Giant Magnetoresistance Pdf

[Landerico Benson]

Giantmagnetoresistance (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 Grnberg 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 (MEMS) and other devices.[1] 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 a multilayer structure.[2][3]

where R(H) is the resistance of the sample in a magnetic field H, and R(0) corresponds to H = 0.[4] Alternative forms of this expression may use electrical resistivity instead of resistance, a different sign for δH,[5] and are sometimes normalized by R(H) rather than R(0).[6]

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.[7][8]

GMR was discovered in 1988 independently[9][10] by the groups of Albert Fert of the University of Paris-Sud, France, and Peter Grnberg of Forschungszentrum Jlich, Germany. The practical significance of this experimental discovery was recognized by the Nobel Prize in Physics awarded to Fert and Grnberg in 2007.[11]

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 δH has been known since the 1960s. By the late 1980s, the anisotropic magnetoresistance had been well explored,[12][13] but the corresponding value of δH did not exceed a few percent.[7] The enhancement of δH 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.[14]

Fert and Grnberg studied electrical resistance of structures incorporating ferromagnetic and non-ferromagnetic materials. In particular, Fert worked on multilayer films, and Grnberg in 1986 discovered the antiferromagnetic exchange interaction in Fe/Cr films.[14]

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).[10] The Grnberg work was performed on multilayers of Fe and Cr on (110) GaAs at room temperature.[9]

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.[10][15] TheGrnberg experiment[9] 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.[9][10] 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,[16] whereas Levy et al. used the quantum formalism.[17] 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.[18] Applications favor the CPP geometry[19] because it provides a greater magnetoresistance ratio (δH),[20] thus resulting in a greater device sensitivity.[21]

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.[7][22]

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.[7]

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.[7][24]

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.[7] The CPP geometry results in more than twice higher GMR, but is more difficult to realize in practice than the CIP configuration.[25][26]

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.[7]

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 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

The GMR phenomenon can be described using two spin-related conductivity channels corresponding to the conduction of electrons, for which the resistance is minimum or maximum. The relation between them is often defined in terms of the coefficient of the spin anisotropy β. This coefficient can be defined using the minimum and maximum of the specific electrical resistivity ρF for the spin-polarized current in the form

If scattering of charge carriers at the interface between the ferromagnetic and non-magnetic metal is small, and the direction of the electron spins persists long enough, it is convenient to consider a model in which the total resistance of the sample is a combination of the resistances of the magnetic and non-magnetic layers.

In this model, there are two conduction channels for electrons with various spin directions relative to the magnetization of the layers. Therefore, the equivalent circuit of the GMR structure consists of two parallel connections corresponding to each of the channels. In this case, the GMR can be expressed as

In 1993, Thierry Valet and Albert Fert presented a model for the giant magnetoresistance in the CPP geometry, based on the Boltzmann equations. In this model the chemical potential inside the magnetic layer is split into two functions, corresponding to electrons with spins parallel and antiparallel to the magnetization of the layer. If the non-magnetic layer is sufficiently thin then in the external field E0 the amendments to the electrochemical potential and the field inside the sample will take the form

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