The Bloch point 3D topological charge induced by the magnetostatic interaction.

A hedgehog or Bloch point is a point-like 3D magnetization configuration in a ferromagnet. Regardless of widely spread treatment of a Bloch point as a topological defect, its 3D topological charge has never been calculated. Here, applying the concepts of the emergent magnetic field and Dirac string, we calculate the 3D topological charge (Hopf index) of a Bloch point and show that due to the magnetostatic energy contribution it has a finite, non-integer value. Thus, Bloch points form a new class of hopfions-3D topological magnetization configurations. The calculated Bloch point non-zero gyrovector leads to important dynamical consequences such as the appearance of topological Hall effect.

Distinct magnetic field dependence of Néel skyrmion sizes in ultrathin nanodots.

We investigate the dependence of the Néel 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.

Magnetization reversal in circular vortex dots of small radius.

We present a detailed study of the magnetic behavior of Permalloy (Ni80Fe20 alloy) circular nanodots with small radii (30 nm and 70 nm) and different thicknesses (30 nm or 50 nm). Despite the small size of the dots, the measured hysteresis loops manifestly display the features of classical vortex behavior with zero remanence and lobes at high magnetic fields. This is remarkable because the size of the magnetic vortex core is comparable to the dot diameter, as revealed by magnetic force microscopy and micromagnetic simulations. The dot ground states are close to the border of the vortex stability and, depending on the dot size, the magnetization distribution combines attributes of the typical vortex, single domain states or even presents features resembling magnetic skyrmions. An analytical model of the dot magnetization reversal, accounting for the large vortex core size, is developed to explain the observed behavior, providing a rather good agreement with the experimental results. The study extends the understanding of magnetic nanodots beyond the classical vortex concept (where the vortex core spins have a negligible influence on the magnetic behavior) and can therefore be useful for improving emerging spintronic applications, such as spin-torque nano-oscillators. It also delimits the feasibility of producing a well-defined vortex configuration in sub-100 nm dots, enabling the intracellular magneto-mechanical actuation for biomedical applications.

Giant moving vortex mass in thick magnetic nanodots.

Magnetic vortex is one of the simplest topologically non-trivial textures in condensed matter physics. It is the ground state of submicron magnetic elements (dots) of different shapes: cylindrical, square etc. So far, the vast majority of the vortex dynamics studies were focused on thin dots with thickness 5-50 nm and only uniform across the thickness vortex excitation modes were observed. Here we explore the fundamental vortex mode in relatively thick (50-100 nm) dots using broadband ferromagnetic resonance and show that dimensionality increase leads to qualitatively new excitation spectra. We demonstrate that the fundamental mode frequency cannot be explained without introducing a giant vortex mass, which is a result of the vortex distortion due to interaction with spin waves. The vortex mass depends on the system geometry and is non-local because of important role of the dipolar interaction. The mass is rather small for thin dots. However, its importance increases drastically with the dot thickness increasing.

Angular dependence of the magnetoresistance in nanoparticle arrays.

The interplay between the ferromagnetism and the charging effects strongly affects the electron transport through nanoparticle arrays when they are placed between two ferromagnetic electrodes with collinear magnetizations. There are oscillations in the current for the parallel orientation of magnetizations, and large values of the tunneling magnetoresistance (TMR). We analyze the transport properties in nanoparticle arrays for the case of noncollinear magnetizations. We show that the I-V and TMR curves strongly depend on the angle θ between the magnetization orientations of both electrodes. Large values of TMR are obtained for several values of θ.

Probing the anharmonicity of the potential well for a magnetic vortex core in a nanodot.

The anharmonicity of the potential well confining a magnetic vortex core in a nanodot is measured dynamically with a magnetic resonance force microscope (MRFM). The stray field of the MRFM tip is used to displace the equilibrium core position away from the nanodot center. The anharmonicity is then inferred from the relative frequency shift induced on the eigenfrequency of the vortex core translational mode. An analytical framework is proposed to extract the anharmonic coefficient from this variational approach. Traces of these shifts are recorded while scanning the tip above an isolated nanodot, patterned out of a single crystal FeV film. We observe a +10% increase of the eigenfrequency when the equilibrium position of the vortex core is displaced to about one-third of its radius. This calibrates the tunability of the gyrotropic mode by external magnetic fields.

Evolution of the magnetic properties of Co10Cu90 nanoparticles prepared by wet chemistry with thermal annealing.

Nanoparticles of Co10Cu90 alloy have been prepared by sonochemical wet method. According to transmission electron microscopy, bimetallic particles with typical diameter of 50-100 nm consisting of nanocrystallites with average diameter of 15-20 nm were obtained. The samples were annealed at 300 degrees C and 450 degrees C. Zero field cooled and field cooled temperature dependences of magnetization in the temperature range of 5-400 K at 50 Oe, as well as magnetization hysteresis loops at 15, 100 and 305 K were measured by vibrating sample magnetometry. Presence of antiferromagnetic phase, most probably of the oxide Co3O4, was observed in as-prepared sample. The lowest coercivity was found for the CoCu sample annealed at-300 degrees C, whereas for as prepared sample and the one annealed at 450 degrees C it was significantly higher. The samples were additionally probed by continuous wave ferromagnetic resonance at room, temperature using a standard X-band electron spin resonance spectrometer. A good correspondence between evolution of the coercivity and the microwave resonance fields with annealing temperature was observed.

Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk.

Microwave spectroscopy of individual vortex-state magnetic nanodisks in a perpendicular bias magnetic field H is performed using a magnetic resonance force microscope. It reveals the splitting induced by H on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field Hr, at which the core polarity is reversed. The difference between the frequencies of the two stable rotational modes corresponding to each core polarity is proportional to H and to the ratio of the disk thickness to its radius. Simple analytic theory in combination with micromagnetic simulations give a quantitative description of the observed bistable dynamics.

Spin wave wells in nonellipsoidal micrometer size magnetic elements.

We show experimentally and by model calculations that in finite, nonellipsoidal, micrometer size magnetic thin film elements the dynamic magnetic eigenexcitations (spin waves) may exhibit strong spatial localization. This localization is due to the formation of a potential well for spin waves in the highly inhomogeneous internal magnetic field within the element.