Efeitos da interação dipolar na nucleação de vórtices em nano-cilindros magnéticos

The effect of confinement on the magnetic structure of vortices of dipolar coupled ferromagnetic nanoelements is an issue of current interest, not only for academic reasons, but also for the potential impact in a number of promising applications. Most applications, such as nano-oscillators for wireless data transmission, benefit from the possibility of tailoring the vortex core magnetic pattern. We report a theoretical study of vortex nucleation in pairs of coaxial iron and Permalloy cylinders, with diameters ranging from 21nm to 150nm, and 12nm and 21nm thicknesses, separated by a non-magnetic layer. 12nm thick iron and Permalloy isolated (single) cylinders do not hold a vortex, and 21nm isolated cylinders hold a vortex. Our results indicate that one may tailor the magnetic structure of the vortices, and the relative chirality, by selecting the thickness of the non-magnetic spacer and the values of the cylinders diameters and thicknesses. Also, the dipolar interaction may induce vortex formation in pairs of 12nm thick nanocylinders and inhibit the formation of vortices in pairs of 21nm thick nanocylinders. These new phases are formed according to the value of the distance between the cylinderes. Furthermore, we show that the preparation route may control relative chirality and polarity of the vortex pair. For instance: by saturating a pair of Fe 81nm diameter, 21nm thickness cylinders, along the crystalline anisotropy direction, a pair of 36nm core diameter vortices, with same chirality and polarity is prepared. By saturating along the perpendicular direction, one prepares a 30nm diameter core vortex pair, with opposite chirality and opposite polarity. We also present a theoretical discussion of the impact of vortices on the thermal hysteresis of a pair of interface biased elliptical iron nanoelements, separated by an ultrathin nonmagnetic insulating layer. We have found that iron nanoelements exchange coupled to a noncompensated NiO substrate, display thermal hysteresis at room temperature, well below the iron Curie temperature. The thermal hysteresis consists in different sequences of magnetic states in the heating and cooling branches of a thermal loop, and originates in the thermal reduction of the interface field, and on the rearrangements of the magnetic structure at high temperatures, 5 produce by the strong dipolar coupling. The width of the thermal hysteresis varies from 500 K to 100 K for lateral dimensions of 125 nm x 65 nm and 145 nm x 65 nm. We focus on the thermal effects on two particular states: the antiparallel state, which has, at low temperatures, the interface biased nanoelement with the magnetization aligned with the interface field and the second nanoelement aligned opposite to the interface field; and in the parallel state, which has both nanoelements with the magnetization aligned with the interface field at low temperatures. We show that the dipolar interaction leads to enhanced thermal stability of the antiparallel state, and reduces the thermal stability of the parallel state. These states are the key phases in the application of pairs of ferromagnetic nanoelements, separated by a thin insulating layer, for tunneling magnetic memory cells. We have found that for a pair of 125nm x 65nm nanoelements, separated by 1.1nm, and low temperature interface field strength of 5.88kOe, the low temperature state (T = 100K) consists of a pair of nearly parallel buckle-states. This low temperature phase is kept with minor changes up to T= 249 K when the magnetization is reduced to 50% of the low temperature value due to nucleation of a vortex centered around the middle of the free surface nanoelement. By further increasing the temperature, there is another small change in the magnetization due to vortex motion. Apart from minor changes in the vortex position, the high temperature vortex state remains stable, in the cooling branch, down to low temperatures. We note that wide loop thermal hysteresis may pose limits on the design of tunneling magnetic memory cells

Vortex state and effect of anisotropy in sub-100 nm magnetic nanodots

Magnetic properties of Fe nanodots are simulated using a scaling technique and Monte Carlo method, in good agreement with experimental results. For the 20-nm-thick dots with diameters larger than 60¿nm, the magnetization reversal via vortex state is observed. The role of magnetic interaction between dots in arrays in the reversal process is studied as a function of nanometric center-to-center distance. When this distance is more than twice the dot diameter, the interaction can be neglected and the magnetic properties of the entire array are determined by the magnetic configuration of the individual dots. The effect of crystalline anisotropy on the vortex state is investigated. For arrays of noninteracting dots, the anisotropy strongly affects the vortex nucleation field and coercivity, and only slightly affects the vortex annihilation field

