Geology Reference
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Fig. 3.14 Magnetic susceptibility per unit mass, ¦
[m 3 /kg] vs. temperature ( ı C) for magnetite (Fe 3 O 4 ).
Arrows indicate the directions of heating and cooling
(Redrawn from Harrison and Putnis 1996 )
Fig. 3.13 Magnetization curve of a ferromagnetic min-
eral, showing the characteristic hysteresis loop of these
materials. M s is the saturation magnetization, M r is the
remanent magnetization, H c is the coercive value of the
external field
of two components: an induced magnetization M ,
which is proportional to H for small values of the
external field, and a remanent magnetization M r .
Therefore,
dissipate internal energy during the progressive
magnetization resulting from increasing exter-
nal field intensity. Therefore, from some point
onward the process is irreversible . For elevated
values of the applied field, most of the work is
done to rotate a little bit the spins and obtain a
better alignment to the external field axis. In these
conditions, there are small increments of mag-
netization even when the increase of magnitude
of H is large. Consequently, the magnetization
curve asymptotically converges to a saturation
value in a similar way as paramagnetic materials
(Fig. 3.10 ). However, in the case of ferromagnetic
minerals the irreversibility of the process for large
external fields determines the appearance of a
hysteresis loop in the magnetization curve, as
illustrated in Fig. 3.13 . The presence of this loop
implies that some residual magnetization persists
even when we remove completely the external
field. It is called remnant magnetization of the
sample. Figure 3.13 shows that in order to remove
completely this remanent magnetization we must
apply an inverse field of magnitude H c ,whichis
called coercive field .
In general, a ferromagnetic solid that has expe-
rienced one or more phases of strong magnetiza-
tion has a total magnetization M T that is the sum
M T D M C M r D ¦H C M r
(3.63)
The magnetic susceptibility ¦ is positive
and depends upon temperature, just as in the
case of paramagnetic substances, but in a more
complicate way. Figure 3.14 illustrates the result
of measurements of susceptibility on a pure
magnetite (Fe 3 O 4 ) sample (Harrison and Putnis
1996 ). The sample was first heated, so that
the temperature raised from room conditions
to 650 ı C, then cooled back to room temperature
at a rate of 11 ı C/min. It is probably not much
surprising that also this plot shows a hysteresis
loop, given the irreversibility of the process of
magnetization. The temperature associated with
the sharp drop of susceptibility at 585 ı Cis
called Curie temperature T c and depends from
the material. For T > T c any ferromagnetic
solid is converted into a paramagnetic material.
This is a consequence of the fact that at high
temperatures the
thermal
energy exceeds the
spin
coupling
energy,
determining
a
random
arrangement of the magnetic moments.
For any ferromagnetic material, the saturation
value of magnetization M s is a decreasing func-
tion of temperature, as illustrated in Fig. 3.15 .
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