1) Paramagnetic Materials.

2) Diamagnetic Materials.

3) Ferromagnetic Materials.

As we shall see, these classifications depend in part on the magnetic dipole moments of the atoms of the material and in part on the interactions among the atoms.

 In a sample of a paramagnetic material with no applied field, the atomic dipole moments initially are randomly oriented in space. The magnetization, is zero, because the random directions of the mi cause the vector sum to vanish, just as the randomly directed velocities of the molecules in a sample of a gas sum to give zerofor the center-of-mass velocity of the entire sample.

 When an external magnetic field is applied to the material (perhaps by placing it within the windings of a solenoid), the resulting torque on the dipoles tends to align them with the field. The vector sum of the individual dipole moments is no longer zero. The field inside the material now has two components: the applied field Bo and the induced field moM from the magnetization of the dipoles. Note that these twofields are parallel; the dipoles enhance the applied field, in contract tothe electrical case in which the dipole field opposed the applied field and reduced the total electric field in the material. The ratio between moM and Bo is determined, which is small and positive for paramagnetic materials.

 The thermal motion of the atoms tends to disturb the alignment of the dipoles, and consequently the magnetization decreases with increasing temperature. The relationship between M and the temperature T was discovered to be an inverse one by Pierre Curie in 1895 and is written              M=(C*Bo)/T

 which is known as Curie's law, the constant C being known as the Curie constant.

 Because the magnetization of a particular sample depends on the vector sum of its atomic magnetic dipoles, the magnetization reaches its maximum value when all the dipoles are parallel. If there are N such dipoles in the volume V, the maximum value of m is Nmi, which occurs when all N magnetic dipoles mi are parallel. In this case

                                              Mmax=(N*mi)/V

 When the magnetization reaches this saturation value, increases in the applied field Bo have no further effect on the magnetization. Curie's law, which requires that M increase linearly with Bo, is valid only when the magnetization is far from saturation, that is, when Bo/T is small. Figure can be drawn to show the measured magnetization M, as a fraction of the maximum value Mmax, as a function of Bo/T for various temperatures for the paramagnetic salt chrome alum, CrK(SO4)2.12H2O. (It is the chromium ions in this salt that are responsible for the paramagnetism.) Note the approach to saturation, and note that Curie's law is valid only at small values of Bo/T (corresponding to small applied fields or high temperatures). A complete treatment using quantum statistical mechanics gives an excellent fit to the data.

 When the external magnetic field is removed from a paramagnetic sample, the thermal motion causes the directions of the magnetic dipole moments to become random again; the magnetic forces between atoms are too weak to hold the alignment and prevent the randomization. This effect can be used to achieve cooling in a process known as adiabatic demagnetization. A sample is magnetized at constant temperature. The dipoles move into a state of minimum energy in full or partial alignment with the applied field, and in doing so they must give up energy to the surrounding material. This energy flows as heat to the thermal reservoir of the environment. Now the sample is thermally isolated from its environment and is demagnetized adiabaticlally. When the dipoles become randomized, the increase in their magnetic energy must be compensated by a corresponding decreae in the internal energy of the system (since heat cannot flow to or from the isolated system in an adiabatic process). The temperature of the sample must therefore decrease. The lowest temperature that can be reached is determined by the residual field caused by the dipoles. The demagnetization of atomic magnetic dipoles can be used to achieve temperatures on the order of 0.001K, while the demagnetization of the much small nuclear magnetic dipoles permits temperatures in the range of 10^-6K to be obtained.

 Diamagnetismis analogous to the effect of induced electric fields in electrostatics. An uncharged bit of material such as paper is attracted to a charged rod of either polarity. The molecules of the paper do not have permanent electric dipole moments but acquire induced dipole moments from the action of the electric field, and these induced moments can then be attracted by the field.

