# Anisotropic magnetoresistive effect

The anisotropic magnetoresistive effect , or AMR effect for short , is the longest known magnetoresistive effect and was discovered in 1857 by William Thomson, 1st Baron Kelvin . It is based on anisotropic (spatial direction dependent) scattering in ferromagnetic metals . This means that it occurs in materials that have their own magnetization .

## Observations

The effect can be observed particularly well in a thin layer (approx. 20 nm) made of permalloy , an alloy of nickel (81%) and iron (19%). It can be seen that the electrical resistance of the layer depends on the external magnetic field . Only magnetic field components in the layer plane have a noticeable influence on the resistance. This is greatest when the external magnetic field is directed in or against the direction of the current. The resistance is lowest when the external magnetic field is directed perpendicular to the direction of the current in the layer plane.

The effect is attributed to a distortion of the atomic orbitals due to the spin alignment in the magnetic field. This changes their scattering cross-section for conduction electrons and thus the resistance.

## Description of the effect

A sample of a ferromagnetic material cuboid is considered for which the following applies: length ≫ width ≫ thickness. The current density vector under consideration and the magnetic field vector lie in the plane that is spanned by length and width.

A magnetic field acting on the material from the outside rotates the internal magnetization of the domains of the material in such a way that, with increasing magnetic field strength, these are increasingly oriented towards the external field. If the field strength of the external field is strong enough, the orientation of the internal magnetization and the external field are the same.

If the current density vector of the current flowing through the material and the magnetic field vector of the internal magnetization are perpendicular to one another, the resistance of the material is minimal, if they are parallel to one another, the resistance is maximal.

The resulting resistance is:, where${\ displaystyle R = R _ {\ parallel} - \ Delta R _ {\ mathrm {max}} \ cdot \ sin ^ {2} (\ Theta _ {JM})}$${\ displaystyle \ Delta R _ {\ mathrm {max}} = R _ {\ parallel} -R _ {\ perp}}$

${\ displaystyle R _ {\ parallel}}$is the resistance if both vectors are parallel, is the resistance if both vectors are perpendicular to each other. ${\ displaystyle R _ {\ perp}}$

As can be seen from the equation, the resistance can be used to determine the magnitude of the angle, but not its sign . Possible values ​​are in the range between and . ${\ displaystyle \ Theta _ {JM} = - 90 ^ {\ circ}}$${\ displaystyle \ Theta _ {JM} = + 90 ^ {\ circ}}$

To solve this problem, the so-called barber pole arrangement has been developed for sensors (named after the well-known rotating decorative cylinders with a continuous horizontal stripe). Conductor strips made of gold or aluminum are applied to the magnetic material (e.g. Permalloy) at an angle of 45 ° . With their help, the angle can be precisely determined in the interval between −45 ° and + 45 °. Another advantage of the Barberpole arrangement is that it has an almost linear behavior for small changes in angle around 0 °.

## Commercial use

AMR is mainly used for read heads (since 1990) in hard disk drives , but also for MRAM chips (from English magneto-resistive random access memory ) for space travel. In favorable cases, the effect size ∆R / R is between 3 and 4%; it is therefore too small for the mass production of inexpensive MRAM memories.

AMR sensors are used in the automotive industry as well as in industrial measurement technology and entertainment electronics. The measuring tasks range from field measurements and compass applications to length and angle measurements to current sensors. AMR sensors are increasingly replacing field plates because they can be used at higher operating temperatures and have better linearity.

In medicine, the effect of magnetic marker monitoring is used to determine motility and transit time in the intestine.

With modern sensors made of narrow strips of permalloy layers, which are switched in the form of a Wheatstone bridge , magnetic fields of the order of 0.01  A / m can be detected.

## Individual evidence

1. Magnetic sensors based on the AMR effect doi : 10.1524 / teme.2001.68.6.269