PL EN


Preferences help
enabled [disable] Abstract
Number of results
2016 | 129 | 6 | RK.129.6.1-1-RK.129.6.1-3
Article title

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

Authors
Content
Title variants
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
Year
Volume
129
Issue
6
Pages
RK.129.6.1-1-RK.129.6.1-3
Physical description
Dates
published
2016-05
received
2016-06-07
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)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv129n6_rk_129_6_1-1kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.