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In this work, we present a theoretical model for domain wall (DW) oscillations in a curved magnetic nanowire with a constant curvature under the action of a uniaxial magnetic field. Our results show that the DW dynamics can be described as that of the mechanical pendulum, and both the NW curvature and the external magnetic field influence its oscillatory frequency. A comparison between our theoretical approach and experimental data in the literature shows an excellent agreement. The results presented here can be used to design devices demanding the proper control of the DW oscillatory motion in NWs.

This work analyzes the propagation of a transverse domain wall (DW) motion under the action of an electric current along a nanowire (NW) with a curvature gradient. Our results evidence that the curvature gradient induces a chiral spin-transfer torque (CSTT) whose effect on the DW motion depends on the direction along which the DW points. The origin of the CSTT is explained in terms of a position and phase-dependent effective field associated with the DW profile and the electric current direction. Finally, our results reveal that this chiral mechanism can also affect the behavior of other magnetization collective modes, such as spin waves. This work shows the emergence of curvature-induced chiral spin transport and highlights a new phenomenon to be considered for designing spintronic devices., Comment: 7 pages, 3 figures

Through micromagnetic simulations, this work analyzes the stability of Bloch points in magnetic nanospheres and the possibility of using an array of such particles to compose a system with the features of a magnetic trap. We show that a BP can be nucleated as a metastable configuration in a relatively wide range of the nanosphere radius compared to a quasi-uniform and vortex state. We also show that the stabilized Bloch point generates a quadrupolar magnetic field outside it, from which we analyze the field profile of different arrays of these nanospheres to show that the obtained magnetic field shares the features of magnetic traps. Some of the highlights of the proposed magnetic traps rely on the magnetic field gradients achieved, which are orders of magnitude higher than standard magnetic traps, and allow three-dimensional trapping. Our results could be useful in trapping particles through the intrinsic magnetization of ferromagnetic nanoparticles while avoiding the commonly used mechanisms associated with Joule heating.

Understanding the domain wall (DW) dynamics in magnetic nanowires (NW) is crucial for spintronic-based applications demanding the use of DWs as information carriers. This work focuses on the dynamics of a DW displacing along a bent NW with an elliptical shape under the action of spin-polarized electric currents and external magnetic fields. Our results evidence that a curvature gradient induces an exchange-driven effective tangential field responsible for pinning a DW near the maximum curvature point in a NW. The DW equilibrium position depends on the competition between the torques produced by the external stimuli and the curvature-induced effective fields. When the external stimuli are below a certain threshold, the DW follows a damped harmonic oscillation around the equilibrium position. Above this threshold, DW displaces along the NW under an oscillatory translational motion.

We investigate the dynamics of two skyrmions lying in distinct layers of an antiferromagnetic bilayer system, consisting of nanostripes with the shape of racetracks. The top and bottom nanostripes are separated by a height offset and they are coupled through a ferromagnetic exchange, allowing the interaction between the skyrmions from both layers. Depending on the distance between the skyrmions they attract each other sufficiently to achieve a bound state. We also analyze their dynamics when an electric current is applied in a unique layer and we determine how the bound-state nucleation depends on the current density and vertical distance between the skyrmions. Finally, we analyzed the robustness of the bound states by considering two situations: 1) a system constituted by clean or homogeneous antiferromagnetic racetracks; 2) a system in which randomly distributed magnetic impurities in both layers are included in the system., Comment: 8 pages, 7 figures

In this work, we study the dynamic range of a neuronal network of excitable neurons with excitatory and inhibitory synapses. We obtain an analytical expression for the critical point as a function of the excitatory and inhibitory synaptic intensities. We also determine an analytical expression that gives the critical point value in which the maximal dynamic range occurs. Depending on the mean connection degree and coupl\-ing weights, the critical points can exhibit ceasing or ceaseless dynamics. However, the dynamic range is equal in both cases. We observe that the external stimulus mask some effects of self-sustained activity (ceaseless dynamic) in the region where the dynamic range is calculated. In these regions, the firing rate is the same for ceaseless dynamics and ceasing activity. Furthermore, we verify that excitatory and inhibitory inputs are approximately equal for a network with a large number of connections, showing excitatory-inhibitory balance as reported experimentally.

