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1
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Rado-Weertman Boundary Equation Revisited in Terms of the Free-Energy Density of a Thin Film

100%
Puszkarski H.
Acta Physica Polonica A
|
2016
|
vol. 129
|
issue 6
RK.129.6.1-1-RK.129.6.1-3
EN
Historically, the first boundary conditions to be formulated and used in the theory of ferromagnetic thin films, the Rado-Weertman (RW) conditions, have a general advantage of being a simple differential equation, 2A_{ex} ∂m/∂n - K_{surf}m = 0. A key role in this equation is played by the phenomenological quantity K_{surf} known as the surface anisotropy energy density; A_{ex} denotes the exchange stiffness constant, and m is the amplitude of the transverse component of dynamic magnetization. In the present paper we use a microscopic theory to demonstrate that the surface anisotropy energy density of a thin film is directly related with its free-energy density, a fact not observed in the literature to date. Using two local free-energy densities F^{surf} and F^{bulk}, defined separately on the surface and in the bulk, respectively, we prove that K_{surf}=d(F^{surf} - F^{bulk}), where d is the lattice constant. The above equation allows to determine the explicit configuration dependence of the surface anisotropy constant K_{surf} on the direction cosines of the magnetization vector for any system with a known formula for the free energy. On the basis of this general formula the physical boundary conditions to be fulfilled for a fundamental uniform mode and surface modes to occur in a thin film are formulated as simple relations between the surface and bulk free-energy densities that apply under conditions of occurrence of specific modes.
2
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Rado-Weertman Boundary Equation Revisited in Terms of the Free-Energy Density of a Thin Film

100%
Puszkarski H.
Acta Physica Polonica A
|
2016
|
vol. 129
|
issue 6
RK.129.6.1-1-RK.129.6.1-3
EN
Historically, the first boundary conditions to be formulated and used in the theory of ferromagnetic thin films, the Rado-Weertman (RW) conditions, have a general advantage of being a simple differential equation, 2A_{ex} ∂m/∂n - K_{surf}m = 0. A key role in this equation is played by the phenomenological quantity K_{surf} known as the surface anisotropy energy density; A_{ex} denotes the exchange stiffness constant, and m is the amplitude of the transverse component of dynamic magnetization. In the present paper we use a microscopic theory to demonstrate that the surface anisotropy energy density of a thin film is directly related with its free-energy density, a fact not observed in the literature to date. Using two local free-energy densities F^{surf} and F^{bulk}, defined separately on the surface and in the bulk, respectively, we prove that K_{surf} = d(F^{surf} - F^{bulk}), where d is the lattice constant. The above equation allows to determine the explicit configuration dependence of the surface anisotropy constant K_{surf} on the direction cosines of the magnetization vector for any system with a known formula for the free energy. On the basis of this general formula the physical boundary conditions to be fulfilled for a fundamental uniform mode and surface modes to occur in a thin film are formulated as simple relations between the surface and bulk free-energy densities that apply under conditions of occurrence of specific modes.
3
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Simplified Solving Procedure for the One-Dimensional Schrodinger Equation with Asymmetrical Boundary Conditions

100%
Puszkarski H.
|
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vol. 96
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issue 3-4
327-331
EN
We propose a new simplified procedure for finding the analytical solutions of the stationary one-dimensional Schrodinger equation, with asymmetric boundary conditions imposed on the equation. The essence of the method consists in expressing the general solution explicitly in terms of the boundary parameters in a form which, by itself, satisfies one of the boundary conditions involved; then, the other boundary condition gives straightforwardly the characteristic equation. This method may turn out to be beneficial with regard to the recently growing interest in one-dimensional quantum systems.
4
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Interface Effective Pinning and Dynamical Coupling of Spin Waves in Bilayer Ferromagnetic Films with Canted Magnetizations

64%
Puszkarski H., Cottam M. G.
Acta Physica Polonica A
|
1991
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vol. 79
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issue 4
549-564
EN
We present a theory for the spin-wave excitations in bilayer magnetic systems with exchange coupling across the interface between two ferromagnetic films having the same crystallographic structure. The Hamiltonian includes exchange and anisotropy terms within each magnetic film of the composite system, as well as at the interface and at the free surfaces. We examine, in particular, the effect of interface canting between the magnetization directions for each film, and we derive effective pinning parameters and dynamic coupling parameters for the interface as functions of the canting angle. We show that, in the special case when the magnetization directions are antiparallel in the bilayer system, the two films may be considered as effectively decoupled as regards the spin-wave dynamics. We discuss the relevance of this theory to recent experimental studies of bilayer ferromagnetic systems that exhibit antiferromagnetic interface exchange.
5
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Treatment of the Periodically Inhomogeneous Surface: Multiple Boundary Condition

