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4 Giant Magnetoresistance (GMR) and Spintronics

4 Giant Magnetoresistance (GMR) and Spintronics

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20



1 Introduction and Some Physical Principles



Fig. 1.20 (a) Temperature dependence of the critical current density Jc of 7 and 9 monolayer (ML)

thick Pb films. Open symbols refer to films with nanovoids, filled symbols to films with nanoscale

mesas. (b) Scanning tunneling microscopy (STM) images (700×700 nm2 ) of a 9 ML Pb film with

nanovoids (dark dots). (c) Critical temperatures Tc derived from the onset of magnetic screening

and Tc∗ from the extra-polated Hc2 (T) data. For d → ∞, Tc∗ extrapolates to a value close to the

bulk Tco = 7.2 K. (Reprinted with permission from [1.103]. © 2006 Nature Publishing Group)



manifestation, the magnetization of a ferromagnet. This picture started to change

when the discovery [1.107, 1.108] of the giant magnetoresistance (GMR) of magnetic multilayers – for which A. Fert and P. Grünberg were awarded the 2007 Nobel

prize in physics [1.109, 1.110] – opened the way to an efficient control of the motion

of electrons by acting on their spin through the orientation of the magnetization.

To employ this spin degree of freedom – i.e., that the spin can assume two different values – for faster switching of electronic components with reduced energy

consumption could lead to the next step in electronics and initiate the age of spin

electronics or spintronics [1.111–1.114]. The progress toward understanding and



1.4



Giant Magnetoresistance (GMR) and Spintronics



21



implementing spintronics in metallic multilayers and in semiconductors is gaining

momentum and spintronic read head sensors are already impacting a multibillion

dollar industry.

To incorporate spins into existing semiconductor technology, one has to resolve

technical issues such as efficient spin injection, transport control and manipulation, and detection of spin polarization as well as spin-polarized currents. There

are visions that the merging of electronics, photonics, and magnetics will ultimately

lead to spin-based multifunctional devices, optical switches operating at terahertz

frequencies, or quantum bits (qubits) for quantum computation and communication.



1.4.1 Giant Magnetoresistance (GMR) and Tunneling

Magnetoresistance (TMR)

GMR (see [1.109, 1.110]) is a quantum mechanical effect observed in layered

magnetic thin film structures that are composed of alternating layers of ferromagnetic and non-magnetic metallic films (Fig. 1.21a). In zero magnetic field the

ferromagnetic layers are antialigned (Fig. 1.23a) with maximum spin-dependent

scattering of the electrons (maximum resistance, see Fig. 1.22). When in an external magnetic field the ferromagnetic layers are aligned in parallel (Fig. 1.23b), the

spin-dependent scattering is minimized (low resistance, Fig. 1.22). For the zerofield antialigned coupling of the two ferromagnetic layers a long-range RKKY-type

(Ruderman–Kittel–Kasuya–Yosida) magnetic coupling of electrons is assumed.

A spin valve (Fig. 1.21a) is a GMR-based device with two ferromagnetic layers (e.g., Fe, Ni, Co) separated by a thin non-magnetic conductor layer (e.g., Cu)

where one of the ferromagnetic layers is “pinned” to an antiferromagnetic layer,

i.e., its magnetization cannot be changed by moderate magnetic fields. The magnetization of the other ferromagnetic layer can be changed easily by a magnetic

field giving rise to a resistance change of 5–10% in a relatively small magnetic

field. Commercial GMR read heads use the spin-valve format for hard drives and

magnetic field sensors.



Fig. 1.21 Spin-dependent transport structures. (a) Spin valve. (b) Magnetic tunneling junction.

(Reprinted with permission from [1.112]. © 2001 American Association for the Advancement of

Science (AAAS))



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1 Introduction and Some Physical Principles



Fig. 1.22 First observations of giant magnetoresistance (GMR) in (a) a multilayer [1.107] and

(b) a double layer [1.108] of Fe interspaced by Cr. In (b), the earlier found anisotropic magnetoresistance (AMR) effect of a Fe film is shown for comparison. (Reprinted with permission from

[1.110]. © 2008 American Physical Society)



Fig. 1.23 Schematics of

electron transport parallel to

the plane of a layered metallic

structure with ferromagnetic

(arrows) and non-magnetic

layers with aligned (low

resistance) and antialigned

(high resistance) magnetization. (Reprinted with

permission from [1.111].

© 1998 AAAS)



A magnetic tunneling junction (MTJ) is a device (Fig. 1.21b) in which a pinned

ferromagnetic layer and a free ferromagnetic layer are separated by a very thin insulating layer (e.g., Al2 O3 , MgO) [1.115, 1.116]. The electron tunneling phenomenon

arises from the wave nature of the electrons while the resulting junction electrical

conductance is determined by the evanescent state of the electron wave function

within the tunneling barrier. The tunneling magnetoresistance (TMR) arises from

the difference in the electronic density of states (DOS) at the Fermi level EF between

spin-up N↑ (EF ) and spin-down N↓ (EF ) electrons. Since electrons preserve their spin

orientation during the tunneling process, electrons can only tunnel into the subbands of the same spin orientation, thus, in the case of the same spin orientation

of the two electrodes, the tunneling conductance is proportional to the product of

the Fermi level DOS values of the two electrodes. A change from a parallel magnetization to an antiparallel magnetization of the two electrodes will result in an

exchange between the two spin sub-bands of one of the electrodes for the tunneling process with a decrease of the conductance, provided that the Fermi level DOS



1.4



Giant Magnetoresistance (GMR) and Spintronics



23



Fig. 1.24 Schematics of magnetic random access memory (MRAM) array with magnetic tunneling junction (MTJ) memory elements. For the toggle MRAM, the long axis of the eliptically

shaped element (magnetic shape anisotropy) is oriented diagonally with respect to the x–y grid of

write lines. Each element is connected to a transistor performing the read selection. (Reprinted

with permission from [1.115]. © 2006 Elsevier)



values are different for the two spin sub-bands [1.115]. High TMR values are found

for Co(001)/MgO(001)/Co(001) tunneling junctions [1.116].

