Nonlinear ac stationary response and dynamic magnetic hysteresis of quantum uniaxial superparamagnets

The nonlinear ac stationary response of uniaxial paramagnets and superparamagnets - nanoscale solids or clasters with spin number S ~ 10^0 - 10^4 - in superimposed uniform ac and dc bias magnetic fields of arbitrary strength, each applied along the easy axis of magnetization, is determined by solving the evolution equation for the reduced density matrix represented as a finite set of three-term differential-recurrence relations for its diagonal matrix elements. The various harmonic components of the magnetization, dynamic magnetic hysteresis loops, etc. are then evaluated via matrix continued fractions indicating a pronounced dependence of the nonlinear response on S arising from the quantum spin dynamics. In the linear response approximation, the results concur with existing solutions.Comment: 28 pages, 10 figures, 33 refererence

Reversal time of the magnetization of magnetic nanoparticles at very low damping

The magnetization reversal time of ferromagnetic nanoparticles is investigated in the very low damping regime. The energy-controlled diffusion equation rooted in a generalization of the Kramers escape rate theory for point Brownian particles in a potential to the magnetic relaxation of a macrospin, yields the reversal time in closed integral form. The latter is calculated for a nanomagnet with uniaxial anisotropy with a uniform field applied at an angle to the easy axis and for a nanomagnet with biaxial anisotropy with the field along the easy axis. The results completely agree with those yielded by independent numerical and asymptotic methods.Comment: An extended version: 28 pages; 5 figures; Mathematica Program

predictions for the dirac phase in the neutrino mixing matrix and sum rules

Using the fact that the neutrino mixing matrix U = U†eUν, where Ue and Uv result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uv has a form dictated by, or associated with, discrete symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uv, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge L' = Le — Lμ — Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for 5 in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2 θ12, sin2 θ23 and sin2 θ13. This allows us, in particular, to assess the accuracy of the predictions for cos δ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges

Phase space master equations for quantum Brownian motion in a periodic potential: comparison of various kinetic models

The dynamics of quantum Brownian particles in a cosine periodic potential are studied using the phase space formalism associated with the Wigner representation of quantum mechanics. Various kinetic phase space master equation models describing quantum Brownian motion in a potential are compared by evaluating the dynamic structure factor and escape rate from the differential recurrence relations generated by the models. The numerical solution is accomplished via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The results of numerical calculations of the escape rate from a well of the cosine potential are compared with those given analytically by the quantum-mechanical reaction rate theory solution of the Kramers turnover problem for a periodic potential, given by Georgievskii and Pollak (1994 Phys. Rev. E 49 5098), enabling one to appraise each model

Predictions for the Dirac CP violation phase in the neutrino mixing matrix

Using the fact that the neutrino mixing matrix U = (UeUv)-U-dagger , where U-e and U-v result from the diagonalization of the charged lepton and neutrino mass matrices, we analyze the predictions based on the sum rules which the Dirac phase delta present in U satisfies when U-v has a form dictated by, or associated with, discrete flavor symmetries and U-e has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to U-v, so that the reactor, atmospheric and solar neutrino mixing angles theta(13), theta(23) and theta(12) have values compatible with the current data. $U_e$ has a ``minimal'' form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_{ u}$, so that the reactor, atmospheric and solar neutrino mixing angles $heta_{13}$, $heta_{23}$ and $heta_{12}$ have values compatible with the current data

Nonlinear frequency-dependent effects in the dc magnetization of uniaxial magnetic nanoparticles in superimposed strong alternating current and direct current fields

International audienceThe dc component of the magnetization of noninteracting fine magnetic particles possessing simple uniaxial anisotropy and subjected to strong ac and dc bias magnetic fields is calculated via the magnetic Langevin equation. In the presence of an ac driving field, the dc component of the magnetization of uniaxial particles alters drastically leading to new nonlinear effects; in particular, it becomes frequency-dependent. In axial symmetry, where the strong ac field is parallel to the easy axis of a particle, two distinct dispersion regions in the dc magnetization at low and mid-frequencies emerge, corresponding to longitudinal overbarrier and intrawell relaxation modes. Such frequency-dependent behavior allows one to estimate the magnetization reversal time via the half-width of the low-frequency dispersion band. Otherwise, by applying the strong ac field at an angle to the easy axis of a particle so breaking the axial symmetry, a third high-frequency nonlinear resonant dispersion in the dc component of the magnetization appears accompanied by parametric resonance behavior due to excitation of transverse modes with frequencies close to the precession frequency

Spin transfer torque and dc bias magnetic field effects on the magnetization reversal time of nanoscale ferromagnets at very low damping: Mean first-passage time versus numerical methods

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Linear and nonlinear stationary ac response of nanomagnets in the presence of thermal agitation and spin-transfer torques

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