Theoretical limit of the minimal magnetization switching field and the optimal field pulse for Stoner particles

Optimal Control of Magnetization Reversal in a Monodomain Particle by Means of Applied Magnetic Field

A complete analytical solution to the optimal reversal of a macrospin with easy-axis anisotropy is presented. An optimal control path minimizing the energy cost of the reversal is identified and used to derive the time-dependent direction and amplitude of the optimal switching field. The minimum energy cost of the reversal scales inversely with the switching time for fast switching, follows exponential asymptotics for slow switching, and reaches the lower limit proportional to the energy barrier between the target states and to the damping parameter at infinitely long switching time. For a given switching time, the energy cost is never smaller than that for a free macrospin. This limitation can be bypassed by adding a hard anisotropy axis that activates the internal torque in the desired switching direction, thereby significantly reducing the energy cost. A comparison between the calculated optimal control path and minimum energy path reveals that optimal control does not translate to the minimization of the energy barrier but signifies effective use of the system's internal dynamics to aid the desired magnetic transition.

Dynamic magnetic susceptibility and electrical detection of ferromagnetic resonance

The dynamic magnetic susceptibility of magnetic materials near ferromagnetic resonance (FMR) is very important in interpreting the dc voltage obtained in its electrical detection. Based on the causality principle and the assumption that the usual microwave absorption lineshape of a homogeneous magnetic material around FMR is Lorentzian, the general forms of the dynamic magnetic susceptibility of an arbitrary sample and the corresponding dc voltage lineshapes of its electrical detection were obtained. Our main findings are as follows. (1) The dynamic magnetic susceptibility is not a Polder tensor for a material with an arbitrary magnetic anisotropy. The two off-diagonal matrix elements of the tensor near FMR are not, in general, opposite to each other. However, the linear response coefficient of the magnetization to the total radio frequency (rf) field (the sum of the external and internal rf fields due to precessing magnetization is a quantity which cannot be measured directly) is a Polder tensor. This may explain why the two off-diagonal susceptibility matrix elements were always wrongly assumed to be opposite to each other in almost all analyses. (2) The frequency dependence of dynamic magnetic susceptibility near FMR is fully characterized by six real numbers, while its field dependence is fully characterized by seven real numbers. (3) A recipe of how to determine these numbers by standard microwave absorption measurements for a sample with an arbitrary magnetic anisotropy is proposed. Our results allow one to unambiguously separate the contribution of the anisotropic magnetoresistance to the dc voltage signals from the anomalous Hall effect. With these results, one can reliably extract the information of spin pumping and the inverse spin-Hall effect, and determine the spin-Hall angle. (4) In the case that resonance frequency is not sensitive to the applied static magnetic field, the field dependence of the matrix elements of dynamic magnetic susceptibility, as well as the dc voltage, may have another non-resonance broad peak. Thus, one should be careful in interpreting the observed peaks.

Phase dependence of microwave-assisted switching of a single magnetic nanoparticle

Microwave-assisted switching of the magnetization is an efficient way to reduce the magnetic field required to reverse the magnetization of nanostructures. Here, the phase sensitivity of microwave-assisted switching of an individual cobalt nanoparticle is studied using a pump-probe technique. The pump microwave pulse prepares an initial state of the magnetization, and the probe pulse tests its stability against switching. Precession states are established, which are stable against switching. Their basin of attraction is measured and is in qualitative agreement with numerical macrospin calculations. The damping parameter is evaluated using the variable delay pump-probe technique.

Probabilistic aspects of magnetization relaxation in single-domain nanomagnets

A single-domain nanomagnet is a basic example of a system where relaxation from high to low energy is probabilistic in nature even when thermal fluctuations are neglected. The reason is the presence of multiple stable states combined with extreme sensitivity to initial conditions. It is demonstrated that for this system the probability of relaxing from high energies to one of the stable magnetization orientations can be tuned to any desired value between 0 and 1 by applying a small transverse magnetic field of appropriate amplitude. In particular, exact analytical predictions are derived for the conditions under which the probability of reaching one of the stable states becomes exactly 0 or 1. Under these conditions, magnetization relaxation is totally insensitive to initial conditions, and the final state can be predicted with certainty, a feature that could be exploited to devise novel magnetization switching strategies or novel methods for the measurement of the magnetization damping constant.

