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Giant magnetoresistance

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   Albert Fert (2011), Scholarpedia, 6(2):6982. [3]doi:10.4249/scholarpedia.6982
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   Curator: [7]Albert Fert
   Contributors:


   0.50 -

   [8]WikiSysop Real Name

   [9]Benjamin Bronner

   [10]Riccardo Guida

   [11]Eugene M. Izhikevich

   [12]Marcelo Rozenberg

   [13]Nicolau Leal Werneck

   [14]Gabriel Kotliar
     * [15]Prof. Albert Fert, Unite Mixte de Physique CNRS/Thales, University
       Paris-Sud 11, France

   The Giant Magnetoresistance (GMR) is the large change in the electrical
   resistance which is induced by the application of a magnetic field to thin films
   composed of alternating ferromagnetic and nonmagnetic layers. This change in
   resistance, in general a reduction, is related to the field-induced alignment of
   the magnetizations of the magnetic layers. In the first experiments, the film was
   composed of layers of Fe (ferromagnetic) and Cr (nonmagnetic) with typical
   thicknesses of a few nm and the current was in the plane of the film. GMR effects
   can also be obtained with the current perpendicular to the layers. The origin of
   the GMR is the dependence of the electrical conduction in ferromagnetic materials
   on the spin state of the carriers (electrons).

Contents

     * [16]1 Discovery and first experiments
     * [17]2 Spin dependent conduction in a ferromagnetic conductor
     * [18]3 Physics and theoretical models of the GMR with Current In the layer
       Planes (CIP-GMR)
     * [19]4 Spin-valves, applications
     * [20]5 GMR with the Current Perpendicular to the layer Planes (CPP-GMR), spin
       accumulation effects
     * [21]6 Concluding remarks
     * [22]7 References
     * [23]8 See also

Discovery and first experiments

   The GMR was discovered in 1988 by the team of Albert Fert (Baibich 1988) in
   France on Fe/Cr(001) multilayers and, independently, by Peter Grünberg (Binash
   1989) and coworkers in Germany on Fe/Cr/Fe(001) trilayers, in both cases on
   samples grown by Molecular Beam Epitaxy (MBE). We show in Figure [24]1 some of
   the first experimental curves. The GMR can be described as the reduction of the
   resistance of the magnetic multilayers due to the alignment of the magnetizations
   of the Fe layers by the applied magnetic field.

   The discovery of 1988 had been preceded in 1986 by Grünberg's Brillouin
   scattering experiments (Grünberg 1986) showing that two layers of Fe separated by
   an ultra-thin (« 1 nm) layer of Cr were antiferromagnetically coupled.
   Consequently, in zero applied field, the magnetizations of the Fe layers are
   antiparallel (in opposite direction) but can be aligned by an applied field. The
   field-induced decrease of the resistance in the experiments of the discovery of
   the GMR (Baibich 1988, Binash 1989) is thus the resistance variation between the
   resistance R[AP] and R[P] of the AP (antiparallel) and P (parallel) magnetic
   configurations. The amplitude of the GMR is generally characterized by the ratio
   \((R_{AP}- R_{P})/ R_{P}\ .\) For example, this ratio reaches 80% for the
   multilayer with 0.9nm thick Cr layers in the results of Figure [25]1 a. The GMR
   decreases rapidly as the layer thickness increases. The interpretation of the GMR
   in terms of spin dependent scattering, proposed by Fert's group (Baibich 1988),
   and the corresponding theoretical models are presented in Section 3.
   Figure 1: First observations of giant magnetoresistance. (a) On Fe/Cr(001)
   multilayers (Baibich 1988). With the current definition of the magnetoresistance
   ratio, \(MR=100 \times (R_{AP}- R_{P})/ R_{P}\ ,\) MR = 80% for the Fe 3nm/Cr
   0.9nm multilayer. (b) On Fe/Cr/Fe trilayers (Binash 1989). (c) Schematic of the
   mechanism of the GMR. In the parallel magnetic configuration (bottom), the
   electrons of one of the spin channels can go easily through all the magnetic
   layers and the short-circuit through this channel leads to a small resistance. In
   the antiparallel configuration (top), the electrons of each channel are slowed
   down every second magnetic layer and the resistance is high. The current is
   horizontal on the figure and it is carried by electrons having velocities in all
   the possible directions with different proportion of rightward and leftward
   orientations (figure from Chappert 2007).

