Abstract
A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual degrees of freedom cannot be resolved and only their mesoscopic properties are relevant. In the present work, the consequences of identifying the effects of dissipation as resulting from interactions with a bath of spins are explored, in addition to elastic, degrees of freedom. The corresponding stochastic differential equations are solved numerically and the moments of the magnetization are computed. The stochastic equations implicitly define a measure on the space of spin configurations, whose moments at equal times satisfy a hierarchy of deterministic, ordinary differential equations. Closure assumptions are used to truncate the hierarchy and the same moments are computed. We focus on the advantages and problems that each approach presents, for the approach to equilibrium and, in particular, the emergence of longitudinal damping.
Graphical abstract
Similar content being viewed by others
References
N. Smith, P. Arnett, Appl. Phys. Lett. 78, 1448 (2001)
G. Bacher, A.A. Maksimov, H. Schömig, V.D. Kulakovskii, M.K. Welsch, A. Forchel, P.S. Dorozhkin, A.V. Chernenko, S. Lee, M. Dobrowolska, J.K. Furdyna, Phys. Rev. Lett. 89, 127201 (2002)
S.A. Crooker, D.G. Rickel, A.V. Balatsky, D.L. Smith, Nature 431, 49 (2004)
C. Degen, F. Reinhard, P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017)
D. Forster, Hydrodynamic fluctuations, broken symmetry, and correlation functions, 1st edn. Advanced book classics (Addison-Wesley, Reading, MA, 1994)
V. Kamberský, Czechoslovak J. Phys. B 26, 1366 (1976)
D.A. Garanin, Phys. Rev. B 55, 3050 (1997)
P. Thibaudeau, T. Nussle, S. Nicolis, J. Magn. Magn. Mater. 432, 175 (2017)
W.F. Brown, Phys. Rev. 130, 1677 (1963)
R. Kubo, N. Hashitsume, Prog. Theor. Phys. Suppl. 46, 210 (1970)
W. Brown, IEEE Trans. Magn. 15, 1196 (1979)
W.T. Coffey, Y.P. Kalmykov, J. Appl. Phys. 112, 121301 (2012)
G. Bertotti, I.D. Mayergoyz, C. Serpico, Nonlinear Magnetization Dynamics in Nanosystems (Elsevier, 2009)
A.O. Caldeira, A.J. Leggett, Ann. Phys. 149, 374 (1983)
R. Zwanzig, J. Stat. Phys. 9, 215 (1973)
A. Rebei, G.J. Parker, Phys. Rev. B 67, 104434 (2003)
E. Rossi, O.G. Heinonen, A.H. MacDonald, Phys. Rev. B 72, 174412 (2005)
T. Nussle, P. Thibaudeau, S. Nicolis, J. Magn. Magn. Mater. 469, 633 (2019)
N. Prokof’ev, P. Stamp, Rep. Prog. Phys. 63, 669 (2000)
R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, G. Nardulli, Phys. Lett. B 299, 139 (1993)
J. Tranchida, P. Thibaudeau, S. Nicolis, J. Phys.: Conf. Ser. 574, 012146 (2015)
G. Bertotti, C. Serpico, I.D. Mayergoyz, Phys. Rev. Lett. 86, 724 (2001)
L.F. Álvarez, O. Pla, O. Chubykalo, Phys. Rev. B 61, 11613 (2000)
S. Blanes, F. Casas, J.A. Oteo, J. Ros, Phys. Rep. 470, 151 (2009)
M. Krech, A. Bunker, D.P. Landau, Comput. Phys. Commun. 111, 1 (1998)
E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd edn. Springer Series in Computational Mathematics (Springer-Verlag, Berlin, Heidelberg, 2006)
P. Thibaudeau, D. Beaujouan, Physica A 391, 1963 (2012)
H.G. Schuster, W. Just, Deterministic Chaos: An Introduction, 4th edn. (Wiley-, 2006)
E. Du Trémolet de Lacheisserie, Magnetostriction: theory and applications of magnetoelasticity (CRC Press, Boca Raton, 1993)
B. Skubic, J. Hellsvik, L. Nordström, O. Eriksson, J. Phys.:Condens. Matter 20, 315203 (2008)
N.G. Van Kampen, Phys. Rep. 24, 171 (1976)
V.E. Shapiro, V.M. Loginov, Physica A 91, 563 (1978)
V. Berdichevsky, M. Gitterman, Phys. Rev. E 60, 1494 (1999)
J. Tranchida, P. Thibaudeau, S. Nicolis, Physica B 486, 57 (2016)
K. Furutsu, J. Res. Natl. Bur. Stand. 67D, 303 (1963)
J. Tranchida, P. Thibaudeau, S. Nicolis, Phys. Rev. E 98, 042101 (2018)
H. Niederreiter, Random number generation and quasi-Monte Carlo methods. No. 63 in CBMS-NSF regional conference series in applied mathematics (Society for Industrial and Applied Mathematics, Philadelphia, 1992)
J.C. Butcher, Numerical methods for ordinary differential equations, 3rd edn. (Wiley, Chichester, West Sussex, 2016)
H.H. Rosenbrock, Comput. J. 5, 329 (1963)
J. Verner, SIAM J. Numer. Anal. 15, 772 (1978)
C. Nicolis, G. Nicolis, Phys. Rev. E 58, 4391 (1998)
J. Kisker, L. Santen, M. Schreckenberg, H. Rieger, Phys. Rev. B 53, 6418 (1996)
M. Ney-Nifle, H.J. Hilhorst, Physica A 193, 48 (1993)
L. Šmejkal, J. Železný, J. Sinova, T. Jungwirth, Phys. Rev. Lett. 118, 106402 (2017)
K. Shen, G.E.W. Bauer, J. Phys. D 51, 224008 (2018)
S. Streib, H. Keshtgar, G.E. Bauer, Phys. Rev. Lett. 121, 027202 (2018)
L. Šmejkal, Y. Mokrousov, B. Yan, A.H. MacDonald, Nat. Phys. 14, 242 (2018)
S.F. Maehrlein, I. Radu, P. Maldonado, A. Paarmann, M. Gensch, A.M. Kalashnikova, R.V. Pisarev, M. Wolf, P.M. Oppeneer, J. Barker, T. Kampfrath, Sci. Adv. 4, eaar5164 (2018)
V.V. Temnov, I. Razdolski, T. Pezeril, D. Makarov, D. Seletskiy, A. Melnikov, K.A. Nelson, J. Optics 18, 093002 (2016)
D.G. Piliposyan, K.B. Ghazaryan, G.T. Piliposian, J. Appl. Phys. 116, 044107 (2014)
H. Sohn, C.y. Liang, M.E. Nowakowski, Y. Hwang, S. Han, J. Bokor, G.P. Carman, R.N. Candler, J. Magn. Magn. Mater. 439, 196 (2017)
M.N. Chernodub, M.A. Zubkov, Phys. Rev. B 95, 115410 (2017)
V. Arjona, M.A.H. Vozmediano, Phys. Rev. B 97, 201404 (2018)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nussle, T., Thibaudeau, P. & Nicolis, S. Probing magneto-elastic phenomena through an effective spin-bath coupling model. Eur. Phys. J. B 92, 29 (2019). https://doi.org/10.1140/epjb/e2019-90539-6
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2019-90539-6