Influence of the dipolar interactions in the magnetization reversal asymmetry of hard-soft magnetic ribbons

Partial crystallization of the metallic glass Co66Si16B12Fe4Mo2 was performed by annealing at temperatures between 500 and 540°C for 10-20 min, resulting in crystallite volume fractions of (0.7-5)×10¿3 and sizes of 50-100 nm. This two-phase alloy presents a remarkable feature: a hysteresis loop shift that can be tailored by simply premagnetizing the sample in the adequate magnetic field. Shifts as large as five times the coercive field have been obtained which make them interesting for application as magnetic cores in dc pulse transformers. The asymetrical magnetic reversal is explained in terms of the magnetic dipolar field interaction and the observed hysteresis loops have been satisfactorily simulated by a modification of Stoner-Wohlfarth¿s model of coherent rotations.

Pulsar timing irregularities and the imprint of magnetic field evolution

Context. The rotational evolution of isolated neutron stars is dominated by the magnetic field anchored to the solid crust of the star. Assuming that the core field evolves on much longer timescales, the crustal field evolves mainly though Ohmic dissipation and the Hall drift, and it may be subject to relatively rapid changes with remarkable effects on the observed timing properties. Aims. We investigate whether changes of the magnetic field structure and strength during the star evolution may have observable consequences in the braking index n. This is the most sensitive quantity to reflect small variations of the timing properties that are caused by magnetic field rearrangements. Methods. We performed axisymmetric, long-term simulations of the magneto-thermal evolution of neutron stars with state-of-the-art microphysical inputs to calculate the evolution of the braking index. Relatively rapid magnetic field modifications can be expected only in the crust of neutron stars, where we focus our study. Results. We find that the effect of the magnetic field evolution on the braking index can be divided into three qualitatively different stages depending on the age and the internal temperature: a first stage that may be different for standard pulsars (with n ~ 3) or low field neutron stars that accreted fallback matter during the supernova explosion (systematically n < 3); in a second stage, the evolution is governed by almost pure Ohmic field decay, and a braking index n > 3 is expected; in the third stage, at late times, when the interior temperature has dropped to very low values, Hall oscillatory modes in the neutron star crust result in braking indices of a high absolute value and both positive and negative signs. Conclusions. Current magneto-thermal evolution models predict a large contribution to the timing noise and, in particular, to the braking index, from temporal variations of the magnetic field. Models with strong (≳ 1014 G) multipolar or toroidal components, even with a weak (~1012 G) dipolar field are consistent with the observed trend of the timing properties.

Magnetization reversal of ferromagnetic nanowires studied by magnetic force microscopy

The magnetization reversal of two-dimensional arrays of parallel ferromagnetic Fe nanowires embedded in nanoporous alumina templates has been studied. By combining bulk magnetization measurements (superconducting quantum interference device magnetometry) with field-dependent magnetic force microscopy (MFM), we have been able to decompose the macroscopic hysteresis loop in terms of the irreversible magnetic responses of individual nanowires. The latter are found to behave as monodomain ferromagnetic needles, with hysteresis loops displaced (asymmetric) as a consequence of the strong dipolar interactions between them. The application of field-dependent MFM provides a microscopic method to obtain the hysteresis curve of the array, by simply registering the fraction of up and down magnetized wires as a function of applied field. The observed deviations from the rectangular shape of the macroscopic hysteresis loop of the array can be ascribed to the spatial variation of the dipolar field through the inhomogeneously filled membrane. The system studied proves to be an excellent example of the two-dimensional classical Preisach model, well known from the field of hysteresis modeling and micromagnetism.