   The publications reporting the discovery of GMR rapidly attracted [26]attention
   for its fundamental interest as well as for the many possibilities of
   applications, and the research on magnetic multilayers became very active. In
   1990 Parkin and coworkers (Parkin 1990) demonstrated the existence of GMR in
   multilayers (Fe/Cr, Co/Ru and Co/Cr) made by the simpler and faster technique of
   sputtering. They could explore very broad thickness ranges and found the
   oscillatory variation of the magnetoresistance which reflects the
   [27]oscillations of the interlayer exchange coupling as a function of the spacer
   thickness. GMR effects exist in the thickness ranges where the coupling is
   antiferromagnetic (AF) and vanishes when the coupling is ferromagnetic, as shown
   in Figure [28]2. The oscillations are modulated by the general decrease of the
   GMR with the thickness. The oscillatory behavior disappears and only a continuous
   decrease subsists in the thickness range where the exchange coupling becomes
   weaker than the coercive field.
   Figure 2: Oscillatory variation of the GMR ratio of Fe/Cr multilayers as a
   function of the thickness of the nonmagnetic layers in Fe/Cr (2 nm thick Fe
   layers), Parkin 1990, and Co/Cu multilayers (1.5 nm thick Co layers), Mosca 1991.

   Other important advances were obtained at the beginning of the nineties. In 1990
   Shinjo and Yamamoto (1990), as well as Dupas et al (1990), demonstrated that GMR
   effects can be found in multilayers without antiferromagnetic interlayer coupling
   but composed of magnetic layers having different coercivities. The first results
   on trilayers of "spin valve" type in which the magnetization of one of the
   magnetic layer is pinned by interaction with an antiferromagnetic layer were also
   obtained in 1991. We will present the spin valves and their applications in
   Section 4. Another important result in 1991, illustrated by Figure [29]2 b, was
   also the observation of large and oscillatory GMR effects in Co/Cu, which became
   an archetypical GMR system. The first observations were obtained at Orsay (Mosca
   1991) with multilayers prepared by sputtering at Michigan State University and at
   about the same time at IBM (Parkin 1991). Finally it can be noted that the
   highest GMR ratio, 220%, was obtained by Schad et al. (1994) on Fe/Cr multilayers
   . All these results are for the GMR with the Current In the layer Planes
   (CIP-GMR). After 1991, measurements have been also performed with the Current
   Perpendicular to the layer Planes (CPP-GMR), which leads to the different
   properties described in Section 5.

Spin dependent conduction in a ferromagnetic conductor

   The origin of the GMR is the dependence of the electrical conduction in
   ferromagnetic materials on the spin state of the carriers (electrons). This is a
   consequence of the spin spitting of the energy bands in the ferromagnetic state
   illustrated in Figure [30]3 a.
   Figure 3: Basics of spintronics. (a) Spin up and spin down density of states
   (DOS), \(n _{\uparrow }(E) \) and \(n _{\downarrow }(E) \ ,\) in a ferromagnetic
   metal. The origin of the spontaneous magnetization is the splitting between the
   DOS of the d electrons (colored DOS). The parabolic DOS are for the non polarized
   s electrons. (b) Schematic for spin dependent conduction through independent spin
   up and spin down channels in the limit of negligible spin mixing (\(\rho
   _{\uparrow \downarrow}=0\) in the formalism of Fert 1976). (c) Resistivities of
   the spin up and spin down conduction channels for nickel doped with 1% of several
   impurity types (measurements at 4.2 K), Fert 1976. The ratio \(\alpha\) between
   the resistivities \(\rho _{0\downarrow}\) and \( \rho _{0 \uparrow}\) can be as
   large as 20 (Co impurities) or, as well, smaller than one (Cr or V impurities).

