Debye formulas for a relaxing system with memory

Rate (master) equations are ubiquitous in statistical physics, yet, to the best of our knowledge, a rate equation with memory has previously never been considered. We write down an integro-differential rate equation for the evolution of a thermally relaxing system with memory. For concreteness we adopt as a model a single-domain magnetic particle driven by a small ac field and derive the modified Debye formulas. For any memory time Θ the in-phase component of the resultant ac susceptibility is positive at small probing frequencies ω, but becomes negative at large ω. The system thus exhibits frequency induced diamagnetism. For comparison we also consider particle pairs with dipolar coupling. The memory effect is found to be enhanced by ferromagnetic coupling and suppressed by antiferromagnetic coupling. Numerical calculations support the prediction of a negative susceptibility which arises from a phase shift induced by the memory effect. It is proposed that the onset of frequency induced diamagnetism represents a viable experimental signature of correlated noise

The oldest magnetic record in our Solar System identified using nanometric imaging and numerical modeling

Recordings of magnetic fields, thought to be crucial to our Solar System’s rapid accretion, are potentially retained in unaltered nanometric low-Ni kamacite (~metallic Fe) grains encased within dusty olivine crystals, found in the chondrules of unequilibrated chondrites. However, most of these kamacite grains are magnetically non-uniform, so their ability to retain four-billion-year-old magnetic recordings cannot be estimated by previous theories, which assume only uniform magnetization. Here, we demonstrate that non-uniformly magnetized nanometric kamacite grains are stable over Solar System timescales and likely the primary carrier of remanence in dusty olivine. By performing in-situ temperature-dependent nanometric magnetic measurements using off-axis electron holography, we demonstrate the thermal stability of multi-vortex kamacite grains from the chondritic Bishunpur meteorite. Combined with numerical micromagnetic modeling, we determine the stability of the magnetization of these grains. Our study shows that dusty olivine kamacite grains are capable of retaining magnetic recordings from the accreting Solar System

First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers

We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled-material, where injected charge current flows parallel to the interface. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide.Comment: 22 pages, 9 figures, PDFLaTeX; prepared for Springer Handbook of Materials Modeling, Volume 2 Applications: Current and Emerging Material

Direct observation of a propagating spin wave induced by spin-transfer torque

Spin torque oscillators with nanoscale electrical contacts(1-4) are able to produce coherent spin waves in extended magnetic films, and offer an attractive combination of electrical and magnetic field control, broadband operation(5,6), fast spin-wave frequency modulation(7-9), and the possibility of synchronizing multiple spin-wave injection sites(10,11). However, many potential applications rely on propagating (as opposed to localized) spin waves, and direct evidence for propagation has been lacking. Here, we directly observe a propagating spin wave launched from a spin torque oscillator with a nanoscale electrical contact into an extended Permalloy (nickel iron) film through the spin transfer torque effect. The data, obtained by wave-vector-resolved micro-focused Brillouin light scattering, show that spin waves with tunable frequencies can propagate for several micrometres. Micromagnetic simulations provide the theoretical support to quantitatively reproduce the results

Magnetic properties of individual Co2FeGa Heusler nanoparticles studied at room temperature by a highly sensitive co-resonant cantilever sensor

The investigation of properties of nanoparticles is an important task to pave the way for progress and new applications in many fields of research like biotechnology, medicine and magnetic storage techniques. The study of nanoparticles with ever decreasing size is a challenge for commonly employed methods and techniques. It requires increasingly complex measurement setups, often low temperatures and a size reduction of the respective sensors to achieve the necessary sensitivity and resolution. Here, we present results on how magnetic properties of individual nanoparticles can be measured at room temperature and with a conventional scanning force microscopy setup combined with a co-resonant cantilever magnetometry approach. We investigate individual Co2FeGa Heusler nanoparticles with diameters of the order of 35 nm encapsulated in carbon nanotubes. We observed, for the first time, magnetic switching of these nanoparticles in an external magnetic field by simple laser deflection detection. Furthermore, we were able to deduce magnetic properties of these nanoparticles which are in good agreement with previous results obtained with large nanoparticle ensembles in other experiments. In order to do this, we expand the analytical description of the frequency shift signal in cantilever magnetometry to a more general formulation, taking unaligned sensor oscillation directions with respect to the magnetic field into account