Influência da interação dipolar nas fases magnéticas de nanopartículas esféricas com estrutura núcleo@camada

Bi-magnetic core@shell nanoparticle has attracted attention several researchers because great applicability that they offer. The possibility of combining different functionalities of magnetic materials make them a key piece in many areas as in data processing permanent magnets and biomagnetics sistems. These nanoparticles are controlled by intrinsic properties of the core and shell materials as well as the interactions between them, besides size and geometry effects. Thus, it was developed in this thesis a theoretical study about dipolar interaction contribution between materials different magnetic properties in bi-magnetic core@shell nanoparticles conventional spherical geometry. The materials were analyzed CoFe2O4, MnFe2O4 e CoFe2 in various combinations and sizes. The results show that the impact of the core dipole field in the shell cause reverse magnetization early its, before of the core, in nanoparticle of CoFe2O4(22nm)@CoFe2(2nm), thereby causing a decrease coercivity field of 65% in comparection with simple nanoparticle of CoFe2O4 (HC=13.6 KOe) of same diameter. The large core anisotropy in conventional nanoparticle makes it the a stable dipolar field source in the shell, that varies length scale of the order of the core radius. Furthermore, the impact of dipolar field is greatly enhanced by the geometrical constraints and by magnetics properties of both core@shell materials. In systems with core coated with a thin shell of thickness less than the exchange length, the interaction interface can hold reversal the shell occurring an uniform magnetization reversal, however this effect only is relevant on systems where the dipole field effects is weak compared with the exchange interaction.

Influência da interação dipolar nas fases magnéticas de nanopartículas esféricas com estrutura núcleo@camada

Bi-magnetic core@shell nanoparticle has attracted attention several researchers because great applicability that they offer. The possibility of combining different functionalities of magnetic materials make them a key piece in many areas as in data processing permanent magnets and biomagnetics sistems. These nanoparticles are controlled by intrinsic properties of the core and shell materials as well as the interactions between them, besides size and geometry effects. Thus, it was developed in this thesis a theoretical study about dipolar interaction contribution between materials different magnetic properties in bi-magnetic core@shell nanoparticles conventional spherical geometry. The materials were analyzed CoFe2O4, MnFe2O4 e CoFe2 in various combinations and sizes. The results show that the impact of the core dipole field in the shell cause reverse magnetization early its, before of the core, in nanoparticle of CoFe2O4(22nm)@CoFe2(2nm), thereby causing a decrease coercivity field of 65% in comparection with simple nanoparticle of CoFe2O4 (HC=13.6 KOe) of same diameter. The large core anisotropy in conventional nanoparticle makes it the a stable dipolar field source in the shell, that varies length scale of the order of the core radius. Furthermore, the impact of dipolar field is greatly enhanced by the geometrical constraints and by magnetics properties of both core@shell materials. In systems with core coated with a thin shell of thickness less than the exchange length, the interaction interface can hold reversal the shell occurring an uniform magnetization reversal, however this effect only is relevant on systems where the dipole field effects is weak compared with the exchange interaction.