Domain wall propagation through spin wave emission

We theoretically study field-induced domain wall motion in an electrically insulating ferromagnet with hard- and easy-axis anisotropies. Domain walls can propagate along a dissipationless wire through spin wave emission locked into the known soliton velocity at low fields. In the presence of damping, the usual Walker rigid-body propagation mode can become unstable for a magnetic field smaller than the Walker breakdown field.

Spin transfer in a ferromagnet-quantum dot and tunnel-barrier-coupled Aharonov-Bohm ring system with Rashba spin-orbit interactions

The spin transfer effect in a ferromagnet-quantum dot (insulator)-ferromagnet Aharonov-Bohm (AB) ring system with Rashba spin-orbit (SO) interactions is investigated by means of the Keldysh nonequilibrium Green function method. It is found that both the magnitude and direction of the spin transfer torque (STT) acting on the right ferromagnet electrode can be effectively controlled by changing the magnetic flux threading the AB ring or the gate voltage on the quantum dot. The STT can be greatly augmented by matching a proper magnetic flux and an SO interaction at a cost of low electrical current. The STT, electrical current and spin current are uncovered to oscillate with the magnetic flux. The present results are expected to be useful for information storage in nanospintronics.

Domain-wall motion in ferromagnetic nanowires driven by arbitrary time-dependent fields: an exact result

We address the dynamics of magnetic domain walls in ferromagnetic nanowires under the influence of external time-dependent magnetic fields. We report a new exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy. The solution holds for applied fields with arbitrary strength and time dependence. We further extend this solution to applied fields slowly varying in space and to multiple domain walls.

Fast domain wall propagation under an optimal field pulse in magnetic nanowires

We investigate field-driven domain wall (DW) propagation in magnetic nanowires in the framework of the Landau-Lifshitz-Gilbert equation. We propose a new strategy to speed up the DW motion in a uniaxial magnetic nanowire by using an optimal space-dependent field pulse synchronized with the DW propagation. Depending on the damping parameter, the DW velocity can be increased by about 2 orders of magnitude compared to the standard case of a static uniform field. Moreover, under the optimal field pulse, the change in total magnetic energy in the nanowire is proportional to the DW velocity, implying that rapid energy release is essential for fast DW propagation.

Switching properties of ferromagnetic nanoparticles driven by a circularly polarized magnetic field

We present a comprehensive study of the magnetization switching of a uniaxial nanoparticle driven by a circularly polarized magnetic field rotated in the plane perpendicular to the easy axis. The conditions for the existence of the uniform and non-uniform precessions of the nanoparticle magnetic moment are derived. In addition, the differences between switchings via uniform and non-uniform precession are determined, and the essential role of field polarization is demonstrated. The dependence of the switching time on the field amplitude and frequency are calculated numerically. We show that a permanent magnetic field can reduce the amplitude and frequency of the switching rotating field, and that the combined action of these fields is characterized by an extremely strong dependence of the switching time on the field parameters. We also demonstrate that the transition process caused by an external magnetic field pulse can decrease the switching amplitude in comparison with the value predicted from analysis of the stability criterion. We discuss the advantages of switching the magnetization by means of the action of a rotating field over the magnetization switching using a steady field applied perpendicular to the easy axis.

Local control of ultrafast dynamics of magnetic nanoparticles

Using the local control theory we derive analytical expressions for magnetic field pulses that steer the magnetization of a monodomain magnetic nanoparticle to a predefined state. Finite-temperature full numerical simulations confirm the analytical results and show that a magnetization switching or freezing is achievable within few precessional periods and that the scheme is exploitable for fast thermal switching.

Theoretical limit in the magnetization reversal of stoner particles

Magnetization reversal of uniaxial Stoner particles under the Slonczewski spin-transfer torques of polarized electric currents is investigated. Based on the modified Landau-Lifshitz-Gilbert equation of magnetization dynamics, the theoretical limit of critical currents required to reverse a magnetization with an arbitrary polarized current is obtained. Under a constant polarization degree and constant current amplitude, the optimal current pulse for the fastest magnetization reversal is derived. These results can be used as benchmarks to evaluate different reversal strategies besides other possible usages.