO 4 , CuCl 2 , and other J 1 − J 2 cuprates.…”

“…Li 2 CuO 2 [17,18] and CuAs 2 O 4 [19] are notable exceptions, where J 1 is also FM, but J 2 /|J 1 | < 1 4 renders spin alignment along the chains purely ferromagnetic. Spin-chain compounds with AFM J 1 are more rare, although tentative indications of the spin-gap formation at J 2 /J 1 > 0.241 have been reported [20].One puzzling case in this series is Cu 2 GeO 4 [21] that reveals an unanticipated antiferromagnetic up-up-downdown (UUDD) order [22] despite the prediction of FM J 1 * altsirlin@gmail.com and AFM J 2 , both of the same magnitude [23]. This parameter regime would normally lead to the incommensurate spiral order, similar to LiCuVO 4 , CuCl 2 , and other J 1 − J 2 cuprates.…”

“…23 on the spiral order was based on the study of an isotropic spin Hamiltonian, so it is natural to suspect, following Ref. 22, that non-Heisenberg terms stabilize the UUDD order. We calculate such terms but find them to be small and largely irrelevant.…”