   The spin dependence of the conduction in ferromagnetic metals or alloys has been
   first suggested by Mott (1936) before being experimentally demonstrated and
   quantitatively described at the end of the sixties by Fert and Campbell (Fert
   1968) for series of iron- and nickel-based alloys. Similar results could be
   rapidly found in several other systems (Loegel 1971, Dorleijn 1977, Fert 1976).
   The experimental results can be accounted for in the "two current model" of the
   conduction in ferromagnetic metals (Fert 1968, 1976). In this model the
   resistivity of a ferromagnetic conductor is expressed as \[\tag{1} \rho = {{\rho
   _ \uparrow \rho _ \downarrow + \rho _{ \uparrow \downarrow } (\rho _ \uparrow +
   \rho _ \downarrow )} \over {\rho _ \uparrow + \rho _ \downarrow + 4\rho _{
   \uparrow \downarrow } }} \]

   \(\rho_\uparrow\) and \(\rho_\downarrow\) are the resistivities of the
   spin\(\uparrow\) (majority spin direction) and spin\(\downarrow\) (minority spin
   direction) channels. \(\rho_{\uparrow \downarrow}\) is the spin mixing
   resistivity term expressing the transfer of momentum between the two channels by
   spin-flip scattering. In the low temperature limit (T {\rm{r}}_{\rm{P}}= \frac{{\rm{r}}_ {+}^{P}{\rm{r}}_ {-} ^{P}}{{\rm{r}}_
   {+}^{P}+{\rm{r}}_ {-} ^{P}} \]

   and to the GMR ratio \[\tag{9} {\rm{GMR}} = {{{\rm{r}}_{{\rm{AP}}} -
   {\rm{r}}_{\rm{P}} } \over {{\rm{r}}_{\rm{P}} }} = {{{\rm{(r}}_ -^{P} - {\rm{r}}_
   +^{P} {\rm{)}}^{\rm{2}} } \over {{\rm{4r}}_ +^{P} {\rm{r}}_ -^{P} }}\]

   For a more realistic picture, one must take into account that the layers are not
   much thinner than the MFP, consider the physical origin of the spin dependent
   scattering and also go beyond free electron models. Figure [37]4 represents
   schematically the potential landscape seen by the electrons. Figure [38]4 (a) and
   (b) are for the spin + and spin - electrons in the parallel (P) configuration and
   (c) is for any spin directions in the antiparallel (AP) configuration. The
   potential can be separated into, (a) the intrinsic potential of the perfect
   multilayered structure (superlattice), which determines the wave functions of the
   electrons carrying the current, and (b) the scattering (extrinsic) potentials due
   to defects (atomic disorder, impurities, interface roughness) and represented by
   spikes. In a magnetic multilayer both the intrinsic and extrinsic potentials are
   spin dependent.
   Figure 4: Potential landscape seen by the spin+ and spin- conduction electrons in
   the P and AP configurations. The intrinsic potential is represented by a periodic
   array of spin dependent steps (Kronig-Penney-like potential); the bulk and
   interface scattering potentials are represented by spin dependent spikes.

   (a) Let us first consider the role of the intrinsic potential represented in
   Figure [39]4 by steps of Kronig-Penney potentials. The spin dependence of these
   steps are related to the exchange splitting of the energy bands in a
   ferromagnetic metal. For a perfectly ordered structure the interferences between
   Bragg-like specular reflections at the interfaces would build the Bloch functions
   of an artificial superlattice. However the superlattice approach is valid for
   coherent interferences between the specular reflections, that only applies if the
   MFP is much longer than the multilayer period. For real multilayers, with bulk
   scattering and also a significant probability of scattering by roughness defects
   at each interface, the MFP cannot be many times longer than the layer thickness.
   Consequently a superlattice approach is rarely appropriate, which is confirmed by
   the absence of most superlattice effects, oscillations of the conductance as a
   function of the layer thickness for example. A more realistic approach is the
   so-called "layer by layer" approach, in which one considers the specular
   reflections of the wave functions in each layer but not the interference between
   the reflections at successive interfaces. Nevertheless the specular reflections
   play an important role for the GMR as they can channel the current in some of the
   layers and lead to different efficiencies for the spin dependent scatterings in
   different layers.

   (b) The extrinsic potentials, represented by spin dependent spikes in Figure
   [40]4, are associated with bulk or interface scatterings. Both are spin dependent
   and contribute to the GMR. Their respective contributions depend on the density
   of interfaces (i.e. on the thicknesses) and also, as described a few lines above,
   on the different channelling of the electrons in the different layers. More
   quantitative data on the respective importance of bulk and interface effects can
   be derived from the analysis of the CPP-GMR (see Section 5). It turns out that
   the interface contribution is generally predominant for a few nm thick layers,
   the bulk contributions becoming larger for thicknesses exceeding the 5-10 nm
   range.

