Strongly anisotropic nonequilibrium phase transition in Ising models with friction

Angst, Sebastian; Hucht, Alfred; Wolf, Dietrich E.

doi:10.1103/physreve.85.051120

Cited by 24 publications

(36 citation statements)

References 33 publications

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“…Previous studies have already proposed models in which two lattices interact with each other [11][12][13][14][15]. However, in our model the shift of the upper lattice δx changes according to Eq.…”

Section: Modelmentioning

confidence: 89%

Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

Komatsu

2019

Phys. Rev. E

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We propose a model of magnetic friction and investigate the relation between the frictional force and the relative velocity of surfaces in the steady state. The model comprises two square lattices adjacent to each other, the upper of which is subjected to an external force, and the magnetic interaction acts as a kind of "potential barrier" that prevents the upper lattice from moving. We consider two surface types for the upper lattice: smooth and rough. The behavior of this model is classified into three domains, which we refer to as domains I,II, and III. In domain I, the external force is weak and cannot move the lattice, whereas in domain III, the external force is dominant compared with other forces. In the intermediate domain II, the frictional force obeys the Dieterich-Ruina law. This characteristic property can be observed regardless of whether the surface is smooth or rough.

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Section: Modelmentioning

confidence: 89%

Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

Komatsu

2019

Phys. Rev. E

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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.…”

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confidence: 99%

Spin waves cause non-linear friction

Magiera

Brendel

Wolf

et al. 2011

EPL

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Abstract. -Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-LifshitzGilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.Introduction. -On the macroscopic scale the phenomenology of friction is well-known. However, investigations of energy dissipation on the micron and nanometer scale have led in recent years to many new insights [1]. This progress was made possible by the development of modern surface science methods, in particular Atomic Force Microscopy, which allows to measure energy dissipation caused by relative motion of a tip with respect to a substrate.Studies concerning the contribution of magnetic degrees of freedom to energy dissipation [2, 3] form a young subfield of nanotribology, which has been attracting increasing interest in recent years. 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. In the second class of models [9][10][11][12][13], there is no symmetry between slider and substrate: The slider, representing e.g. the tip of a Magnetic Force Microscope, interacts only locally with a planar magnetic surface. While scanning the surface, the tip in general excites substrate spins and hence experiences friction, even at zero temperature. The present study belongs to the second class of models.We investigate the nature of the substrate excitations caused by the tip motion for a classical Heisenberg model with Landau-Lifshitz-Gilbert (LLG, [14,15]) dynamics (precession around, and relaxation into the local field di-

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“…Several experimental facts suggest that physical degrees of freedom, such as phonon [14][15][16][17][18][19][20], orbital motion of electrons [20][21][22][23] and magnetic moment of spins [24,25], play roles of dissipation channels. Especially for the magnetic moment, Monte Carlo simulations of classical spin systems by the use of the Monte Carlo simulations and the analysis based on the Landau-Lifshitz-Gilbert equation [26][27][28][29][30][31][32][33][34][35][36][37] have revealed several facts regarding the friction due to magnetism from the viewpoints of statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

“…Many facts with the magnetic friction have been revealed, but almost all of them are related to the model of infinite size ( Fig. 1(a)) [28,30,31,33,35,37], where almost exclusively nonequilibrium phase transitions are discussed. In order to understand the non-equilibrium nature of classical spin systems, however, finite-size extension is one of the most important directions.…”

Section: Introductionmentioning

confidence: 99%

Effects of boundary conditions on magnetic friction

Sugimoto

2019

Phys. Rev. E

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We consider magnetic friction between two square lattices of the ferromagnetic Ising model of finite thickness. We analyze the dependence on the boundary conditions and the sample thickness. Monte Carlo results indicate that the setup enables us to control the frictional force by magnetic fields on the boundaries. In addition, we confirm that the temperature derivative of the frictional force as well as that of the boundary energy has singularity at a velocity-dependent critical temperature.

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Strongly anisotropic nonequilibrium phase transition in Ising models with friction

Cited by 24 publications

References 33 publications

Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

Spin waves cause non-linear friction

Effects of boundary conditions on magnetic friction

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