Magnetic shape-memory alloys owe their exceptional properties primarily to the
accompanying effects of a martensitic phase transformation. The twinning disconnection as
elementary carrier of magnetic-field-induced deformation is the starting point of the present study.
A disconnection is a line defect similar to a dislocation but located at an interface and exhibiting a
step character besides a dislocation character. The mutual interaction of disconnections is fully
tractable by the theory of dislocations. Due to the martensitic transformation, a hierarchical twin
microstructure evolves, details of which are controlled through disconnection-disconnection
interaction. Depending on the mutual orientation of twin boundaries on different hierarchical levels,
twinning disconnections are incorporated in higher hierarchical twin boundaries forming
disclination walls, or they stand off individually from those interfaces. Disconnections which stand
off from interfaces contribute to magnetoelasticity, i.e. recoverable magnetic-field-induced
deformation. Disconnections in disclination walls contribute to magnetoplasticity, i.e. permanent
magnetic-field-induced deformation, if the twin thickness is large. In self-accommodated martensite
with very thin twins, resulting from a martensitic transformation without training, the deformation is
fully magnetoelastic and small. In single-domain crystals, resulting from effective thermo-magnetomechanical
training, the deformation is fully magnetoplastic and large. Between these limiting
cases, there is a continuous spectrum where, as a rule, the fraction of magnetoplastic strain and the
total strain increase with increasing effectiveness of training.
Martensitic Transformation in Shape Memory Alloys under Magnetic Field and Hydrostatic Pressure