Giant magnetoresistance (GMR) is a 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 Albert Fert and Peter Grünberg for the discovery of GMR.
The effect is observed as a significant change in the electrical resistance depending on whether the magnetization of adjacent ferromagnetic layers are in a parallel or an antiparallel alignment. The overall resistance is relatively low for parallel alignment and relatively high for antiparallel alignment. The magnetization direction can be controlled, for example, by applying an external magnetic field. The effect is based on the dependence of electron scattering on the spin orientation.
The main application of GMR is magnetic field sensors, which are used to read data in hard disk drives, biosensors, microelectromechanical systems (MEMS) and other devices. GMR multilayer structures are also used in magnetoresistive random-access memory (MRAM) as cells that store one bit of information.
In literature, the term giant magnetoresistance is sometimes confused with colossal magnetoresistance of ferromagnetic and antiferromagnetic semiconductors, which is not related to the multilayer structure.
Magnetoresistance is the dependence of the electrical resistance of a sample on the strength of an external magnetic field. Numerically, it is characterized by the value
δH = [R(H) – R(0)] / R(0)
where R(H) is the resistance of the sample in a magnetic field H, and R(0) corresponds to H = 0. Alternative forms of this expression may use electrical resistivity instead of resistance, a different sign for δH, and are sometimes normalized by R(H) rather than R(0).
The term "giant magnetoresistance" indicates that the value δH for multilayer structures significantly exceeds the anisotropic magnetoresistance, which has a typical value within a few percent.
Experiment and its interpretation
Fert and Grünberg studied electrical resistance of structures incorporating ferromagnetic and non-ferromagnetic materials. In particular, Fert worked on multilayer films, and Grünberg in 1986 discovered the antiferromagnetic exchange interaction in Fe/Cr films.
The GMR discovery work was carried out by the two groups on slightly different samples. The Fert group used (001)Fe/(001) Cr superlattices wherein the Fe and Cr layers were deposited in a high vacuum on a (001) GaAs substrate kept at 20 °C and the magnetoresistance measurements were taken at low temperature (typically 4.2 K). The Grünberg work was performed on multilayers of Fe and Cr on (110) GaAs at room temperature.
In Fe/Cr multilayers with 3-nm-thick iron layers, increasing the thickness of the non-magnetic Cr layers from 0.9 to 3 nm weakened the antiferromagnetic coupling between the Fe layers and reduced the demagnetization field, which also decreased when the sample was heated from 4.2 K to room temperature. Changing the thickness of the non-magnetic layers led to a significant reduction of the residual magnetization in the hysteresis loop. Electrical resistance changed by up to 50% with the external magnetic field at 4.2 K. Fert named the new effect giant magnetoresistance, to highlight its difference with the anisotropic magnetoresistance. The Grünberg experiment made the same discovery but the effect was less pronounced (3% compared to 50%) due to the samples being at room temperature rather than low temperature.
The discoverers suggested that the effect is based on spin-dependent scattering of electrons in the superlattice, particularly on the dependence of resistance of the layers on the relative orientations of magnetization and electron spins. The theory of GMR for different directions of the current was developed in the next few years. In 1989, Camley and Barnaś calculated the "current in plane" (CIP) geometry, where the current flows along the layers, in the classical approximation, whereas Levy et al. used the quantum formalism. The theory of the GMR for the current perpendicular to the layers (current perpendicular to the plane or CPP geometry), known as the Valet-Fert theory, was reported in 1993. Applications favor the CPP geometry because it provides a greater magnetoresistance ratio (δH), thus resulting in a greater device sensitivity.
In magnetically ordered materials, the electrical resistance is crucially affected by scattering of electrons on the magnetic sublattice of the crystal, which is formed by crystallographically equivalent atoms with nonzero magnetic moments. Scattering depends on the relative orientations of the electron spins and those magnetic moments: it is weakest when they are parallel and strongest when they are antiparallel; it is relatively strong in the paramagnetic state, in which the magnetic moments of the atoms have random orientations.
