It is shown that the nonselfadjoint (and non-normal) linear ordinary differential operators of a certain class are spectral operators of scalar type in the sense of Dunford and Bade. Operators of this kind appear in physical problems such as the scattering of spin waves by magnetic solitons.

The equilibrium state of a monoaxial chiral magnet surrounded by a non-magnetic medium (such as air or vacuum) is a helical texture characterized by a single, well-defined wave vector. No metastable states have ever been observed in such systems. Recently, however, it was demonstrated that when a chiral magnet is in close contact with two uniaxial ferromagnets, a large number of metastable helical states emerge in addition to the equilibrium state [Phys. Rev. B 109, 214424]. These helical states are distinguished by their wave number (helicity). In the present work, we elucidate the topological origin of the stabilization of these states –a mechanism we term dynamical topological protection– and investigate their static and dynamic properties. We find that, as a consequence of this dynamical topological protection, the winding number of the helical states remains constant under the application of sufficiently weak magnetic fields and polarized electric currents. Furthermore, when a polarized current is applied to a metastable helical state, a static configuration is reached. This state retains the original winding number, but its winding number density becomes non-homogeneously distributed, concentrating near the interface with one of the ferromagnets. The dynamic response to sufficiently large magnetic fields and currents provides mechanisms to switch between different helical states. Since the magnetic properties depend on helicity, these metastable helical states are highly promising for applications in spintronics and magnonics.

The magnon spectral problem is solved in terms of the spectrum of a diagonalizable operator for a generic class of magnetic states that includes several types of domain walls and the chiral solitons of monoaxial helimagnets. Focusing on the isolated solitons of monoaxial helimagnets, it is shown that the spin waves scattered (reflected and transmitted) by the soliton suffer a lateral displacement analogous to the Goos-Hanchen effect of optics. The displacement is a fraction of the wavelength, but can be greatly enhanced by using an array of well separated solitons. Contrarily to the Goos-Hanchen effect recently studied in some magnetic systems, which takes place at interfaces between different magnetic systems, the effect predicted here takes place at the soliton position, what it is interesting from the point of view of applications since solitons can be created at different places and moved across the material. This kind of Goos-Hanchen effect is not particular of monoaxial helimagnets, but it is generic of a class of magnetic states, including domain walls in systems with interfacial Dzyaloshinskii-Moriya interaction.

The spin wave spectral problem is solved in terms of the spectrum of a diagonalizable operator for a class of magnetic states that includes several types of domain walls and the chiral solitons of monoaxial helimagnets. Focusing on these latter solitons, it is shown that the spin waves reflected and transmitted by them suffer a lateral displacement analogous to the Goos-Hänchen effect of optics. The displacement is a fraction of the wavelength, but can be greatly enhanced by using an array of well separated solitons. Contrarily to the Goos–Hänchen effect recently studied in some magnetic systems, which takes place at the interfaces between different magnetic systems, the effect predicted here takes place at the soliton position, which is interesting for applications since solitons can be created at different places and moved across the material by suitable means. Moreover, the effect predicted here is not particular to monoaxial helimagnets, but it is generic of 1D solitons, although it is accidentally absent in the domain walls of ferromagnets with uniaxial anisotropy. Even though in this work the dipolar interaction is ignored for simplicity, we argue that the Goos–Hänchen shift is also present when it is taken into account.

It is known that a Bloch domain wall in an anisotropic ferromagnet is transparent to spin waves. This result is derived by approximating the dipolar interaction between magnetic moments by an effective anisotropy interaction. In this paper we study the the scattering of spin waves by a domain wall taking into account the full complexity of the dipolar interaction, treating it perturbatively in the distorted wave Born approximation. Due to the peculiarities of the dipolar interaction, the implementation of this approximation is not straightforward. The difficulties are circumvented here by realizing that the contribution of the dipolar interaction to the spin wave operator can be split into two terms: i) an operator that commutes with the spin wave operator in absence of dipolar interaction, and ii) a local operator suitable to be treated as a perturbation in the distorted wave Born approximaton. We analyze the scattering parameters obtained within this approach. It turns out that the reflection coefficient does not vanish in general, and that the transmitted waves suffer a lateral shift even at normal incidence. This lateral shift can be greatlty enhanced by making the spin wave go through an array of well separated domain walls. The outgoing spin wave will no be attenuated by the scattering at the domain walls since the reflection coefficient vanishes at normal incidence. This effect may be very useful to control the spin waves in magnonic devices.

