An improved discretization of Schrodinger-like radial equations

A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a pathology, related to the singular behaviour of the radial function at the origin, that suffers in some cases the discretization of the second derivative with respect to the radial coordinate. This pathology causes an enormous slowing down of the convergence to the continuum limit when the two point boundary value problem posed by the radial equation is solved as a discrete matrix eigenvalue problem. The proposed discretization is a simple solution to that problem. Some illustrative examples are discussed.Comment: 21 pages, 12 figure

Stability of the skyrmion lattice near the critical temperature in cubic helimagnets

The phase diagram of cubic helimagnets near the critical temperature is obtained from a Landau-Ginzburg model, including fluctuations to gaussian level. The free energy is evaluated via a saddle point expansion around the local minima of the Landau-Ginzburg functional. The local minima are computed by solving the Euler-Lagrange equations with appropriate boundary conditions, preserving manifestly the full nonlinearity that is characteristic of skyrmion states. It is shown that the fluctuations stabilize the skyrmion lattice in a region of the phase diagram close to the critical temperature, where it becomes the equilibrium state. A comparison of this approach with previous computations performed with a different approach (truncated Fourier expansion of magnetic states) is given.Comment: 6 pages, 6 color figure

Nucleation, instability, and discontinuous phase transitions in monoaxial helimagnets with oblique fields

The phase diagram of the monoaxial chiral helimagnet as a function of temperature (T ) and magnetic field with components perpendicular (H x ) and parallel (H z ) to the chiral axis is theoretically studied via the variational mean field approach in the continuum limit. A phase transition surface in the three dimensional thermodynamic space separates a chiral spatially modulated phase from a homogeneous forced ferromagnetic phase. The phase boundary is divided into three parts: two surfaces of second order transitions of instability and nucleation type, in De Gennes terminology, are separated by a surface of first order transitions. Two lines of tricritical points separate the first order surface from the second order surfaces. The divergence of the period of the modulated state on the nucleation transition surface has the logarithmic behavior typical of a chiral soliton lattice. The specific heat diverges on the nucleation surface as a power law with logarithmic corrections, while it shows a finite discontinuity on the other two surfaces. The soliton density curves are described by a universal function of H x if the values of T and H z determine a transition point lying on the nucleation surface; otherwise, they are not universal.Comment: Phase diagram refined, with a new tricritical point located; 9 pages, 8 figures; version shortened, published in Phys. Rev.

Understanding the H-T phase diagram of the mono-axial helimagnet

Some unexpected features of the phase diagram of the monoaxial helimagnet in presence of an applied magnetic field perpendicular to the chiral axis are theoretically predicted. A rather general hamiltonian with long range Heisenberg exchange and Dzyaloshinskii--Moriya interactions is considered. The continuum limit simplifies the free energy, which contains only a few parameters which in principle are determined by the many parameters of the hamiltonian, although in practice they may be tuned to fit the experiments. The phase diagram contains a Chiral Soliton Lattice phase and a forced ferromagnetic phase separated by a line of phase transitions, which are of second order at low T and of first order in the vicinity of the zero-field ordering temperature, and are separated by a tricritical point. A highly non linear Chiral Soliton Lattice, in which many harmonics contribute appreciably to the spatial modulation of the local magnetic moment, develops only below the tricritical temperature, and in this case the scaling shows a logarithmic behaviour similar to that at T=0, which is a universal feature of the Chiral Soliton Lattice. Below the tricritical temperature, the normalized soliton density curves are found to be independent of T, in agreement with the experimental results of magnetorresistance curves, while above the tricritical temperature they show a noticeable temperature dependence. The implications in the interpretation of experimental results of CrNb3S6 are discussed.Comment: 11 pages, 17 figures. Enlarged version, with more details and results. To be publisehd in Phys. Rev.

Thermal fluctuations in the conical state of monoaxial helimagnets

The effect of thermal fluctuations on the phase structure of monoaxial helimagnets with external magnetic field parallel to the chiral axis is analyzed by means of a saddle point expansion of the free energy. The phase transition that separates the conical and forced ferromagnetic phases is changed to first order by the thermal fluctuations. In a purely monoaxial system the pitch of the conical state remains independent of temperature and magnetic field, as in mean field theory, even when fluctuations are taken into account. However, in presence of weak Dzyaloshinskii-Moriya interactions in the plane perpendicular to the chiral axis, thermal fluctuations induce a dependence of the pitch on temperature and magnetic field. This may serve to determine the nature of magnetic interactions in such systems.Comment: 9 pages, 4 figure