Local spin dynamics of magnetic moments on metal surfaces

We present a theory of the local spin dynamics of an isolated magnetic moment either embedded within or adsorbed on a metal surface, within the framework of an itinerant electron description of the combined system. We explore issues that are relevant to probes of local spin dynamics via scanning tunneling microscope (STM) tips. Explicit calculations are presented for Co and Mn moments on the Cu(100) surface. We describe the system via a mean-field description of the ground state, and a treatment of the spin dynamics via the random-phase approximation. Thus, the discussion is appropriate to a system at temperatures above the Kondo temperature, and in a magnetic field sufficiently high the moment is pinned parallel to the field. Attention is directed to the following issue. If, in the absence of spin-orbit coupling or other terms in the Hamiltonian that breaks spin rotation invariance, any experiment (such as electron-spin resonance) which measures the total magnetic moment of the system necessarily sees a response with zero linewidth, at precisely $g=2.\mathrm{}$ However, we show that a local probe such as a STM tip will see a broad structure with origin in decay of the moment’s precession to particle-hole pairs, whose peak displays an appreciable g shift. We illustrate with explicit calculations directed to the systems mentioned above.