Wasp-waist and pot-belly hysteresis loops have been observed in many materials. When only the major loop is reported, the results are insufficient to establish which processes are involved. We present two models for wasp-waist materials that produce virtually indistinguishable major loops, but show that first-order reversal curves can be used to separate the effects. In the simplest model, we take a soft magnetic material and a hard material and exchange couple them. When the exchange is positive, the loop is conventional. However, for negative (antiferromagnetic) exchange, the wasp-waist loop is obtained. Negative coupling of two materials with different switching field distributions leads to pot-bellied loops.
We report a newly observed phenomenon, namely, the observation of a visible anomaly in the Bloch T(3/2) law for the temperature dependence of magnetization of nanostructured ferromagnets, for which we give a thermodynamic explanation. Our interpretation extends the Bloch law by introducing the system's chemical potential and assumes a finite Bose-Einstein condensation temperature T(BE) of the magnons. Our extension involves accounting for the possibility of a magnon or magnetic entropy term, leading to a magnon chemical potential (hitherto omitted in the traditional derivation) which varies with temperature. The result is a subtle upturn of the magnetization curves of ferromagnetic nanoparticles in the 10 to 50 K temperature range. Here we show experimental data for nanomaterials and an outline of the extended theory which includes T(BE).
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