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Dispersion relations and isofrequency curves are of critical importance for understanding the behavior of waves, including what frequencies can be excited, how the waves will propagate, and how waves in one system will couple to another. Here, we present methods to extract the dispersion relations and isofrequency curves automatically and conveniently, each from a single micromagnetic simulation run. These methods have significant advantages in that they provide a means to obtain rapid insight into spin wave behavior in complex situations where analytic approaches are difficult or impossible. We present multiple examples to illustrate the methodology and discuss specific issues that need to be considered for the different situations. 

Ultrasoft magnetorheological elastomers (MREs) offer convenient real-time magnetic field control of mechanical properties that provides a means to mimic mechanical cues and regulators of cells in vitro. Here, we systematically investigate the effect of polymer stiffness on magnetization reversal of MREs using a combination of magnetometry measurements and computational modeling. Poly-dimethylsiloxane-based MREs with Young’s moduli that range over two orders of magnitude were synthesized using commercial polymers Sylgard™ 527, Sylgard 184, and carbonyl iron powder. The magnetic hysteresis loops of the softer MREs exhibit a characteristic pinched loop shape with almost zero remanence and loop widening at intermediate fields that monotonically decreases with increasing polymer stiffness. A simple two-dipole model that incorporates magneto-mechanical coupling not only confirms that micrometer-scale particle motion along the applied magnetic field direction plays a defining role in the magnetic hysteresis of ultrasoft MREs but also reproduces the observed loop shapes and widening trends for MREs with varying polymer stiffnesses.