Giant magnetoresistance

Giant magnetoresistance 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, which also sets the foundation for the study of spintronics.
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 spin orientation.
The main application of GMR is in magnetic field sensors, which are used to read data in hard disk drives, biosensors, microelectromechanical systems and other devices. GMR multilayer structures are also used in magnetoresistive random-access memory 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 a multilayer structure.
File:GMR.svg|thumb|340px|The founding results of Albert Fert and Peter Grünberg : change in the resistance of Fe/Cr superlattices at 4.2 K in external magnetic field H. The current and magnetic field were parallel to the miller indices| axis. The arrow to the right shows maximum resistance change. H_s is saturation field.

Formulation

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
where R is the resistance of the sample in a magnetic field H, and R corresponds to H = 0. Alternative forms of this expression may use electrical resistivity instead of resistance, a different sign for δ_H, and are sometimes normalized by R rather than R.
The term "giant magnetoresistance" indicates that the value δ_H for multilayer structures significantly exceeds the anisotropic magnetoresistance, which has a typical value within a few percent.

History

GMR was discovered in 1988 independently by the groups of Albert Fert of the University of Paris-Sud, France, and Peter Grünberg of Forschungszentrum Jülich, Germany. The practical significance of this experimental discovery was recognized by the Nobel Prize in Physics awarded to Fert and Grünberg in 2007.

Early steps

The first mathematical model describing the effect of magnetization on the mobility of charge carriers in solids, related to the spin of those carriers, was reported in 1936. Experimental evidence of the potential enhancement of δ_H has been known since the 1960s. By the late 1980s, the anisotropic magnetoresistance had been well explored, but the corresponding value of δ_H did not exceed a few percent. The enhancement of δ_H became possible with the advent of sample preparation techniques such as molecular beam epitaxy, which allows manufacturing multilayer thin films with a thickness of several nanometers.

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 Fe/ Cr superlattices wherein the Fe and Cr layers were deposited in a high vacuum on a GaAs substrate kept at 20 °C and the magnetoresistance measurements were taken at low temperature. The Grünberg work was performed on multilayers of Fe and Cr on 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 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" 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, known as the Valet-Fert theory, was reported in 1993. Applications favor the CPP geometry because it provides a greater magnetoresistance ratio, thus resulting in a greater device sensitivity.

Theory

Fundamentals

Spin-dependent scattering

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, 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 geometry, the current flows along the layers, and the electrodes are located on one side of the structure. In the current perpendicular to plane 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:
The coefficient J is an oscillatory function of the thickness of the non-magnetic layer d_s; therefore J can change its magnitude and sign. If the d_s value corresponds to the antiparallel state then an external field can switch the superlattice from the antiparallel state to the parallel state. The total resistance of the structure can be written as
where R₀ is the resistance of ferromagnetic superlattice, ΔR is the GMR increment and θ is the angle between the magnetizations of adjacent layers.