Anisotropia magnética em nanofilmes com assimetria cristalográfica

This Thesis comprises a theoretical study about the influence of the magnetocrystalline anisotropy on the static and dynamic magnetic properties of nanofilms: monolayers and trilayers coupled through the bilinear and biquadratic exchange fields, for situations in which the systems are grown in unusual [hkl] asymmetric directions. Using a theory based on a realistic phenomenological model for description of nanometric systems, we consider the total free magnetic energy including the Zeeman interaction, cubic and uniaxial anisotropies, demagnetizing and surface anysotropy energies, as well as the exchange terms. Numerical calculations are conducted by minimizing the total magnetic energy from the determination of equilibrium static configurations. We consider experimental parameters found in the literature to illustrate our results for Fe/Cr/Fe trilayer systems. In particular, a total of six different magnetic scenarios are analyzed for three regimens of exchange fields and the [211] and [321] asymmetric growth directions. After numerically minimize the total energy, we use the equilibrium configurations to calculate magnetization and magnetoresistance curves with the respective magnetic phases and corresponding critical fields. These results are also used to establish the boundary for occurrence of saturated states. Within the context of the spin waves, we solve the equation of motion for these systems in order to find the respective associated dispersion relations. The results show similar magnetization and magnetoresistance curves for both [211] and [321] growth scenarios, including an equivalent magnetic transition behavior. However, the combination of those peculiar symmetries and influence of the exchange energies results in attractive properties, including the generation of magnetic states as a function of the asymmetric degree imposed in the [hkl] growth orientations. There is also an increasing incompatibility between the values of saturation fields of magnetization and magnetoresistance for the cases in which a magnetic field acts along intermediate cubic anisotropic axes, particularly in the situations where the bilinear and biquadratic exchange fields are comparable. The dispersion relations and static results are consistent, the corresponding magnetic states are also present in both acoustic and optical modes. Furthermore, Goldstone excitations are also observed for that particular cases of a magnetic field acting in the intermediate axes, an effect related to transitions of second order and to the spontaneous symmetry breaking imposed by the combination of the biquadratic energy with the cubic and uniaxial anisotropies.

Magnetic polarization currents in double quantum dot devices

We investigate coherent electron transport through a parallel circuit of two quantum dots (QDs), each of which has a single tunable. energy level. Electrons tunnelling via each dot from the left lead interfere with each other at the right lead. It is shown that due to the quantum interference of tunnelling electrons the double QD device is magnetically polarized by coherent circulation of electrons on the closed path through the dots and the leads. By varying the energy level of each dot one can make the magnetic states of the device be up-, non- or down-polarized. It is shown that for experimentally accessible temperatures and applied biases the magnetic polarization currents Should be sufficiently large to observe with current nanotechnology.

Resonant spin tunneling in small antiferromagnetic particles

The paper reports a detailed experimental study on magnetic relaxation of natural horse-spleen ferritin. ac susceptibility measurements performed on three samples of different concentration show that dipole-dipole interactions between uncompensated moments play no significant role. Furthermore, the distribution of relaxation times in these samples has been obtained from a scaling of experimental X" data, obtained at different frequencies. The average uncompensated magnetic moment per protein is compatible with a disordered arrangement of atomic spins throughout the core, rather than with surface disorder. The observed field dependence of the blocking temperature suggests that magnetic relaxation is faster at zero field than at intermediate field values. This is confirmed by the fact that the magnetic viscosity peaks at zero field, too. Using the distribution of relaxation times obtained independently, we show that these results cannot be explained in terms of classical relaxation theory. The most plausible explanation of these results is the existence, near zero field, of resonant magnetic tunneling between magnetic states of opposite orientation, which are thermally populated.

Ferromagnetic properties of pyrolytic nanocarbon

The work reported in this thesis is dedicated to irreversible magnetic properties in pyrolytic nanocarbon samples. Based on atomic force microscope images, the samples consist of carbon clusters with radius 30..120 nm. These are treated as single-domain nanoparticles. Magnetic hysteresis, field cooled, zero field cooled and thermoremanent magnetization measurements were performed using an RF SQUID magnetometer and ferromagnetic behaviour was observed. Analysis suggests that the ferromagnetic ordering is associated with defects in a thin surface layer, whose thickness is independent of particle size. Critical radius for single-domain particles, critical radius for coherent rotation, magnetic layer thickness, distance between elementary magnetic moments, saturation magnetization, exchange stiffness constant and anisotropy energy density are also presented.

Resonant spin tunneling in small antiferromagnetic particles

The paper reports a detailed experimental study on magnetic relaxation of natural horse-spleen ferritin. ac susceptibility measurements performed on three samples of different concentration show that dipole-dipole interactions between uncompensated moments play no significant role. Furthermore, the distribution of relaxation times in these samples has been obtained from a scaling of experimental X" data, obtained at different frequencies. The average uncompensated magnetic moment per protein is compatible with a disordered arrangement of atomic spins throughout the core, rather than with surface disorder. The observed field dependence of the blocking temperature suggests that magnetic relaxation is faster at zero field than at intermediate field values. This is confirmed by the fact that the magnetic viscosity peaks at zero field, too. Using the distribution of relaxation times obtained independently, we show that these results cannot be explained in terms of classical relaxation theory. The most plausible explanation of these results is the existence, near zero field, of resonant magnetic tunneling between magnetic states of opposite orientation, which are thermally populated.

