Relaxation effects in magnetic-field-induced martensitic transformation of an Ni–Mn–In–Co alloy

The effect of isothermal stepwise changes of an applied magnetic field in an Ni–Mn–In–Co metamagnetic shape memory alloy has been studied. It has been found that relaxations towards equilibrium states occur under isothermal and isofield conditions, in both direct and reverse martensitic transformations (upon decreasing or increasing field sequences, respectively). In all cases, the relaxation follows a logarithmic time dependence, which can be monitored through the time dependence of magnetization M(t). The logarithmic dependence brings close analogies with the thermal fluctuation magnetic after-effect, associated with the thermally assisted rearrangement of magnetic domains after a sudden variation of the magnetic field. Following this analogy, it has been found that the viscosity coefficient Z (slope of M(t) vs. ln t) is directly proportional to the transformation rate in a continuous cycle. This result generalizes what has been found in temperature-induced transformations, although in field-induced transformations the proportionality is temperature dependent. This result also allows for an understanding of the existence of isothermal–isofield “windows” where the relaxations can take place, and the experimental results found in quite different systems can be easily rationalized in this way. Finally, the features of pseudo-transformation–temperature–time diagrams in this alloy can be rationalized according to the proposed dependence of Z.