   To sum up, a realistic description of the GMR demands to treat the bulk and
   interface spin dependent scatterings of wave functions more or less channelled
   inside the layers by interface specular reflections. The MFP fixes the range in
   which the different spin dependent scatterings must be averaged. The main
   difficulty for quantitative theoretical predictions is the limited information we
   have on the defects at the origin of the bulk and interface spin scattering
   potentials and on their spin dependence. However the theoretical models can
   describe qualitatively all the main features, as it turns out from the review of
   models in the next lines.

   The first model of GMR was the semi-classical free electron model of Camley and
   Barnas (1989). This is a free electron model in which the GMR is calculated from
   bulk scattering probabilities and interface scattering, reflection and
   transmission coefficients. The scattering probabilities inside the magnetic
   layers and the interface coefficients are spin dependent. The major success of
   this model was to predict the thickness dependence of the GMR. In the limit of
   thick nonmagnetic layers the GMR decreases exponentially as a function of the
   ratio of the thickness to the MFP. As a function of the thickness of the magnetic
   layers, the GMR vanishes as the inverse of the thickness.

   The first quantum mechanical model of the GMR was introduced by Levy and
   coworkers (1990) who used the Kubo formalism to calculate the conductivity of
   free electrons scattered by a distribution of spin dependent potentials. The
   model, as the one of Camley of Barnas (1989), explains the thickness dependence
   of the GMR. However, for a realistic comparison with experimental results, it is
   necessary to replace the free electron picture by an accurate description of the
   spin-polarized band structure. This has been done first using tight-binding
   models and then in several types of ab initio models based on the Local Spin
   Density Approximation (LSDA). One of the important results of such ab initio
   calculations is the concept of quantum channelling discussed above (Zahn 1998).
   For quantitative predictions, the scattering potentials of defects, interface
   roughness or impurities must be introduced into the models but little is know on
   these imperfections of the multilayers. Consequently the theory of the GMR cannot
   be really predictive. For an extensive review of the theoretical models, we refer
   to a review article of Levy and Mertig (2002).

Spin-valves, applications

   GMR requires that an antiparallel configuration of the magnetizations in the
   multilayers can be switched into a parallel one by applying a magnetic field. In
   the first GMR experiments the AP configuration was induced by antiferromagnetic
   interlayer exchange but this is not the only way to obtain an antiparallel
   configuration. For example, in multilayers combining hard and soft magnetic
   layers, the GMR effects can be obtained by switching only the soft layer (Shinjo
   1990, Dupas 1990). The best known structure in which interlayer exchange is not
   used to obtain an AF configuration and GMR effects, is the spin valve structure,
   introduced in 1991 by Dieny et al (1991) and now used in most applications of
   GMR.
   Figure 5: (a) Typical layered structure of a spin valve. (b) Hysteresis (top) and
   magnetoresistance (bottom) loops of a [NiFe(6 nm)/Cu(2.2 nm)/NiFe(4 nm)/FeMn(7
   nm)] spin valve at room temperature (Dieny 1991).

   A spin valve structure, in its simplest form shown in Figure [41]5 a, consists of
   a magnetically soft layer separated by a nonmagnetic layer from a second magnetic
   layer which has its magnetization pinned by an exchange biasing interaction with
   an antiferromagnetic (FeMn) or ferrimagnetic layer. The operation of the spin
   valve can be understood from the magnetization and magnetoresistance curves shown
   in Figure [42]5 b. One of the permalloy layers has its magnetization pinned by
   the FeMn in the negative direction. When the magnetic field is increased from
   negative to positive values, the magnetization of the free layer reverses in a
   small field range close to H=0, whereas the magnetization of the pinned layer
   remains fixed in the negative direction. Consequently, the resistance increases
   steeply in this small field range. Magnetic multilayers of the spin valve type
   are used in most applications of GMR, in particular the read heads of hard discs,
   see Figure [43]6. More details about the applications of GMR can be found in
   review articles (Parkin 2002, Chappert 2007).
   Figure 6: GMR head for hard disc recording. Figure from Chappert 2007.

