Treatment of the Periodically Inhomogeneous Surface: Multiple Boundary Condition

Puszkarski, H.; Krawczyk, Maciej

doi:10.12693/aphyspola.97.1017

Cited by 6 publications

(12 citation statements)

References 10 publications

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“…In particular, theoretically it has been shown that systems of continuous spins (XY and Heisenberg) in two dimensions (2D) with short-range interaction cannot have long-range order at finite temperature [4]. In the case of thin films, it has been shown that low-lying localized spin waves can be found at the film surface [5] and effects of these localized modes on the surface magnetization at finite temperature (T ) and on the critical temperature have been investigated by the Green's function technique [6,7]. Experimentally, objects of nanometric size such as ultrathin films and nanoparticles have also been intensively studied because of numerous and important applications in industry.…”

Section: Introductionmentioning

confidence: 99%

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Hoang¹,

Kasperski²,

Puszkarski³

et al. 2013

J. Phys.: Condens. Matter

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We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper which correspond to the 3-state Potts model. The Hamiltonian of the system includes: (i) the exchange interaction Jij between nearest-neighbor sites i and j (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance rc (iii) a single-ion perpendicular anisotropy of amplitude A. We allow Jij = Js between surface spins, and Jij = J otherwise. We show that the ground state depends on the the ratio D/A and rc. For a single layer, for a given A, there is a critical value Dc below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near Dc: the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T , below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio Js/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.

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Section: Introductionmentioning

confidence: 99%

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Hoang¹,

Kasperski²,

Puszkarski³

et al. 2013

J. Phys.: Condens. Matter

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“…Introduced in papers [8,9], the concept of surface pinning parameter A was proposed to describe the degree of freedom of surface spins in their precession. By definition the surface pinning parameter value A = 1 corresponds to the natural freedom of the surface spins resulting from breaking their bonds with neighbors eliminated from the system by surface cut.…”

Section: Surface Pinning Diagram Vs Swr Spectramentioning

confidence: 99%

On the Existence Conditions of Surface Spin Wave Modes in (Ga,Mn)As Thin Films

Puszkarski

Tomczak

2016

Acta Phys. Pol. A

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Spin-wave resonance is a newly emerged method for studying surface magnetic anisotropy and surface spinwave modes in (Ga,Mn)As thin films. The existence of surface spin-wave modes in (Ga,Mn)As thin films has recently been reported in the literature; surface spin-wave modes have been observed in the in-plane configuration (with variable azimuth angle ϕM between the in-plane magnetization of the film and the surface [100] crystal axis), in the azimuth angle range between two in-plane critical angles ϕc1 and ϕc2. We show here that cubic surface anisotropy is an essential factor determining the existence conditions of the above-mentioned surface spin-wave modes: conditions favorable for the occurrence of surface spin-wave modes in a (Ga,Mn)As thin film in the inplane configuration are fulfilled for those azimuth orientations of the magnetization of the sample that lie around the hard axes of cubic magnetic anisotropy. This implies that a hard cubic anisotropy axis can be regarded in (Ga,Mn)As thin films as an easy axis for surface spin pinning.

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“…Note, on the other hand, that we have previously [3][4][5] expressed this surface parameter in the frame of the SI model by the following equation:…”

Section: On Puttingmentioning

confidence: 99%

“…The fulfillment of the other condition (2) requires that |K surf (ϑ, ϕ) | → ∞, and an infinite value of the surface anisotropy constant is considered to result in a situation in which surface spins are completely pinned. * e-mail: henpusz@amu.edu.plWe will now show that the differential form of the RW equation written above is equivalent to the microscopic boundary equation derived within the surface inhomogeneity (SI) model; the latter is based on a discrete model of magnetization and has the form of difference equation [3,4]:where m 0 ≡ m surf is the surface amplitude of the transversal (dynamic) magnetization component m, and m −d is its analytical continuation beyond the surface, denoting the amplitude in the first fictitious layer parallel to the surface, separated from it by one lattice constant d. …”

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confidence: 96%

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

Puszkarski

2016

Acta Phys. Pol. A

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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, 2Aex ∂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; Aex 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. The Rado-Weertman (RW) boundary equation is the earliest boundary condition to have been proposed in the theory of thin-film magnetism [1,2] with the aim of taking into account the specific dynamics of motion of the surface magnetization, as distinct from that of the bulk magnetization. The RW equation is based on a continuum model of magnetization and in the circular approximation readswhere m is the amplitude of the transversal (dynamic) component of the magnetization, A ex is the exchange stiffness constant, n denotes the direction normal to the surface of the film, K surf (ϑ, ϕ) is the surface anisotropy energy density, and magnetization angles ϕ and ϑ are azimuth and polar angles, respectively. The RW Eq. (1) is mostly used for the description of two extreme situations, defined by the conditions:The first condition (2) implies zero surface anisotropy constant, K surf (ϑ, ϕ) ≡ 0; this is considered to correspond to completely unpinned surface spins. The fulfillment of the other condition (2) requires that |K surf (ϑ, ϕ) | → ∞, and an infinite value of the surface anisotropy constant is considered to result in a situation in which surface spins are completely pinned. * e-mail: henpusz@amu.edu.plWe will now show that the differential form of the RW equation written above is equivalent to the microscopic boundary equation derived within the surface inhomogeneity (SI) model; the latter is based on a discrete model of magnetization and has the form of difference equation [3,4]:where m 0 ≡ m surf is the surface amplitude of the transversal (dynamic) magnetization component m, and m −d is its analytic...

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Treatment of the Periodically Inhomogeneous Surface: Multiple Boundary Condition

Cited by 6 publications

References 10 publications

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

On the Existence Conditions of Surface Spin Wave Modes in (Ga,Mn)As Thin Films

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

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