For good conductors such as gold or copper, the Fermi level lies within the sp band, and the d band is completely filled. In ferromagnets, the dependence of electron-atom scattering on the orientation of their magnetic moments is related to the filling of the band responsible for the magnetic properties of the metal, e.g., 3d band for iron, nickel or cobalt. The d band of ferromagnets is split, as it contains a different number of electrons with spins directed up and down. Therefore, the density of electronic states at the Fermi level is also different for spins pointing in opposite directions. The Fermi level for majority-spin electrons is located within the sp band, and their transport is similar in ferromagnets and non-magnetic metals. For minority-spin electrons the sp and d bands are hybridized, and the Fermi level lies within the d band. The hybridized spd band has a high density of states, which results in stronger scattering and thus shorter mean free path λ for minority-spin than majority-spin electrons. In cobalt-doped nickel, the ratio λ↑/λ↓ can reach 20.
According to the Drude theory, the conductivity is proportional to λ, which ranges from several to several tens of nanometers in thin metal films. Electrons "remember" the direction of spin within the so-called spin relaxation length (or spin diffusion length), which can significantly exceed the mean free path. Spin-dependent transport refers to the dependence of electrical conductivity on the spin direction of the charge carriers. In ferromagnets, it occurs due to electron transitions between the unsplit 4s and split 3d bands.
In some materials, the interaction between electrons and atoms is the weakest when their magnetic moments are antiparallel rather than parallel. A combination of both types of materials can result in a so-called inverse GMR effect.
CIP and CPP geometries
Electric current can be passed through magnetic superlattices in two ways. In the current in plane (CIP) geometry, the current flows along the layers, and the electrodes are located on one side of the structure. In the current perpendicular to plane (CPP) configuration, the current is passed perpendicular to the layers, and the electrodes are located on different sides of the superlattice. The CPP geometry results in more than twice higher GMR, but is more difficult to realize in practice than the CIP configuration.
Carrier transport through a magnetic superlattice
Magnetic ordering differs in superlattices with ferromagnetic and antiferromagnetic interaction between the layers. In the former case, the magnetization directions are the same in different ferromagnetic layers in the absence of applied magnetic field, whereas in the latter case, opposite directions alternate in the multilayer. Electrons traveling through the ferromagnetic superlattice interact with it much weaker when their spin directions are opposite to the magnetization of the lattice than when they are parallel to it. Such anisotropy is not observed for the antiferromagnetic superlattice; as a result, it scatters electrons stronger than the ferromagnetic superlattice and exhibits a higher electrical resistance.
Applications of the GMR effect require dynamic switching between the parallel and antiparallel magnetization of the layers in a superlattice. In first approximation, the energy density of the interaction between two ferromagnetic layers separated by a non-magnetic layer is proportional to the scalar product of their magnetizations:
w = -J(M1 . M2)
The coefficient J is an oscillatory function of the thickness of the non-magnetic layer ds; therefore J can change its magnitude and sign. If the ds value corresponds to the antiparallel state then an external field can switch the superlattice from the antiparallel state (high resistance) to the parallel state (low resistance). The total resistance of the structure can be written as
R = R0 + ∆Rsin2(θ/2)
where R0 is the resistance of ferromagnetic superlattice, ΔR is the GMR increment and θ is the angle between the magnetizations of adjacent layers.
Types of GMR
In multilayer GMR, two or more magnetic layers are separated by a very thin (about 1 nm) non-magnetic (insulating) layer. Ferrite, a form of iron, is a magnetic layer and chrome is an insulating layer. At certain thickness, the strength of magnetism between the layers becomes easy to measure and adjust. The strength of electrical current between the layers can change by up to 10%.
The GMR effect was first observed in stacks of 10 or more layers.
Spin valve GMR
In spin valve GMR, two magnetic layers are separated by a thin (~3 nm) non-magnetic (insulating) layer. It is possible to measure and adjust the strength of magnetism between these layers.
It is hoped that research into spinning electrons will improve spin valves.
Materials used in spin valves are copper and an alloy of nickel and iron.
Spin valve GMR is the most useful sort for hard drives and is tested carefully to meet industry standards.
Granular GMR is an effect found in copper containing grains of cobalt. It is not possible to control the strength of granular GMR in the same manner as Multilayer GMR.
