Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

Abstract

-Spin dynamics in the Kondo impurity model, initiated by suddenly switching the direction of a local magnetic field, is studied by means of the time-dependent density-matrix renormalization group. Quantum effects are identified by systematic computations for different spin quantum numbers S and by comparing with tight-binding spin-dynamics theory for the classical-spin Kondo model. We demonstrate that, besides the conventional precessional motion and relaxation, the quantum-spin dynamics shows nutation, similar to a spinning top. Opposed to semiclassical theory, however, the nutation is efficiently damped on an extremely short time scale. The effect is explained in the large-S limit as quantum dephasing of the eigenmodes in an emergent two-spin model that is weakly entangled with the bulk of the system. We argue that, apart from the Kondo effect, the damping of nutational motion is essentially the only characteristics of the quantum nature of the spin. Qualitative agreement between quantum and semiclassical spin dynamics is found down to S = 1/2.Introduction.-The paradigmatic system to study the real-time dynamics of a spin-1/2 coupled to a Fermi sea is the Kondo model [1]. It is mainly considered as a generic model for the famous Kondo effect [2], namely screening of the impurity spin by a mesoscopically large number of electrons in a thermal state with temperature below the Kondo temperature T K ∼ exp(−1/Jρ), where J is the strength of the exchange coupling and ρ is the density of states. The Kondo effect is a true quantum effect which originates from the two-fold spin degeneracy and is protected by time-reversal symmetry. Longitudinal spin dynamics, such as the time-dependent Kondo screening, has been studied recently [3,4] by starting from an initial state with a fully polarized spin, which can be prepared with the help of local magnetic field. The longitudinal dynamics is initiated by suddenly switching off the field.

Anomalous Spin Precession under a Geometrical Torque

“…Using the time-dependent density-matrix renormalization group (t-DMRG, see Refs. [32,38,39]), we have also qualitatively verified the effect for L > 1 in the quantum-spin case, see Fig. 1 ("quantum").…”

“…Damping and finally relaxation S(t) → Sẑ is phenomenologically described by the LLG equation [27] and is also found microscopically from the model (2) for J > 0 [19,21,23,29]. Besides precession and damping, the electronic system causes a weak nutation of the spin [30][31][32]. While damping ∝Ṡ and nutation ∝S are higher-order effects [33], spin precession is the most elementary phenomenon in this context.…”

Topological spin torque emerging in classical-spin systems with different time scales

“…An important question concerns the conditions for which the constraints (3) are (approximately) satisfied. Previous work on spin dynamics in the s-d impurity model [43][44][45][46] has shown that the real-time evolution of the classical spin is almost adiabatic in large regions of parameter space. It is thus tempting to expect almost adiabatic motion in a certain parameter range and hence an anomalous precession frequency, as predicted by Eq.…”

Non-Hamiltonian dynamics of indirectly coupled classical impurity spins

“…In the RKKY case, it is the ground-state magnetic susceptibility χ 12 (ω = 0) that determines the RKKY effective interaction. Besides this, full linearresponse theory and ground-state response functions also describe other effects, such as Gilbert damping or inertia effects [20,21,[24][25][26][27], but those come at higher order in an expansion in the typical memory time scale and can thus be classified as being of secondary importance.…”