Magnetic Friction in Ising Spin Systems

Abstract

A new contribution to friction is predicted to occur in systems with magnetic correlations: Tangential relative motion of two Ising spin systems pumps energy into the magnetic degrees of freedom. This leads to a friction force proportional to the area of contact. The velocity and temperature dependence of this force are investigated. Magnetic friction is strongest near the critical temperature, below which the spin systems order spontaneously. Antiferromagnetic coupling leads to stronger friction than ferromagnetic coupling with the same exchange constant. The basic dissipation mechanism is explained. A surprising effect is observed in the ferromagnetically ordered phase: The relative motion can act like a heat pump cooling the spins in the vicinity of the friction surface.PACS numbers: 68.35. Af, 75.30.Sg, 05.50+q, 05.70.Ln As friction is an intriguingly complex phenomenon of enormous practical importance, the progress in experimental techniques on the micro-and nano-scale [1,2] as well as the improved computational power for atomic simulations [3,4,5] has led to a renaissance of this old research field in recent years. Currently a large variety of microscopic models compete with one another [1,6,7]. Major complications are wear, plastic deformation at the contact, impurities, and lubricants. It is unlikely that in the general case only a single dissipation mechanism will be active. Defect motion, phononic and electronic excitations may be involved in a very complex blend. In order to reduce these complications and to focus on the elementary dissipation processes, increasing attention has been paid to non-contact friction: It can be measured as damping of an atomic force microscope tip which oscillates in front of a surface without touching it [8,9]. For this setup, too, phononic [10,11] as well as electronic dissipation mechanisms [12,13] have been discussed. Recently, a Heisenberg model with magnetic dipole-dipole interactions was studied at zero temperature as a model for magnetic force microscopy. In this case the moving tip excites spin waves, which dissipate part of the energy [14].In this paper a different mechanism is considered, by which the spin degrees of freedom of an Ising model contribute to friction. We imagine two magnetic materials with planar surfaces sliding on each other. Of course, if one of the materials is metallic, their relative motion will induce eddy currents [15]. The corresponding Joule heat is commonly associated with the term "magnetic friction", although the energy is not dissipated into the spin degrees of freedom, which can even be considered as frozen. By contrast, here we are interested in the case that both materials are non-metallic (e.g. magnetite Fe 3 O 4 ). In order to highlight the role of the spin degrees of freedom we do not take phononic and electronic excitations into account explicitly, but regard them as a heat bath of fixed temperature T to which all spins are coupled. Energy dissipation in Ising spin systems was studied previously [16,17], but there it was du...

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“…Two classes of models have been considered, which show different phenomena. The first one is Ising-like spin systems with two equivalent half spaces moving relative to each other [4][5][6][7][8]. In this case, friction is induced by thermal fluctuations, and hence is not present at zero temperature.…”