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Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction of a magnetic moment with a bath of colored noise. The parameter of the expansion is the ratio of the colored noise timescale to the precession period. In the process we obtain the Gilbert damping from the same expansion. We recover the known results, when the coefficients of the two terms are proportional to one another, in the white noise limit; and show how colored noise leads to situations where this simple relation breaks down, but what replaces it can be understood by the appropriate generalization of the fluctuation--dissipation theorem. Numerical simulations of the stochastic equations support the analytic approach. In particular we find that the equilibration time is about an order of magnitude longer than the timescale set by the colored noise for a wide range of values of the latter and we can identify the presence of nutation in the non-uniform way the magnetization approaches equilibrium.
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We present a study of the magnetic order and the structural stability of two-dimensional quantum spin systems in the presence of spin-lattice coupling. For a square lattice it is shown that the plaquette formation is the most favourable form of static two-dimensional dimerization. We also demonstrate that such distortions may coexist with long range magnetic order, in contrast to the one-dimensional case. Similarly, the coupling to Einstein phonons is found to reduce, but not to eliminate the staggered magnetic moment. In addition, we consider the renormalization of the square lattice phonon spectrum due to spin-phonon coupling in the adiabatic approximation. Towards low temperatures significant softening mainly of zone boundary phonons is found, especially around the $(pi,0)$ point of the Brillouin zone. This result is compatible with the tendency to plaquette formation in the static limit. We also point out the importance of a magnetic pressure on the lattice due to spin-phonon coupling. At low temperatures, this results in a tendency towards shear instabilities of the lattice.
The multifrequency resonance has been widely explored in some of the single-particle models, in which the modulating Rabi model has been most widely investigated. It has been found that with the diagonal periodic modulation, a steady dynamics can be realized in some well-defined discrete frequencies. These frequencies are independent of the off-diagonal couplings. In this work, we generalize this physics to the many-body seesaw realized using the tilted Bose-Hubbard model. We find that the wave function will recover to its initial condition when the modulation frequency is commensurate with the initial energy level spacing between the ground and the first excited levels. The period is determined by the driving frequency and commensurate ratio. In this case, the wave function will almost be restricted to the lowest two instantaneous energy levels. By projecting the wave function to these two relevant states, the dynamics is exactly the same as that for the spin precession dynamics and nutation dynamics around an oscillating axis. We map out the corresponding phase diagram and show that in the low-frequency regime the state is thermalized and in the strong modulation limit, the dynamics is determined by the effective Floquet Hamiltonian. The measurement of these dynamics from the mean position and mean momentum in phase space are also discussed. Our results provide a new thought about the multifrequency resonance in the many-body system.
We examine the presence and evolution of magnetic Dirac nodes in the Heisenberg honeycomb lattice. Using linear spin theory, we evaluate the collinear phase diagram as well as the change in the spin dynamics with various exchange interactions. We show that the ferromagnetic structure produces bosonic Dirac and Weyl points due to the competition between superexchange interactions. Furthermore, it is shown that the criteria for magnetic Dirac nodes are coupled to the magnetic structure and not the overall crystal symmetry, where the breaking of inversion symmetry greatly affects the antiferromagnetic configurations. The tunability of the nodal points through variation of the exchange parameters leads to the possibility of controlling Dirac symmetries through an external manipulation of the orbital interactions.
Non-collinear magnets exhibit a rich array of dynamic properties at microwave frequencies. They can host nanometre-scale topological textures known as skyrmions, whose spin resonances are expected to be highly sensitive to their local magnetic environment. Here, we report a magnetic resonance study of an [Ir/Fe/Co/Pt] multilayer hosting Neel skyrmions at room temperature. Experiments reveal two distinct resonances of the skyrmion phase during in-plane ac excitation, with frequencies between 6-12 GHz. Complementary micromagnetic simulations indicate that the net magnetic dipole moment rotates counterclockwise (CCW) during both resonances. The magnon probability distribution for the lower-frequency resonance is localised within isolated skyrmions, unlike the higher-frequency mode which principally originates from areas between skyrmions. However, the properties of both modes depend sensitively on the out-of-plane dipolar coupling, which is controlled via the ferromagnetic layer spacing in our heterostructures. The gyrations of stable isolated skyrmions reported in this room temperature study encourage the development of new material platforms and applications based on skyrmion resonances. Moreover, our material architecture enables the resonance spectra to be tuned, thus extending the functionality of such applications over a broadband frequency range.
Since the 1950s Heisenberg and others have attempted to explain the appearance of countable particles in quantum field theory in terms of stable localized field configurations. As an exception Skyrmes model succeeded to describe nuclear particles as localized states, so-called skyrmions, within a non-linear field theory. Skyrmions are a characteristic of non-linear continuum models ranging from microscopic to cosmological scales. Skyrmionic states have been found under non-equilibrium conditions, or when stabilised by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids, spin textures in quantum Hall magnets, or the blue phases in liquid crystals, respectively. However, it is believed that skyrmions cannot form spontaneous ground states like ferromagnetic or antiferromagnetic order in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model, that is based on a few material-specific parameters that may be determined from experiment. As a new condition not considered before, we allow for softened amplitude variations of the magnetisation - a key property of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist quite generally in a large number of materials, notably at surfaces and in thin films as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.
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