Dissipation in quasistatically driven disordered systems

Ortı́n, Jordi; Goicoechea, J.

doi:10.1103/physrevb.58.5628

Cited by 17 publications

(19 citation statements)

References 21 publications

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“…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 due to an oscillating magnetic field rather than the tangential relative motion of two lattices. The competition between the time scales for driving the system out of equilibrium and for its relaxation gave rise to hysteretic, and hence dissipative behavior.…”

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confidence: 99%

Magnetic Friction in Ising Spin Systems

2008

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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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confidence: 99%

Magnetic Friction in Ising Spin Systems

2008

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“…We present the behavior of the different physical quantities of interest [12]: the internal energy H 0 (a), the input energy −B M (b), the total energy H = H 0 − B M (c), and the magnetization M (d). A detailed comparison between the metastable and stable evolution will be presented elsewhere.…”

Section: Algorithm Formulationmentioning

confidence: 99%

Efficient Algorithm for Finding Ground-States in the Random Field Ising Model with an External Field

Frontera

Goicoechea

Ortı́n

et al. 2000

Journal of Computational Physics

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“…Then one assumes that there exist elements of the algebra giving rise to values of q [g] inside any arbitrarily small neighborhood of a given value q [g] = x, and uses the measure of these subsets to calculate the Lebesgue integral of q [g] over G, represented by Eq. (7). To make this loose description mathematically rigorous, one should resort to the language and the methods of measure theory [23,24].…”

Section: Ii2 Hysteresis In System Ensemblesmentioning

confidence: 99%

“…As a first step, let us apply Eq. (7) to the definition of ensemble equilibrium states. The main difference with respect to Section II.1 is that we can no longer identify an equilibrium state by its output value.…”

Section: Ii2 Hysteresis In System Ensemblesmentioning

confidence: 99%

“…The study of hysteresis has been a challenge to physicists and mathematicians for a long time. In physics, hysteresis brings all the conceptual difficulties of out-of-equilibrium thermodynamics [1][2][3][4][5], first of all the fact that we do not know the general principles controlling the balance between stored and dissipated energy in hysteretic transformations [6,7]. In mathematics, on the other hand, the central issue is the formulation of sufficiently general mathematical descriptions grasping the essence of hysteresis beyond the limited interest of ad hoc models [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Functional integration approach to hysteresis

Bertotti¹,

Mayergoyz

Basso

et al. 1999

Phys. Rev. E

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A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free-energy landscapes. Second, the average hysteresis response of an ensemble of such systems is expressed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure mu has been introduced in G. The consequences of the formulation are analyzed in detail in the case where the measure mu is generated by a continuous, Markovian stochastic process. The calculation of the hysteresis properties of the ensemble is reduced to the solution of the level-crossing problem for the stochastic process. In particular, it is shown that, when the process is translationally invariant (homogeneous), the ensuing hysteresis properties can be exactly described by the Preisach model of hysteresis, and the associated Preisach distribution is expressed in closed analytic form in terms of the drift and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder and the interpretation of critical state models of superconducting hysteresis.

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Dissipation in quasistatically driven disordered systems

Cited by 17 publications

References 21 publications

Magnetic Friction in Ising Spin Systems

Magnetic Friction in Ising Spin Systems

Efficient Algorithm for Finding Ground-States in the Random Field Ising Model with an External Field

Functional integration approach to hysteresis

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