Geology Reference
In-Depth Information
In shape anisotropy, a magnetic particle is more easily magnetized along
its long axis, so an ellipsoidal grain will be magnetized along its long
axis. Perpendicular to the long axis is the hard magnetization direction,
which provides an energy barrier to the magnetization flipping over to the
opposite long axis direction. The height of the energy barrier is a function
of the microscopic coercivity, h
c
, of the grain. In fact, the long-term stability
of the magnetic grain is a function of the trade-off between the energy
barrier, vh
c
j
s
, holding the magnetization along the easy axis direction and
the thermal energy (kT) that can on occasion provide enough energy to flip
a grain's magnetization.
vh j
kT
=
1
t
exp
cs
(2.4)
C
2
where t is the relaxation time, C is a constant called the frequency factor (10
−8
s
−1
), v is the volume of the grain, h
c
is the grain's microscopic coercivity, j
s
is the
spontaneous magnetization of the grain, k is the Boltzmann's constant, and T is
the temperature. This equation shows that a ferromagnetic grain's size is critical
in determining its stability. Magnetite grains as small as 10-20 nanometers have
short relaxation times of 100s of seconds and are called superparamagnetic
grains. They are ferromagnetic but behave like paramagnetic grains; they line
up with an applied field causing an induced magnetization, but their directions
randomize when the field is turned off. As ferromagnetic grains increase in size
up to 40-50 nanometers, their relaxation times quickly increase to billions of
years and they are paleomagnetically stable.
2.4.3
Domain State
As the ferromagnetic grains of magnetite grow larger into the several micron
size range, their magnetostatic energy increases. One way of picturing the
increase in energy is that as the grain increases in size, more and more of the
grain's surface is covered with magnetic “charges” of the same sign. Since
charges of the same sign repel each other, the magnetostatic energy of the grain
increases. To reduce its overall energy, the grain subdivides into uniformly
magnetized subregions, or domains, which are magnetized in opposite direc-
tions. There is a critical diameter where the energy required for building the
wall or boundary between these magnetic domains is just equal to the energy
saved by subdividing into a MD grain. The grain has reduced its overall energy,
but the overall magnetization of the grain is also reduced. Domain walls can
move to readjust a grain's magnetization to agree, energetically, with an applied
field. The domain with a magnetization parallel to the applied field grows at
the expense of the domain with a magnetization opposite to the applied
magnetic field. MD wall movement and superparamagnetism, mentioned
above, are important mechanisms for ferromagnetic susceptibility. The MD
grains also are less magnetically stable than the smaller stable SD grains.