64%
Puszkarski H., Krawczyk M.
Acta Physica Polonica A
|
2000
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vol. 97
|
issue 6
1017-1022
EN
We deal with the following question: how can the composite nature of a boundary condition formulated for a periodically inhomogeneous surface and involving the composite surface parameter, be treated analytically? We show that when the appropriate Fourier transformation is applied, the composite boundary condition reduces to a specific eigenproblem condition, which constitutes the spectrum of eigenvalues of an "effective" surface parameter, a novel quantity we introduced to account for the nonhomogeneity of the surface.
6
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Magnonic Spectra of Ferromagnetic Composites Versus Magnetization Contrast

64%
Krawczyk M., Puszkarski H.
Acta Physica Polonica A
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1998
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vol. 93
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issue 5-6
805-810
EN
It had been shown recently that the calculated magnonic spectra of two-dimensional periodic ferromagnetic composites can present frequency ranges forbidden for the propagation of magnon excitations throughout the composite. However, those forbidden energy gaps were found to be highly sensitive to the exchange contrast between the component ferromagnetic materials but were very weakly sensitive to the contrast in spontaneous magnetizations of the two materials. Accordingly, in this paper we introduce a new mathematical definition of the exchange field acting in inhomogeneous medium. With this new definition the present theory gives magnonic spectra reasonably sensitive to magnetization contrast, as they should be from the physical viewpoint; moreover, the magnetization contrast now becomes a gap-creating factor as well.
7
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Model for the Surface Anisotropy Field Observed in Spin-Wave Resonance in (Ga,Mn)As Thin Films

64%
Puszkarski H., Tomczak P.
Acta Physica Polonica A
|
2015
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vol. 127
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issue 2
508-510
EN
In this study we show why spin-wave resonance in a (Ga,Mn)As thin film may, in different conditions, meet the assumptions of either the surface inhomogeneity (SI) or the volume inhomogeneity (VI) model.
8
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Hybridization of Surface and Impurity Spin Waves Induced by their Propagation in the Plane of a Thin Ferromagnetic Film

64%
Kołodziejczak B., Puszkarski H.
Acta Physica Polonica A
|
1991
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vol. 80
|
issue 5
675-687
EN
Spin waves of a thin ferromagnetic film containing in its bulk two impurity layers, each parallel to the film surface and symmetrically disposed with regard to the film centre, are theoretically investigated within the framework of the Heisenberg model. The existence conditions for surface-localized and impurity-layer localized spin waves are established. Particular attention is given to the effect of a possible hybridization of these localized excitations; it is shown that this phenomenon does in fact occur for certain specified directions of the in-plane wave vector k_{||}.
9
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Effect of Interface Coupling on the Energy Spectrum of Triple-Layer Film. Interface-Localized Modes

64%
Słomian M., Puszkarski H.
Acta Physica Polonica A
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1991
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vol. 79
|
issue 6
873-888
EN
Numerical results of a new (interface-rescaling) theory of normal excitations in a triple-layer film are reported. The film is modelled by three one dimensional finite chains coupled together; the coupling across the interface is properly taken into account. The formation process of the film energy spectrum as a result of interface (i.e. inter-chain) coupling is studied, and the exact conditions for the existence of interface-localized modes are established.
10
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Two-Dimensional Brillouin Zones in Thin Magnetic Films and a Mapping of the Regions of Existence of Magnetic Surface States

64%
Kołodziejczak B., Puszkarski H.
Acta Physica Polonica A
|
1993
|
vol. 83
|
issue 5
661-676
EN
We consider the model of a thin ferromagnetic film, described by a standard Heisenberg Hamiltonian involving interactions between nearest neighbours. The surface inhomogeneities are introduced by means of "surface parameters" describing strictly the conditions at the surfaces. We consider the surface orientations SC(111) and FCC(111), for which we diagonalize the Hamiltonian by standard procedure obtaining the characteristic equation for the permitted eigenvalues (and eigenvectors perpendicular to the surface) versus the two-dimensional wave vector in the plane of the reciprocal lattice. It is found that the existence of a surface state (at fixed surface conditions) requires an appropriate propagation direction of the spin wave in the plane of the film. This requirement is visualized graphically by plotting the existence regions of the surface states in the two-dimensional Brillouin zone. These regions are studied as to their form and size versus the surface parameters. For the two surface orientations studied, the existence regions are found to be identical and hence they are not sensitive to the differences in cubic structure between SC and FCC.
11
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On the Interpretation of the Angular Dependence of the Main FMR/SWR Line in Ferromagnetic Thin Films

