Ferromagnetism

   Iron, nickel, cobalt and some of the rare earths (gadolinium, dysprosium) exhibit
   a unique magnetic behavior which is called ferromagnetism because iron (ferrum in
   Latin) is the most common and most dramatic example. Samarium and neodymium in
   alloys with cobalt have been used to fabricate very strong [1]rare-earth magnets.

   Ferromagnetic materials exhibit a [2]long-range ordering phenomenon at the atomic
   level which causes the unpaired electron spins to line up parallel with each
   other in a region called a [3]domain. Within the domain, the magnetic field is
   intense, but in a bulk sample the material will usually be unmagnetized because
   the many domains will themselves be randomly oriented with respect to one
   another. Ferromagnetism manifests itself in the fact that a small externally
   imposed [4]magnetic field, say from a [5]solenoid, can cause the magnetic domains
   to line up with each other and the material is said to be magnetized. The driving
   magnetic field will then be increased by a large factor which is usually
   expressed as a [6]relative permeability for the material. There are many
   practical [7]applications of ferromagnetic materials, such as the
   [8]electromagnet.

   Ferromagnets will tend to stay magnetized to some extent after being subjected to
   an external magnetic field. This tendency to "remember their magnetic history" is
   called [9]hysteresis. The fraction of the saturation magnetization which is
   retained when the driving field is removed is called the [10]remanence of the
   material, and is an important factor in permanent magnets.

   All ferromagnets have a maximum temperature where the ferromagnetic property
   disappears as a result of thermal agitation. This temperature is called the
   [11]Curie temperature.

   Ferromagntic materials will respond mechanically to an impressed magnetic field,
   changing length slightly in the direction of the applied field. This property,
   called [12]magnetostriction, leads to the familiar hum of transformers as they
   respond mechanically to 60 Hz AC voltages.

          [13]Magnetic properties of solids [14]Table of magnetic properties

                            [15]Table of Curie temperatures

   [16]Index

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                           Long Range Order in Ferromagnets

   The long range order which creates [21]magnetic domains in [22]ferromagnetic
   materials arises from a quantum mechanical interaction at the atomic level. This
   interaction is remarkable in that it locks the magnetic moments of neighboring
   atoms into a rigid parallel order over a large number of atoms in spite of the
   thermal agitation which tends to randomize any atomic-level order. Sizes of
   domains range from a 0.1 mm to a few mm. When an external magnetic field is
   applied, the domains already aligned in the direction of this field grow at the
   expense of their neighbors. If all the spins were aligned in a piece of iron, the
   field would be about 2.1 Tesla. A magnetic field of about 1 T can be produced in
   annealed iron with an external field of about 0.0002 T, a multiplication of the
   external field by a factor of 5000! For a given ferromagnetic material the long
   range order abruptly disappears at a certain temperature which is called the
   [23]Curie temperature for the material. The Curie temperature of iron is about
   1043 K.
   [24]Index
   Reference
   [25]Ohanian
   Sec 33-3

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                                 The Curie Temperature

   For a given [30]ferromagnetic material the [31]long range order abruptly
   disappears at a certain temperature which is called the Curie temperature for the
   material. The Curie temperature of iron is about 1043 K. The Curie temperature
   gives an idea of the amount of energy it takes to break up the long-range
   ordering in the material. At 1043 K the [32]thermal energy is about 0.135 eV
   compared to about 0.04 eV at room temperature.

           [33]Magnetic properties of solids [34]Table of Curie temperatures

   [35]Index

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                                   Magnetic Domains

   The [40]microscopic ordering of electron spins characteristic of
   [41]ferromagnetic materials leads to the formation of regions of magnetic
   alignment called domains.

                                     [domain.png]

   The main implication of the domains is that there is already a high degree of
   magnetization in ferromagnetic materials within individual domains, but that in
   the absence of external magnetic fields those domains are randomly oriented. A
   modest applied magnetic field can cause a larger degree of alignment of the
   magnetic moments with the external field, giving a large multiplication of the
   applied field.

   These illustrations of domains are conceptual only and not meant to give an
   accurate scale of the size or shape of domains. The microscopic evidence about
   magnetization indicates that the net magnetization of ferromagnetic materials in
   response to an external magnetic field may actually occur more by the growth of
   the domains parallel to the applied field at the expense of other domains rather
   than the reorientation of the domains themselves as implied in the sketch.

