Magnetoresistance · BPhO 2017 #2
Physics · electromagnetism
Problem
Magnetic properties of electrons are intrinsically related to their spin. In ferromagnetic materials, unpaired electron spins line up with each other within regions called domains. Within domains the magnetic field is therefore intense, though domains will generally be randomly orientated with respect to one another so that a bulk sample will usually be unmagnetised. However, an externally applied magnetic field can cause the magnetic domains to line up with each other; the material is said to be magnetised. Electrons, although point particles, behave as if they were spinning and act like tiny magnets. Electrons in a ferromagnet whose spins are oriented in the direction of (parallel), or opposite to (antiparallel), the internal magnetisation carry independent currents, leading to the material behaving as if it has different resistivities ρₚ and ρₐ for each of the two current components. Two ferromagnetic layers with identical dimensions (length ℓ, cross-sectional area A) but opposite magnetisation are placed next to each other in parallel with a cell of e.m.f. ε and internal resistance r. The resistance of the rest of the external circuit is modelled by a resistance R in series with the ferromagnetic layers. (a) Draw a diagram of the circuit described above. (b) Find the total resistance of the circuit. (c) An external magnetic field is now applied to the ferromagnetic layers causing their magnetisation to line up. Draw a new circuit diagram and find the total resistance in this case. (d) The current component parallel flows much more easily than that antiparallel, meaning that ρₚ ≪ ρₐ. (i) Find an expression for the change in current between the two situations before and after the external field is applied. (ii) For fixed resistances (and fixed resistivities ρₚ ≪ ρₐ), under what conditions is the change in current maximised? (e) The effect described above is known as magnetoresistance, and can be employed in the construction of hard disk read/write heads. Suggest how one of these might work and how the result of (d)(ii) is relevant. What other considerations are there?Intuitive explanation
The key to this problem is understanding how two ferromagnetic layers with opposite magnetisation act as parallel resistors with different resistivities. When spins are misaligned (antiparallel to each other), electrons experience both and pathways in parallel; when an external field aligns them, the resistance changes dramatically. The insight is that the total resistance depends on how these two resistivity components combine, and since , the parallel combination is dominated by the low-resistance path—so alignment causes a significant drop in total resistance.
Intuitive explanation
The key to this problem is understanding how two ferromagnetic layers with opposite magnetisation act as parallel resistors with different resistivities. When spins are misaligned (antiparallel to each other), electrons experience both and pathways in parallel; when an external field aligns them, the resistance changes dramatically. The insight is that the total resistance depends on how these two resistivity components combine, and since , the parallel combination is dominated by the low-resistance path—so alignment causes a significant drop in total resistance.