Starting from \textit{ab-initio} calculations, we derive a five-band Hubbard model to describe the CuO$_2$ chains of LiCu$_2$O$_2$. This model is further simplified to a low-energy effective Heisenberg model with nearest-neighbor (NN) $J_1$, and next-nearest-neighbor (NNN) $J_2$ interactions, combining perturbation theory, exact diagonalization calculations and Density Matrix Renormalization Group results. For realistic parameters we find the corresponding values of these interactions. The obtained effective model is consistent with a spiral-magnetic ground state as experimentally observed. Using symmetry arguments, the spiral state is a sufficient condition for the ferroelectricity observed in the system.
The spin-1/2 Cu2+ ions of LiCuVO4 form one-dimensional chains along the b-direction, and the spin frustration in LiCuVO4 is described in terms of the nearest-neighbor ferromagnetic exchange J1 and the next-nearest-neighbor antiferromagnetic exchange J2 in these chains. Recently, it has become controversial whether or not J1 is stronger in magnitude than J2. To resolve this controversy, we determined the crystal structure of LiCuVO4 at 1.6 K by neutron diffraction, analyzed the magnetic susceptibility of LiCuVO4 to deduce the Curie-Weiss temperature θand the J2/J1 ratio, and finally extracted t…
Spin Susceptibility and Superexchange Interaction in the Antiferromagnet CuO
在Heisenberg模型的框架下给出了CuO准一维反铁磁性的证据。通过$^{63}$ Cu NMR位移测量，从总磁化率中分别减去轨道磁化率，得到了CuO顺磁自旋磁化率的实验绝对值，并与理论预测进行了比较。结果是最好的一维$S=1/2$反铁磁海森堡（AFH）模型描述，支持早期作者援引的推测。我们还提出了一个半定量的原因，为什么CuO，似乎是一个3D结构，出乎意料的准一维反铁磁体。
We present ab initio calculations of the superexchange antiferromagnetic spin coupling $J$ for two cuprates, Sr$_2$CuO$_3$ and La$_2$CuO$_4$. Good agreement with experimental estimates is obtained. We find that $J$ increases substantially as the distance between Cu and apical O is increased. There is an important synergetic effect of the Coulomb interaction, expanding the Cu $3d$ orbital when an electron hops into this orbital, and the O-Cu hopping, being increased by this orbital expansion (breathing). This is a new ingredient in superexchange models. In a model with a fixed basis, breathing …
We study the zero-point and thermal ionic motion in La$_2$CuO$_4$ by means of high-resolution neutron diffraction experiments. Our results demonstrate anisotropic motion of O and to a lesser extent of Cu ions, both consistent with the structure of coupled CuO$_6$ octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of $^{18}$O, we find that the oxygen isotope effect on the lattice dimensions is small and negative ($-0.01\%$), while the isotope effect on the ionic displacement parameters is significant ($-6$ to $50\%$). We use our…
In view of the continuous theoretical efforts aimed at an accurate microscopic description of the strongly correlated transition metal oxides and related materials, we show that with continuum quantum Monte Carlo (QMC) calculations it is possible to obtain the value of the spin superexchange coupling constant of a copper oxide in a quantitatively excellent agreement with experiment. The variational nature of the QMC total energy allows us to identify the best trial wave function out of the available pool of wave functions, which makes the approach essentially free from adjustable parameters an…
We have studied the superexchange interaction $J_{ij}$ in doped $2D$ cuprates. The AFM interaction strongly depends on the state of the lattice of a CuO$_2$ layer surrounded by two LaO rock salt layers. In a static $U$ and $D$ stripe nanostructure, the homogeneous AFM interaction is impossible due to the $U/D/U...$ periodic stripe sequence and $T_N=0$. In a dynamic stripe nanostructure, the ideal CuO$_2$ layer with nonlocal effects and the homogeneous AFM interaction are restored. However the interaction $J_{ij}$ decreases by the exponential factor due to partial dynamic quenching. The meaning…
