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Tunnel magnetoresistance (TMR) sensor is a highly sensitive magnetic field sensor and is expected to be applied in various fields, such as magnetic recording, industrial sensing, and bio-medical sensing. To improve the detection capability of TMR sensors in low frequency regime it is necessary to suppress the 1/f noise. We theoretically study 1/f noise of a tiny TMR sensor using the macrospin model. Starting from the generalized Langevin equation, 1/f noise power spectrum and the Hooge parameter are derived. The calculated Hooge parameter of a tiny TMR sensor is much smaller than that of a conventional TMR sensor with large junction area. The results provide a new perspective on magnetic 1/f noise and will be useful for improvement of TMR sensors., Comment: 8 pages, 3 figures

Voltage-controlled magnetoresistive random access memory (VC-MRAM) based on voltage-induced dynamic switching in magnetic tunnel junctions (MTJs) is a promising ultimate non-volatile memory with ultralow power consumption. However, the dynamic switching in a conventional MTJ is accompanied by a relatively high write error rate (WER), hindering the reliable operation of VC-MRAM. Here, we propose a reliable writing scheme using the in-plane demagnetizing field (IDF) and voltage-induced negative out-of-plane anisotropy field (NOAF). Numerical simulations based on macrospin model demonstrate that the voltage-induced NOAF modifies the switching dynamics and increases the torque due to the IDF, thereby reducing the switching time. The IDF and voltage-induced NOAF also reduce the mean energy difference between the magnetization direction at the end of the pulse and the equilibrium direction. As a result, an appropriate combination of the IDF and voltage-induced NOAF reduces the WER by one order of magnitude compared with that of the dynamic switching in a conventional MTJ.

Voltage-induced dynamic switching in magnetic tunnel junctions (MTJs) is a writing technique for voltage-controlled magnetoresistive random access memory (VCMRAM), which is expected to be an ultimate non-volatile memory with ultra-low power consumption. In conventional dynamic switching, the width of sub-nanosecond write voltage pulses must be precisely controlled to achieve a sufficiently low write-error rate (WER). This very narrow tolerance of pulse width is the biggest technical difficulty in developing VCMRAM. Heavily damped precessional switching is a writing scheme for VCMRAM with a substantially high tolerance of pulse width although the minimum WER has been much higher than that of conventional dynamic switching with an optimum pulse width. In this study, we theoretically investigate the effect of MTJ shape and the direction of the applied magnetic field on the WER of heavily damped precessional switching. The results show that the WER in elliptical-cylinder MTJ can be several orders of magnitude smaller than that in usual circular-cylinder MTJ when the external magnetic field is applied parallel to the minor axis of the ellipse. The reduction in WER is due to the fact that the demagnetization field narrows the component of the magnetization distribution perpendicular to the plane direction immediately before the voltage is applied.

Distribution of write error rate (WER) of spin-transfer-torque magnetoreistive random access memory (STT MRAM) caused by a distribution of resistance area product and anisotropy constant is theoretically studied. Assuming that WER is much smaller than unity, and junction parameters obey a normal distribution, we show that the WER obeys a logarithmic normal distribution. We derive analytical expressions for the probability density function and statistical measures. We find that the coefficient of variation of WER can be reduced by decreasing the pulse width. We also perform numerical simulations based on the Fokker-Planck equation and confirm the validity of the analytical expressions. The results are useful for designing reliable STT MRAMs., Comment: 8 pages, 4 figures, typos corrected, hyperlinks added

Recent advances in experimental techniques have made it possible to manipulate and measure the magnetization dynamics on the femtosecond time scale which is the same order as the correlation time of the bath degrees of freedom. In the equations of motion of magnetization, the correlation of the bath is represented by the non-Markovian damping. For development of the science and technologies based on the ultrafast magnetization dynamics it is important to understand how the magnetization dynamics depend on the correlation time. It is also important to determine the correlation time experimentally. Here we study the precession dynamics of a small magnet with the non-Markovian damping. Extending the theoretical analysis of Miyazaki and Seki [J. Chem. Phys. 108, 7052 (1998)] we obtain analytical expressions of the precession angular velocity and the effective damping constant for any values of the correlation time under assumption of small Gilbert damping constant. We also propose a possible experiment for determination of the correlation time., Comment: 6 pages, 3 figures

Effects of a microwave voltage on magnetization precession are analyzed based on a macrospin model. The microwave voltage induces the oscillating anisotropy field through the voltage controlled magnetic anisotropy (VCMA) effect, and then stimulates the magnetization. The large angle precession is maintained if the magnetization synchronizes with the microwave voltage. The effective equations of motion of the magnetization with an oscillating anisotropy field are derived, and the mechanism of the synchronization is clarified by analyzing the derived equations of motion. The conditions of the angular frequency detuning and the amplitude of the oscillating anisotropy field for synchronization are obtained. The results are useful for development of the VCMA-based energy-efficient spintronics devices using magnetization precession such as a VCMA-based magnetoresistive random access memory and a nano-scale microwave magnetic field generator., Comment: 7 pages, 5 figures

A low power magnetization switching scheme based on the voltage control of magnetic anisotropy (VCMA) is proposed. In contrast to the conventional switching scheme using VCMA, where the magnetic anisotropy is eliminated during the voltage pulse, the magnetic anisotropy is enhanced to induce precession around the axis close to the easy axis. After turning off the voltage proximately at a half of precession period, the magnetization relaxes to the opposite equilibrium direction. We perform numerical simulations and show that the pulse duration of the proposed switching scheme is as short as a few tens of pico seconds. Such a short pulse duration is beneficial for low power consumption because of the reduction of energy loss by Joule heating., Comment: 15 pages, 3 figures