During the last years, topologically protected collective modes of the magnetization have called much attention. Among these, skyrmions and merons have been the object of intense study. In particular, topological skyrmions are objects with an integer skyrmion number $Q$ while merons have a half-integer skyrmion charge $q$. In this work, we consider a $Q=1$ skyrmion, composed by a meron and an antimeron (bimeron), displacing in a ferromagnetic racetrack, disputing a long-distance competition with its more famous counterpart, the typical $Q=1$ cylindrically symmetrical skyrmion. Both types of topological structures induce a Magnus force and then are subject to the Hall effect. The influence of the Dzyaloshinskii-Moriya interaction ($DMI$) present in certain materials and able to induces $DMI$-skyrmions is also analyzed. Our main aim is to compare the motions (induced by a spin-polarized current) of these objects along with their own specific racetracks. We also investigate some favorable factors which are able to give breath to the competitors, impelling them to remain in the race for longer distances before their annihilation at the racetrack lateral border. An interesting result is that the $DMI$-skyrmion loses this hypothetical race due to its larger rigidity., Comment: 6 pages, 5 figures

Curvature of nanomagnets can be used to induce chiral textures in the magnetization field. Here we perform analytical calculations and micromagnetic simulations aiming to analyze the stability of in-surface magnetization configurations in toroidal nanomagnets. We have obtained that despite toroidal vortex-like configurations are highly stable in magnetic nanotori, the interplay between geometry and magnetic properties promotes the competition between effective interactions yielding the development of a core in a vortex state when the aspect ratio between internal and external radii of nanoturus is $\gtrsim0.75$.

Magnetic nanorings have been widely studied due to their potential applications in spintronic and magnonic devices. In this work, by means of analytical calculations and micromagnetic simulations we have analyzed the magnetic energy of nanorings with variable anisotropy along their radius. Four magnetic states, including two new magnetic configurations, here called meron and knot-like states, are considered, looking to the relative lower energy states as a function of anisotropy. Phase diagrams with this states are presented., Comment: 6 pages, 4 figures

A discussion on the interaction between skyrmions in a bi-layer system connected by a non-magnetic metal is presented. From considering a free charge carrier model, we have shown that the Ruderman-Kittel-Kasuya-Yosida (RKKY ) inter- action can induce attractive or repulsive interaction between the skyrmions depending on the spacer thickness. We have also shown that due to an increasing in RKKY energy when the skyrmions are far from each other, their widths are diminished. Finally, we have obtained analytical solutions to the skyrmion position when the in-plane distance between the skyrmions is small and it is shown that an attractive RKKY interaction yields a skyrmion precessory motion. This RKKY-induced coupling could be used as a skyrmion drag mechanism to displace skyrmions in multilayers., Comment: 5 Pages, 7 Figures

Understanding the domain wall dynamics is an important issue in modern magnetism. Here we present results of domain wall displacement in curved cylindrical nanowires at a constant magnetic field. We show that the average velocity of a transverse domain wall increases with curvature. Contrary to what it is observed in stripes, in a curved wire the transverse domain wall oscillates along and rotates around the nanowire with the same frequency. These results open the possibility of new oscillation-based applications., Comment: 6 Figures

An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology., Comment: New version, accepted for publication in EPJB, 6 pages, 1 figure

We have demonstrated that Lorentz-violating terms stemming from the fermion sector of the SME are able to generate geometrical phases on the wave function of electrons confined in 1-dimensional rings, as well as persistent spin currents, in the total absence of electromagnetic fields. We have explicitly evaluated the eigenenergies and eigenspinors of the electrons modified by the Lorentz-violating terms, using them to calculate the dynamic and the Aharonov-Anandan phases in the sequel. The total phase presents a pattern very similar to the Aharonov-Casher phase accumulated by electrons in rings under the action of the Rashba interaction. Finally, the persistent spin current were carried out and used to impose upper bounds on the Lorentz-violating parameters., Comment: 8 pages, revtex, two columns, final and revised version published in Phys.Lett.B (2015)

We show that, after a transformation, the dynamics of linear perturbations (spin waves) around a singular Bloch point soliton is formally equivalent to a quantum system of an electron in a magnetic monopole field. The analytical solution to this problem is known and allows us to find the spectrum and the scattering of a wave in a Bloch point field., Comment: 6 pages, 4 figures

Curvature effects are important for a proper description of the properties of magnetic systems. In this paper the exchange and dipolar energy of vortices on a paraboloidal shell is studied. Using analytical calculations it is shown that the in-plane component of vortices has larger energy on a paraboloidal shell than in a planar disk with same thickness. On the other hand, the dipolar energy associated to the vortex core diminishes if the vortex core is on a paraboloidal surface. This reduction in the dipolar energy may cause a vortex pinning mechanism by a paraboloidal shaped defect in a planar nanomagnet. Regarding skyrmions, by using an in-plane anisotropy approximation to the dipolar energy, it is shown that the skyrmion must have its width shrunk in order to diminishes the magnetostatic energy and satisfy geometrical constraints of the system.