Efeitos de interface em bicamadas magnéticas

We study magnetic interface roughness in F/AF bilayers. Two kinds of roughness were considered. The first one consists of isolated defects that divide the substrate in two regions, each one with an AF sub-lattice. The interface exchange coupling is considered uniform and presents a sudden change in the defects line, favoring Neel wall nucleation. Our results show the interface field dependence of the threshold thickness for the reorientation of the magnetization in the ferromagnetic film. Angular profiles show the relaxation of the magnetization, from Neel wall, at the interface, to reoriented state, at the surface. External magnetic field, perpendicular to the easy axis of the substrate, favors the reoriented state. Depending, of the external magnetic field intensity, parallel to the easy axis of the AF, the magnetization profile at surface can be parallel or perpendicular to the field direction. The second one treats of distributed deffects, periodically. The shape hysteresis curves, exchange bias and coercivity were characterized by interface field intensity and roughness pattern. Our results show that dipolar effects decrease the exchange bias and coercivity

Nucleação de vortices e paredes de domínio em nanoestruturas magnéticas

We report a theoretical investigation of the magnetic phases and hysteresis of exchange biased ferromagnetic (F) nanoelements for three di erent systems: exchange biased nanoparticles, exchange biased narrow ferromagnetic stripes and exchange biased thin ferromagnetic lms. In all cases the focus is on the new e ects produced by suitable patterns of the exchange energy coupling the ferromagnetic nanoelement with a large anisotropy antiferromagnetic (AF) substrate. We investigate the hysteresis of iron and permalloy nanoparticles with a square basis, with lateral dimensions between 45 nm and 120 nm and thickness between 12 nm and 21 nm. Interface bias is aimed at producing large domains in thin lms. Our results show that, contrary to intuition, the interface exchange coupling may generate vortex states along the hysteresis loop. Also, the threshold value of the interface eld strength for vortex nucleation is smaller for iron nanoelements. We investigate the nucleation and depinning of an array of domain walls pinned at interface defects of a vicinal stripe/AF bilayer. The interface exchange eld displays a periodic pattern corresponding to the topology of the AF vicinal substrate. The vicinal AF substrate consists of a sequence of terraces, each with spins from one AF subalattice, alternating one another. As a result the interface eld of neighboring terraces point in opposite direction, leading to the nucleation of a sequence of domain walls in the ferromagnetic stripe. We investigated iron an permalloy micrometric stripes, with width ranging from 100 nm and 300 nm and thickness of 5 nm. We focused in domain wall sequences with same chirality and alternate chirality. We have found that for 100nm terraces the same chiraility sequence is more stable, requiring a larger value of the external eld for depinning. The third system consists of an iron lm with a thickness of 5 nm, exchange coupled to an AF substrate with a periodic distribution of islands where the AF spins have the opposite direction of the spins in the background. This corresponds to a two-sublattice noncompensated AF plane (such as the surface of a (100) FeF2 lm), with monolayer-height islands containing spins of one sublattice on a surface containing spins of the opposite sublattice. The interface eld acting in the ferromagnetic spins over the islands points in the opposite direction of that in the spins over the background. This a model system for the investigation of interface roughness e ects. We have studied the coercicivity an exchange bias hysteresis shift as a function of the distance between the islands and the degree of interface roughness. We have found a relevant reduction of coercivity for nearly compensated interfaces. Also the e ective hysteresis shift is not proportional to the liquid moment of the AF plane. We also developed an analytical model which reproduces qualitatively the results of numerical simulations

Dipolar Bose-Einstein condensate in a ring or in a shell

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)