- Access by Xinjiang University
Temperature effects on drift of suspended single-domain particles induced by the Magnus force
Phys. Rev. E 97, 032608 – Published 27 March, 2018
DOI: https://doi.org/10.1103/PhysRevE.97.032608
Abstract
We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models. Using these solutions, we calculate the drift velocity and show that the out-of-plane fluctuations of magnetization, which are not accounted for in the planar rotor model, play an important role. In the general case of arbitrary fluctuations, we investigate the temperature dependence of the drift velocity by numerically simulating a set of effective stochastic differential equations for the magnetization dynamics.
Physics Subject Headings (PhySH)
Article Text
References (31)
- S. I. Denisov and B. O. Pedchenko, Drift of suspended ferromagnetic particles due to the Magnus effect, J. Appl. Phys. 121, 043912 (2017).
- S. I. Denisov, B. O. Pedchenko, O. V. Kvasnina, and E. S. Denisova, Exactly solvable model for drift of suspended ferromagnetic particles induced by the Magnus force, J. Magn. Magn. Mater. 443, 89 (2017).
- R. Skomski, Simple Models of Magnetism (Oxford University Press, New York, 2008).
- A. P. Guimarães, Principles of Nanomagnetism, 2nd ed. (Springer-Verlag, Berlin, 2017).
- W. Horsthemke and R. Lefever, Noise-Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology (Springer-Verlag, Berlin, 1984).
- C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences, 3rd ed. (Springer-Verlag, Berlin, 2004).
- W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation: With Applications in Physics, Chemistry and Electrical Engineering, 2nd ed. (World Scientific, Singapore, 2004).
- N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (Elsevier, North Holland, 2007).
- H. Risken, The Fokker-Planck Equation: Methods of Solutions and Applications, 2nd ed. (Springer-Verlag, Berlin, 1989).
- W. F. Brown, Jr., Thermal fluctuations of a single-domain particle, Phys. Rev. 130, 1677 (1963).
- G. Bertotti, I. Mayergoyz, and C. Serpico, Nonlinear Magnetization Dynamics in Nanosystems (Elsevier, Oxford, 2009).
- S. I. Denisov, T. V. Lyutyy, and P. Hänggi, Magnetization of Nanoparticle Systems in a Rotating Magnetic Field, Phys. Rev. Lett. 97, 227202 (2006).
- S. I. Denisov, T. V. Lyutyy, P. Hänggi, and K. N. Trohidou, Dynamical and thermal effects in nanoparticle systems driven by a rotating magnetic field, Phys. Rev. B 74, 104406 (2006).
- S. I. Denisov, K. Sakmann, P. Talkner, and P. Hänggi, Mean first-passage times for an ac-driven magnetic moment of a nanoparticle, Europhys. Lett. 76, 1001 (2006).
- S. I. Denisov, K. Sakmann, P. Talkner, and P. Hänggi, Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment, Phys. Rev. B 75, 184432 (2007).
- S. I. Denisov, A. Yu. Polyakov, and T. V. Lyutyy, Resonant suppression of thermal stability of the nanoparticle magnetization by a rotating magnetic field, Phys. Rev. B 84, 174410 (2011).
- N. A. Usov and B. Ya. Liubimov, Dynamics of magnetic nanoparticle in a viscous liquid: Application to magnetic nanoparticle hyperthermia, J. Appl. Phys. 112, 023901 (2012).
- K. D. Usadel and C. Usadel, Dynamics of magnetic single domain particles embedded in a viscous liquid, J. Appl. Phys. 118, 234303 (2015).
- K. D. Usadel, Dynamics of magnetic nanoparticles in a viscous fluid driven by rotating magnetic fields, Phys. Rev. B 95, 104430 (2017).
- T. V. Lyutyy, O. M. Hryshko, and A. A. Kovner, Power loss for a periodically driven ferromagnetic nanoparticle in a viscous fluid: The finite anisotropy aspects, J. Magn. Magn. Mater. 446, 87 (2018).
- A. Engel, H. W. Müller, P. Reimann, and A. Jung, Ferrofluids as Thermal Ratchets, Phys. Rev. Lett. 91, 060602 (2003).
- A. Engel and P. Reimann, Thermal ratchet effects in ferrofluids, Phys. Rev. E 70, 051107 (2004).
- T. V. Lyutyy, S. I. Denisov, V. V. Reva, and Yu. S. Bystrik, Rotational properties of ferromagnetic nanoparticles driven by a precessing magnetic field in a viscous fluid, Phys. Rev. E 92, 042312 (2015).
- S. I. Rubinow, J. B. Keller, The transverse force on a spinning sphere moving in a viscous fluid, J. Fluid Mech. 11, 447 (1961).
- R. L. Stratonovich, A new representation for stochastic integrals and equations, SIAM J. Control 4, 362 (1966).
- K. Itô, Stochastic differential equations in a differentiable manifold, Nagoya Math. J. 1, 35 (1950).
- V. Méndez, S. I. Denisov, D. Campos, and W. Horsthemke, Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises, Phys. Rev. E 90, 012116 (2014).
- M. Raible and A. Engel, Langevin equation for the rotation of a magnetic particle, Appl. Organometal. Chem. 18, 536 (2004).
- K. V. Mardia, Statistics of Directional Data (Academic, London, 1972).
- S. R. Jammalamadaka and A. SenGupta, Topics in Circular Statistics (World Scientific, Singapore, 2001).
- D. S. Viswanath, T. K. Ghosh, D. H. L. Prasad, N. V. K. Dutt, and K. Y. Rani, Viscosity of Liquids (Springer, Dordrecht, 2007).
