Spin excitations in a monolayer scanned by a magnetic tip

Energy dissipation via spin excitations is investigated for a hard ferromagnetic tip scanning a soft magnetic monolayer. We use the classical Heisenberg model with Landau-LifshitzGilbert (LLG) dynamics including a stochastic field representing finite temperatures. The friction force depends linearly on the velocity (provided it is small enough) for all temperatures. For low temperatures, the corresponding friction coefficient is proportional to the phenomenological damping constant of the LLG equation. This dependence is lost at high temperatures, where the friction coefficient decreases exponentially. These findings can be explained by properties of the spin polarisation cloud dragged along with the tip. Copyright © EPLA, 2009 Introduction. While on the macroscopic scale the . phenomenology of friction is well known, several new aspects are currently being investigated on the micron and nanometer scale [1,2]. During the last two decades, the research on microscopic friction phenomena has advanced enormously, thanks to the development of Atomic Force Microscopy (AFM, [3]), which allows to measure energy dissipation caused by relative motion of a tip with respect to a substrate. Recently the contribution of magnetic degrees of freedom to energy dissipation processes has attracted increasing interest [4-8]. Today, magnetic materials can be controlled down to the nanometer scale. New developments in the data storage industry, spintronics and quantum computing require a better understanding of tribological phenomena in magnetic systems. For example, the reduction of heat generation in reading heads of hard disks which work at nanometer distances is an important issue, as heat can cause data loss. Magnetic Force Microscopy (MFM) , where both tip and surface are magnetic, is used to investigate surface magnetism and to visualise domain walls. Although recent studies have attempted to measure energy dissipation between an oscillating tip and a magnetic sample [9,10], the dependence of the friction force on the tip's sliding velocity has not been considered yet apart from a work by Fusco et al. [8] which is extended by the present work to temperatures T iO. The relative motion of the tip with (a) E-mail: martin.magieratDuni-due.de respect to the surface can lead to the creation of spin waves which propagate inside the sample and dissipate energy, giving rise to magnetic friction. We will first present a simulation model and define magnetic friction. The model contains classical Heisenberg spins located on a rigid lattice which interact by exchange interaction with each other. Analogous to the reading head of a hard disc or a MFM tip, an external fixed magnetic moment is moved across the substrate. Using Langevin dynamics and damping, it is possible to simulate systems at finite temperatures. The main new results concern the temperature dependence of magnetic friction. Simulation model and friction definition. To simulate a solid magnetic monolayer (on a nonmagnetic substrate), we consider a two-dimensional rigid Lx x Ly lattice of classical normalised dipole moments ("spins") Si = P,i/ Ms, where Ms denotes the material-dependent magnetic saturation moment (typically a few Bohr magnetons). These spins, located at z = 0 and with lattice spacing a, represent the magnetic moments of single atoms. They can change their orientation but not their absolute value, so that there are two degrees of freedom per spin. We use open boundary conditions. A constant point dipole Stip pointing in the z-direction and located at z = 2a represents the magnetic tip. It is moved parallel to the surface with constant velocity v. This model has only magnetic degrees of freedom and thus focusses on their contributions to friction. For a real tip one could expect that magnetic, just like