# Tunnel magnetoresistance

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Tunnel magnetoresistance
Magnetic tunnel junction (schematic)

The Tunnel magnetoresistance (TMR) is a magnetoresistive effect that occurs in magnetic tunnel junctions (MTJs). This is a component consisting of two ferromagnets separated by a thin insulator. If the insulating layer is thin enough (typically a few nanometers), electrons can tunnel from one ferromagnet into the other. Since this process is forbidden in classical physics, the tunnel magnetoresistance is a strictly quantum mechanical phenomenon.

Magnetic tunnel junctions are manufactured in thin film technology. On an industrial scale the film deposition is done by magnetron sputter deposition; on a laboratory scale molecular beam epitaxy, pulsed laser deposition and electron beam physical vapor deposition are also utilized. The junctions are prepared by photolithography.

## Phenomenological description

The direction of the two magnetizations of the ferromagnetic films can be switched individually by an external magnetic field. If the magnetizations are in a parallel orientation it is more likely that electrons will tunnel through the insulating film than if they are in the oppositional (antiparallel) orientation. Consequently, such a junction can be switched between two states of electrical resistance, one with low and one with very high resistance.

## History

The effect was originally discovered in 1975 by M. Jullière (University of Rennes, France) in Fe/Ge-O/Co-junctions at 4.2 K. The relative change of resistance was around 14%, and did not attract much attention.[1] In 1991 T. Miyazaki (University Tohoku, Japan) found an effect of 2.7% at room temperature. Later, in 1994, Miyazaki found 18% in junctions of iron separated by an amorphous aluminum oxide insulator [2] and J. Moodera found 11.8% in junctions with electrodes of CoFe and Co.[3] The highest effects observed to date with aluminum oxide insulators are around 70% at room temperature.

Since the year 2000, tunnel barriers of crystalline magnesium oxide (MgO) are under development. In 2001 Butler and Mathon independently made the theoretical prediction that using iron as the ferromagnet and MgO as the insulator, the tunnel magnetoresistance can reach several thousand percent [4] .[5] The same year, Bowen et al. were the first to report experiments showing a significant TMR in a MgO based magnetic tunnel junction [Fe/MgO/FeCo(001)].[6] In 2004, Parkin and Yuasa were able to make Fe/MgO/Fe junctions that reach over 200% TMR at room temperature.[7][8] Today (2009) effects of up to 600% at room temperature and more than 1100% at 4.2 K are observed in junctions of CoFeB/MgO/CoFeB .[9]

## Applications

The read-heads of modern hard disk drives work on the basis of magnetic tunnel junctions. TMR, or more specifically the magnetic tunnel junction, is also the basis of MRAM, a new type of non-volatile memory. The 1st generation technologies relied on creating cross-point magnetic fields on each bit to write the data on it, although this approach has a scaling limit at around 90-130 nm.[10] There are two 2nd generation techniques currently being developed: Thermal Assisted Switching (TAS)[10] and Spin Torque Transfer (STT) on which several companies are working[11] Further, magnetic tunnel junctions are also used for sensing applications.

## Physical explanation

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

The relative resistance change—or effect amplitude—is defined as

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

where Rap is the electrical resistance in the anti-parallel state, whereas Rp is the resistance in the parallel state.

The TMR effect was explained by Jullière with the spin polarizations of the ferromagnetic electrodes. The spin polarization P is calculated from the spin dependent density of states (DOS) $\mathcal{D}$ at the Fermi energy:

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

The spin-up electrons are those with spin orientation parallel to the external magnetic field, whereas the spin-down electrons have anti-parallel alignment with the external field. The relative resistance change is now given by the spin polarizations of the two ferromagnets, P1 and P2:

$\mathrm{TMR} = \frac{2 P_1 P_2}{1 - P_1 P_2}$

If no voltage is applied to the junction, electrons tunnel in both directions with equal rates. With a bias voltage U, electrons tunnel preferentially to the positive electrode. With the assumption that spin is conserved during tunneling, the current can be described in a two-current model. The total current is split in two partial currents, one for the spin-up electrons and another for the spin-down electrons. These vary depending on the magnetic state of the junctions.