GMR with the Current Perpendicular to the layer Planes (CPP-GMR), spin accumulation
effects

   During the first years of the research on GMR, the experiments were performed
   only in the CIP geometry, that is with currents flowing along the layer planes.
   It is only in 1991 that experiments of GMR with the Current Perpendicular to the
   layer Planes (CPP-GMR) begun to be performed. This was done first by sandwiching
   a magnetic multilayer between superconducting electrodes (Pratt 1991, Bass 1999),
   then by electrodepositing multilayers into the pores of a polycarbonate membrane
   (Piraux 1994, Fert 1999) and, more recently, in vertical nanostructures (pillars)
   fabricated by e-beam lithographic techniques (Albert 2000). In the CPP-geometry,
   the GMR is not only definitely higher than in CIP but also subsists in
   multilayers with relatively thick layers, up to the micron range in Figure [44]7
   a for example. Actually, as explained in the Valet-Fert model of the CPP-GMR
   (Valet 1993), spin-polarized currents flowing perpendicularly to the layers
   induce spin accumulation effects and the final result is that the length scale
   governing the thickness dependence becomes the "long" spin diffusion length
   (related to the spin relaxation) in place of the "short" mean free path in the
   CIP-geometry. Similar effects for single interfaces had already been described by
   Johnson and Sisbee (1987).

   The physics of the spin-accumulation occurring when an electron flux crosses an
   interface between a ferromagnetic (F) and a nonmagnetic (N) material is explained
   in Figure [45]8 for a simple situation (single interface, no interface
   resistance, no band bending, single polarity). In Figure [46]8 a, the incoming
   electron flux is predominantly carried by the spin up direction whereas the
   outgoing flux is carried equally by both spins. Consequently there is
   accumulation of spin up electrons at the interface and this accumulation diffuses
   on both sides of a F/N interface to a distance of the order of the spin diffusion
   length. In terms of electron distribution the spin accumulation is described as a
   splitting of the spin up and spin down Fermi energies (chemical potentials), as
   shown in Figure [47]8 b. The spin-flips generated by this out of [48]equilibrium
   electron distribution in the spin accumulation zone provide the mechanism of the
   adjustment between the incoming and outgoing spin currents. To sum up, the spin
   polarization of the current decreases progressively as it goes through this broad
   spin accumulation zone. In a similar way, for the current in the opposite
   direction, a similar mechanism progressively polarizes the current. In both
   cases, the current spin-polarization just at the interface depends on the
   proportion of the depolarizing (or polarizing, depending on the direction of the
   current), spin-flips induced by the spin accumulation in F and N.

   In the multi-interface structure of a CPP-GMR experiment, there is an interplay
   between the spin accumulation effects at successive interfaces. The spin
   accumulation in a non-magnetic layer is larger for an AP magnetic configuration
   in which the easily injected spin direction is the less easily extracted. The
   CPP-GMR is related to the difference between the spin accumulation in the P and
   AP configuration. The GMR ratio vanishes only when the thickness becomes larger
   than the spin diffusion length, in agreement with the persistence of the GMR up
   to much thicker layer than in the CIP geometry, see Figure [49]7.

   The physics of spin accumulation can be described by new types of transport
   equations (Valet 1993), often called drift/diffusion equations, in which the
   electrical potential is replaced by a spin and position dependent
   electro-chemical potential. The electro-chemical potentials in different layers
   are coupled by boundary conditions involving spin dependent interface
   resistances. These equations have been extensively applied to the interpretation
   of the experimental results of CPP-GMR (Pratt 1991, Bass 1999, Fert 1999) and an
   example is shown in Figure [50]7 b.
   Figure 7: (left) \(\Delta{R}/R_P\) vs. Co thickness for Co/Cu/Co multilayers,
   Fert 1999 (\(\Delta R\) is the resistance change between P and AP states).
   (right) \(\Delta R\) vs. CoFe and Co thickness for CoFe/Cu/CoFe and Co/Cu/Co
   multilayers, Reilly 1999. For CoFe \(\Delta R\) flattens off for CoFe layers
   thicker than 40nm. In the thickness range where \(\Delta R\) becomes constant,
   \(\Delta R / R_P \) decreases to zero as \(R_P\) increases progressively with the
   thickness of CoFe. For Co the saturation of \(\Delta R\) is not reach at 50nm
   yet, in agreement with the decrease of \(\Delta R / R_P \) down to zero at
   definitely thicker layers in the experiment of Figure [51]7 left.

