Electricity and Magnets are a Heady Mix

The Hall Effect is a very common thing. If you have ever done high school level physics you will have been taught the effects of the Hall Effect. If you remember sitting in exams with three fingers pointed out in orthogonal (at right angles to each other) directions, you will know what this means. If not, read on...

When a charged particle such as an electron travels through a magnetic field, it experiences a force. What this means, is that if you run a wire between the poles of a magnet, and then switch the current on, the wire will move out of the magnetic field. This is illustrated by the Left Hand Motor Rule¹, where your index finger indicates the direction of current flow and your second finger, sticking out at right angles from the first, indicates the direction of the magnetic field. If you then stick your thumb straight up, this is the direction that the wire will move. This is the basis on which electric motors work, just with a lot more wires all trying to move out of the magnetic field.

So, what happens if the wire can't move? The force still exists, so the electrons within the wire move to one side. Hence, if there are more electrons at one side than the other, a potential difference (voltage) can be measured. Thus, if you measure the current running through the wire, then with this new voltage you can calculate a value similar to resistance, just as you would normally for a resistor (V=IRh where V = Voltage, I = Current, Rh = Hall Coefficent, measured in Ohms just like resistance). Also, as you increase the magnetic field, more and more electrons cram up against the one side of the wire, making the voltage (and hence this new value) larger. This is the Hall Effect, named after EH Hall who discovered it in the 19th Century. It makes for a nice straight line graph (which always keeps physicists happy) of R against B (the magnetic field and is most useful for calculating the number of electrons in a wire.

Big Brains and Even Bigger Magnets

You can see this effect in any conductor (school railings, coat hangers, people) but it is best observed at very cold temperatures of the order of tens of Kelvins. The effect is also easier to detect with pseudo two dimensional semiconductors. These are materials, such as silicon, which modern industry uses to make all those microchips in your PC, TV and washing machine. When carefully made and cooled down to single Kelvin, or even milli Kelvin temperatures, the electrons that travel through these samples encounter very little electrical and thermal noise². If a very large magnetic field is then applied much more interesting effects can be seen.

Basically, the electrons split up into separate energy levels under the effect of the magnetic field (just like the energy levels in atoms that lead to light) and you get what is called the Quantum Hall Effect. This shows up as plateaux (flat bits) in the straight line graph of the basic Hall Effect at a magnetic field of one Tesla and higher. It should be born in mind that the average magnetic field of the Earth is 0.00005 Tesla so you don't need to worry about this happening to your television and it's best not to get too close to these experiments with your bank cards.

Now, this phenomenon would be only mildly interesting to beardy scientists wearing sandals if it were not for one very interesting point. These plateaux always appear at the same value of resistance. To a value so exact it makes their toes curl. No matter what temperature or in what type of metal or semi-conductor you measure it in. This means you can take any sample and, without any calibration or checking whatsoever state that plateau number two has a resistance of 12,949 Ohms (to the nearest whole Ohm) and plateau number one has a resistance of 25,938 Ohms. Hence, from this you can then calibrate all those instruments you have had lying about the lab for years, and suddenly all your scientific results become much more accurate, which Physicists like.

Because this was such an astounding discovery Klaus von Klitzing, the very clever man who first observed this effect, won the Nobel Prize in 1985.

If you then take the magnetic field even higher, and use an even cleaner sample you will eventually observe the Fractional Quantum Hall Effect (Tsui, Stormer, Laughlin - Nobel Prize 1998).

But what Is it Good for?

The Hall Effect can be put to use in a number of ways. For instance, if you wish to measure a magnetic field you can use a Hall probe. This is simply a device that passes a constant current through a small probe, and measures the voltage. If a magnetic field is present, then a Hall coefficient will exist, and a simple calculation will tell you the magnetic field that is causing the effect. This is particularly useful in modern solid state physics. Here you may want to study a tiny magnetic particle, say, part of a computer hard disk. It is now possible to build Hall probes that are only nanometres (0.000000001 of a metre) in size. This allows very accurate study of your magnetic particle, which in turn leads to the sort of discoveries that give you the huge storage spaces your PCs currently have.