The Quantum Pontiff

The Nobel Prize in physics for 2007 has been awarded to Albert Fert and Peter Grünberg . First of all this is very cool, because (1) condensed matter physicist never get enough respect IMHO and (2) once again the physics Nobel goes to a piece of physics research whose exciting use is…information technology 🙂 Giant magnetoresistance forms the basis for magnetic field reading heads in our hard drives, albeit in a slightly different form than that of the original discovery work for which the Nobel prize was awarded.
The basic idea of the GMR effect can be explained by a very simplistic model. First you need to know what to compare to, i.e. what is ordinary magnetoresistance. Ordinary magnetoresistance is simply the change of electrical resistance to a current flowing through a material in response to an applied magnetic field. This effect was first discovered way back in 1856 by Lord Kelvin (you can see the paper here if you have the proper insitution subscription.) But the effect is rather small, with changes of only about five percent or so possible (the effect is usually also anisotropic, having a differing magnitude depending on what direction the current is in comparison to the magnet field.)
Okay, now with ordinary magnetoresistance down, onward and upward to giant magnetoresistance. Suppose you have two ferromagnetic metals separated by a nonmagnetic layer only a few atoms thick. Then, under the proper circumstance, there is an antiferromagnetic coupling between these two materials. This means that the two layers will allign their spin in different directions, call one spin up and one spin down. Well this is what will happen at zero external magnetic field. If you crank up a magnetic field, then this external field will overwelm this antiferromagnetic coupling and both layers will allign in the same direction.
Okay so what does this have to do with resistance? Well in a ferromagnetic metal like iron, the spin up and spin down have different resistances. Call the resistance of the spin up [tex]$R_{uparrow}$[/tex] and the resistance of spin down [tex]$R_{downarrow}$[/tex] where “up” and “down” are defined with respect to the magnetic moment of the ferromagnetic material your traveling through.
What does this simple picture mean for the setup we’ve described above? First consider the case where the external magnetic field is zero. Consider a current starting in one ferromagnetic layer, then going through the nonmagnetic spacing layer and coming out in the other ferromagnetic later. In this case, a spin up electron will start in one layer, experiencing a resistance of [tex]$R_{uparrow}$[/tex], it will then traverse the nonmagnetic layer and enter into the other ferromagnetic layer. But remember at zero field, this layer has a magnetic moment pointing in the opposite direction. So the spin up electron, spin up relative to the first layer, will now experience a resistance as if it was a spin down electron in the first layer, [tex]$R_{downarrow}$[/tex]. Reistances add in series, so the total resistance for this spin up electron will be [tex]$R_{uparrow}+R_{downarrow}[/tex]. A spin down electron in the first layer will similarly experience the same resistance (in the opposite order, but reistance commutes 🙂 ) [tex]$R_{uparrow}+R_{downarrow}[/tex]. A current coming from and leaving to a non-ferromagnetic layer can be thought of as splitting into the spin up or spin down currents and then experiencing these two resistances, now in series. Thus the total resistance when the external magnetic field is [tex]${1 over 2}(R_{uparrow}+R_{downarrow})[/tex].
Okay what about when there is a magnetic field. Well now a spin up always experiences the same resistance in both layers, so the resistance for this current will be [tex]$2R_{uparrow}$[/tex]. Similarly a spin down electron will experience the same resistance in both layers, [tex]$2R_{downarrow}$[/tex]. Combining these in parallel gives, [tex]$2 R_{uparrow} R_{downarrow} over (R_{uparrow}+R_{downarrow})$[/tex].
Okay so now we can figure out what the change in resistance is between there being an external magnetic field and there not being an external magnetic field. It is just the difference of the two resistances we just derived, i.e.
[tex]$Delta R={2 R_{uparrow} R_{downarrow} over (R_{uparrow}+R_{downarrow})}-{1 over 2}(R_{uparrow}+R_{downarrow})=-{1 over 2} {(R_{uparrow}-R_{downarrow})^2 over (R_{uparrow}+R_{downarrow})}$[/tex].
So now we see that the larger the difference between the two resistances, the larger the change in the resistance is, i.e. the larger giant magnetic resistance is. What has happened, of course, is that in the case of zero external magnetic field, any electron must traverse a bad region where its resistance is the higher of the two resistances, thus creating a high resistance. When an external magnetic field is applied, however, there are now pathways where the electron only travels through the low restistance pathway, thus lowering the resistance. This is the origin of giant magnetoresistance.
By the way, there are even larger magnetoresistances possible. Since “giant” has already been taken, these are called “colossal” magnetoresistance. While the effects for colossal magnetoresistance are even larger, these results haven’t made their way into technology because of the large magnetic fields needed to induce the effects. And, interstingly, last I remember there wasn’t a consensus on what causes colossal magnetoresistance (allthough some quick googling leads me to here for some very recent interesting work.)
Anyway, happy times for the Nobel prize winners and thanks to them for the discovery that led directly to my hard drive being so big! Err, I mean small. Okay: dense!