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Magnetoresistance is the tendency of a material (preferably ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance: some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov de Haas oscillations, or the common positive magnetoresistance in metals.[1] Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets[2] or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions), giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed.

The first magnetoresistive effect was discovered by William Thomson, better known as Lord Kelvin, in 1856, but he was unable to lower the electrical resistance of anything by more than 5%. Nowadays, systems, e.g. semimetals[3] or concentric ring EMR structures, are known where a magnetic field can change resistance by orders of magnitude. As the resistance may depend on magnetic field through various mechanisms, it is useful to separately consider situations where it depends on magnetic field directly, e.g. geometric magnetoresistance and multiband magnetoresistance, and those where it does so indirectly through magnetisation, e.g. AMR, TMR.



Animation about the magnetoresistance discovery Graphs
Corbino disc. With the magnetic field turned off, a radial current flows in the conducting annulus due to the battery connected between the (infinite) conductivity rims. When a magnetic field along the axis is turned on,(B points directly out of the page) the Lorentz force drives a circular component of current, and the resistance between the inner and outer rims goes up. This increase in resistance due to the magnetic field is called magnetoresistance.

In 2007, Albert Fert and Peter Grünberg were jointly awarded the Nobel Prize for the discovery of Giant Magnetoresistance.[5]

Geometrical magnetoresistance[edit]

An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a Corbino disc (see Figure). It consists of a conducting annulus with perfectly conducting rims. Without a magnetic field, the battery drives a radial current between the rims. When a magnetic field perpendicular to the plane of the annulus is applied, (either into or out of the page) a circular component of current flows as well, due to Lorentz force. Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911.[6]


where μ is the carrier mobility. Solving for the velocity, we find:

where the effective reduction in mobility due to the B-field (for motion perpendicular to this field) is apparent. Electric current (proportional to the radial component of velocity) will decrease with increasing magnetic field and hence the resistance of the device will increase. Critically, this magnetoresistive scenario depends sensitively on the device geometry and current lines and it does not rely on magnetic materials.


Anisotropic magnetoresistance (AMR)[edit]



In polycrystalline ferromagnetic materials, the AMR can only depend on the angle between the magnetization and current direction and (as long as the resistivity of the material can be described by a rank-two tensor), it must follow[9]

where is the (longitudinal) resistivity of the film and are the resistivities for and , respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed (somewhat confusingly[1]) the planar Hall effect. In monocrystals, resistivity depends also on individually.



See also[edit]


  • 1. The (ordinary) Hall effect changes sign upon magnetic field reversal and it is an orbital effect (unrelated to spin) due to the Lorentz force. Transversal AMR (planar Hall effect[10]) does not change sign and it is caused by spin-orbit interaction.


  1. ^ A.B. Pippard: Magnetoresistance in Metals, Cambridge University Press (1989)
  2. ^ Coleman, R.V.; Isin, A. (1966), "Magnetoresistance in Iron Single Crystals", Journal of Applied Physics, 37 (3): 1028–1029, Bibcode:1966JAP....37.1028C, doi:10.1063/1.1708320
  3. ^ "Unstoppable Magnetoresistance".
  4. ^ a b Thomson, W. (18 June 1857), "On the Electro-Dynamic Qualities of Metals:—Effects of Magnetization on the Electric Conductivity of Nickel and of Iron", Proc. Royal Soc. Lond., 8: 546–550, doi:10.1098/rspl.1856.0144
  5. ^ The Nobel Prize in Physics 2007, Nobel Media AB, 9 Oct 2007, retrieved 25 Jun 2014
  6. ^ G Giuliani (2008). "A general law for electromagnetic induction". EPS. 81 (6): 60002. arXiv:1502.00502. Bibcode:2008EL.....8160002G. doi:10.1209/0295-5075/81/60002.
  7. ^ McGuire, T.; Potter, R. (1975). "Anisotropic magnetoresistance in ferromagnetic 3d alloys" (PDF). IEEE Transactions on Magnetics. 11 (4): 1018–1038. Bibcode:1975ITM....11.1018M. doi:10.1109/TMAG.1975.1058782.
  8. ^ Wiśniewski, P. (2007). "Giant anisotropic magnetoresistance and magnetothermopower in cubic 3:4 uranium pnictides". Applied Physics Letters. 90 (19): 192106. Bibcode:2007ApPhL..90s2106W. doi:10.1063/1.2737904.
  9. ^ De Ranieri, E.; Rushforth, A. W.; Výborný, K.; Rana, U.; Ahmed, E.; Campion, R. P.; Foxon, C. T.; Gallagher, B. L.; Irvine, A. C.; Wunderlich, J.; Jungwirth, T. (10 June 2008), "Lithographically and electrically controlled strain effects on anisotropic magnetoresistance in (Ga,Mn)As" (PDF), New J. Phys., 10 (6): 065003, arXiv:0802.3344, Bibcode:2008NJPh...10f5003D, doi:10.1088/1367-2630/10/6/065003
  10. ^ Tang, H. X.; Kawakami, R. K.; Awschalom, D. D.; Roukes, M. L. (March 2003), "Giant Planar Hall Effect in Epitaxial (Ga,Mn)As Devices" (PDF), Phys. Rev. Lett., 90 (10): 107201, arXiv:cond-mat/0210118, Bibcode:2003PhRvL..90j7201T, doi:10.1103/PhysRevLett.90.107201