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Magnetic tunnel junctions operating in the superparamagnetic regime are promising devices in the field of probabilistic computing, which is suitable for applications like high-dimensional optimization or sampling problems. Further, random number generation is of interest in the field of cryptography. For such applications, a device's uncorrelated fluctuation time-scale can determine the effective system speed. It has been theoretically proposed that a magnetic tunnel junction designed to have only easy-plane anisotropy provides fluctuation rates determined by its easy-plane anisotropy field and can perform on a nanosecond or faster time-scale as measured by its magnetoresistance's autocorrelation in time. Here, we provide experimental evidence of nanosecond scale fluctuations in a circular-shaped easy-plane magnetic tunnel junction, consistent with finite-temperature coupled macrospin simulation results and prior theoretical expectations. We further assess the degree of stochasticity of such a signal.

A practical problem for memory applications involving perpendicularly magnetized magnetic tunnel junctions is the reliability of switching characteristics at high-bias voltage. Often it has been observed that at high-bias, additional error processes are present that cause a decrease in switching probability upon further increase of bias voltage. We identify the main cause of such error-rise process through examination of switching statistics as a function of bias voltage and applied field, and the junction switching dynamics in real time. These experiments show a coincidental onset of error-rise and the presence of a new low-frequency microwave emission well below that dictated by the anisotropy field. We show that in a few-macrospin coupled numerical model, this is consistent with an interface region with concentrated perpendicular anisotropy, and where the magnetic moment has limited exchange coupling to the rest of the layers. These results point to the important role high-frequency interface magnetic moment dynamics play in determining the switching characteristics of these tunnel junction devices.

International audience; The field-and current-induced magnetization reversal of a Co-Fe-B layer in a perpendicular magnetic tunnel junction (pMTJ) is studied at room temperature. The magnetization switching probability from the parallel (P) state to the antiparallel (AP) state and from AP to P is found to be asymmetric. We observe that this asymmetry depends on the magnetic configuration of the synthetic antiferromagnetic (SAF). The state diagram and the energy landscape are compared for two SAF configurations. We conclude that the asymmetry is due to the inhomogeneity of the fringe field generated by the SAF. Our study highlights the role of the reference-layer fringe field on the free layer's energy barrier height, which has to be carefully controlled for memory applications.

Binary stochastic neurons (BSNs) form an integral part of many machine learning algorithms, motivating the development of hardware accelerators for this complex function. It has been recognized that hardware BSNs can be implemented using low-barrier magnets (LBMs) by minimally modifying present-day magnetoresistive random-access memory (MRAM) devices. A crucial parameter that determines the response of these LBM-based BSN designs is the correlation time of magnetization $\tau _c$ . In this letter, we show that, for magnets with low-energy barriers ( $\Delta \approx k_BT$ and below), circular disk magnets with in-plane magnetic anisotropy (IMA) lead to $\tau _c$ values that are two orders of magnitude smaller than $\tau _c$ of magnets with perpendicular magnetic anisotropy (PMA). Analytical descriptions demonstrate that this striking difference in $\tau _c$ is due to a precessionlike fluctuation mechanism that is enabled by the large demagnetization field in IMA magnets. We provide a detailed energy-delay performance evaluation of previously proposed BSN designs based on spin-orbit torque MRAM and spin-transfer torque MRAM employing low-barrier circular IMA magnets by SPICE simulations. The designs exhibit subnanosecond response times leading to energy requirements of approximately a few femtojoules to evaluate the BSN function, orders of magnitude lower than digital CMOS implementations with a much larger surface area. While modern MRAM technology is based on PMA magnets, results in this letter suggest that low-barrier circular IMA magnets may be more suitable for this application.

