We report upon a theoretical study of collective magnonic modes in pairs of magnetic nano-elements with quasi-uniform magnetization. The mode spectrum and character are numerically computed for an individual isolated nano-element and then used to analytically calculate the splitting of the modes due to the inter-element magneto-dipole interaction. The results are compared with those obtained using direct simulations for the pairs of elements, yielding a generally good agreement. For the edge mode the interaction between the edges of the neighboring elements can exceed that between the edges of the same element, leading to softening of the mode profile and hence to the violation of the assumptions of the analytical approach. The softening has to be taken into account in the interpretation of dynamical studies of closely packed arrays of magnetic elements (magnonic crystals). V
The dispersion relations of collective oscillations of the magnetic moment of magnetic dots arranged in square-planar arrays and having magnetic moments perpendicular to the array plane are calculated. The presence of the external magnetic field perpendicular to the plane of array, as well as the uniaxial anisotropy for single dot are taken into account. The ferromagnetic state with all the magnetic moments parallel, and chessboard antiferromagnetic state are considered. The dispersion relation yields information about the stability of different states of the array. There is a critical magnetic field below which the ferromagnetic state is unstable. The antiferromagnetic state is stable for small enough magnetic fields. The dispersion relation is non-analytic as the value of the wave vector approaches zero. Non-trivial Van Hove anomalies are also found for both ferromagnetic and antiferromagnetic states.
The state of the art in modern nanolithography makes it possible to create regular arrays of magnetic superstructures with large numbers of nanodimen sional elements [1]. Of these systems, two dimen sional (2D) arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates are of spe cial interest. The distances between these particles are much greater than the exchange length of the magnet; they can only interact by means of magnetic dipole interaction. These arrays have important practical applications in systems of high density magnetic recording [1, 2] and they are of interest for various new areas of study in the applied physics of magnetism, such as magnonics, spintronics, and physics of mag nonic crystals. It is also important to note that these systems represent a new implementation of dipole magnets, which are basic objects of the fundamental physics of magnetism (see, e.g., review [3]).It should be noted that all artificial superstructures are large, yet finite, systems. Therefore, it is expected that boundary elements play a large role in the forma tion of properties of these systems and, hence, an anal ysis of the role of boundaries in samples of finite 2D arrays is of considerable interest. The presence of boundaries in an arbitrary periodic structure implies that the system loses translational symmetry in the direction perpendicular to the boundary. This decrease in the symmetry allows us to expect the appearance of qualitatively new solutions that are localized at the boundary-solutions of the type of Tamm surface states [4,5]. These states are usually studied in systems with a small number of interacting neighbors, e.g., in a simple approximation of nearest neighbor interactions [5], where a local decrease in the coordination number at the boundary is an important factor. For dipole coupled systems, this effect is expected to be not as important as in systems with short range interactions. On the other hand, in view of the long range character of magnetic dipole interac tions, some other effects of finiteness of the system that are manifested by the presence of macroscopically inhomogeneous fields may become much more signif icant. Therefore, the issues concerning the character of the ground state and the surface localization of modes in finite systems with long range interactions are of special interest.For a wave localized on the boundary, the ampli tude of oscillations at a given site depends on a discrete argument (site number) and is described by the corre sponding matrix equation [5]. The presence of a boundary can be treated as some local perturbation. Since the rank of the matrix for a long range interac tion is large, the exact problem in this case was studied by numerical methods and analytic estimations were obtained using the nearest neighbor approximation. It was found that this simple approximation still reflects important features of the problem.Consider an array of magnetic particles in the form of a semi infinite square lattice in the xy plane and let the boundar...
A simple model of magnetization dynamics in a ferromagnet/doped semiconductor hybrid structure with Rashba spin-orbit interaction (SOI) driven by an applied pulse of the electric field is proposed. The electric current excited by the applied field is spin-polarized due to the SOI and therefore it induces the magnetization rotation in the ferromagnetic layer via s-d exchange coupling. Magnetization dynamics dependence on the electric pulse shape and magnitude is analyzed for realistic values of parameters. We show that it is similar to the dynamics of a damped nonlinear oscillator with the time-dependent frequency proportional to the square root of the applied electric field. The magnetization switching properties of an elliptic magnetic element are examined as a function of the applied field magnitude and direction.
Long term surgical treatment results were studied for 30 patients (10 male and 20 female) with two- and three-fragment proximal humeral fractures with short intramedullary nail. Mean age of patients was 68.8 (37-84) years. All patients were examined clinically and roentgenologically. In postoperative period secondary varus deformity was observed in18 (60%) patients and made up 4.3° at an average. Roentgenologic signs of delayed fracture consolidation due to the loss of reposition and decrease of neck-shaft angle under 120° were observed in one case. Evaluation by ASES scale made up 90.73±7.01 points, by SST scale - 10.47±1.41 points. Treatment results for three-fragment fractures were not as good as for two-fragment ones however the difference was not statistically significant ( p >0.05). Obtained data showed the high efficacy of short straight intramedullary nail application in two- and three-fragment proximal humeral fractures.
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