Lattice Distortion and Magnetism of 3d-t2gt_{2g} Perovskite Oxides

Several puzzling aspects of interplay of the experimental lattice distortion and the the magnetic properties of four narrow $t_{2g}$-band perovskite oxides (YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$) are clarified using results of first-principles electronic structure calculations. First, we derive parameters of the effective Hubbard-type Hamiltonian for the isolated $t_{2g}$ bands using newly developed downfolding method for the kinetic-energy part and a hybrid approach, based on the combination of the random-phase approximation and the constraint local-density approximation, for the screened Coulomb interaction part. Then, we solve the obtained Hamiltonian using a number of techniques, including the mean-field Hartree-Fock (HF) approximation, the second-order perturbation theory for the correlation energy, and a variational superexchange theory. Even though the crystal-field splitting is not particularly large to quench the orbital degrees of freedom, the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favor the formation of the experimentally observed magnetic structures in YTiO$_3$, YVO_, and LaVO$_3$ even at the HF level. Beyond the HF approximation, the correlations effects systematically improve the agreement with the experimental data. Using the same type of approximations we could not reproduce the correct magnetic ground state of LaTiO$_3$. However, we expect that the situation may change by systematically improving the level of approximations for dealing with the correlation effects.Comment: 30 pages, 17 figures, 8 tables, high-quality figures are available via e-mai

FPGA Implementation of Convolutional Neural Networks with Fixed-Point Calculations

Neural network-based methods for image processing are becoming widely used in practical applications. Modern neural networks are computationally expensive and require specialized hardware, such as graphics processing units. Since such hardware is not always available in real life applications, there is a compelling need for the design of neural networks for mobile devices. Mobile neural networks typically have reduced number of parameters and require a relatively small number of arithmetic operations. However, they usually still are executed at the software level and use floating-point calculations. The use of mobile networks without further optimization may not provide sufficient performance when high processing speed is required, for example, in real-time video processing (30 frames per second). In this study, we suggest optimizations to speed up computations in order to efficiently use already trained neural networks on a mobile device. Specifically, we propose an approach for speeding up neural networks by moving computation from software to hardware and by using fixed-point calculations instead of floating-point. We propose a number of methods for neural network architecture design to improve the performance with fixed-point calculations. We also show an example of how existing datasets can be modified and adapted for the recognition task in hand. Finally, we present the design and the implementation of a floating-point gate array-based device to solve the practical problem of real-time handwritten digit classification from mobile camera video feed

Ferromagnetic zigzag chains and properties of the charge ordered perovskite manganites

The low-temperature properties of the so-called ''charge ordered'' state in 50% doped perovskite manganites are described from the viewpoint of the magnetic spin ordering. In these systems, the zigzag antiferromagnetic ordering, combined with the double-exchange physics, effectively divides the whole sample into the one-dimensional ferromagnetic zigzag chains and results in the anisotropy of electronic properties. The electronic structure of one such chain is described by an effective 3$\times$3 Hamiltonian in the basis of Mn($3de_g$) orbitals. We treat this problem analytically and consider the following properties: (i) the nearest-neighbor magnetic interactions; (ii) the distribution of the Mn($3de_g$) and Mn($4p$) states near the Fermi level, and their contribution to the optical conductivity and the resonant x-ray scattering near the Mn $K$-absorption edge. We argue that the anisotropy of magnetic interactions in the double-exchange limit, combined with the isotropic superexchange interactions, readily explains both the local and the global stability of the zigzag antiferromagnetic state. The two-fold degeneracy of $e_g$ levels plays a very important role in the problem and explains the insulating behavior of the zigzag chain, as well as the appearance of the orbital ordering in the double-exchange model. Importantly, however, the charge ordering itself is expected to play only a minor role and is incompatible with the ferromagnetic coupling within the chain. We also discuss possible effects of the Jahn-Teller distortion and compare the tight-binding picture with results of band structure calculations in the local-spin-density approximation.Comment: 35 pages, 8 figure

Low-Temperature Spin Dynamics of Doped Manganites: roles of Mn-t2g and eg and O-2p states

The low-temperature spin dynamics of doped manganites have been analyzed within a tight-binding model, the parameters of which are estimated by mapping the results of ab initio density functional calculations onto the model. This approach is found to provide a good description of the spin dynamics of the doped manganites, observed earlier within the ab initio calculations. Our analysis not only provides some insight into the roles of the eg and the t2g states but also indicates that the oxygen p states play an important role in the spin dynamics. This may cast doubt on the adaptability of the conventional model Hamiltonian approaches to the analysis of spin dynamics of doped manganites.Comment: 12 pages; Includes 5 figure

Spectroscopy of orbital ordering in La0.5Sr1.5MnO4 : A many-body cluster calculation

We have studied the orbital ordering (OO) in La0.5Sr1.5MnO4 and its soft x-ray resonant diffraction spectroscopic signature at the Mn L2, L3 edges. We have modelled the system in second quantization as a small planar cluster consisting of a central Mn atom, with the first neighbouring shells of oxygen and Mn atoms. For the effective Hamiltonian we consider Slater-Koster parameters, charge transfer and electron correlation energies obtained from previous measurements on manganites. We calculate the OO as a function of oxygen distortion and spin correlation used as adjustable parameters. Their contribution as a function of temperature is clearly distinguished with a good spectroscopic agreement.Comment: 5 pages 3 figure

Doping dependence of the exchange energies in bilayer manganites: Role of orbital degrees of freedom

Recently, an intriguing doping dependence of the exchange energies in the bilayer manganites $La_{2-2x}Sr_{1+2x}Mn_2O_7$ has been observed in the neutron scattering experiments. The intra-layer exchange only weakly changed with doping while the inter-layer one drastically decreased. Here we propose a theory which accounts for these experimental findings. We argue, that the observed striking doping dependence of the exchange energies can be attributed to the evaluation of the orbital level splitting with doping. The latter is handled by the interplay between Jahn-Teller effect (supporting an axial orbital) and the orbital anisotropy of the electronic band in the bilayer structure (promoting an in-plane orbital), which is monitored by the Coulomb repulsion. The presented theory, while being a mean-field type, describes well the experimental data and also gives the estimates of the several interesting energy scales involved in the problem.Comment: Added references, corrected typos. To appear in Phys. Rev.