64%
Puszkarski H., Kasperski M.
|
EN
The reported measurements of the angular dependence of ferromagnetic resonance spectra and their theoretical interpretation lead to the observation that a discrepancy occurs between the theory and the experiment in certain ranges of the configuration angle. This disagreement cannot be eliminated within the Smit-Beljers model commonly used in the literature for the description of ferromagnetic resonance in thin films since the main ferromagnetic resonance line observed in thin films is not necessarily associated with the excitation of a uniform mode, as the Smit-Beljers model does assume for bulk samples. Instead, we associate this line with the excitation of a surface mode or the thin-film principal nonuniform mode. By taking into account the occurrence of a surface spin-pinning anisotropy, this assumption allows to obtain an agreement between the theoretical description of the ferromagnetic resonance and the experimental data in the whole range of angular configuration of the external field. As an example, on the basis of this modified ferromagnetic resonance model, we make some observations on the angular resonant dependence in uniaxial thin films.
12
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Content available

Ferromagnetic Layered Composites. Transfer Matrix Approach

51%
Puszkarski H., Krawczyk M., Lévy J., Mercier D.
Acta Physica Polonica A
|
2001
|
vol. 100
|
issue Supplement
195-214
EN
A theoretical analysis of spin-wave excitations in a ferromagnetic layered composite (ABAB... ABA; A and B are different homogeneous ferromagnetic materials) is performed by means of the transfer matrix approach. We focus our attention on two features not yet well studied in the present literature, namely, the existence of forbidden energy gaps in the spin-wave mode spectrum, as well as the properties of multilayer spin-wave mode profiles. These features are discussed in relation to several multilayer characteristics, such as the filling fraction, and the exchange or magnetization contrast; surface pinning conditions and dipolar interactions are also taken into account. The existence of forbidden gaps as well as properties of mode profiles are successfully explained by having recourse to an approximate model of indepe ndent constituent sublayers. Finally, as a byproduct of our investigation, we ascertain that the conventional test for computational convergence within the finite difference method demands to be completed by symmetry mode profile verification, in addition to standard verification of the frequency convergence alone.
13
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The Emergence of Subsurface Spin-Waves in fcc (110) Magnetic Films

51%
Mamica S., Puszkarski H., Lévy J.
Acta Physica Polonica A
|
2000
|
vol. 97
|
issue 3
483-486
EN
We show that the emergence of subsurface branches in the spin-wave spectra of thin films is due to the deficiency of interactions with next-nearestneighbours, the position vectors of which are oblique to the film surface.
14
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The Role of Oblique-to-Surface Disposition of Neighbours in the Emergence of Surface Spin Waves in Magnetic Films

51%
Mamica S., Józefowicz R., Puszkarski H.
Acta Physica Polonica A
|
1998
|
vol. 94
|
issue 1
79-91
EN
This work is aimed at a numerical investigation of the spin-wave energies and respective band structures throughout the two-dimensional Brillouin zone in magnetic (cubic) thin films for the surface orientations sc(001), bcc(001) and fcc(001). We apply the Heisenberg localized spin model assuming exchange nearest (NN) and next-nearest (NNN) neighbour interactions and elucidate the role of the geometrical disposition of the NN and NNN neighbourhoods for the emergence of the surface spin-waves. The necessary condition for the emergence of the surface spin-waves is turned out to require the bonds to be cut at the surface obliquely thereto irrespective of whether these "oblique" interactions are of the NN or NNN type.
15
Publication available in full text mode
Content available

Enhanced Photonic Band Gaps of Periodic Dielectric Structures Composed of Double Cylindrical Rods