Barrier interface condition is critical for spin-polarized tunneling and spin-transfer torque switching in CoFeB∣MgO∣CoFeB-based magnetic tunnel junctions. The differential tunnel conductance gV contains information on CoFeB’s magnetic properties at tunnel interfaces. Experimentally, we find gV to follow a “cross-normalization” relationship between the parallel and antiparallel alignments. This we show originates from the leading order spin-flip scatter terms related to CoFeB interface magnetic properties such as its exchange-stiffness. By connecting the observable gV slopes to electrode-specific spin-flip scatter rates, we obtain an efficient measurement for mass-screening of junctions for interface magnetic differences. This provides valuable information for device and fabrication process optimization.Barrier interface condition is critical for spin-polarized tunneling and spin-transfer torque switching in CoFeB∣MgO∣CoFeB-based magnetic tunnel junctions. The differential tunnel conductance gV contains information on CoFeB’s magnetic properties at tunnel interfaces. Experimentally, we find gV to follow a “cross-normalization” relationship between the parallel and antiparallel alignments. This we show originates from the leading order spin-flip scatter terms related to CoFeB interface magnetic properties such as its exchange-stiffness. By connecting the observable gV slopes to electrode-specific spin-flip scatter rates, we obtain an efficient measurement for mass-screening of junctions for interface magnetic differences. This provides valuable information for device and fabrication process optimization.

Équipe 101 : Nanomagnétisme et électronique de spin; International audience; We present a systematic experimental study of the spin-torque-induced magnetic switching statistics at room temperature, using all-perpendicularly magnetized spin-valves as a model system. Three physical regimes are distinguished: a short-time ballistic limit below a few nanoseconds, where spin-torque dominates the reversal dynamics from a thermal distribution of initial conditions; a long time limit, where the magnetization reversal probability is determined by spin-torque-amplified thermal activation; and a cross-over regime, where the spin-torque and thermal agitation both contribute. For a basic quantitative understanding of the physical processes involved, an analytical macrospin model is presented which contains both spin-torque dynamics and finite temperature effects. The latter was treated rigorously using a Fokker-Plank formalism, and solved numerically for specific sets of parameters relevant to the experiments to determine the switching probability behavior in the short time and cross over regimes. This analysis shows that thermal fluctuations during magnetization reversal greatly affect the switching probability over all the time scales studied, even in the short time limit. (C) 2014 Elsevier B.V. All rights reserved

We give an abstraction of verifiable multi-secret sharing schemes that is accessible to a fully mechanized analysis. This abstraction is formalized within the applied pi-calculus by using an equational theory which characterizes the cryptographic semantics of secret share. We also present an encoding from the equational theory into a convergent rewriting system, which is suitable for the automated protocol verifier ProVerif. Based on that, we verify the threshold certificate protocol in ProVerif.

International audience; The spin-torque switching of metallic nanopillar spin valves showing strong perpendicular anisotropy are studied. The magnetic states of the layers depend on extrinsic parameters such as the magnetic field and the dc current applied to the device. A state diagram presents a comprehensive graph of the role of those parameters on the spin-valve magnetic response. After explaining how state diagrams can be built and the different possible representation, experimental state diagrams are studied for perpendicular devices and the influence of lateral size, temperature, and field orientation are shown. An analytical model of a purely uniaxial system is presented. It is shown that this simple model does not properly reflect the experimental results, whereas if the symmetry is broken a qualitative agreement is obtained. Finally, the possible origins of the symmetry break are discussed in light of an analytical model and numerical simulations.

International audience; Magnetization excitation and reversal induced by spin-transfer torques is described in terms of power received or dissipated in a macrospin system. This approach provides a clear and intuitive understanding of the effect of both applied magnetic fields and injected spin-polarized currents on magnetization reversal. It is illustrated by solving the case of magnetization reversal in a nanopillar spin valve with perpendicular magnetizations although the approach can be applied more generally. The appearance of critical currents below which spin-transfer torque is no longer efficient is explained by a break in the uniaxial symmetry of such structures.

