# Magnetic tunnel resistance

The magnetic tunnel resistance ( English tunnel magnetoresistance , TMR ) or TMR effect is a magnetoresistive effect that is used in magnetic tunnel contacts . The TMR effect cannot be explained with the help of classical physics and is therefore a purely quantum mechanical phenomenon.

## history

The effect was discovered in 1975 by M. Jullière (University of Rennes, France) in Fe / Ge - O / Co contacts at 4.2 K. Since the relative change in resistance at room temperature was less than 1%, the discovery initially received little attention. In 1991 Terunobu Miyazaki (University of Tohoku, Japan) found an effect of 2.7% at room temperature and in 1994 a “giant TMR effect” of 18% at room temperature (iron layers separated by an amorphous aluminum oxide insulator). The highest effects observed to date with aluminum oxide-based contacts were 70% at room temperature. With tunnel barriers made of magnesium oxide (MgO) up to 600% at room temperature and at 4.2 K even over 1100%.

## Physical explanation

Dual current model for parallel and anti-parallel alignment of the magnetizations

The relative change in resistance, or the effect amplitude, is defined as

${\ displaystyle {\ text {TMR}}: = {\ frac {R_ {ap} -R_ {p}} {R_ {p}}}}$

where describes the electrical resistance in the anti-parallel state and the electrical resistance in the parallel state. ${\ displaystyle R _ {\ mathrm {ap}}}$${\ displaystyle R _ {\ mathrm {p}}}$

Jullière attributed the TMR effect to the spin polarization of the individual ferromagnetic electrodes of a magnetic tunnel contact. The spin polarization arises from the spin-dependent density of states (Engl. Density of states , abbr .: DOS ) of electrons at the Fermi level : ${\ displaystyle P}$ ${\ displaystyle {\ mathcal {D}}}$

${\ displaystyle P = {\ frac {{\ mathcal {D}} _ {\ uparrow} (E _ {\ mathrm {F}}) - {\ mathcal {D}} _ {\ downarrow} (E _ {\ mathrm { F}})} {{\ mathcal {D}} _ {\ uparrow} (E _ {\ mathrm {F}}) + {\ mathcal {D}} _ {\ downarrow} (E _ {\ mathrm {F}} )}}}$

The spin-up electrons are those whose spin alignment is parallel to the magnetization, the spin-down electrons are those with an anti-parallel spin alignment. The relative change in resistance results from the spin polarizations of the two ferromagnets, and : ${\ displaystyle P_ {1}}$${\ displaystyle P_ {2}}$

${\ displaystyle {\ text {TMR}} = {\ frac {2P_ {1} P_ {2}} {1-P_ {1} P_ {2}}}}$

If no voltage is applied to the electrodes, electrons tunnel in both directions at the same rate. If a voltage is applied , electrons tunnel preferentially in the direction of the positive electrode. Assuming that the spin is retained during tunneling , the current can be described with a two-current model; the total current is broken down into a spin-up and a spin-down component. These vary in size depending on the magnetic state of the contact. ${\ displaystyle U}$

There are two possibilities to obtain a defined anti-parallel state. On the one hand, ferromagnetic electrodes with different coercive field strengths (due to different materials or different layer thicknesses) can be used. On the other hand, one of the two layers can be coupled with an antiferromagnet ( exchange bias ). In this case, the magnetization of the uncoupled electrode remains “free”.

The TMR decreases both with increasing temperature and with increasing voltage. In principle, both can be understood through magnon excitation or interaction with magnons.

Obviously, the TMR becomes infinite if and are equal to 1, or both electrodes are 100% spin-polarized. In this case the magnetic tunnel junction becomes a switch that can switch between finite (small) resistance and infinite resistance on a magnetic basis. Materials that come into question for this are referred to as ferromagnetic semi-metals . Their conduction electrons are completely spin polarized. Theoretically, this property has been predicted for a number of materials (e.g. CrO 2 , various Heusler alloys ), but has not yet been confirmed experimentally. ${\ displaystyle P_ {1}}$${\ displaystyle P_ {2}}$

Tunnel barriers made of MgO play a special role. If the interfaces between the ferromagnets and the MgO are epitaxial , i.e. the crystal lattices fit together without dislocation, additional filtering effects can occur. Electrons with a certain orbital symmetry are suppressed, while others can tunnel almost unhindered. The electrons, which can then pass almost unhindered, come from bands that have a particularly high polarization.