A ferromagnetic or ferrimagnetic element is used to control the temperature and applied magnetic field of the element to cause the state of the element as represented on a temperature-magnetic entropy diagram to repeatedly traverse a loop. The loop may have a first portion of concurrent substantially isothermal or constant temperature and increasing applied magnetic field, a second portion of lowering temperature and constant applied magnetic field, a third portion of isothermal and decreasing applied magnetic field, and a fourth portion of increasing temperature and constant applied magnetic field. Other loops may be four-sided, with two isotherms and two adiabats. Preferably, a regenerator is used to enhance desired cooling or heating effects, with varied magnetic fields, or varying temperatures including three-sided figures traversed by the representative point