We study the influence of curvature on the exchange energy of skyrmions and vortices on a paraboloidal surface. It is shown that such structures appear as excitations of the Heisenberg model, presenting topological stability, unlike what happens on other simply-connected geometries such as pseudospheres. We also show that the skyrmion width depends on the geometrical parameters of the paraboloid. The presence of a magnetic field leads to the appearance of $2\pi$-skyrmions, introducing a new characteristic length into the system. Regarding vortices, the geometrical parameters of the paraboloid play an important role in the exchange energy of this excitation.

We study the stability and energetics associated to skyrmions appear- ing as excitations on curved surfaces. Using a continuum model we show that the presence of cylindrically radial and azimuthal fields destabilizes the skyrmions that appear in the absence of an external field. Weak fields generate fractional skyrmions while strong magnetic fields yield stable 2{$\pi$}- skyrmions, which have their widths diminished by the magnetic field strength. Under azimuthal fields vortex appear as stable states on the curved surface.

We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time reversal invariant or if there are more phases that has different topological invariants. From a mathematical point of view may exist more topological phases of matter as a subclass of one well established phase., Comment: revised version with some misprints corrected

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler-Lagrange static equations, derived from the Hamiltonian lead to the inhomogeneous double sine-Gordon equation (DSG). However, if the magnetic field is coupled with the metric elements of the surface, and consequently, its curvature, the homogeneous DSG appears and a $2\pi$-soliton is obtained as a solution for this model. In order to obey the self-dual equations, surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. The model was used to particularize the characteristic lenght of the 2$\pi$-soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. Fractional 2$\pi$-solitons must appear on finite surfaces, as the sphere, torus and barrels, for example., Comment: 15 pages, 1 figure, to appear in volume 43 of the Brazilian Journal of Physics. arXiv admin note: substantial text overlap with arXiv:1206.6228

The most general combination of couplings of fermions with external potentials in 1+1 dimensions, must include vector, scalar and pseudoscalar potentials. We consider such a mixing of potentials in a PT-symmetric time-independent Dirac equation. The Dirac equation is mapped into an effective PT-symmetric Schr\"{o}dinger equation. Despite the non-hermiticity of the effective potential, we find real energies for the fermion., Comment: 11 pages

We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are $r$ and $R$, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, $R\to\infty$, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R=0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus ($R>r$) such excitations present no core where energy could blow up. At the limit $R\to\infty$ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus ($R=r$) a singular core takes place, while for $R

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum chemistry, which consists of an oscillator with time-dependent mass and frequency under the action of a time-dependent imaginary potential. The propagator for a general time-dependence of the parameters and the wave-functions are obtained explicitly for constant frequency and mass and a linear time-dependence in the potential. The wave-functions are used to obtain the expectation value of the Hamiltonian. Although it is neither Hermitian nor PT symmetric, the case under study exhibits real values of energy., Comment: 8 pages - title and content changed

Static field classical configurations in (1+1)-dimensions for new non-linear potential models are investigated from an isospectral potential class and the concept of bosonic zero- mode solution. One of the models here considered has a static non-topological configuration with a single vacuum state that breaks supersymmetry., Comment: Revtex, 14 pages, 4 figures. To appear in the Phys. Lett. A ( Accepted in 04.04.2002)

In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the energy expression respect the correct quantum limits, which is a very important quality. The similarity of this kind of problem with the quasi exactly solvable potentials is explored in order to accomplish our goals., Comment: Latex, 13 pages

The hcp-fcc transformation induced in cobalt powder by ball milling at room temperature was studied using the excess Gibbs free energy for the metals, in nanometric form, to calculate the activation energy that the atoms need for the phase transformation to occur. The crystalline component of the nanocrystalline cobalt produced in our laboratory, via ball milling, was analized using the radial distribution function technique. The results suggest that the crystalline component has the same structure as the bulk, contradicting results already reported., Comment: 6 pages, 4 figures