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Register a new userMicromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites
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We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hard phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.
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We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for non-equilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, than the super-cell approximation.
Using Brillouin spectroscopy, the first observation has been made of the band structures of nanostructured defect magnonic crystals. The samples are otherwise one-dimensional periodic arrays of equal-width Ni80Fe20 and cobalt nanostripes, where the defects are stripes of a different width. A dispersionless defect branch emerges within the bandgap with a frequency tunable by varying the defect stripe width, while the other branches observed are similar to those of a defect-free crystal. Micromagnetic and finite-element simulations performed unveil additional tiny bandgaps and the frequency-dependent localization of the defect mode in the vicinity of the defects.
We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.
The solution of differential problems, and in particular of quantum wave equations, can in general be performed both in the direct and in the reciprocal space. However, to achieve the same accuracy, direct-space finite-difference approaches usually involve handling larger algebraic problems with respect to the approaches based on the Fourier transform in reciprocal space. This is the result of the errors that direct-space discretization formulas introduce into the treatment of derivatives. Here, we propose an approach, relying on a set of sinc-based functions, that allows us to achieve an exact representation of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.
We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain of N sites and correlation length xi, the computational cost formally scales as g(D,xi /N)D^3, where g(D,xi /N) is a nontrivial function. For xi << N, this scaling reduces to D^3, independent of the system size N, making our algorithm N times faster than previous proposals. We apply the method to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system.
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