Approximating the longest path length of a stochastic DAG by a normal distribution in linear time

AbstractThis paper presents a linear time algorithm for approximating, in the sense below, the longest path length of a given directed acyclic graph (DAG), where each edge length is given as a normally distributed random variable. Let F(x) be the distribution function of the longest path length of the DAG. Our algorithm computes the mean and the variance of a normal distribution whose distribution function F˜(x) satisfies F˜(x)⩽F(x) as long as F(x)⩾a, given a constant a (1/2⩽a<1). In other words, it computes an upper bound 1−F˜(x) on the tail probability 1−F(x), provided x⩾F−1(a). To evaluate the accuracy of the approximation of F(x) by F˜(x), we first conduct two experiments using a standard benchmark set ITC'99 of logical circuits, since a typical application of the algorithm is the delay analysis of logical circuits. We also perform a worst case analysis to derive an upper bound on the difference F˜−1(a)−F−1(a)

Modulation of Hanle magnetoresistance in an ultrathin platinum film by ionic gating

Hanle magnetoresistance (HMR) is a type of magnetoresistance where interplay of the spin Hall effect, Hanle-type spin precession, and spin-dependent scattering at the top/bottom surfaces in a heavy metal controls the effect. In this study, we modulate HMR in ultrathin Pt by ionic gating, where the surface Rashba field created by a strong electric field at the interface between the ionic gate and Pt plays the dominant role in the modulation. This finding can facilitate investigations of gate-tunable, spin-related effects and fabrication of spin devices.Comment: 10 pages, 3 figures (To appear in Applied Physics Express

Anomalous sign inversion of spin-orbit torque in ferromagnetic/nonmagnetic bilayer systems due to self-induced spin-orbit torque

Self-induced spin-orbit torques (SI-SOTs) in ferromagnetic (FM) layers have been overlooked when estimating the spin Hall angle (SHA) of adjacent nonmagnetic (NM) layers. In this work, we observe anomalous sign inversion of the total SOT in the spin-torque ferromagnetic resonance due to the enhanced SI-SOT, and successfully rationalize the sign inversion through a theoretical calculation considering the SHE in both the NM and FM layers. The findings show that using an FM layer whose SHA sign is the same as that of the NM achieves efficient SOT-magnetization switching with the assistance of the SI-SOT. The contribution of the SI-SOT becomes salient for a weakly conductive NM layer, and conventional analyses that do not consider the SI-SOT can overestimate the SHA of the NM layer by a factor of more than 150.Comment: 9 pages, 4 figure

Significant suppression of two-magnon scattering in ultrathin Co by controlling the surface magnetic anisotropy at the Co/nonmagnet interfaces

To enable suppression of two-magnon scattering (TMS) in nanometer-thick Co (ultrathin Co) layers and realize low-magnon damping in such layers, the magnon damping in ultrathin Co layers grown on various nonmagnetic seed layers with different surface magnetic anisotropy (SMA) energies are investigated. We verify the significantly weak magnon damping realized by varying the seeding layer species used. Although TMS is enhanced in ultrathin Co on Cu and Al seeding layers, the insertion of a Ti seeding layer below the ultrathin Co greatly suppresses the TMS, which is attributed to suppression of the SMA at the interface between Co and Ti. The Gilbert damping constant of the ultrathin Co layer on Ti (3 nm), 0.020, is comparable to the value for bulk Co, although the Co layer thickness here is only 2 nm. Realization of such weak magnon damping can open the door to tunable magnon excitation, thus enabling coupling of magnons with other quanta such as photons, given that the magnetization of ultrathin ferromagnets can be tuned using an external electric field

Enhancement of low-frequency spin-orbit-torque ferromagnetic resonance signals by frequency tuning observed in Pt/Py, Pt/Co, and Pt/Fe bilayers

DC voltages via spin rectification effect (SRE), VDC, under microwave irradiation are investigated for three platinum (Pt)/ferromagnetic metal (FM) bilayer structures: Pt/Ni₈₀Fe₂₀, Pt/Co, and Pt/Fe. At the microwave frequency region lower than the resonant frequency, large VDC is obtained at zero DC magnetic field for all devices. In frequency dependence just around the resonant frequency, sharp rise and drop of magnitude in VDC are observed. These behaviors are well explained by the numerically calculated magnetic susceptibility. It is also found that the magnitude of VDC is strongly dependent on the slope of magnetoresistance spectrum. These findings lead to developments of sensitive detection technique for nano-scale magnetization switching