Magnetic heat pumping

The method employs ferromagnetic or ferromagnetic elements, preferably of rare-earth based material, for example gadolinium, and preferably employs a regenerator. The steps comprise controlling the temperature and applied magnetic field of the element to cause the state of the element as represented on a temperature-magnetic entropy diagram repeatedly to 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, for example, two isotherms and two adiabats (constant entropy portions