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In physics, conserved quantities are key to understanding and describing physical phenomena. These conserved quantities are related to Noether's theorem and the Lagrangian description both in classical mechanics and in field theory. In this article we have found the equation of the vortex core trajectory in terms of two conserved physical quantities, namely the energy, $E$, and a vector perpendicular to the orbit plane, $\vec{A} = -\vec{L} + \vec{G} \, |\vec{r}_c|^2/2$ where $\vec{G}$, $\vec{L}$ and $\vec{r}_c$ are the topological gyrovector, the angular momentum and the position of the vortex core, respectively. We find that in the absence of a dissipative term, for small deviations of the vortex core, the trajectory is bounded between two concentric circles. On the contrary, under the action of a dissipative term proportional to the damping coefficient, $\vec{A}$ is no longer conservative and the vortex core moves either towards the center or out of the cylinder, depending on the circularity of the magnetic vortex and the intensity of the magnetic field applied in the plane of the cylinder., Comment: the results obtained are not valid in ferromagnets, in particular for the system that we have studied

Skyrmions have become one of the most visited topics during the last decade in condensed matter physics. In this work, and by means of analytical calculations and micromagnetic simulations, we explore the effect of the magnetostatic field generated by a magnetic tip on the stability of skyrmions. Our results show that the interaction energy between the tip and the skyrmion plays a fundamental role in the stabilization of N\'eel skyrmions confined in nanodisks, allowing its nucleation and annihilation, and also providing precise control of its size and polarity. Based on our results, we propose a very simple and cyclic method to nucleate and annihilate skyrmions, as well as to control their polarity and chirality. This proposal could open new possibilities for logic devices taking advantage of all the degrees of freedom that skyrmionic textures have.

In this article we investigate the induction of a surface anisotropy due to the displacement of the vortex core in a cylindrical nanostructure. In fact, the effect of the displacement of the vortex core in the dipolar energy can be modeled simply as a surface anisotropy of the form $E_s = K_s \int_{\mathcal{S}_m} d\mathcal{S} \, (\hat{n} \cdot \hat{m})^2/2$. Moreover, the surface anisotropy constant $K_s$ is proportional to the cylinder in-plane demagnetizing factor in the direction of the core deviation, $N_y(L/R)$, i.e., $K_s = \mu_0 M_0^2 R \, N_y(L/R)$, where $R$ and $L$ are the radius and the thickness of the cylinder, respectively. Our results show that the term of the nontrivial dipolar energy caused by the charges in the cylinder mantle can be replaced by a simple integral $E_s$ that increases the efficiency of the numerical calculations in the analytical study of the displacement of the vortex core in magnetic vortices., Comment: 5 pages, 6 figures

We investigate the dependence of the N\'eel skyrmion size and stability on perpendicular magnetic field in ultrathin circular magnetic dots with out-of-plane anisotropy and interfacial Dzyaloshinskii-Moriya exchange interaction. Our results show the existence of two distinct dependencies of the skyrmion radius on the applied field and dot size. In the case of skyrmions stable at zero field, their radius strongly increases with the field applied parallel to the skyrmion core until skyrmion reaches the metastability region and this dependence slows down. More common metastable skyrmions demonstrate a weaker increase of their size as a function of the field until some critical field value at which these skyrmions drastically increase in size showing a hysteretic behavior with coexistence of small and large radius skyrmions and small energy barriers between them. The first case is also characterized by a strong dependence of the skyrmion radius on the dot diameter, while in the second case this dependence is very weak., Comment: 15 pages, 9 figures

In this letter we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the external magnetic field applied. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any $\psi$ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields., Comment: 5 pages, 4 figures

An analytical expression for the energy of N\'eel skyrmions in ultra-thin nanodots considering exchange, uniaxial anisotropy, Dzyaloshinskii-Moriya, and dipolar contributions has been obtained. In particular, we have proposed for the N\'eel skyrmion, a general ansatz for the component of the magnetization perpendicular to the dot, given by $m_z(r) = [1-(r/R_s)^n]/[1 + (r/R_s)^n]$, where $R_s$ is the radius of the skyrmion and $n$ is an integer and even number. As proof of concept, we calculate the energy of a N\'eel skyrmion in an ultra-thin Co/Pt dot, and we find that the dipolar contribution cannot be neglected and that both Dzyaloshinskii-Moriya interaction and anisotropy play an important role to stabilize the skyrmion. Additionally, we have obtained a good agreement between our analytical calculations and previously published micromagnetic simulations for $n = 10$. For this reliable value of $n$, we have obtained that for a Dzyaloshinski Moriya constant $D = 5.5 \, (mJ/m^2)$, it is possible to stabilize a N\'eel skyrmion for $K_u$ in the range, $0.4 \, (MJ/m^3)< K_u <1.3 \, (MJ/m^3)$, whereas for $K_u = 0.8 \, (MJ/m^3)$, the skyrmion stabilizes for $5.0 \, (mJ/m^2) < D <6.0 \, (mJ/m^2) $. Thus, this analytical equation can be widely used to predict stability ranges for the N\'eel skyrmion in spintronic devices., Comment: 10 pages, 6 figures

