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Register a new userSpin-density fluctuations and the fluctuation-dissipation theorem in 3d ferromagnetic metals
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Spatial and time scales of spin density fluctuations (SDF) were analyzed in 3d ferromagnets using ab initio linear response calculations of complete wavevector and energy dependence of the dynamic spin susceptibility tensor. We demonstrate that SDF are spread continuously over the entire Brillouin zone and while majority of them reside within the 3d bandwidth, a significant amount comes from much higher energies. A validity of the adiabatic approximation in spin dynamics is discussed. The SDF spectrum is shown to have two main constituents: a minor low-energy spin wave contribution and a much larger high-energy component from more localized excitations. Using the fluctuation-dissipation theorem (FDT), the on-site spin correlator (SC) and the related effective fluctuating moment were properly evaluated and their universal dependence on the 3d band population is further discussed.
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The full spin density fluctuations (SDF) spectra in 3d paramagnetic metals are analyzed from first principles using the linear response technique. Using the calculated complete wavevector and energy dependence of the dynamic spin susceptibility, we obtain the most important, but elusive, characteristic of SDF in solids: on-site spin correlator (SC). We demonstrate that the SDF have a mixed character consisting of interacting collective and single-particle excitations of similar strength spreading continuously over the entire Brillouin zone and a wide energy range up to femtosecond time scales. These excitations cannot be adiabatically separated and their intrinsically multiscale nature should be always taken into account for a proper description of metallic systems. Overall, in all studied systems, despite the lack of local moment, we found a very large SC resulting in an effective fluctuating moment of the order of several Bohr magnetons.
When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin equation, for mapping the noise to the dynamical degrees of freedom. When the spin dynamics is discretized in time, a general fluctuation-dissipation theorem, valid for non-Markovian noise, can be established, even when zero modes are present. We discuss the subtleties that arise, when Gilbert damping is present and the mapping between noise and spin degrees of freedom is non--linear.
We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium effective temperature. Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by ATP hydrolysis illustrate these points.
The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter.By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the linear response regime, the theorem interrelates the spontaneous fluctuations of microscopic variables with the kinetic coefficients that are responsible for energy dissipation.In the quantum form provided by Callen and Welton in their pioneer paper of 1951 for the case of conductors, electrical noise detected at the terminals of a conductor was given in terms of the spectral density of voltage fluctuations, $S_V({omega})$, and was related to the real part of its impedance, $Re[Z({omega})]$, by a simple relation.The drawbacks of this relation concern with: (I) the appearance of a zero point contribution which implies a divergence of the spectrum at increasing frequencies; (ii) the lack of detailing the appropriate equivalent-circuit of the impedance, (iii) the neglect of the Casimir effect associated with the quantum interaction between zero-point energy and boundaries of the considered physical system; (iv) the lack of identification of the microscopic noise sources beyond the temperature model. These drawbacks do not allow to validate the relation with experiments. By revisiting the FDT within a brief historical survey, we shed new light on the existing drawbacks by providing further properties of the theorem, focusing on the electrical noise of a two-terminal sample under equilibrium conditions. Accordingly, we will discuss the duality and reciprocity properties of the theorem, its applications to the ballistic transport regime, to the case of vacuum and to the case of a photon gas.
An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly-bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be$_2$ and Ne$_2$.
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