On a generalization of distance sets

A subset $X$ in the $d$-dimensional Euclidean space is called a $k$-distance set if there are exactly $k$ distinct distances between two distinct points in $X$ and a subset $X$ is called a locally $k$-distance set if for any point $x$ in $X$, there are at most $k$ distinct distances between $x$ and other points in $X$. Delsarte, Goethals, and Seidel gave the Fisher type upper bound for the cardinalities of $k$-distance sets on a sphere in 1977. In the same way, we are able to give the same bound for locally $k$-distance sets on a sphere. In the first part of this paper, we prove that if $X$ is a locally $k$-distance set attaining the Fisher type upper bound, then determining a weight function $w$, $(X,w)$ is a tight weighted spherical $2k$-design. This result implies that locally $k$-distance sets attaining the Fisher type upper bound are $k$-distance sets. In the second part, we give a new absolute bound for the cardinalities of $k$-distance sets on a sphere. This upper bound is useful for $k$-distance sets for which the linear programming bound is not applicable. In the third part, we discuss about locally two-distance sets in Euclidean spaces. We give an upper bound for the cardinalities of locally two-distance sets in Euclidean spaces. Moreover, we prove that the existence of a spherical two-distance set in $(d-1)$-space which attains the Fisher type upper bound is equivalent to the existence of a locally two-distance set but not a two-distance set in $d$-space with more than $d(d+1)/2$ points. We also classify optimal (largest possible) locally two-distance sets for dimensions less than eight. In addition, we determine the maximum cardinalities of locally two-distance sets on a sphere for dimensions less than forty.Comment: 17 pages, 1 figur

Stochastic simulation of thermally assisted magnetization reversal in sub-100 nm dots with perpendicular anisotropy

Thermally assisted magnetization reversal of sub-100 nm dots with perpendicular anisotropy has been investigated using a micromagnetic Langevin model. The performance of the two different reversal modes of (i) a reduced barrier writing scheme and (ii) a Curie point writing scheme are compared. For the reduced barrier writing scheme, the switching field Hswt decreases with an increase in writing temperature but is still larger than that of the Curie point writing scheme. For the Curie point writing scheme, the required threshold field Hth, evaluated from 50 simulation results, saturates at a value, which is not simply related to the energy barrier height. The value of Hth increases with a decrease in cooling time owing to the dynamic aspects of the magnetic ordering process. Dependence of Hth on material parameters and dot sizes has been systematically studied

A Nuclear Magnetic Resonance Study on Rubrene-cobalt Nano-composites

We implemented a nuclear magnetic resonance (NMR) study on rubrene(C42H28)-Co nano-composites that exhibit an enhanced magnetoresistance (MR) ratio of 80%. The 59Co NMR spin echo experiment enabled clarification of the hyperfine field of Co at the interface between the ferromagnet and the molecules, which has not been investigated for molecular spintronics. An enhanced hyperfine field of the Co was observed in the rubrene-Co nano-composites, which may be related to the enhancement of the MR ratio. This study demonstrates the importance of microscopic investigation of the interface between molecules and ferromagnets that governs spin-dependent transport in molecular spin devices.Comment: 12pages, 3 figures, 1 tabl

Spin Injection into a Graphene Thin Film at Room Temperature

We demonstrate spin injection into a graphene thin film with high reliability by using non-local magnetoresistance (MR) measurements, in which the electric current path is completely separated from the spin current path. Using these non-local measurements, an obvious MR effect was observed at room temperature; and the MR effect was ascribed to magnetization reversal of ferromagnetic electrodes. This result is a direct demonstration of spin injection into a graphene thin film. Furthermore, this is the first report of spin injection into molecules at room temperature.Comment: 12 pages, 3 figure

Ferroelectricity driven-resistive switching and Schottky barrier modulation at CoPt/MgZnO interface for non-volatile memories

Ferroelectric memristors have attracted much attention as a type of nonvolatile resistance switching memories in neuromorphic computing, image recognition, and information storage. Their resistance switching mechanisms have been studied several times in perovskite and complicated materials systems. It was interpreted as the modulation of carrier transport by polarization control over Schottky barriers. Here, we experimentally report the isothermal resistive switching across a CoPt/MgZnO Schottky barrier using a simple binary semiconductor. The crystal and texture properties showed high-quality and single-crystal Co$_{0.30}$Pt$_{0.70}$/Mg$_{0.20}$Zn$_{0.80}$O hetero-junctions. The resistive switching was examined by an electric-field cooling method that exhibited a ferroelectric T$_C$ of MgZnO close to the bulk value. The resistive switching across CoPt/MgZnO Schottky barrier was accompanied by a change in the Schottky barrier height of 26.5 meV due to an interfacial charge increase and/or orbital hybridization induced reversal of MgZnO polarization. The magnitude of the reversed polarization was estimated to be a reasonable value of 3.0 (8.25) $\mu$ C/cm$^2$ at 300 K (2 K). These findings demonstrated the utilities of CoPt/MgZnO interface as a potential candidate for ferroelectric memristors and can be extended to probe the resistive switching of other hexagonal ferroelectric materials