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The Effect of Magnetic Fields
on the Resistance of a Conductor

When a magnetic field is applied to a conductor in which charges are flowing it produces a curvature in their paths as a result of the Lorentz force. The curvature of the paths of the charges increases the distance the charges must travel through the conductor and increases the expected number of collisions with impurities and lattice imperfections and thus the resistance of the conductor is increased.

When the flowing charges possess spin there will be an additional effect because the charges with spin have a magnetic moment which interacts with the magnetic field. The two spin orientations with respect to the magnetic field have different energies. At equilibrium the population of the higher energy orientation is suppressed by a factor of

exp(-ΔE)/kT)/[1+exp(-ΔE/kT)]

where ΔE is the energy difference of the two orientations and kT is the thermal energy.

The current is effectively carried by two channels in parallel.

When the conductor is ferromagnetic charges with spin such as electrons are affected by the residual magnetic field even when there is no external magnetic field applied. But at a sufficiently high level of the external field the magnetization of the ferromagnetic conductor will be aligned with the external field.

A multilayer conductor is one that contains alternating layers of magnetic and nonmagnetic materials. For example, one type of multilayer contains thirty thin layers of iron sandwiched between thirty layers of chromium. The magnetic domains of the iron layers are coordinated. When the chromium layers are thin the successive iron layers are coupled antiferromagnetically. This means the directions of magnetization are reversed in successive layers. This means that half of the iron layers are oriented in a way that interfers with the transport of electrons with one spin. This creates an enhanced resistance.

When an external magnetic field is applied it tends to change the direction of magnetization of the domains in such a way that resistance is reduced. At sufficiently high level of the external field the iron layers all have the same direction of magnetization and resistance is minimized. The difference between the resistance at zero external field and the minimum resistance can be quite larges, a reduction of fifty percent. This is called Giant Magnetoresistance.

The thickness of the nonmagnetic layers determines the nature of the magnetic coupling of the successive iron layers. As indicated in the Howson article, there is an optimal domain width. If the thickness of the nonmagnetic layer results in the magnetic layers being separated by this optimal domain distance then the successive iron layers will be coupled antiferromagnetically. But larger thickness may result in the successive iron layers being coupled ferromagnetically.

The argument for higher resistance when successive magnetic layers are coupled with opposite directions of magnetization (antiferromagnetic coupling) seems to be based upon the resistance of a circuit involving two or more channels connected in parallel. For the case of two subcircuits of resistance R1 and R2 the resistance R of the parallel circuit is given by:

1/R = 1/R1 + 1/R2.

Thus if R2/R1 is represented as n then:

R = R1[n/(n+1)].

Suppose the resistance of a channel with magnetization that opposes the flow of electrons is 4 times as great at a channel in which the magnetization enhances the flow. Then the resistance of the two channels is (4/5) of the resistance of a sinle good channel. If a magnetic field reverses the direction of magnetization of the channel which opposes electron flow then the resistance of the combined channels drops to one half the resistance of a single good channel. A drop in resistance of this magnitude would be called giant magnetoresistance.

Other structures besides multilayers show large values for magnetoresistance. One such structure is granules of cobalt in a matrix of silver. Another is stacked permalloy disks in a matrix of silver.

Sources:

Agnes Barthélémy, Albert Fert, Robert Morel and Laua Steren, "Giant steps with tiny magnets," Physics World, (November 1994), pp. 34-39.

Mark Howson, "Magnetism of thin films and multilayers," Contemporary Physics (1994) Vol 35, no 5, pp. 347-359.

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