Tunnel magnetoresistance
Encyclopedia
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), electron
s 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
.
s 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 electron
s 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.
/Ge
-O
/Co
-junctions at 4.2 K. The relative change of resistance was around 14%, and did not attract much attention. 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 and J. Moodera found 11.8% in junctions with electrodes of CoFe and Co. 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
. 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)].
In 2004, Parkin and Yuasa were able to make Fe/MgO/Fe junctions that reach over 200% TMR at room temperature. 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
.
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. There are two 2nd generation techniques currently being developed: Thermal Assisted Switching
(TAS) and Spin Torque Transfer
(STT) on which several companies are working Further, magnetic tunnel junctions are also used for sensing applications.
where
is the electrical resistance in the anti-parallel state, whereas 
is the resistance in the parallel state.
The TMR effect was explained by Jullière with the spin polarization
s of the ferromagnetic electrodes. The spin polarization
is calculated from the spin
dependent density of states
(DOS)
at the Fermi energy
:
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,
and 
:
If no voltage
is applied to the junction, electrons tunnel in both directions with equal rates. With a bias voltage
, 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
and 
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 alloy
s) but has not been experimentally confirmed to date.
Magnetoresistance
Magnetoresistance is the property of a material to change the value of its electrical resistance when an external magnetic field is applied to it. The effect was first discovered by William Thomson in 1856, but he was unable to lower the electrical resistance of anything by more than 5%. This...
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), electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s can tunnel from one ferromagnet into the other. Since this process is forbidden in classical physics, the tunnel magnetoresistance is a strictly quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
phenomenon.
Magnetic tunnel junctions are manufactured in thin film
Thin film
A thin film is a layer of material ranging from fractions of a nanometer to several micrometers in thickness. Electronic semiconductor devices and optical coatings are the main applications benefiting from thin film construction....
technology. On an industrial scale the film deposition is done by magnetron sputter deposition
Sputter deposition
Sputter deposition is a physical vapor deposition method of depositing thin films by sputtering, that is ejecting, material from a "target," that is source, which then deposits onto a "substrate," such as a silicon wafer...
; on a laboratory scale molecular beam epitaxy
Molecular beam epitaxy
Molecular beam epitaxy is one of several methods of depositing single crystals. It was invented in the late 1960s at Bell Telephone Laboratories by J. R. Arthur and Alfred Y. Cho.-Method:...
, pulsed laser deposition
Pulsed laser deposition
Pulsed laser deposition is a thin film deposition technique where a high power pulsed laser beam is focused inside a vacuum chamber to strike a target of the material that is to be deposited...
and electron beam physical vapor deposition
Electron Beam Physical Vapor Deposition
Electron Beam Physical Vapor Deposition or EBPVD is a form of physical vapor deposition in which a target anode is bombarded with an electron beam given off by a charged tungsten filament under high vacuum. The electron beam causes atoms from the target to transform into the gaseous phase...
are also utilized. The junctions are prepared by photolithography
Photolithography
Photolithography is a process used in microfabrication to selectively remove parts of a thin film or the bulk of a substrate. It uses light to transfer a geometric pattern from a photomask to a light-sensitive chemical "photoresist", or simply "resist," on the substrate...
.
Phenomenological description
The direction of the two magnetizationMagnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...
s of the ferromagnetic films can be switched individually by an external magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. If the magnetizations are in a parallel orientation it is more likely that electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s 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
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, 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 FeIron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
/Ge
Germanium
Germanium is a chemical element with the symbol Ge and atomic number 32. It is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors tin and silicon. The isolated element is a semiconductor, with an appearance most similar to elemental silicon....
-O
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
/Co
Cobalt
Cobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....
-junctions at 4.2 K. The relative change of resistance was around 14%, and did not attract much attention. 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 and J. Moodera found 11.8% in junctions with electrodes of CoFe and Co. 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
Magnesium oxide
Magnesium oxide , or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium . It has an empirical formula of and consists of a lattice of Mg2+ ions and O2– ions held together by ionic bonds...
(MgO) are under development. In 2001 Butler and Mathon independently made the theoretical prediction that using iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
as the ferromagnet and MgO
MGO
MGO may refer to:*Magnesium oxide, the chemical formula MgO*Methylglyoxal, abbreviated MGO*Metal Gear Online, a PlayStation 3 online multiplayer spin-off of the Metal Gear video game series...
as the insulator, the tunnel magnetoresistance can reach several thousand percent
. 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)].
In 2004, Parkin and Yuasa were able to make Fe/MgO/Fe junctions that reach over 200% TMR at room temperature. 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
.
Applications
The read-headsDisk read-and-write head
Disk read/write heads are the small parts of a disk drive, that move above the disk platter and transform platter's magnetic field into electrical current or vice versa – transform electrical current into magnetic field...
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
Non-volatile memory
Non-volatile memory, nonvolatile memory, NVM or non-volatile storage, in the most basic sense, is computer memory that can retain the stored information even when not powered. Examples of non-volatile memory include read-only memory, flash memory, ferroelectric RAM, most types of magnetic computer...
. 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. There are two 2nd generation techniques currently being developed: Thermal Assisted Switching
Thermal Assisted Switching
Thermal Assisted Switching, or TAS, is one of the new 2nd generation approaches to MRAM currently being developed. A few different designs have been proposed, but all rely on the idea of reducing the required switching fields by heating...
(TAS) and Spin Torque Transfer
Spin Torque Transfer
Spin-transfer torque is an effect in which the orientation of a magnetic layer in a tunnel magnetoresistance or spin valve can be modified using a spin-polarized current....
(STT) on which several companies are working Further, magnetic tunnel junctions are also used for sensing applications.
Physical explanation
The relative resistance change—or effect amplitude—is defined aswhere
is the electrical resistance in the anti-parallel state, whereas is the resistance in the parallel state.The TMR effect was explained by Jullière with the spin polarization
Spin polarization
Spin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in ferromagnetic metals, such as iron, giving rise to...
s of the ferromagnetic electrodes. The spin polarization
is calculated from the spinSpin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
dependent density of states
Density of states
In solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...
(DOS)
at the Fermi energyFermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
:
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,
and :If no voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
is applied to the junction, electrons tunnel in both directions with equal rates. With a bias voltage
, electrons tunnel preferentially to the positive electrode. With the assumption that spin is conservedConservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
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
Coercivity
In materials science, the coercivity, also called the coercive field or coercive force, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation...
(by using different materials or different film thicknesses). And second, one of the ferromagnets can be coupled with an antiferromagnet (exchange bias
Exchange bias
Exchange bias or exchange anisotropy occurs in bilayers of magnetic materials where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the soft magnetization curve of a ferromagnetic film...
). 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
Magnon
A magnon is a collective excitation of the electrons' spin structure in a crystal lattice. In contrast, a phonon is a collective excitation of the crystal lattice atoms or ions. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. As a...
excitations and interactions with magnons.
It is obvious that the TMR becomes infinite if
and 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 alloyHeusler alloy
A Heusler alloy is a ferromagnetic metal alloy based on a Heusler phase. Heusler phases are intermetallics with particular composition and face-centered cubic crystal structure. They are ferromagnetic—even though the constituting elements are not—as a result of the double-exchange mechanism between...
s) but has not been experimentally confirmed to date.
See also
- Quantum tunnellingQuantum tunnellingQuantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...
- MagnetoresistanceMagnetoresistanceMagnetoresistance is the property of a material to change the value of its electrical resistance when an external magnetic field is applied to it. The effect was first discovered by William Thomson in 1856, but he was unable to lower the electrical resistance of anything by more than 5%. This...