51%
Woźniak T., Krawczyk M., Puszkarski H.
Acta Physica Polonica A
|
2001
|
vol. 99
|
issue 5
611-625
EN
On the basis of Maradudin and McGurn's model we investigate the spectral properties of a two-dimensional photonic crystal, consisting of cylindrical rods disposed periodically throughout a dielectric matrix (the crystal is limited by two surfaces perpendicular to the axes of the rods). The model is supplemented by a new structural element in the form of dielectric rods (also cylindrical in shape) disposed coaxially within the original rods. The centers of both kinds of rods overlap forming a two-dimensional rectangular lattice in the plane parallel to the surface. Thus, the object of our study is a Maradudin-McGurn's model in which the individual rods are replaced by coaxial double rods. For this modified model we search for the optimal set of structural parameter values for which the forbidden energy gaps become greatest, giving especial attention to the role played by the additional inner rods in the emergence of gaps. We arrive at the conclusion that the condition for the opening of absolutely forbidden gaps become more favourable in a photonic crystal with double rods compared with those required in a crystal with simple rods.
16
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A Monte Carlo Study of Critical Properties of Strongly Diluted Magnetic Semiconductor (Ga,Mn)As

51%
Tomczak P., Diep H., Jabłoński P., Puszkarski H.
Acta Physica Polonica A
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2018
|
vol. 133
|
issue 3
514-516
EN
Within a Monte Carlo technique we examine critical properties of diluted bulk magnetic semiconductor (Ga,Mn)As modeled by a strongly diluted ferromagnetic Heisenberg spin-5/2 system on a face centered cubic lattice. We assumed that 5% of Ga atoms is substituted by Mn atoms and the interaction between them is of the RKKY-type. The considered system is randomly quenched and a double average was performed: firstly, over the Boltzmann probability distribution and secondly - over 2048 configurations related to the quenched disorder. We estimated the critical temperature: T_{c}=97±6 K, which is in agreement with the experiment.
17
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SWR Studies of Higher-Order Surface Anisotropy Terms in (Ga,Mn)As Thin Films

51%
Puszkarski H., Tomczak P., Diep H.
Acta Physica Polonica A
|
2018
|
vol. 133
|
issue 3
635-638
EN
We extend the theory of spin-wave resonance (SWR) by introducing a new formula representing the surface pinning parameter as a series of contributions from different anisotropies existing in (Ga,Mn)As thin films. Comparing our theory with the reported experimental studies of SWR in thin films of the ferromagnetic semiconductor (Ga,Mn)As, we find that besides the first-order cubic anisotropy, higher-order cubic anisotropies (in the second and third orders) as well as uniaxial anisotropies (perpendicular in the first and second orders, and in-plane diagonal) occur on the surface of this material. To our best knowledge this is the first report of the existence of higher-order surface anisotropy fields in (Ga,Mn)As thin films.
18
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On the Magnon Spectrum of Antiferromagnetically Aligned Bilayer Films

45%
Puszkarski H., Kołodziejczak B., Akjouj A., Djafari-Rouhani B., Dobrzynski L.
Acta Physica Polonica A
|
1993
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vol. 83
|
issue 5
677-683
EN
We deal with spin-wave propagation in two antiferromagnetically aligned sublayers forming one bilayer film owing to the antiferromagnetic exchange coupling assumed to exist at the film interface. We get the following picture: as the spin wave traverses the interface, the creation of a spin-reversal in the one sublayer becomes an annihilation in the other sublayer. This feature is expressed by the non-conventional type of normalization condition of the spin-wave amplitudes.
19
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Brillouin Zone Mapping of the Existence Conditions for Interface Bilayer Spin-Waves. Effects of the Configuration of the Film Magnetization

39%
Puszkarski H., Józefowicz R., Kołodziejczak B., Akjouj A., Djafari-Rouhani B., Dobrzynski L.
Acta Physica Polonica A
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1996
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vol. 89
|
issue 5-6
675-688
EN
For the two interface cubic cuts: sc(110) and sc(111) we consider the existence regions of interface spin-waves of a ferromagnetic bilayer film on the two-dimensional Brillouin zone as to their size and shape versus the respective interface related parameters (interface exchange coupling and intrinsic interface anisotropy) applying the approximation of a very thick bilayer film and the method of Brillouin zone mapping (the three (100) interface cubic orientations have been dealt with earlier [Phys. Rev. B 51, 16008 (1995)]). Of particular interest to us still remains the emergence of interface spin-waves induced by varying dynamic quantities such as the in-plane propagation wave vector k_{∥}. Moreover, in our present investigation, we put especial emphasis on the effect exerted on the Brillouin zone mapping by varying (in the plane perpendicular to the film) the configuration angle 𝜗 of the film magnetization with respect to the film normal. We predict the existence of (at the most two) critical angles 𝜗_{c} at which the interface spin-waves emerge. These critical angles are functions of the in-plane wave vector k_{∥} of interface spin-wave propagation along the interface. Finally, we discuss the effects due to the presence of critical angles with a view to their exploitation in experimental measurements.
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