We study the influence of the porosity on the domain structure of cobalt antidots thin films with controlled and circular defects of 20, 40 and 60 nm of diameter. Micromagnetic simulations, combined with First-order reversal curves analysis of classical magnetometry measurements, have been used to track the evolution of the magnetic domain configurations. The found coercivity enhancement with the increase of the pore diameter is correlated to the domain reversibility. Moreover, we found that when the pores diameter increases the domain-domain interactions become dominant., Comment: 10 pages, 6 figures

A detailed investigation of the scaling relations recently proposed by [J. d'Albuquerque e Castro, D. Altbir, J. C. Retamal, and P. Vargas, Phys. Rev. Lett. 88, 237202 (2002)] to study the magnetic properties of nanoparticles is presented. Analytical expressions for the total energy of three characteristic internal configurations of the particles are obtained, in terms of which the behavior of the magnetic phase diagram for those particles upon scaling of the exchange interaction is discussed. The exponent $\eta $ in scaling relations is shown to be dependent on the geometry of the vortex core, and results for specific cases are presented., Comment: 6 pages, 4 figures

The magnetic behavior of truncated conical nanoparticles in patterned thin films is investigated as a function of their size and shape. Using a scaling technique, phase diagrams giving the relative stability of characteristic internal magnetic structures of the particles are obtained. The role of the uniaxial anisotropy in determining the magnetic properties of such systems is discussed, and a simple method for stablishing its strength is proposed., Comment: 4 pages, 4 figures

The magnetization reversal in ordered arrays of iron oxide nanotubes of 50 nm outer diameter grown by atomic layer deposition is investigated theoretically as a function of the tube wall thickness, $d_{w}$. In thin tubes ($d_{w}<13$ nm) the reversal of magnetization is achieved by the propagation of a vortex domain boundary, while in thick tubes ($d_{w}>13$ nm) the reversal is driven by the propagation of a transverse domain boundary. Magnetostatic interactions between the tubes are responsible for a decrease of the coercive field in the array. Our calculations are in agreement with recently reported experimental results. We predict that the crossover between the vortex and transverse modes of magnetization reversal is a general phenomenon on the length scale considered., Comment: 8 pages, 7 figures

The hysteresis curves of multilayer microwires consisting of a soft magnetic nucleus, intermediate non-magnetic layers, and an external hard magnetic layer are investigated. The magnetostatic interaction between magnetic layers is proved to give rise to an antiferromagnetic-like coupling resulting in a magnetostatic bias in the hysteresis curves of the soft nucleus. This magnetostatic biasing effect is investigated in terms of the microwire geometry. The experimental results are interpreted considering an analytical model taking into account the magnetostatic interaction between the magnetic layers., Comment: 6 pages, 7 figures

The investigation of interactions between magnetic nanotubes is complex and often involves substantial simplifications. In this letter an analytical expression for the magnetostatic interaction, taking into account the geometry of the tubes, has been obtained. This expression allows for the definition of a critical vertical separation for relative magnetization between nanotubes and can be used for tailoring barcode-type nanostructures with prospective applications such as biological separation and transport., Comment: 4 pages, 5 figures

The magnetostatic interaction between two ferromagnetic microwires is calculated as a function of their geometric parameters and compared with those measured through magnetic hysteresis loops of glass-coated amorphous Fe% $_{77.5}$Si$_{7.5}$B$_{15}$ microwires. The hysteresis loops are characterized by well-defined Barkhausen jumps corresponding each to the magnetization reversal of individual microwires, separated by horizontal plateaux. It is shown that the magnetostatic interaction between them is responsible for the appearance of these plateaux. Finally, using the expression for the magnetostatic interaction is trivial to obtain the interacting force between microwires. Our results are intended to provide guidelines for the use of these microwires with technological purpose such as the fabrication of magnetic sensors., Comment: 5 pages, 5 figures

The non-uniform magnetostatic field produced by the equilibrium and non equilibrium magnetic states of magnetic nanotubes has been investigated theoretically. We consider magnetic fields produced by actual equilibrium states and transverse and vortex domain walls confined within the nanostructure. Our calculations allow us to understand the importance of the magnetostatic field in nanomagnetism, which is frequently considered as a uniform field. Moreover, our results can be used as a basis for future research of others properties, such as the investigation of spin waves when domain walls are present, or the motion of a magnetic particle near a magnetic field., Comment: 8 pages, 8 figures

During the last years great attention has been given to the encapsulation of magnetic nanoparticles. In this work we investigated the stability of small magnetic particles inside magnetic nanotubes. Multisegmented nanotubes were tested in order to optimize the stability of the particle inside the nanotubes. Our results evidenced that multisegmented nanotubes are more efficient to entrap the particles at temperatures up to hundreds of kelvins., Comment: 4 pages, 4 figures

