Magnetic Friction in Ising Spin Systems

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.

Figure 1

Accumulated energy $\Delta E_{\mathrm{bath}}$ per spin which is transferred to the heat bath during a time interval $t$, without motion ($v=0$) and with motion ($v=1$) of the two half-spaces. Simulation with Metropolis rates. The total energy per spin fluctuates around the exact value $E/N\approx -1.10608$ [20] in both cases.

Figure 2

Energy dissipation rate $P$ per unit length as a function of the relative velocity $v$ of the two half-spaces (averaged over 100 runs). Dashed line: Metropolis rates. Dotted line: Glauber rates. Solid line: Exact solution for the limit $v\to 0$.

Figure 3

Temperature dependence of the friction force per unit length, $F/L$. Solid line: Exact quasistatic limit $v\to 0$. Simulation results with Metropolis rates (circles) for $v=0.1$ agree with the quasistatic limit. For $v=1$ the friction forces for Metropolis rates (dashed line), respectively, Glauber rates (dotted line) are larger corresponding to the upward curvature in Fig. 2. All data are averaged over 100 runs. The critical temperature is indicated by the dashed vertical line.

Figure 4

Magnetization profile along the $z$ axis perpendicular to the slip plane (at $z=40$ in units of the lattice constant $a$) at $T=2.1<T_C$ for Glauber rates at different velocities. The local magnetization near the slip plane is enhanced. This effect becomes stronger for increasing velocity and saturates for the same reason as in Fig. 2. When using Metropolis rates this effect is less pronounced (not shown).