Internal energy versus moment for ferromagnets and pyroelectrics

Since the internal energy

E

is a monotonically increasing function of the temperature

T

, the moment

M (T)

can be expressed as a function of internal energy

E

. The corresponding form of

E (M)

is focused on in this paper. For ferromagnets, the two-dimensional Ising model is used to obtain the exact form of

E (M)

and this is discussed both near

T = 0

and near the critical temperature

T_{c}

. In three dimensions, we are only able to discuss the forms of

E (M)

near

T = 0

and

T = T_{c}

. For low temperatures, spin-wave theory readily yields the result that, for insulating ferromagnets,

Δ E = E - E (0)

is proportional to

{(Δ M)}^{\frac{5}{3}}

with

Δ M = M (0) - M (T)

while for the metallic case

Δ E \propto {(Δ M)}^{\frac{4}{3}}

. Though the theory is much less complete than for ferromagnets, some results are very briefly discussed for pyroelectrics.

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