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

Abstract

We use density-functional band-structure calculations to explore the origin of the up-up-downdown (UUDD) magnetic order in Cu2GeO4 with the frustrated J1 − J2 spin chains coupled into layers within the spinel-like crystal structure. In contrast to earlier studies, we find that the nearestneighbor coupling J1 may be negligibly small, owing to a nearly perfect compensation of the ferromagnetic direct exchange and antiferromagnetic superexchange. Under this condition, weak symmetric anisotropy of the exchange couplings gives rise to the UUDD order observed experimentally and also elucidates the non-trivial ordering pattern between the layers, whereas a small Dzyaloshinsky-Moriya interaction causes a spin canting that may generate local electric polarization. We argue that the buckling of the copper chains plays a crucial role in the suppression of J1 in Cu2GeO4 and sets this compound apart from other J1 − J2 chain magnets. I. INTRODUCTIONCopper oxides built by chains of edge-sharing CuO 4 plaquettes serve as material prototypes of frustrated spin-1 2 chains with competing nearest-neighbor and nextnearest-neighbor interactions J 1 and J 2 , respectively. This simple spin model received ample attention [1] triggered by the prospects of chiral, multipolar, and spinnematic phases that may occur therein [2][3][4][5][6][7][8]. Whereas long-range order does not take place in one dimension (1D), interchain couplings in real materials will usually cause three-dimensional (3D) collinear or noncollinear order depending on the J 2 /J 1 ratio. On the classical level, incommensurate spiral order appears for J 2 /|J 1 | > 1 4 , whereas at J 2 /|J 1 | < 1 4 the second-neighbor coupling is not strong enough to tilt the spins, and the collinear ferromagnetic or up-down-up-down antiferromagnetic order form depending on the sign of J 1 . Quantum effects preserve the spiral state in the case of ferromagnetic (FM) J 1 [9], but destroy the order and open a spin gap for antiferromagnetic (AFM) J 1 at J 2 /J 1 > 0.241 [10][11][12].Real-world prototypes of the J 1 − J 2 spin chains will typically follow one of these scenarios. The majority of quasi-1D copper oxides reveal J 2 /|J 1 | > 1 4 with FM J 1 and develop the incommensurate spiral order [13][14][15][16]. 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. Here, we address this discrepancy and first analyze whether additional terms beyond J 1 and J 2 could...

Magnetic order and multipoles in the 5d2 rhenium double perovskite Ba2YReO6Thompson1, Marjerisson2, Badrtdinov3 et al. 2021Phys. Rev. BSelf Cite7180View full textAdd to dashboardCite

“…This is illustrated by the example of K 2 IrCl 6 , where the space group and Wyckoff site of the magnetic Ir 4+ (d 4 ) ions are the same as in Ba 2 YReO 6 , and which shows drastic (up to 50%) departures from the dipolar approximation even at κ ∼ 1 Å −1 [29]. We attempt to account for these effects by calculating the j 0 (κ ) contribution to the dipolar form factor by Fourier transforming the moment density obtained by density functional theory [30]; see also [31][32][33][34][35][36][37][38]. The delocalization of spin density onto the O 2− surrounding the Re 5+ leads to a sharper drop in f (κ ) with increasing κ than in the free-ion case.…”

SrCu$_2$(BO$_3$)$_2$ under pressure: a first-principle study

“…where t ij is the hopping integral between the ith and jth Wannier functions. On the basis of these Wannier functions, one can perform a microscopic analysis of the exchange interactions by using a superexchange theory approach 29 :…”

“…(4). The former involves a significant error bar when calculated by DFT 29 , but its microscopic origin is well known and for cuprates it comes from the Hund's coupling on the ligand site 37 . The size of J F depends on the contribution of the ligand orbitals to the Cu d x 2 −y 2 Wannier function 37 .…”

Interplay between breathing-mode distortions and magnetic order in rare-earth nickelates from $ab$ $initio$ magnetic models

“…Correlation effects were taken into account on the static mean-field level using the DFT+U method 35 , where we considered an effective on-site Coulomb U and Hund's exchange J H interactions in the rotationally invariant form 36 . A value of J H = 1 eV can be used for compounds with 3d orbitals 37,38 , while the on-site Coulomb parameter depends on the specific system. Previous results showed that the best agreement with experiment can be obtained using a relatively small value of U = 2 eV 1,2,39 .…”