Magnetoresistance is the tendency of a material (often

ferromagnetic Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagne ...

) to change the value of its

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paral ...

in an externally-applied

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

. 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. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions),

giant magnetoresistance Giant magnetoresistance (GMR) is a quantum mechanics, quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Alb ...

(GMR),

tunnel magnetoresistance Tunnel magnetoresistance (TMR) is a magnetoresistance, magnetoresistive effect that occurs in a magnetic tunnel junction (MTJ), which is a component consisting of two ferromagnets separated by a thin Insulator (electrical), insulator. If the insula ...

(TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed. The first magnetoresistive effect was discovered in 1856 by William Thomson, better known as Lord Kelvin, but he was unable to lower the electrical resistance of anything by more than 5%. Today, systems including

semimetal A semimetal is a material with a small energy overlap between the bottom of the Electrical conduction, conduction Electronic band structure, band and the top of the valence band, but they do not overlap in momentum space. According to Band theory ...

s and concentric ring EMR structures are known. In these, a magnetic field can adjust the resistance by orders of magnitude. Since different mechanisms can alter the resistance, it is useful to separately consider situations where it depends on a magnetic field directly (e.g. geometric magnetoresistance and multiband magnetoresistance) and those where it does so indirectly through magnetization (e.g. AMR and TMR).

Discovery

William Thomson (Lord Kelvin) first discovered ordinary magnetoresistance in 1856. He experimented with pieces of iron and discovered that the resistance increases when the current is in the same direction as the magnetic force and decreases when the current is at 90° to the magnetic force. He then did the same experiment with nickel and found that it was affected in the same way but the magnitude of the effect was greater. This effect is referred to as anisotropic magnetoresistance (AMR). In 2007,

Albert Fert Albert Fert (; born 7 March 1938) is a French physicist and one of the discoverers of giant magnetoresistance which brought about a breakthrough in gigabyte hard disks. Currently, he is an emeritus professor at Paris-Saclay University in Orsay ...

and

Peter Grünberg Peter Andreas Grünberg (; 18 May 1939 – 7 April 2018) was a German physicist, and Nobel Prize in Physics laureate for his discovery with Albert Fert of giant magnetoresistance which brought about a breakthrough in gigabyte hard disk drive ...

were jointly awarded the Nobel Prize for the discovery of

Geometrical magnetoresistance

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 In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...

. Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911. In a simple model, supposing the response to the Lorentz force is the same as for an electric field, the carrier velocity is given by:

\mathbf = \mu \left( \mathbf + \mathbf \right),

where is the

carrier mobility In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term ca ...

. Solving for the velocity, we find:

semiconductor

A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

Anisotropic magnetoresistance (AMR)

are an example of AMR, a property of a material in which a dependence of electrical resistance on the angle between the direction of electric current and direction of magnetization is observed. The effect arises in most cases from the simultaneous action of magnetization and

spin–orbit interaction In quantum mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin– ...

(exceptions related to non-collinear magnetic order notwithstanding) and its detailed mechanism depends on the material. It can be for example due to a larger probability of s-d scattering of electrons in the direction of magnetization (which is controlled by the applied magnetic field). The net effect (in most materials) is that the electrical resistance has maximum value when the direction of current is parallel to the applied magnetic field. AMR of new materials is being investigated and magnitudes up to 50% have been observed in some uranium (but otherwise quite conventional) ferromagnetic compounds. Materials with extreme AMR have been identified driven by unconventional mechanisms such as a metal-insulator transition triggered by rotating the magnetic moments (while for some directions of magnetic moments, the system is semimetallic, for other directions a gap opens). 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

\rho(\varphi) = \rho_\perp + (\rho_\parallel - \rho_\perp) \cos^2 \varphi

where is the (longitudinal)

resistivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...

of the film and are the resistivities for and , respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed (somewhat confusingly) the planar Hall effect. In monocrystals, resistivity depends also on and individually. To compensate for the non-linear characteristics and inability to detect the polarity of a magnetic field, the following structure is used for sensors. It consists of stripes of aluminum or gold placed on a thin film of

permalloy Permalloy () is a nickel–iron magnetic alloy, with about 80% nickel and 20% iron content. Invented in 1914 by physicist Gustav Elmen at Bell Telephone Laboratories, it is notable for its very high magnetic permeability, which makes it useful ...

(a ferromagnetic material exhibiting the AMR effect) inclined at an angle of 45°. This structure forces the current not to flow along the “easy axes” of thin film, but at an angle of 45°. The dependence of resistance now has a permanent offset which is linear around the null point. Because of its appearance, this sensor type is called '

barber pole A barber's pole is a type of sign used by barbers to signify the place or shop where they perform their craft. The trade sign is, by a tradition dating back to the Middle Ages, a staff or pole with a helix of colored stripes (often red and w ...

'. The AMR effect is used in a wide array of sensors for measurement of Earth's magnetic field (electronic

compass A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with No ...

), for electric current measuring (by measuring the magnetic field created around the conductor), for traffic detection and for linear position and angle sensing. The biggest AMR sensor manufacturers are

Honeywell Honeywell International Inc. is an American publicly traded, multinational conglomerate corporation headquartered in Charlotte, North Carolina. It primarily operates in four areas of business: aerospace, building automation, industrial automa ...

NXP Semiconductors NXP Semiconductors N.V. is a Dutch semiconductor manufacturing and design company with headquarters in Eindhoven, Netherlands. It is the third largest European semiconductor company by market capitalization as of 2024. The company employs approx ...

STMicroelectronics STMicroelectronics Naamloze vennootschap, NV (commonly referred to as ST or STMicro) is a European multinational corporation, multinational semiconductor contract manufacturing and design company. It is the largest of such companies in Europe. ...

, an
Sensitec GmbH
As theoretical aspects, I. A. Campbell, A. Fert, and O. Jaoul () derived an expression of the AMR ratio for Ni-based alloys using the two-current model with s-s and s-d scattering processes, where 's' is a conduction electron, and 'd' is 3d states with the spin-orbit interaction. The AMR ratio is expressed as

\frac= \frac=\gamma (\alpha - 1),

with

\gamma=(3/4)(A/H)^2

and

\alpha=\rho_\downarrow/\rho_\uparrow

, where

A

H

, and

\rho_\sigma

are a spin-orbit coupling constant (so-called

\zeta

), an exchange field, and a resistivity for spin

\sigma

, respectively. In addition, recently, Satoshi Kokado et al. have obtained the general expression of the AMR ratio for 3d transition-metal ferromagnets by extending the theory to a more general one. The general expression can also be applied to half-metals.

Footnotes

References

{{Authority control 1856 introductions 1856 in science Magnetic ordering Spintronics Articles containing video clips

Discovery

Geometrical magnetoresistance

Anisotropic magnetoresistance (AMR)

See also

Footnotes

References