The effect of thermal fluctuations on spin-transfer switching has been studied for a broad range of time scales (sub-ns to seconds) in a model system, a uniaxial thin film nanomagnet. The nanomagnet is incorporated into a spin-valve nanopillar, which is subject to spin-polarized current pulses of variable amplitude and duration. Two physical regimes are clearly distinguished: a long pulse duration regime, in which reversal occurs by spin-transfer assisted thermal activation over an energy barrier, and a short time large pulse amplitude regime, in which the switching probability is determined by the spin angular momentum in the current pulse., 4 page, 3 figures

We use spin-transfer-driven ferromagnetic resonance (ST-FMR) to measure the spin-transfer torque vector T in MgO-based magnetic tunnel junctions as a function of the offset angle between the magnetic moments of the electrodes and as a function of bias, V. We explain the conflicting conclusions of two previous experiments by accounting for additional terms that contribute to the ST-FMR signal at large |V|. Including the additional terms gives us improved precision in the determination of T(V), allowing us to distinguish among competing predictions. We determine that the in-plane component of has a weak but non-zero dependence on bias, varying by 30-35% over the bias range where the measurements are accurate, and that the perpendicular component can be large enough to be technologically significant. We also make comparisons to other experimental techniques that have been used to try to measure T(V)., 30 pages, 8 figures. Expanded with additional data and discussion. In press at PRB

Spin-torque driven ferromagnetic resonance (ST-FMR) is used to study thin Co/Ni synthetic layers with perpendicular anisotropy confined in spin-valve based nanojunctions. Field swept ST-FMR measurements were conducted with a magnetic field applied perpendicular to the layer surface. The resonance lines were measured under low amplitude rf excitation, from 1 to 20 GHz. These results are compared with those obtained using conventional rf field driven FMR on extended films with the same Co/Ni layer structure. The layers confined in spin valves have a lower resonance field, a narrower resonance linewidth and approximately the same linewidth vs frequency slope, implying the same damping parameter. The critical current for magnetic excitations is determined from measurements of the resonance linewidth vs dc current and is in accord with the one determined from I-V measurements., 3 pages, 3 figures

Spin-polarized currents can transfer spin angular momentum to a ferromagnet, generating a torque that can efficiently reorient its magnetization. Achieving quantitative measurements of the spin-transfer-torque vector in magnetic tunnel junctions (MTJs) is important for understanding fundamental mechanisms affecting spin-dependent tunneling, and for developing magnetic memories and nanoscale microwave oscillators. Here we present direct measurements of both the magnitude and direction of the spin torque in Co60Fe20B20/MgO/Co60Fe20B20 MTJs. At low bias V, the differential torque vector d{tau}/dV lies in the plane defined by the electrode magnetizations, and its magnitude is in excellent agreement with a prediction for highly-spin-polarized tunneling. With increasing bias, the in-plane component d{tau}_{parallel}/dV remains large, in striking contrast to the decreasing magnetoresistance ratio. The differential torque vector also rotates out of the plane under bias; we measure a perpendicular component tau_{perp}(V) with bias dependence proportional to V^2 for low V, that becomes as large as 30% of the in-plane torque., 33 pages, 9 figures

The switching probability of a single-domain ferromagnet under spin-current excitation is evaluated using the Fokker-Planck equation(FPE). In the case of uniaxial anisotropy, the FPE reduces to an ordinary differential equation in which the lowest eigenvalue $\lambda_1$ determines the slowest switching events. We have calculated $\lambda_1$ by using both analytical and numerical methods. It is found that the previous model based on thermally distributed initial magnetization states \cite{Sun1} can be accurately justified in some useful limiting conditions., Comment: The 10th Joint MMM/Intermag, HA-09

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries., 12 pages, 3 figures. A preliminary version of this paper appeared in the 21st ACM Symp. Comp. Geom., Pisa, 2005, pp. 296-305

Direct observations of the half-integer flux quantum effect in rings, disks, and blanket films of the high-Tc cuprate superconductorsY Ba 2 Cu 3O 7−δ (YBCO),GdBa 2 Cu 3O 7−δ (GdBCO),Tl 2 Ba 2 CuO 6+δ (Tl2201), andBi 2 Sr 2 CaCu 2O 8+δ (BSCCO) with three tricrystal substrate geometries show that their gaps have sign changes consistent with d-wave symmetry. The blanket geometry gives the Josephson penetration depth directly, and provides a means for symmetry tests without patterning. Tl2201 is a tetragonal, single-layer, cuprate without chains. When combined with photoemission results, our BSCCO results imply that the gap followsd x 2−y2 symmetry closely. Asymmetric 45 degree bicrystal grain boundary samples show spontaneous magnetization, as expected for d-wave superconductors with interface roughness.