Magnetically-controlled actuator materials are provided that produce large actuation stroke, that exhibit fast actuation response time and corresponding high-frequency operation, and that enable efficient actuation energy conversion at convenient operating temperatures. The actuator materials exhibit an austenitic crystal structure above a characteristic phase transformation temperature and exhibit a martensitic twinned crystal structure below the phase transformation temperature. One actuator material provided by the invention is an alloy composition that can be defined generally as (Ni.sub.a Fe.sub.b Co.sub.c).sub.65-x-y (Mn.sub.d Fe.sub.e Co.sub.f).sub.20+x (Ga.sub.g Si.sub.h Al.sub.i).sub.15+y, where x is between about 3 atomic % and about 15 atomic % and y is between about 3 atomic % and about 12 atomic %, and where a+b+c=1, where d+e+f=1, and g+h+i=1. The actuator material is characterized by a magnetocrystalline anisotropy energy that is sufficient for enabling motion of twin boundaries of the martensitic twinned crystal structure in response to application of a magnetic field to the martensitic twinned crystal structure. This enables the material to produce an actuation stroke in response to the magnetic field. Based on this actuation mechanism, the actuator materials of the invention overcome the thermal, stroke, and frequency response limitations typically associated with actuator materials, and enable a class of actuators with large stroke and high speed at convenient temperatures.