A novel method to estimate integral parameters of the orientation distribution function (ODF) in textured polycrystals from the wavelength-resolved neutron transmission is presented. It is based on the expression of the total coherent elastic cross section as a function of the Fourier coefficients of the ODF. This method is broken down in detail for obtaining Kearns factors in hexagonal crystals, and other material properties that depend on the average of second- and fourth-rank tensors. The robustness of the method against three situations was analyzed: effects of sample misalignment, of cutoff value l max of the series expansion and of experimental standard deviation. While sample misalignment is shown not to be critical for the determination of Kearns factors and second-order-rank properties, it can be critical for fourth-rank and higher-order tensor properties. The effect of the cutoff value on the method robustness is correlated to the standard deviation of the experimental data. In order to achieve a good estimation of the Fourier coefficients, it is recommended that the experimental standard deviation be around 3–5% of the total scattering cross section of the material for the method to be stable. The method was applied for the determination of Kearns factors from transmission measurements performed at the instrument ENGIN-X (ISIS) on a Zr–2.5 Nb pressure tube along two sample directions and was shown to be able to estimate Kearns factors with an error below 5%.

Chiral solitons are one dimensional localized magnetic structures that are metastable in some ferromagnetic systems with Dzyaloshinskii-Moriya interactions and/or uniaxial magnetic anisotropy. Though topological textures in general provide a very interesting playground for new spintronics phenomena, how to properly create and control single chiral solitons is still unclear. We show here that chiral solitons in monoaxial helimagnets, characterized by a uniaxial Dzyaloshinskii-Moriya interaction, can be stabilized with external magnetic fields. Once created, the soliton moves steadily in response to a polarized electric current, provided the induced spin-transfer torque has a dissipative (nonadiabatic) component. The structure of the soliton depends on the applied current density in such a way that steady motion exists only if the applied current density is lower than a critical value, beyond which the soliton is no longer stable.

A method of simulating the neutron scattering by a textured polycrystal is presented. It is based on an expansion of the scattering cross sections in terms of the spherical harmonics of the incident and scattering directions, which is derived from the generalized Fourier expansion of the polycrystal orientation distribution function. The method has been implemented in a Monte Carlo code as a component of the McStas software package, and it has been validated by computing some pole figures of a Zircaloy-4 plate and a Zr-2.5Nb pressure tube, and by simulating an ideal transmission experiment. The code can be used to estimate the background generated by components of neutron instruments such as pressure cells, whose walls are made of alloys with significant crystallographic texture. As a first application, the effect of texture on the signal-to-noise ratio was studied in a simple model of a diffraction experiment, in which a sample is placed inside a pressure cell made of a zirconium alloy. With this setting, the results of two simulations were compared: one in which the pressure-cell wall has a uniform distribution of grain orientations, and another in which the pressure cell has the texture of a Zr-2.5Nb pressure tube. The results showed that the effect of the texture of the pressure cell on the noise of a diffractogram is very important. Thus, the signal-to-noise ratio can be controlled by appropriate choice of the texture of the pressure-cell walls.

Resumen del trabajo presentado a la 21st International Conference on Magnetism (ICM), celebrada en San Francisco (US) del 15 al 20 de julio de 2018.

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.

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 the 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.

A new method to compute the incoherent scattering function of harmonic lattices is introduced. It is based in a saddle point approximation for each term of the phonon expansion, and is simple enough to be used in practice. The method gives very accurate results even for the tails of the scattering function, and is more accurate than the usual gaussian approximation, which can be derived from this saddle point approximation in the limit in which the order of the phonon expansion term becomes large. Numerical comparisons are provided using vanadium as a test case.

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 Schrödinger equation in a central potential) is presented. It cures a pathology, related to the singular behavior 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.

Trabajo presentado al SkyMag: Challenges for Magnetic Skyrmions and opportunities for skyrmionic devices, celebrado en Paris (Francia) del 2 al 5 de mayo de 2017.

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 DeGennes 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 a 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 Hx if the values of T and Hz determine a transition point lying on the nucleation surface; otherwise, they are not universal.

Resumen del trabajo presentado al IV International Workshop Dzyaloshinskii-Moriya Interaction and Exotic Spin Structures (DMI), celebrado en Peterhof (Rusia) del 23 al 26 de mayo de 2017.

Resumen del trabajo presentado al IV International Workshop Dzyaloshinskii-Moriya Interaction and Exotic Spin Structures (DMI), celebrado en Peterhof (Rusia) del 23 al 26 de mayo de 2017.

The stability of the four known stationary points of the cubic helimagnet energy functional: the ferromagnetic state, the conical helix, the conical helicoid, and the skyrmion lattice, is studied by solving the corresponding spectral problem. The only stable points are the ferromagnetic state at high magnetic field and the conical helix at low field, and there is no metastable state. Thermal fluctuations around the stationary point, included to quadratic order in the saddle point expansion, destabilize the conical helix in a region where the ferromagnetic state is unstable. Thus, a new intermediate phase appears which, in a region of the phase diagram, is a skyrmion lattice stabilized by thermal fluctuations. The skyrmion lattice lost the stability by lowering temperature, and a new intermediate phase of unknown type, presumably with three-dimensional modulations, appears in the lower temperature region.