In condensed matter physics, an Arrott plot is a plot of the square of the magnetization
M
2
of a substance, against the ratio of the applied magnetic field to magnetization
H
/
M
at one (or several) fixed temperature(s). Arrott plots are an easy way of determining the presence of ferromagnetic order in a material. They are named after American physicist Anthony Arrott who introduced them as a technique for studying magnetism in 1957.
According to the Ginzburg-Landau mean field picture for magnetism, the free energy of a ferromagnetic material close to a phase transition can be written as:
F
(
M
)
=
−
H
M
+
a
T
−
T
c
T
c
M
2
+
b
M
4
+
…
where
M
, the magnetization, is the order parameter,
H
is the applied magnetic field,
T
c
is the critical temperature, and
a
,
b
are material constants.
Close to the phase transition, this gives a relation for the magnetization order parameter:
M
2
=
1
4
b
H
M
−
a
2
b
ϵ
where
ϵ
=
T
−
T
c
T
c
is a dimensionless measure of the temperature.
Thus in a graph plotting
M
2
vs.
H
/
M
for various temperatures, the line without an intercept corresponds to the dependence at the critical temperature. Thus along with providing evidence for the existence of a ferromagnetic phase, the Arrott plot can also be used to determine the critical temperature for the phase transition.