Asymmetric dots as a function of their geometry have been investigated using three-dimensional (3D) object oriented micromagnetic framework (OOMMF) code. The effect of shape asymmetry of the disk on coercivity and remanence is studied. Angular dependence of the remanence and coercivity is also addressed. Asymmetric dots are found to reverse their magnetization by nucleation and propagation of a vortex, when the field is applied parallel to the direction of asymmetry. However, complex reversal modes appear when the angle at which the external field is applied is varied, leading to a non monotonic behavior of the coercivity and remanence., Comment: 5 pages, 7 figures

We have used Monte Carlo simulations to investigate the magnetic properties of asymmetric dots as a function of their geometry. The asymmetry of round dots is produced by cutting off a fraction of the dot and is characterized by an asymmetry parameter $\alpha$. This shape asymmetry has interesting effects on the coercivity ($H_{c}$), remanence ($M_{r}$), and barrier for vortex and C- state formation. The dependences of $H_{c}$ and $M_{r}$ are non monotonic as a function of $\alpha$ with a well defined minima in these parameters. The vortex enters the most asymmetric part and exits through the symmetric portion of the dot. With increasing $\alpha $ the vortex formation starts with a C-state which persists for longer fields and the barrier for vortex exit diminishes with increasing asymmetry, thus providing control over the magnetic chirality. This implies interesting, naively-unexpected, magnetic behavior as a function of geometry and magnetic field., Comment: 6 pages, 6 figures

The angular dependence of the remanence and coercivity of Ni nanowire arrays produced inside the pores of anodic alumina membranes has been studied. By comparing our analytical calculations with our measurements, we conclude that the magnetization reversal in this array is driven by means of the nucleation and propagation of a transverse wall. A simple model based on an adapted Stoner-Wohlfarth model is used to explain the angular dependence of the coercivity.

The magnetic configurations of barcode-type magnetic nanostructures consisting of alternate ferromagnetic and nonmagnetic layers arranged within a multilayer nanotube structure are investigated as a function of their geometry. Based on a continuum approach we have obtained analytical expressions for the energy which lead us to obtain phase diagrams giving the relative stability of characteristic internal magnetic configurations of the barcode-type nanostructures.

The magnetic configurations of bi-phase micro- and nanotubes consisting of a ferromagnetic internal tube, an intermediate non-magnetic spacer, and an external magnetic shell are investigated as a function of their geometry. Based on a continuum approach we obtained analytical expressions for the energy which lead us to obtain phase diagrams giving the relative stability of characteristic internal magnetic configurations of the bi-phase tubes.

The effect of dipolar interactions among cylindrical nanodots, with a vortex-core magnetic configuration, is analyzed by means of analytical calculations. The cylinders are placed in a N x N square array in two configurations - core oriented parallel to each other and with antiparallel alignment between nearest neighbors. Results comprise the variation in the core radius with the number of interacting dots, the distance between them and dot height. The dipolar interdot coupling leads to a decrease (increase) of the core radius for parallel (antiparallel) arrays.

The influence of the macroscopic size of the Ni nanowire array system on their remanence state has been investigated. A simple magnetic phenomenological model has been developed to obtain the remanence as a function of the magnetostatic interactions in the array. We observe that, due to the long range of the dipolar interactions between the wires, the size of the sample strongly influence the remanence of the array. On the other hand, the magnetic state of nanowires has been studied by variable field magnetic force microscopy for different remanent states. The distribution of nanowires with the magnetization in up or down directions and the subsequent remanent magnetization has been deduced from the magnetic images. The existence of two short-range magnetic orderings with similar energies can explain the typical labyrinth pattern observed in magnetic force microscopy images of the nanowire arrays.

The nucleation field for infinite magnetic nanotubes, in the case of a magnetic field applied parallel to the long axis of the tubes, is calculated as a function of their geometric parameters and compared with those produced inside the pores of anodic alumina membranes by atomic layer deposition. We also extended this result to the case of an angular dependence. We observed a transition from curling-mode rotation to coherent-mode rotation as a function of the angle in which the external magnetic field is applied. Finally, we observed that the internal radii of the tubes favors the magnetization curling reversal.

The investigation of the role of interactions in magnetic wire arrays is complex and often subject to strong simplifications. In this paper we obtained analytical expressions for the magnetostatic interactions between wires and investigate the range of validity of dipole-dipole, first order and second order approximations. We also analyze the extension of the interwire magnetostatic interactions in a sample and found that the number of wires required to reach energy convergence in the array strongly depends on the relative magnetic orientation between the wires., Comment: 7 pages and 5 figures

The magnetic switching of ferromagnetic nanotubes is investigated as a function of their geometry. Two independent methods are used: Numerical simulations and analytical calculations. It is found that for long tubes the reversal of magnetization is achieved by two mechanism: The propagation of a transverse or a vortex domain wall depending on the internal and external radii of the tube., Comment: 4 pages, 4 figures

The relative stability of the vortex, onion and ferromagnetic phases in nanorings is examined as a function of the ring geometry. Total energy calculations are carried out analytically, based on simple models for each configuration. Results are summarized by phase diagrams, which might be used as a guide to the production of rings with specific magnetic properties., Comment: To appear in Journal of Applied Physics