Magnetic Cooling: Effects of External Field

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orthovector
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The degrees of freedom associated with the possible orientations of the spins of the magnetic atoms constitute a spin system, which is in thermal interaction with the degrees of freedom of translational motion of all the atoms which constitute the lattice system.

If the external magnetic field acts on the spin system alone, what happens when the field is NOT changed too rapidly to the lattice and spin systems and temperature and total heat capacity?
 
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Are you simply referring to adiabatic demagnetization refrigeration (ADR)?
Or to something else?