One of the main applications of GMR materials is in magnetic field sensors, e.g., in hard disk drives and biosensors, as well as detectors of oscillations in MEMS. A typical GMR-based sensor consists of seven layers:
- Silicon substrate,
- Binder layer,
- Sensing (non-fixed) layer,
- Non-magnetic layer,
- Fixed layer,
- Antiferromagnetic (Pinning) layer,
- Protective layer.
The binder and protective layers are often made of tantalum, and a typical non-magnetic material is copper. In the sensing layer, magnetization can be reoriented by the external magnetic field; it is typically made of NiFe or cobalt alloys. FeMn or NiMn can be used for the antiferromagnetic layer. The fixed layer is made of a magnetic material such as cobalt. Such a sensor has an asymmetric hysteresis loop owing to the presence of the magnetically hard, fixed layer. Spin valves may exhibit anisotropic magnetoresistance, which leads to an asymmetry in the sensitivity curve.
Hard disk drives
In hard disk drives (HDDs), information is encoded using magnetic domains, and a change in the direction of their magnetization is associated with the logical level 1 while no change represents a logical 0. There are two recording methods: longitudinal and perpendicular.
In the longitudinal method, the magnetization is normal to the surface. A transition region (domain walls) is formed between domains, in which the magnetic field exits the material. If the domain wall is located at the interface of two north-pole domains then the field is directed outward, and for two south-pole domains it is directed inward. To read the direction of the magnetic field above the domain wall, the magnetization direction is fixed normal to the surface in the antiferromagnetic layer and parallel to the surface in the sensing layer. Changing the direction of the external magnetic field deflects the magnetization in the sensing layer. When the field tends to align the magnetizations in the sensing and fixed layers, the electrical resistance of the sensor decreases, and vice versa.
A cell of magnetoresistive random-access memory (MRAM) has a structure similar to the spin-valve sensor. The value of the stored bits can be encoded via the magnetization direction in the sensor layer; it is read by measuring the resistance of the structure. The advantages of this technology are independence of power supply (the information is preserved when the power is switched off owing to the potential barrier for reorienting the magnetization), low power consumption and high speed.
In a typical GMR-based storage unit, a CIP structure is located between two wires oriented perpendicular to each other. These conductors are called lines of rows and columns. Pulses of electric current passing through the lines generate a vortex magnetic field, which affects the GMR structure. The field lines have ellipsoid shapes, and the field direction (clockwise or counterclockwise) is determined by the direction of the current in the line. In the GMR structure, the magnetization is oriented along the line.
The direction of the field produced by the line of the column is almost parallel to the magnetic moments, and it can not reorient them. Line of the row is perpendicular, and regardless of the magnitude of the field can rotate the magnetization by only 90 °. With the simultaneous passage of pulses along the row and column lines, of the total magnetic field at the location of the GMR structure will be directed at an acute angle with respect to one point and an obtuse to others. If the value of the field exceeds some critical value, the latter changes its direction.
There are several storage and reading methods for the described cell. In one method, the information is stored in the sensing layer; it is read via resistance measurement and is erased upon reading. In another scheme, the information is kept in the fixed layer, which requires higher recording currents compared to reading currents.
Tunnel magnetoresistance (TMR) is an extension of spin-valve GMR, in which the electrons travel with their spins oriented perpendicularly to the layers across a thin insulating tunnel barrier (replacing the non-ferromagnetic spacer). This allows to achieve a larger impedance, a larger magnetoresistance value (~10x at room temperature) and a negligible temperature dependence. TMR has now replaced GMR in MRAMs and disk drives, in particular for high area densities and perpendicular recording.Giant Magnetoresistance of (001)Fe (001)Cr Magnetic Superlattices
American Physical Society. Available in: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.61.2472. Access in: 28/10/2018.
Wikipedia. Available in: https://en.wikipedia.org/wiki/Giant_magnetoresistance. Access in: 28/10/2018.
Wikipedia. Available in: https://simple.wikipedia.org/wiki/Giant_magnetoresistance. Access in: 28/10/2018.