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Scanning Hall probe microscopy is attractive for minimally invasive characterization of magnetic thin films and nanostructures by measurement of the emanating magnetic stray field. Established sensor probes operating at room temperature employ highly miniaturized spin-valve elements or semimetals, such as Bi. As the sensor layer structures are fabricated by patterning of planar thin films, their adaption to custom-made sensor probe geometries is highly challenging or impossible. Here we show how nanogranular ferromagnetic Hall devices fabricated by the direct-write method of focused electron beam induced deposition (FEBID) can be tailor-made for any given probe geometry. Furthermore, we demonstrate how the magnetic stray field sensitivity can be optimized in situ directly after direct-write nanofabrication of the sensor element. First proof-of-principle results on the use of this novel scanning Hall sensor are shown.
Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait –the propensity to compare one’s own success with that of others– expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.