Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. Previous studies proposed a strategy updating mechanism, which successfully demonstrated that the scale-free network can provide a fr
amework for the emergence of cooperation. Instead, individuals in random graphs and small-world networks do not favor cooperation under this updating rule. However, a recent empirical result shows the heterogeneous networks do not promote cooperation when humans play a Prisoners Dilemma. In this paper, we propose a strategy updating rule with payoff memory. We observe that the random graphs and small-world networks can provide even better frameworks for cooperation than the scale-free networks in this scenario. Our observations suggest that the degree heterogeneity may be neither a sufficient condition nor a necessary condition for the widespread cooperation in complex networks. Also, the topological structures are not sufficed to determine the level of cooperation in complex networks.
We determine the composition of intrinsic as well as extrinsic contributions to the anomalous Hall effect (AHE) in the isoelectronic L1o FePd and FePt alloys. We show that the AHE signal in our 30 nm thick epitaxially deposited films of FePd is mainl
y due to extrinsic side-jump, while in the epitaxial FePt films of the same thickness and degree of order the intrinsic contribution is dominating over the extrinsic mechanisms of the AHE. We relate this crossover to the difference in spin-orbit strength of Pt and Pd atoms and suggest that this phenomenon can be used for tuning the origins of the AHE in complex alloys.
The field of spin electronics (spintronics) was initiated by the discovery of giant magnetoresistance (GMR) for which Fert[1] and Grunberg[2] were awarded the 2007 Nobel Prize for Physics. GMR arises from differential scattering of the majority and m
inority spin electrons by a ferromagnet (FM) so that the resistance when the FM layers separated by non-magnetic (NM) spacers are aligned by an applied field is different to when they are antiparallel. In 1996 Slonczewski[3] and Berger[4] predicted that a large spin-polarised current could transfer spin-angular momentum and so exert a spin transfer torque (STT) sufficient to switch thin FM layers between stable magnetisation states[5] and, for even higher current densities, drive continuous precession which emits microwaves[6]. Thus, while GMR is a purely passive phenomenon which ultimately depends on the intrinsic band structure of the FM, STT adds an active element to spintronics by which the direction of the magnetisation may be manipulated. Here we show that highly non-equilibrium spin injection can modify the scattering asymmetry and, by extension, the intrinsic magnetism of a FM. This phenomenon is completely different to STT and provides a third ingredient which should further expand the range of opportunities for the application of spintronics.
Using a three-dimensional focused-ion beam lithography process we have fabricated nanopillar devices which show spin transfer torque switching at zero external magnetic fields. Under a small in-plane external bias field, a field-dependent peak in the
differential resistance versus current is observed similar to that reported in asymmetrical nanopillar devices. This is interpreted as evidence for the low-field excitation of spin waves which in our case is attributed to a spin-scattering asymmetry enhanced by the IrMn exchange bias layer coupled to a relatively thin CoFe fixed layer.
We present the results of experimental investigations of magnetic switching and magnetotransport in a new generation of magnetic devices containing artificially patterned domains. Our devices are realised by locally reducing the coercive field of a p
erpendicularly magnetised Pt (3.5 nm)/Co (0.5 nm)/Pt (1.6 nm) trilayer structure using a gallium focused ion beam (FIB). Artificial domain walls are created at the interfaces between dosed and undosed regions when an external magnetic field switches the former but not the latter. We have exploited this property to create stripe-like domains with widths down to sub-micron lengthscales, separated by undosed regions. Using the extraordinary Hall effect to monitor the local magnetisation we have investigated the reversal dynamics of these artificial domains by measuring major and minor hysteresis loops. The coercive field of regions irradiated with identical doses systematically increases as their size decreases. In the lower branch of minor loops, reversal is seen to occur via a few large Barkhausen events. Preliminary measurements of transport across domain walls reveal a positive domain wall resistance, that does not change sign from 4.2 K to 300 K.
In this paper, we present a correct proof of an $L_p$-inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmunds inequality to the polar derivative of a polynomial.
