AC-driven quantum spins: resonant enhancement of transverse DC magnetization

Magnetic resonance effects have been long studied and used for various spectroscopic methods1–3. Timedependent external fields being an integral part of the physical setups, become also very interesting in their action when entering the field of spintronics and processing of quantum information. While the linear response of a system (probe) to external fields may be typically understood in a rather complete way, nonlinear and perhaps nonadiabatic response effects are usually much harder to be analyzed. Some studies have been devoted to the effect of second-harmonic generation. Much less is known about zeroth-harmonic generation, i.e. about the induction of static fields by pure ac fields. The understanding of such processes is very important in any application involving ac fields, as additional induced dc fields may strongly influence the desired effects. The principal possibility of the zeroth-harmonic generation can be studied using symmetry considerations,. Analytical approaches which may also estimate the magnitude of the induced fields are typically restricted to various perturbation techniques with a suitable small parameter involved. Two of us have recently applied these methods to the simplest cases of a spin s = 1/2 coupled to an environment (heat bath) in the presence of an external magnetic dc field (in z-direction). While an additional ac field applied in x-direction leads to the standard spin resonance setup used e.g. for nuclear spins, a tilt of the ac field direction in the x−z-plane leads to a broken symmetry and to a generation of a nonzero magnetic moment in y-direction, i.e. perpendicular to the applied fields. Similar results have been also obtained for a spin s = 1 where the external dc field in z-direction is replaced by a magnetic ion anisotropy in z-direction. This work is devoted to the analysis of spin-spin interaction and its action on the above described effects. The first goal is to study the generalization of the symmetry considerations in the presence of an interaction. The second goal is to demonstrate that the interaction is capable of increasing the induced field strength by an order of magnitude, and to give an explanation for this result. The paper is organized as follows. In the next section we introduce the density matrix approach. Section III is devoted to a reconsideration of the single spin problem. Section IV contains the central results on two interacting spins. Section V concludes the paper.