Spectroscopic ellipsometry was used to study the dielectric function of LiCuVO$_{4}$, a compound comprised of chains of edge-sharing CuO$_4$ plaquettes, in the spectral range (0.75 - 6.5) eV at temperatures (7-300) K. For photon polarization along the chains, the data reveal a weak but well-resolved two-peak structure centered at 2.15 and 2.95 eV whose spectral weight is strongly enhanced upon cooling near the magnetic ordering temperature. We identify these features as an exciton doublet in the Mott-Hubbard gap that emerges as a consequence of the Coulomb interaction between electrons on near…
With wavefunction-based electronic-structure calculations we determine the Cu d-d excitation energies in quasi-one-dimensional spin-chain and ladder copper oxides. A complete set of local excitations has been calculated for cuprates with corner-sharing (Sr2CuO3 and SrCuO2) and edge-sharing (LiVCuO4, CuGeO3, LiCu2O2 and Li2CuO2) CuO4 plaquettes, with corner-sharing CuF6 octahedra (KCuF3), for the ladder system CaCu2O3, and for multiferroic cupric oxide CuO. Our data compare well with available results of optical absorption measurements on KCuF3 and the excitation energies found by resonant inel…
We propose a multielectron approach to calculate superexchange interaction in magnetic Mott- Hubbard insulator La2CuO4(further La214) that allows to obtain the effect of optical pumping on the superexchange interaction. We use the cell perturbation theory with exact diagonalization of the multiband pd Hamiltonian inside each CuO6 unit cell and treating the intercell hopping as perturbation. To incorporate effect of optical pumping we include in this work the excited singlehole local states as well as all two-hole singlets and triplets. By projecting out the interband intercell electron hopping…
While the dominant magnetic interaction in La$_2$CuO$_4$ is superexchange between nearest-neighbor Cu moments, the pinning of the spin direction depends on weak anisotropic effects associated with spin-orbit coupling. The symmetry of the octahedral tilt pattern allows an out-of-plane canting of the Cu spins, which is compensated by an opposite canting in nearest-neighbor layers. A strong magnetic field applied perpendicular to the planes can alter the spin canting pattern to induce a weak ferromagnetic phase. In light of recent evidence that the lattice symmetry is lower than originally assume…
By means of resonant inelastic x-ray scattering at the Cu L$_3$ edge, we measured the spin wave dispersion along $\langle$100$\rangle$ and $\langle$110$\rangle$ in the undoped cuprate Ca$_2$CuO$_2$Cl$_2$. The data yields a reliable estimate of the superexchange parameter $J$ = 135 $\pm$ 4 meV using a classical spin-1/2 2D Heisenberg model with nearest-neighbor interactions and including quantum fluctuations. Including further exchange interactions increases the estimate to $J$ = 141 meV. The 40 meV dispersion between the magnetic Brillouin zone boundary points (1/2,\,0) and (1/4,\,1/4) indicat…
A new spin-1/2 quasi-one-dimensional antiferromagnet KCuMoO_4(OH) is prepared by the hydrothermal method. The crystal structures of KCuMoO_4(OH) and the already-known Na-analogue, NaCuMoO_4(OH), are isotypic, comprising chains of Cu^{2+} ions in edge-sharing CuO_4(OH)_2 octahedra. Despite the structural similarity, their magnetic properties are quite different because of the different arrangements of d_{x2-y2} orbitals carrying spins. For NaCuMoO_4(OH), d_{x2-y2} orbitals are linked by superexchange couplings via two bridging oxide ions, which gives a ferromagnetic nearest-neighbor interaction…
Weak antiferromagnetism due to Dzyaloshinskii-Moriya interaction in Ba$_3$Cu$_2$O$_4$Cl$_2$
反铁磁绝缘铜氧化物Ba $_3$ Cu $_2$ O $_4$ Cl $_2$含有折叠的CuO $_2$链，每个晶胞具有四个磁性铜离子（$S=1/2$）。一个潜在的多轨道哈伯德模型制定和超交换理论的发展，以获得一个有效的自旋哈密顿量的铜酸盐。得到的自旋哈密顿量除了包含各向同性交换作用外，还包含一个Dzyaloshinskiii-Moriya项和一个更弱的对称各向异性交换项.相应的Dzyaloshinskiii-Moriya矢量的每个磁性Cu-Cu键链中揭示了一个定义良好的空间秩序。超交换理论和互补群理论的考虑，都导致了关于这种秩序的性质的相同结论。的基态磁特性的推导模型的分析导致预测的反铁磁结构的一个额外的非共线调制。这种弱反铁磁性仅限于其中一个铜亚晶格。
