Daniele Pinna

Thermally assisted spin-transfer torque dynamics in energy space

We consider the general Landau-Lifshitz-Gilbert theory underlying the magnetization dynamics of a macrospin magnet subject to spin-torque effects and thermal fluctuations. Thermally activated dynamical properties are analyzed by averaging the full magnetization equations over constant-energy orbits. After averaging, all the relevant dynamical scenarios are a function of the ratio between hard and easy axis anisotropies. We derive analytically the range of currents for which limit cycles exist and discuss the regimes in which the constant energy orbit averaging technique is applicable.

Thermally assisted spin-transfer torque magnetization reversal in uniaxial nanomagnets

We simulate the stochastic Landau-Lifshitz-Gilbert dynamics of a uniaxial nanomagnet out to sub-millisecond timescales using a graphical processing unit based micromagnetic code and determine the effect of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted reversal dynamics. The asymptotic behavior of the switching time (I→0, 〈τ〉∝exp(−ξ(1−I)2)) is approached gradually, indicating a broad crossover regime between the ballistic and thermally assisted spin transfer reversal. Interestingly, the functional form of the mean switching time is shown to be independent of the angle between the spin current and magnets uniaxial axes. These results have important implications for modeling the energetics of thermally assisted magnetization reversal of spin transfer magnetic random access memory bit cells.

Spin-torque oscillators with thermal noise: A constant energy orbit approach

We study the magnetization dynamics of spin-torque oscillators in the presence of thermal noise and as a function of the spin-polarization angle in a macrospin model. The macrospin has biaxial magnetic anisotropy, typical of thin film magnetic elements, with an easy axis in the film plane and a hard axis out of the plane. Using a method that averages the energy over precessional orbits, we derive analytic expressions for the current that generates and sustains out-of-plane precessional states. We find that there is a critical angle of the spin polarization necessary for the occurrence of such states and predict a hysteretic response to applied current. This model can be tested in experiments on orthogonal spin-transfer devices, which consist of both an in-plane and out-of-plane magnetized spin polarizers, effectively leading to an angle between the easy and spin-polarization axes.

Spin-transfer torque magnetization reversal in uniaxial nanomagnets with thermal noise

We consider the general Landau-Lifshitz-Gilbert (LLG) dynamical theory underlying the magnetization switching rates of a thin film uniaxial magnet subject to spin-torque effects and thermal fluctuations. After discussing the various dynamical regimes governing the switching phenomena, we present analytical results for the mean switching time behavior. Our approach, based on explicitly solving the first passage time problem, allows for a straightforward analysis of the thermally assisted, low spin-torque, switching asymptotics of thin film magnets. To verify our theory, we have developed an efficient Graphics Processing Unit (GPU)-based micromagnetic code to simulate the stochastic LLG dynamics out to millisecond timescales. We explore the effects of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted dynamics. We find that even in the absence of axial symmetry, the switching times can be functionally described in a form virtually identical to the collinear case.

Micromagnetic study of spin transfer switching with a spin polarization tilted out of the free layer plane

We present the results of zero temperature macrospin and micromagnetic simulations of spin transfer switching of thin film nanomagnets in the shape of an ellipse with a spin-polarization tilted out of the layer plane. The perpendicular component of the spin-polarization is shown to increase the reversal speed, leading to a lower current for switching in a given time. However, for tilt angles larger than a critical angle, the layer magnetization starts to precess about an out-of-plane axis, which leads to a final magnetization state that is very sensitive to simulation conditions. As the ellipse lateral size increases, this out-of-plane precession is suppressed, due to the excitation of spatially non-uniform magnetization modes.

Large fluctuations and singular behavior of nonequilibrium systems.

We present a general geometrical approach to the problem of escape from a metastable state in the presence of noise. The accompanying analysis leads to a simple condition, based on the norm of the drift field, for determining whether caustic singularities alter the escape trajectories when detailed balance is absent. We apply our methods to systems lacking detailed balance, including a nanomagnet with a biaxial magnetic anisotropy and subject to a spin-transfer torque. The approach described within allows determination of the regions of experimental parameter space that admit caustics.

State diagram of an orthogonal spin transfer spin valve device

We present the switching characteristics of a spin-transfer device that incorporates a perpendicularly magnetized spin-polarizing layer with an in-plane magnetized free and fixed magnetic layer, known as an orthogonal spin transfer spin valve device. This device shows clear switching between parallel (P) and antiparallel (AP) resistance states and the reverse transition (AP → P) for both current polarities. Further, hysteretic transitions are shown to occur into a state with a resistance intermediate between that of the P and AP states, again for both current polarities. These unusual spin-transfer switching characteristics can be explained within a simple macrospin model that incorporates thermal fluctuations and considers a spin-polarized current that is tilted with respect to the free layers plane, due to the presence of the spin-transfer torque from the polarizing layer.

Reliable spin-transfer torque driven precessional magnetization reversal with an adiabatically decaying pulse

We show that a slowly decaying current pulse can lead to nearly deterministic precessional switching in the presence of noise. We consider a biaxial macrospin, with an easy axis in the plane and a hard axis out-of-the plane, typical of thin film nanomagnets patterned into asymmetric shapes. Out-of-plane precessional magnetization orbits are excited with a current pulse with a component of spin polarization normal to the film plane. By numerically integrating the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation we show that thermal noise leads to strong dephasing of the magnetization orbits. However, an adiabatically decreasing pulse amplitude overwhelmingly leads to magnetization reversal, with a final state that {\em only} depends on the pulse polarity, not on the pulse amplitude. We develop an analytic model to explain this phenomena and to determine the pulse decay time necessary for adiabatic magnetization relaxation and thus precessional magnetization switching.