Impact of spin transfer torque (STT) on the write error rate of a voltage-torque-based magnetoresistive random access memory is theoretically analyzed by using the macrospin model. During the voltage pulse the STT assists or suppresses the precessional motion of the magnetization depending on the initial magnetization direction. The characteristic value of the current density is derived by balancing the STT and the external-field torque, which is about 5$\times$ 10$^{11}$ A/m$^{2}$. The results show that the write error rate is insensitive to the STT below the current density of $10^{10}$ A/m$^{2}$., Comment: 8 pages, 5 figures, submitted to Physical Review Applied

Spintronic neurons which emit sharp voltage spikes are required for the realization of hardware neural networks enabling fast data processing with low-power consumption. In many neuroscience and computer science models, neurons are abstracted as non-linear oscillators. Magnetic nano-oscillators called spin-torque nano-oscillators are interesting candidates for imitating neurons at nanoscale. These oscillators, however, emit sinusoidal waveforms without spiking while biological neurons are relaxation oscillators that emit sharp voltage spikes. Here we propose a simple way to imitate neuron spiking in high-magnetoresistance nanoscale spin valves where both magnetic layers are free and thin enough to be switched by spin torque. Our numerical-simulation results show that the windmill motion induced by spin torque in the proposed spintronic neurons gives rise to spikes whose shape and frequency, set by the charging and discharging times, can be tuned through the amplitude of injected dc current. We also found that these devices can exhibit chaotic oscillations. Chaotic-like neuron dynamics has been observed in the brain, and it is desirable in some neuromorphic computing applications whereas it should be avoided in others. We demonstrate that the degree of chaos can be tuned in a wide range by engineering the magnetic stack and anisotropies and by changing the dc current. The proposed spintronic neuron is a promising building block for hardware neuromorphic chips leveraging non-linear dynamics for computing.

Memristors are non-volatile nano-resistors. Their resistance can be tuned by applied currents or voltages and set to a large number of levels between two limit values. Thanks to these properties, memristors are ideal building blocks for a number of applications such as multilevel non-volatile memories and artificial nano-synapses, which are the focus of this work. A key point towards the development of large scale memristive neuromorphic hardware is to build these neural networks with a memristor technology compatible with the best candidates for the future mainstream non-volatile memories. Here we show the first experimental achievement of a memristor compatible with Spin-Torque Magnetic Random Access Memory. The resistive switching in our spin-torque memristor is linked to the displacement of a magnetic domain wall by spin-torques in a perpendicularly magnetized magnetic tunnel junction. We demonstrate that our magnetic synapse has a large number of intermediate resistance states, sufficient for neural computation. Moreover, we show that engineering the device geometry allows leveraging the most efficient spin torque to displace the magnetic domain wall at low current densities and thus to minimize the energy cost of our memristor. Our results pave the way for spin-torque based analog magnetic neural computation., Comment: 9 pages, 3 figures

We use spin-torque resonance to probe simultaneously and separately the dynamics of a magnetic domain wall and of magnetic domains in a nanostripe magnetic tunnel junction. Thanks to the large associated resistance variations we are able to analyze quantitatively the resonant properties of these single nanoscale magnetic objects. In particular, we find that the magnetic damping of both domains and domain walls is doubled compared to the damping value of their host magnetic layer. We estimate the contributions to damping arising from dipolar couplings between the different layers in the junction and from the intralayer spin pumping effect. We find that they cannot explain the large damping enhancement that we observe. We conclude that the measured increased damping is intrinsic to large amplitudes excitations of spatially localized modes or solitons such as vibrating or propagating domain walls

We present an experimental study of phase-locking in a stochastic magnetic oscillator. The system comprises a magnetic tunnel junction with a superparamagnetic free layer, whose magnetization dynamics is driven with spin torques through an external periodic driving current. We show that synchronization of this stochastic oscillator to the input current is possible for current densities below $3 \times 10^6$ A/cm$^2$, and occurs for input frequencies lower than the natural mean frequency of the stochastic oscillator. We show that such injection-locking is robust and leads to a drastic reduction in the phase diffusion of the stochastic oscillator, despite the presence of a frequency mismatch between the oscillator and the excitation.

We present time-resolved measurements of the displacement of magnetic domain-walls (DWs) driven by vertical spin-polarized currents in track-shaped magnetic tunnel junctions. In these structures we observe very high DW velocities (600 m/s) at current densities below $10^7 A/cm^2$. We show that the efficient spin-transfer torque combined with a short propagation distance allows to avoid the Walker breakdown process, and achieve deterministic, reversible and fast ($\approx$ 1 ns) DW-mediated switching of magnetic tunnel junction elements, which is of great interest to the implementation of fast DW-based spintronic devices.

The discovery that a spin polarized current can exert a large torque on a ferromagnet through a transfusion of spin angular momentum, offers a new way to control a magnetization by simple current injection, without the help of an applied external field. Spin transfer can be used to induce magnetization reversals and oscillations, or to control the position of a magnetic domain wall. In this review, we focus on this last mechanism, which is today the subject of an extensive research, both because the microscopic details for its origin are still debated, but also because promising applications are at stake for non-volatile magnetic memories.