   More generally, the spin accumulation effects govern the propagation of a
   spin-polarized current through any succession of magnetic and nonmagnetic
   materials and play an important role in all most recent developments of
   spintronics. The diffusion current induced by the accumulation of spins at the
   magnetic/nonmagnetic interface is the mechanism driving a spin-polarized current
   at a long distance from the interface, well beyond the ballistic range (i.e. well
   beyond the mean free path) up to the distance of the spin diffusion length (SDL).
   The drift-diffusion equations of the CPP-GMR can be applied to understand the
   spin transport in various types of devices. In particular they have been applied
   to explain the difficulty of the spin injection from a magnetic metal into a
   semiconductor, the so-called "conductivity mismatch" problem (Schmidt 2000), and
   to show how this problem can be solved by the insertion of spin dependent
   interface resistances (Rashba 2000, Fert 2001).
   Figure 8: Schematic representation of the spin accumulation at an interface
   between a ferromagnetic metal and a non magnetic conductor. (a) Incoming and
   outgoing spin-up and spin-down currents (b) Splitting of the chemical potentials,
   E[Fup] and E[Fdown], in the interface region (spin accumulation). The arrows
   symbolize the spin flips induced by this out of equilibrium distribution. These
   spin-flips govern the progressive depolarization of the current. With an opposite
   direction of the current, the spin accumulation is in the opposite direction and
   opposite spin flips polarize progressively the current. (c) Variation of the
   current spin polarization when there is an approximate balance between the spin
   flips on both sides (metal/metal curve) and when the spin flips on the magnetic
   side are predominant (metal/semiconductor curve in the situation without
   spin-dependent interface resistance). Figures from Chappert 2007.

Concluding remarks

   GMR is best known by the grand public for its application to the hard disc drives
   and the resulting considerable increase of the disc capacities. However more
   important, in my opinion, is that the GMR boosted the research of other
   spin-induced transport effects and, finally, triggered the development of the new
   field of research and technology called spintronics. An important second stage,
   after 1995, was the research on the magnetoresistance of the magnetic tunnel
   junctions (TMR) (Moodera 1995, Miyasaki 1995). The TMR has now replaced the GMR
   in a majority of hard disc drives and is also applied in the type of [52]memory
   called M-RAM (Magnetic Random Access Memory). The physics of spin accumulation
   revealed by the CPP-GMR has also been extended to the situation of spin transport
   in a lateral nonmagnetic channel between magnetic contacts. The channel can be a
   metal, a semiconductor or a carbon-based conductor like carbon nanotubes (CNT) or
   graphene, the lateral geometry introducing the possibility of a gate to
   manipulate the spin polarization for [53]logic or transistor-like applications.
   Promising results have been obtained with CNT (Hueso 2007) in which
   spin-polarized currents turn out to be propagated to distances well above the
   micron range. Similar spin propagations at long distances can be expected for
   graphene and probably other carbonic materials, which can lead to new concepts of
   information processing based on the manipulation of spin currents. Of particular
   importance is also the concept of spin transfer introduced by Slonclewski
   (Slonczewski 1996). Spin transfer is the opposite of magnetoresistance effects
   like GMR or TMR. Whereas, in GMR or TMR, a magnetic configuration is detected by
   a current, in spin transfer a magnetic configuration is created by a "spin
   transfusion" from a spin polarized current. Spin transfer will be applied to
   write MRAM memories or to generate oscillations in the microwave frequency range.
   Many other fascinating directions of research are emerging today on the road of
   spintronics: spin photonics, Spin Hall Effect, [54]topological insulators, spin
   [55]quantum computing, neuromorphic electronics...GMR was only the first step.

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       Rev. Lett. 80, 4309

See also

     * Fert, A., Barthélémy, A. and Petroff, F. (2006). Spin transport in Magnetic
       Multilayers and Tunnel Junctions. In Nanomagnetism: Ultrathin Films and
       Nanostructures, ed. F. Mills and J. A.C. Bland, 153-226 Amsterdam : Elsevier
     * Parkin, S.S.P. (2002). Applications of magnetic nanostructures. In Spin
       Dependent Transport in Magnetic nanostructures, ed S. Maekawa and T. Shinjo,
       237-279. Taylor and Francis.

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