There are two possibilities to obtain a defined anti-parallel state. First, one can use ferromagnets with different coercivities (by using different materials or different film thicknesses). And second, one of the ferromagnets can be coupled with an antiferromagnet (exchange bias). In this case the magnetization of the uncoupled electrode remains "free".

The TMR decreases with both increasing temperature and increasing bias voltage. Both can be understood in principle by magnon excitations and interactions with magnons.

It is obvious that the TMR becomes infinite if P1 and P2 equal 1, i.e. if both electrodes have 100% spin polarization. In this case the magnetic tunnel junction becomes a switch, that switches magnetically between low resistance and infinite resistance. Materials that come into consideration for this are called ferromagnetic half-metals. Their conduction electrons are fully spin polarized. This property is theoretically predicted for a number of materials (e.g. CrO2, various Heusler alloys) but has not been experimentally confirmed to date.

## References

1. ^ * M. Julliere (1975). "Tunneling between ferromagnetic films". Phys. Lett. 54A: 225–226.  sciencedirect
2. ^ * T. Miyazaki and N. Tezuka (1995). "Giant magnetic tunneling effect in Fe/Al2O3/Fe junction". J. Magn. Magn. Mater. 139: L231–L234. Bibcode 1995JMMM..139L.231M. doi:10.1016/0304-8853(95)90001-2.  mit
3. ^ * J. S. Moodera et al. (1995). "Large Magnetoresistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions". Phys. Rev. Lett. 74 (16): 3273–3276. Bibcode 1995PhRvL..74.3273M. doi:10.1103/PhysRevLett.74.3273. PMID 10058155.  aps
4. ^ * W. H. Butler, X.-G. Zhang, T. C. Schulthess, and J. M. MacLaren (2001). "Spin-dependent tunneling conductance of Fe/MgO/Fe sandwiches". Phys. Rev. B 63 (5): 054416. Bibcode 2001PhRvB..63e4416B. doi:10.1103/PhysRevB.63.054416.  aps
5. ^ * J. Mathon and A. Umerski (2001). "Theory of tunneling magnetoresistance of an epitaxial Fe/MgO/Fe (001) junction". Phys. Rev. B 63 (22): 220403. Bibcode 2001PhRvB..63v0403M. doi:10.1103/PhysRevB.63.220403.  aps
6. ^ * M. Bowen et al. (2001). "Large magnetoresistance in Fe/MgO/FeCo(001) epitaxial tunnel junctions on GaAs(001)". Appl. Phys. Lett. 79 (11): 1655. Bibcode 2001ApPhL..79.1655B. doi:10.1063/1.1404125.  [1]
7. ^ * S Yuasa, T Nagahama, A Fukushima, Y Suzuki, and K Ando (2004). "Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions". Nat. Mat. 3 (12): 868–871. Bibcode 2004NatMa...3..868Y. doi:10.1038/nmat1257. PMID 15516927.  nature
8. ^ * S. S. P. Parkin et al. (2004). "Giant tunnelling magnetoresistance at room temperature with MgO (100) tunnel barriers". Nat. Mat. 3 (12): 862–867. Bibcode 2004NatMa...3..862P. doi:10.1038/nmat1256. PMID 15516928.  nature
9. ^ * S. Ikeda, J. Hayakawa, Y. Ashizawa, Y.M. Lee, K. Miura, H. Hasegawa, M. Tsunoda, F. Matsukura and H. Ohno (2008). "Tunnel magnetoresistance of 604% at 300 K by suppression of Ta diffusion in CoFeB/MgO/CoFeB pseudo-spin-valves annealed at high temperature". Appl. Phys. Lett. 93 (8): 082508. Bibcode 2008ApPhL..93h2508I. doi:10.1063/1.2976435.  aip
10. ^ a b The Emergence of Practical MRAM http://www.crocus-technology.com/pdf/BH%20GSA%20Article.pdf
11. ^ http://www.eetimes.com/news/latest/showArticle.jhtml?articleID=218000269

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