 In diamagnetic materials, atoms having no permanent magnetic dipole moments acquire induced dipole moments when they are placed in an external magnetic field. Consider the orbiting electrons in an atom to behave like current loops. When an external field Bo is applied, the flux through the loop changes. By Lenz' law, the motion must change in such a way that an induced field opposes this increase in flux. A calculation based on circular orbits shows that the change in motion is accomplished by a slight speeding up or slowing down of the orbital motion, such that the circular frequency associated with the orbital motion changes by change in w = +/- e*Bo/2m

 where Bo is the magnitude of the applied field and m is the mass of an electron. This change in the orbital frequency in effect changes the orbital magnetic moment of an electron. If we were to bring a single atom of a material such as bismuth near the north pole of a magnet, the field (which points away from the pole) tends to increase the flux through the current loop that represents the circulating electron. According to Lenz' law, there must be an induced field pointing in the opposite direction (toward the pole). The induced north pole is on the side of the loop toward the magnet, and the two north poles repel one another.

 This effect occurs no matter what the sense of rotation of the original orbit, so the magnetization in a dismagnetic material opposes the applied field. The ratio of the magnetization contribution to the field moM to the applied field Bo, given by Km-1 according to Equation, amounts to about -10^-6 to -10^-5 for typical diamagnetic materials.

 We can decrease the effectiveness of the coupling between neighboring atoms that causes ferromagnetism by increasing the temperature of a substance. The temperature at which a ferromagnetic material becomes paramagnetic is called its Curie temperature. The Curie temperature of iron, for instance, is 770 degree C; above this temperature, iron is paramagnetic. The Curie temperature of gadolinium metal is 16 degree C; at room temperature, gadolinium is paramagnetic, while at temperatures below 16 C, gadolinium becomes ferromagnetic.

 The enhancement of the applied field in ferromagnets is considerable. The total magnetic field B inside a ferromagnet may be 10^3 or 10^4 times the applied field Bo. The permeability Km of a ferromagnetic material is not a constant; neither the field B nor the magnetization M increases linearly with Bo, even at small values of Bo.

 Let us insert a ferromagnetic material such as iron into a solenoid.. We assume that the current is initially zero and that the iron is unmagnetized, so that initially both Bo and M are zero. We increase Bo by increasing the current in the solenoid. The magnetization increases rapidly toward a saturation value by the sigment ab. Now we decrease the current to zero. The magnetization does not retrace its original path, but instead the iron remains magnetized (at point c) even when the applied field Bo is zero. If we then reverse the direction of the current in the solenoid, we reach a saturated magnetization in the opposite direction (point d), and returning the current to zero we find that the sample retains a permanent magnetization at point e. We can then increase the current again to return to the saturated magnetization in the original direction (point b). The path bcdeb can be repeatedly followed.

 This behavior is called hysteresis. At points c and e, the iron is magnetized, even though there is no current in the solenoid. Furthermore, the iron "remembers" how it became magnetized, a negative current producing a magnetization different from a positive one. This "memory" is essential to the operation of magnetic storage of information, such as on cassette tapes or computer disks.

 The approach of a ferromagnet to saturation occurs through a mechanism different from that of a paramagnet (which we described by means of the rotation of individual magnetic dipoles into alignment with the applied field). A material such as iron is composed of a large number of microscopic crystals. Within each crystal are magnetic domains, regions of roughly 0.01 mm in size in which the coupling of atomic magnetic dipoles produces essentially perfect alignment of all the atoms. There are many domains, each with its dipoles pointing in a different direction, and the net result of adding these dipole moments in an unmagnetized ferromagnet gives a magnetization of zero.

 When the ferromagnet is placed in an external field, two effects may occur: (1) dipoles outside the walls of domains that are aligned with the field can rotate into alignment, in effect allowing such domains to grow at the expense of neighboring domains; and (2) the dipoles of nonaligned domains may swing entirely into alignment with the applied field. In either case, there are now more dipoles aligned with the field, and the material has a large magnetization. When the field is removed, the domain walls do not move completely back to their former positions, and the material retains a magnetization in the direction of the applied field.