When an external magnetic field is applied to a ferromagnet such as iron,
the atomic dipoles align themselves with it. Even when the field is removed, part
of the alignment will be retained: the material has become magnetized. Once
magnetized, the magnet will stay magnetized indefinitely. To demagnetize
it requires heat or a magnetic field in the opposite direction. This is the
effect that provides the element of memory in a hard disk drive.
The relationship between field strength H and magnetization M is not linear in
such materials. If a magnet is demagnetized and the relationship
between H and M is plotted for increasing levels of field strength, M
follows the initial magnetization curve. This curve increases rapidly at first
and then approaches an asymptote called magnetic saturation. If the magnetic
field is now reduced monotonically, M follows a different curve. At zero field
strength, the magnetization is offset from the origin by an amount called the
remanence. If the H-M relationship is plotted for all strengths of applied
magnetic field the result is a hysteresis loop called the main loop.
The width of the middle section is twice the coercivity of the material.
A closer look at a magnetization curve generally reveals a series of small,
random jumps in magnetization called Barkhausen jumps. This effect is due to
crystallographic defects such as dislocations.
Magnetic hysteresis loops are not exclusive to materials with
ferromagnetic ordering. Other magnetic orderings, such as spin glass ordering,
also exhibit this phenomenon. Physical origin
The phenomenon of hysteresis in ferromagnetic materials is the result of
two effects: rotation of magnetization and changes in size or number of
magnetic domains. In general, the magnetization varies across a magnet,
but in sufficiently small magnets, it does not. In these single-domain
magnets, the magnetization responds to a magnetic field by rotating.
Single-domain magnets are used wherever a strong, stable magnetization is
needed. Larger magnets are divided into regions
called domains. Within each domain, the magnetization does not vary; but between
domains are relatively thin domain walls in which the direction of magnetization
rotates from the direction of one domain to another. If the magnetic field
changes, the walls move, changing the relative sizes of the domains. Because
the domains are not magnetized in the same direction, the magnetic moment per
unit volume is smaller than it would be in a single-domain magnet; but domain
walls involve rotation of only a small part of the magnetization, so it is much
easier to change the magnetic moment. The magnetization can also change by
addition or subtraction of domains. Models
The most known empirical models in hysteresis are Preisach and
Jiles-Atherton models. These models allow an accurate modeling of the
hysteresis loop and are widely used in the industry. However, these models lose
the connection with thermodynamics and the energy consistency is not ensured.
Latest models rely on a consistent thermodynamic formulation. VINCH model
is inspired by the kinematic hardening laws and by the thermodynamics of
irreversible processes. In particular, in addition to provide an accurate
modeling, the stored magnetic energy and the dissipated energy are known at all
times. The obtained incremental formulation is variationally consistent,
i.e., all internal variables follow from the minimization of a thermodynamic
potential. That allows to obtain easily a vectorial model while Preisach and
Jiles-Atherton are fundamentally scalar models.
Applications There are a great variety of
applications of the hysteresis in ferromagnets. Many of these make use of
their ability to retain a memory, for example magnetic tape, hard disks, and
credit cards. In these applications, hard magnets like iron are desirable so
the memory is not easily erased. Soft magnets are used as cores in
electromagnets. The nonlinear response of the magnetic moment to a magnetic
field boosts the response of the coil wrapped around it. The low coercivity
reduces that energy loss associated with hysteresis.
See also Degaussing
Neodymium magnet Jiles-Atherton model
References External links