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

• Authors: H. Puszkarski
• Languages of publication: EN

Abstracts

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.

Keywords

EN

75.70.-i; 75.40.Gb; 75.30.Ds; 75.30.Gw; 75.10.-b

Discipline

• 75.70.-i: Magnetic properties of thin films, surfaces, and interfaces(for magnetic properties of nanostructures, see 75.75.-c)
• 75.30.Ds: Spin waves(for spin-wave resonance, see 76.50.+g)
• 75.30.Gw: Magnetic anisotropy
• 75.40.Gb: Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
• 75.10.-b: General theory and models of magnetic ordering(see also 05.50.+q Lattice theory and statistics)

• Journal: Acta Physica Polonica A
• Year: 2016
• Volume: 129
• Issue: 6
• Pages: RK.129.6.1-1-RK.129.6.1-3

Dates

published

2016-05

received

2016-06-07

Contributors

author

H. Puszkarski

• Surface Physics Division, Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

References

• [1] G.T. Rado, J.R. Weertman, J. Phys. Chem. Solids 11, 315 (1959), doi: 10.1016/0022-3697(59)90233-1
• [2] C. Vittoria, Microwave Properties of Magnetic Films, World Sci., Singapore 1993, doi: 10.1142/9789814354387
• [3] H. Puszkarski, Acta Phys. Pol. A 38, 217, 899 (1970)
• [4] H. Puszkarski, Progr. Surf. Sci. 9, 191 (1979), doi: 10.1016/0079-6816(79)90013-3
• [5] H. Puszkarski, P. Tomczak, Sci. Rep. 4, 6135 (2014), doi: 10.1038/srep06135
• [6] H.T. Diep, Theory of Magnetism - Application to Surface Physics, World Sci., Singapore 2014, doi: 10.1142/8994
• [7] L. Wojtczak, Magnetic Thin Films, Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2009 (in Polish)

Identifiers

DOI

10.12693/APhysPolA.129.RK.129.6.1-1