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Ferromagnetic thin Films with Simple Cubic Structure as Described by Fourth Order Perturbed Heisenberg Hamiltonian

Pubudu Samarasekara, E.M.P. Ekanayake


For the first time, fourth order perturbed Heisenberg Hamiltonian has been applied to study the properties of simple cubic structured ferromagnetic ultrathin films with two spin layers. Only the spin exchange interaction, second order magnetic anisotropy constant and the short-range magnetic dipole interaction were taken into account. Only when the second order anisotropy constant varies from one spin plane to the other spin plane, perturbation becomes nonzero. 3-D plots of total energy versus spin exchange interaction and angle, total energy versus second order anisotropy constant in bottom spin layer and angle, and total energy versus second order anisotropy constant in top layer and angle were plotted. Peaks in the plots are closely packed in fourth order perturbed case compared to the plots obtained using third order perturbed case. All the graphs were plotted using MATLAB program


Heisenberg Hamiltonian, perturbation, ferromagnetic thin films

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Radomska A, Balcerzak T. Theoretical studies of model thin EuTe films with surface elastic stresses. Cent. Eur. 2003; 1(1): 100–17p.

James C. Cates, Chester Alexander Jr. Theoretical study of magnetostriction of in FeTaN thin films. J. Appl. Phys. 1994; 75: 6754–56p.

Ernst A, Lueders M, Temmerman WM, et al. Theoretical study of magnetic layers of nickel on copper; dead or live? J. Phys. Condens. Matter. 2000; 12(26): 5599–606p.

Kovachev S, Wesselinowa JM. Theoretical study of multiferroic thin films based on a microscopic model. J. Phys. Condens. Matter. 2009; 21(22): 225007p.

Zhao D, Liu F, D.L. Huber, et al. Step-induced magnetic-hysteresis anisotropy in ferromagnetic thin films. J. Appl Phys. 2002; 91(5): 3150–53p.

Spisak D, Hafner J. Theoretical study of FeCo/W(110) surface alloys. J. Magn. Magn. Mater. 2005; 286: 386–9p.

Usadel KD, Hucht A. Anisotropy of ultrathin ferromagnetic films and the spin reorientation transition. Phys. Rev. B. 2002; 66: 024419p.

Hucht A, Usadel KD. Reorientation transition of ultrathin ferromagnetic films. Phys. Rev. B. 1997; 55: 12309–1p.

Hucht A, Usadel KD. Theory of the spin reorientation transition of ultra-thin ferromagnetic films. J.Magn. Magn. Mater. 1999; 203(1): 88–90p.

Nowak U. Magnetisation reversal and domain structure in thin magnetic films: Theory and computer simulation. IEEE Trans. Magn. 1995; 31(6–2): 4169–71p.

Dantziger M, Glinsmann B, Scheffler S, et al. In-plane dipole coupling anisotropy of a square ferromagnetic Heisenberg monolayer. Phys, Rev. B 2002; 66: 094416p.

Tsai SH, Landau DP, Schulthess TC. Effect of interracial coupling on the magnetic ordering in ferro-antiferromagntic bilayers. J. Appl. Phys. 2003; 93(10): 8612–14p.

Hegde H, Samarasekara P, Cadieu FJ. Nonepitaxial sputter synthesis of aligned strontium hexaferrites, SrO.6(Fe2O3), films. J. Appl. Phys. 1994; 75(10): 6640–42p.

Samarasekara P. A Pulsed RF Sputtering Method for Obtaining Higher Deposition Rates. Chin. J. Phys. 2003; 41(1): 70–4p.

Samarasekara P. Easy Axis Oriented Lithium Mixed Ferrite Films Deposited by the PLD Method. Chin. J. Phys. 2002; 40(6): 631–6p.

Samarasekara P. Determination of Energy of thick spinel ferrite films using Heisenberg Hamiltonian with second order perturbation” GESJ: Phys. 2010; 1(3): 46–52p.

Samarasekara P, Gunawardhane NHPM. Explanation of easy axis orientation of ferromagnetic films using Heisenberg Hamiltonian. GESJ: Phys. 2011; 2(6): 62–9p.

Samarasekara P, Saparamadu U. Investigation of Spin Reorientation in Nickel Ferrite Films. GESJ: Phys. 2012; 1(7): 15–20p.

Samarasekara P, Saparamadu U. In plane oriented Strontium ferrite thin films described by spin reorientation. Res. Rev.: J. Phys: STM J. 2013; 2(2): 12–6p.

Samarasekara P, Abeyratne MK, Dehipawalage S. Heisenberg Hamiltonian with Second Order Perturbation for Spinel Ferrite Thin Films. Electron. J. Theor. 2009; 6(20): 345–56p.

Samarasekara P. Influence of third order perturbation on Heisenberg Hamiltonian of thick ferromagnetic films. Electron. J. Theor. 2008; 5(17): 227–36p.

Samarasekara P, Mendoza WA. Effect of third order perturbation on Heisenberg Hamiltonian for non-oriented ultra-thin ferromagnetic films. Electron. J. Theor 2010; 7(24): 197–210p.

Samarasekara P, Mendoza WA. Third Order Perturbed Heisenberg Hamiltonian of Spinel Ferrite Ultra-thin films. GESJ: Phys. 2011; 1(5): 15–24p.

Samarasekara P. Investigation of Third Order Perturbed Heisenberg Hamiltonian of Thick Spinel Ferrite Films. Inventi Rapid: Algo. J. 2011; 2(1): 1–3p



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