                                    [domains2.png]

   Some of the more direct evidence we have about domains comes from imaging of
   domains in single crystals of ferromagnetic materials. The sketches above are
   after Young and are adapted from magnified images of domain boundaries in single
   crystals of nickel. They suggest that the effect of external magnetic fields is
   to cause the domain boundaries to shift in favor of those domains which are
   parallel to the applied field. It is not clear how this applies to bulk magnetic
   materials which are polycrystalline. Keep in mind the fact that the internal
   magnetic fields which come from the [42]long range ordering of the electron spins
   are much stronger, sometimes hundreds of times stronger, than the external
   magnetic fields required to produce these changes in domain alignment. The
   effective multiplication of the external field which can be achieved by the
   alignment of the domains is often expressed in terms of the [43]relative
   permeability.

   Domains may be made visible with the use of magnetic colloidal suspensions which
   concentrate along the domain boundaries. The domain boundaries can be imaged by
   polarized light, and also with the use of electron diffraction. Observation of
   domain boundary movement under the influence of applied magnetic fields has aided
   in the development of theoretical treatments. It has been demonstrated that the
   formation of domains minimizes the magnetic contribution to the free energy.
   [44]Index
   References
   [45]Young
   Sec 29-8
   [46]Myers
   Ch. 11

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                                 Relative Permeability

   The [51]magnetic constant µ[0] = 4p x 10^-7 T m/A is called the [52]permeability
   of space. The permeabilities of most materials are very close to µ[0] since most
   materials will be classified as either [53]paramagnetic or [54]diamagnetic. But
   in [55]ferromagnetic materials the permeability may be very large and it is
   convenient to characterize the materials by a relative permeability.

   [relper.png]
   [56]Table of magnetic properties

   When ferromagnetic materials are used in applications like an [57]iron-core
   solenoid, the relative permeability gives you an idea of the kind of
   multiplication of the applied magnetic field that can be achieved by having the
   ferromagnetic core present. So for an ordinary iron core you might expect a
   magnification of about 200 compared to the magnetic field produced by the
   solenoid current with just an air core. This statement has exceptions and limits,
   since you do reach a saturation magnetization of the iron core quickly, as
   illustrated in the discussion of [58]hysteresis.

                           [59]Magnetic properties of solids

   [60]Index

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                            Applications of Ferromagnetism

[65]Electromagnets

[66]Magnetic tape recording

[67]Transformers

                                  [68]Ferromagnetism

   [69]Index

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References

   1. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magperm.html#c2
   2. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c2
   3. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c4
   4. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c4
   5. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c4
   6. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c5
   7. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c6
   8. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c5
   9. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/hyst.html#c1
  10. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magperm.html#c1
  11. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c3
  12. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magstrict.html#c1
  13. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magpr.html#c1
  14. http://hyperphysics.phy-astr.gsu.edu/hbase/tables/magprop.html#c2
  15. http://hyperphysics.phy-astr.gsu.edu/hbase/tables/curie.html#c1
  16. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  17. http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
  18. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html
  19. http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  20. Javascript:history.go(-1)
  21. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c4
  22. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c1
  23. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c3
  24. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  25. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/eleref.html#c1
  26. http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
  27. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html
  28. http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  29. Javascript:history.go(-1)
  30. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c1
  31. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c2
  32. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html#c2
  33. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magpr.html#c1
  34. http://hyperphysics.phy-astr.gsu.edu/hbase/tables/curie.html#c1
  35. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  36. http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
  37. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html
  38. http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  39. Javascript:history.go(-1)
  40. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c2
  41. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c1
  42. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c2
  43. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c5
  44. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  45. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/eleref.html#c1
  46. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/solref.html#c1
  47. http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
  48. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html
  49. http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  50. Javascript:history.go(-1)
  51. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html#c3
  52. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html#c3
  53. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magpr.html#c3
  54. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magpr.html#c2
  55. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c1
  56. http://hyperphysics.phy-astr.gsu.edu/hbase/tables/magprop.html#c2
  57. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c4
  58. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/hyst.html#c2
  59. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magpr.html#c1
  60. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  61. http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
  62. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html
  63. http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  64. Javascript:history.go(-1)
  65. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c5
  66. http://hyperphysics.phy-astr.gsu.edu/hbase/audio/tape.html#c1
  67. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html#c1
  68. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c1
  69. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  70. http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
  71. http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html
  72. http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon
  73. Javascript:history.go(-1)