A high-temperature expansion method for calculating paramagnetic exchange interactions

The method for calculating the isotropic exchange interactions in the paramagnetic phase is proposed. It is based on the mapping of the high-temperature expansion of the spin-spin correlation function calculated for the Heisenberg model onto Hubbard Hamiltonian one. The resulting expression for the exchange interaction has a compact and transparent formulation. The quality of the calculated exchange interactions is estimated by comparing the eigenvalue spectra of the Heisenberg model and low-energy magnetic part of the Hubbard model. By the example of quantum rings with different hopping setups we analyze the contributions from the different part of the Hubbard model spectrum to the resulting exchange interaction.Comment: 8 pages, 8 figure

Electronic Structure and Exchange Interactions of Na2_{2}V3_{3}O7_{7}

We have performed first-principle calculations of the electronic structure and exchange couplings for the nanotube compound Na$_{2}$V$_{3}$O$_{7}$ using the LDA+U approach. Our results show that while the intra-ring exchange interactions are mainly antiferromagnetic, the inter-ring couplings are {\it ferromagnetic}. We argue that this is a consequence of the strong hybridization between filled and vacant 3d vanadium orbitals due to the low symmetry of Na$_{2}$V$_{3}$O$_{7}$, which results into strong - and often dominant - ferromagnetic contributions to the total exchange interaction between vanadium atoms. A comparison with results of previous works is included.Comment: 6 pages, 5 figure

Magnetism of sodium superoxide

By combining first-principles electronic-structure calculations with the model Hamiltonian approach, we systematically study the magnetic properties of sodium superoxide (NaO2), originating from interacting superoxide molecules. We show that NaO2 exhibits a rich variety of magnetic properties, which are controlled by relative alignment of the superoxide molecules as well as the state of partially filled antibonding molecular \pi_g-orbitals. The orbital degeneracy and disorder in the high-temperature pyrite phase gives rise to weak isotropic antiferromagnetic (AFM) interactions between the molecules. The transition to the low-temperature marcasite phase lifts the degeneracy, leading to the orbital order and formation of the quasi-one-dimensional AFM spin chains. Both tendencies are consistent with the behavior of experimental magnetic susceptibility data. Furthermore, we evaluate the magnetic transition temperature and type of the long-range magnetic order in the marcasite phase. We argue that this magnetic order depends on the behavior of weak isotropic as well as anisotropic and Dzyaloshinskii-Moriya exchange interactions between the molecules. Finally, we predict the existence of a multiferroic phase, where the inversion symmetry is broken by the long-range magnetic order, giving rise to substantial ferroelectric polarization.Comment: 10 pages, 7 figure

Magnetic structure and ferroelectric activity in orthorhombic YMnO3: relative roles of magnetic symmetry breaking and atomic displacements

We discuss relative roles played by the magnetic inversion symmetry breaking and the ferroelectric (FE) atomic displacements in the multiferroic state of YMnO3. For these purposes we derive a realistic low-energy model, using results of first-principles calculations and experimental parameters of the crystal structure. Then, we solve this model in the Hartree-Fock approximation. We argue that the multiferroic state in YMnO3 has a magnetic origin, and the centrosymmetric Pbnm structure is formally sufficient for explaining details of the noncentrosymmetric magnetic ground state. The relativistic spin-orbit interaction lifts the degeneracy, caused by the frustration of isotropic interactions, and stabilizes a twofold periodic magnetic state, which is similar to the E-state apart from the spin canting. The noncentrosymmetric atomic displacements in the P2_1nm phase reduce the spin canting, but do not change the symmetry of the magnetic state. The effect of the P2_1nm distortion on the FE polarization P_a is twofold: (i) it gives rise to ionic contributions, associated with the Y and O sites; (ii) it affects the electronic polarization, through the change of the spin canting. The relatively small value of P_a, observed in the experiment, is caused by a partial cancelation of the electronic and ionic contributions in the experimental P2_1nm structure. Finally, we theoretically optimize the crystal structure, by using the LSDA+U approach and assuming the collinear E-type alignment. We have found that the agreement with the experimental data in this case is less satisfactory and P_a is largely overestimated. Although the magnetic structure can be formally tuned by varying the Coulomb repulsion U as a parameter, apparently LSDA+U fails to reproduce some fine details of the experimental structure, and the cancelation of different contributions in P_a does not occur.Comment: 24 pages, 5 figures, 5 table

Magnetic structure of hexagonal YMnO3 and LuMnO3 from a microscopic point of view

The aim of this work is to unravel a basic microscopic picture behind complex magnetic properties of hexagonal manganites. For these purposes, we consider two characteristic compounds: YMnO3 and LuMnO3, which form different magnetic structures in the ground state. First, we establish an electronic low-energy model, which describes the behavior of the Mn 3d bands of YMnO3 and LuMnO3, and derive parameters of this model from the first-principles calculations. From the solution of this model, we conclude that, despite strong frustration effects in the hexagonal lattice, the relativistic spin-orbit interactions lift the degeneracy of the magnetic ground state so that the experimentally observed magnetic structures are successfully reproduced by the low-energy model. Then, we analyze this result in terms of interatomic magnetic interactions, which were computed using different approximations (starting from the model Hamiltonian as well as directly from the first-principles electronic structure calculations in the local-spin-density approximation). We argue that the main reason why YMnO3 and LuMnO3 tend to form different magnetic structures is related to the behavior of the single-ion anisotropy, which reflects the directional dependence of the lattice distortion: namely, the expansion and contraction of the Mn-trimers, which take place in YMnO3 and LuMnO3, respectively. On the other hand, the magnetic coupling between the haxagonal planes is controlled by the next-nearest-neighbor interactions, which are less sensitive to the direction of the trimerization. Finally, using the Berry-phase formalism, we evaluate the magnetic-state dependence of the ferroelectric polarization, and discuss potential applications of the latter in magnetoelectric switching phenomena.Comment: 22 pages, 2 figures, 4 table

Neural network agent playing spin Hamiltonian games on a quantum computer

Quantum computing is expected to provide new promising approaches for solving the most challenging problems in material science, communication, search, machine learning and other domains. However, due to the decoherence and gate imperfection errors modern quantum computer systems are characterized by a very complex, dynamical, uncertain and fluctuating computational environment. We develop an autonomous agent effectively interacting with such an environment to solve magnetism problems. By using the reinforcement learning the agent is trained to find the best-possible approximation of a spin Hamiltonian ground state from self-play on quantum devices. We show that the agent can learn the entanglement to imitate the ground state of the quantum spin dimer. The experiments were conducted on quantum computers provided by IBM. To compensate the decoherence we use local spin correction procedure derived from a general sum rule for spin-spin correlation functions of a quantum system with even number of antiferromagnetically-coupled spins in the ground state. Our study paves a way to create a new family of the neural network eigensolvers for quantum computers.Comment: Local spin correction procedure was used to compensate real device errors; comparison with variational approach was adde