While damped spin dynamics is important for the understanding of magnetic materials, clear signatures of \emph{quantum corrections} to the Gilbert damping mechanism remain elusive. We propose a route to distinguish quantum and classical Gilbert spin damping using ferroelectric control of a magnetic dimer. Ab initio calculations for dimers on ferroelectric substrates show that polarization reversal switches the inter-spin exchange between ferromagnetic and antiferromagnetic regimes. We formulate a magnetization-based diagnostic that relates magnetization traces to entanglement dynamics, which enables ferroelectrical on/off control of dimer entanglement. Material-informed quantum Landau-Lifshitz-Gilbert simulations illustrate how the signature of magnetization dynamics can, in principle, be used to infer the existence of quantum Gilbert spin damping. This minimal and non-volatile platform connects first-principles modeling to experimentally accessible observables and provides a starting point for voltage-controlled quantum entanglement in magnetic spin networks.
While damped spin dynamics is important for the understanding of magnetic materials, clear signatures of \emph{quantum corrections} to the Gilbert damping mechanism remain elusive. We propose a route to distinguish quantum and classical Gilbert spin damping using ferroelectric control of a magnetic dimer. Ab initio calculations for dimers on ferroelectric substrates show that polarization reversal switches the inter-spin exchange between ferromagnetic and antiferromagnetic regimes. We formulate a magnetization-based diagnostic that relates magnetization traces to entanglement dynamics, which enables ferroelectrical on/off control of dimer entanglement. Material-informed quantum Landau-Lifshitz-Gilbert simulations illustrate how the signature of magnetization dynamics can, in principle, be used to infer the existence of quantum Gilbert spin damping. This minimal and non-volatile platform connects first-principles modeling to experimentally accessible observables and provides a starting point for voltage-controlled quantum entanglement in magnetic spin networks.
Understanding the microscopic origin of magnetic damping is essential for describing magnetization dynamics in nanoscale magnetic systems. In this work, we develop a microscopic framework to derive Gilbert damping terms from specific interactions in ferromagnetic conductors and magnetic insulators. In ferromagnetic conductors, magnetic damping is dominated by the s d exchange interaction between the localized magnetic moments and the itinerant electrons, which is effectively equivalent to an electronmagnon interaction. From the spin diffusion equation and the spin transfer torque therein, we obtain the corresponding quantum LLG equation. In magnetic insulators, where free electrons are absent, spin phonon interactions become the primary source of the damping.Starting from an effective spin phonon interaction and using linear response theory, we derive a quantum LLG equation with a Gilbert damping tensor analytically. Our results demonstrate that different microscopic interactions lead to qualitatively different structures of magnetic damping. Instead of being described by a universal scalar parameter, Gilbert damping can exhibit spatial dependence and tensorial characteristics determined by the underlying microscopic interactions.
The Landau-Lifshitz-Gilbert (LLG) and Landau-Lifshitz (LL) equations play an essential role for describing the dynamics of magnetization in solids. While a quantum analog of the LL dynamics has been proposed in [Phys. Rev. Lett. 110, 147201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.147201], the corresponding quantum version of LLG remains unknown. Here, we propose such a quantum LLG equation that inherently conserves purity of the quantum state. We examine the quantum LLG dynamics of a dimer consisting of two interacting spin-1/2 particles. Our analysis reveals that, in the case of ferromagnetic coupling, the evolution of initially uncorrelated spins mirrors the classical LLG dynamics. However, in the antiferromagnetic scenario, we observe pronounced deviations from classical behavior, underscoring the unique dynamics of becoming a spinless state, which is nonlocally correlated. Moreover, when considering spins that are initially entangled, our study uncovers an unusual form of revival-type quantum correlation dynamics, which differs significantly from what is typically seen in open quantum systems.
The Landau-Lifshitz-Gilbert (LLG) equation provides the fundamental description of dissipative magnetization dynamics. A recently proposed quantum analog, the quantum Landau-Lifshitz-Gilbert (QLLG) equation, extends this framework to quantum spin systems. However, whether the QLLG equation recovers the LLG equation in the classical large-spin limit for interacting spin systems remains an open question. Here, we demonstrate this connection by deriving the LLG equation as the classical large-spin limit of the QLLG equation. We establish this correspondence analytically and verify it numerically for an interacting spin system. These results provide a quantum-to-classical description of dissipative spin dynamics, offering a microscopic foundation for the LLG equation. From numerical calculations provided here, we also conclude that quantum effects become much less noticeable for systems with larger number of spins in the Hamiltonian.
We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is, with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uniaxial ferromagnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction accelerates the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., those produced with the large magnetic-dipole-moment atoms 166Er. This enables experimental access to the dissipation parameter $\mathrm{\ensuremath{\Gamma}}$ in the Gross-Pitaevskii mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $\mathrm{\ensuremath{\Gamma}}$ is a single scalar independent of spin indices.
We introduce a distinct route for extending classical atomistic spin dynamics into the quantum regime for arbitrary spin s, based on a variational product-state \textit{ansatz} that includes both pure and mixed local states. By construction, intersite entanglement -- expected to remain negligible even on very short time scales in many real materials -- is excluded, while local quantum effects are retained through the nonclassical structure of s≥1 density operators. Nonlinear dynamics arise from both the mean-field interdependence of the local states and the state-dependent dissipative terms. The framework recovers classical spin dynamics for s=21 while allowing genuinely quantum local dynamics for higher spins. It clarifies the variational and geometric origin of the inequivalence between quantum Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics, provides a criterion for their equivalence under a common time rescaling, establishes connections with the classical theory through two qualitatively distinct limits (s→∞ and a large number of quantum spins N), and allows realistic O(N) simulations of quantum spin dynamics in materials.
The entanglement of many localized spins (LSs) within solid magnetic materials is a topic of great basic and applied interest, particularly after becoming amenable to experimental scrutiny where recent neutron scattering experiments have witnessed macroscopic entanglement in the ground state (GS) of antiferromagnets persisting even at elevated temperatures. On the other hand, spintronics and magnonics studies assume that LSs of antiferromagnets are in unentangled N\'eel GS, as well as that they evolve, when pushed out of equilibrium by current or external fields, according to the Landau-Lifshitz-Gilbert (LLG) equation viewing LSs as classical vectors of fixed length. The prerequisite for applicability of the LLG equation is zero entanglement in the underlying many-body quantum state of LSs. In this study, we initialize quantum Heisenberg ferro- or antiferromagnetic chains hosting S=1/2,S=1, or S=5/2 LSs into an unentangled pure state and then evolve them by quantum master equations (QMEs) of Lindblad or non-Markovian type, derived by coupling LSs weakly to a bosonic bath (due to phonons in real materials) or by using additional ``reaction coordinate'' in the latter case. The time evolution is initiated by applying an external magnetic field, and entanglement of the ensuing mixed quantum states is monitored by computing its negativity. We find that non-Markovian dynamics never brings entanglement to zero, in the presence of which the vector of spin expectation value changes its length to render the LLG equation inapplicable. Conversely, Lindbladian (i.e., Markovian) dynamics ensures that entanglement goes to 0, thereby enabling quantum-to-classical transition in all cases---S=1/2,S=1, and S=5/2 ferromagnets or S=5/2 antiferromagnets---except for S=1/2 and S=1 antiferromagnets. Finally, we investigate the stability of an entangled antiferromagnetic GS upon suddenly coupling it to bosonic baths.