GMR sensors in the spin-valve format as originally proposed by IBM [1.117] or

MTJ sensors [1.118] have been used as read heads in hard disk drives (HDD; see

Sect. 9.5) with data rates exceeding 1 Gbit/s [1.115].

Magnetoresistive devices such as MTJs can be employed as components of a

magnetic random access memory (MRAM) which may be the “dream memory”

because this is capable of the speed of the semiconductor SRAM (static random

access memory), the density of a DRAM (dynamic random access memory), and

the non-volatility of an HDD for integration of a computer system on a single chip.

To date, Freescale’s toggle MRAM (see Sect. 9.5) with a 4 Mbit chip of MTJ elements is in production (see Fig. 1.24). The storage layer of the memory elements is a

synthetic antiferromagnet (SAF) as, e.g., CoFe (2.5 nm)/Ru(0.8 nm)/CoFe(2.5 nm),

oriented at 45◦ to the orthogonally arranged current lines. Two current pulses on the

two write lines effectuate a 180◦ rotation of the magnetic moment of the SAF storage layer of the selected element. Calculations based on the so-called spin-torque

switching [1.115] suggest that such a design may enable MRAMs to reach a storage

capacity of many Gbits per chip with low operating power.



1.4.2 Spintronics in Semiconductors

Recently, efforts have been made to exploit electron spin degrees of freedom in

semiconductors, where the spin orientation can be actively controlled [1.113]. In a

spin transistor the current of the spin-polarized electrons can be controlled by a gate



24



1 Introduction and Some Physical Principles



Fig. 1.25 In a spin transistor [1.119] spin-polarized electrons (red arrows) are injected from a

ferromagnetic source contact into a semiconductor channel where they migrate to a spin selective

drain contact. A voltage perpendicular to the current gives rise to a spin–orbit coupling corresponding to an effective magnetic field (blue arrows) perpendicular to the directions of current and

electrical field which effectuates a spin precession. Only when the electron spins arriving at the

drain are parallel to the spins there, then the electrons can leave via the drain and a current flows in

the transistor. (Reprinted with permission from [1.113]. © 2004 Wiley-VCH)



voltage via spin–orbit coupling (see Fig. 1.25). Another example is a spin-controlled

semiconductor laser where the intensity and the polarization of the emission can be

manipulated by the spin orientation without changing the electron density [1.113].

In addition, spintronics is correlated to quantum information processing where

entangled quantum mechanical states are employed for designing new computer

architectures and safe quantum communication systems.

For spintronics, first spin-polarized electrons must be injected into the semiconductor by optical or electrical procedures. By optical excitation the angular

momentum of a circularly polarized photon can be used to transfer exclusively

electrons of a particular spin orientation from the valence band to the conduction band in order to generate an effective electron spin polarization. By electrical

methods spin-polarized electrons can be transferred from ferromagnetic contacts

into a semiconductor with degrees of polarization of 30% [1.120].

The spin polarization of charge carriers injected from magnetic layers as, e.g.,

n-ZnBeMgSe into a semiconductor can be detected optically by the polarization of

the luminescence in a light-emitting diode (LED; see Fig. 1.26) – a direct inversion

of the optical generation of spin-polarized charge carriers. Considerable progress

in electron spin polarization in semiconductors has been achieved by the discovery of ferromagnetism in strongly Mn-doped GaAs [1.121] or in Zn0.8 Cr0.2 Te films

[1.122]. In these dilute magnetic semiconductors (DMS, see [1.123]), owing to the

short-range character of the direct exchange interaction between the tightly localized magnetic orbitals of the magnetic dopants, the coupling between the d spins

proceeds indirectly (superexchange) via sp bands in the tetrahedrally coordinated



1.4



Giant Magnetoresistance (GMR) and Spintronics



25



Fig. 1.26 (a) Layer sequence of a AlGaAs light-emitting diode (LED) (green) with an Mn-doped

contact (orange) for spin polarization. The lower part shows the position-dependent conduction

band edge (EL ) and the valence band (Ev ). By an electric field the spin-polarized electrons (red)

are transported from the ZnBeMnSe layer into the non-magnetic AlGaAs and GaAs layers forming

the LED which – according to the spin polarization – emits circularly polarized light. (b) Degree of

polarization of the light emitted from the LED in dependence of the external magnetic field B for a

) and with a non-magnetic ZnBeMgSe (∇∇∇)

diode with a paramagnetic ZnBeMnSe layer (

layer. [1.125]. (Reprinted with permission from [1.113]. © 2004 Wiley-VCH)



Fig. 1.27 Schematics of carrier-mediated ferromagnetism in p-type dilute magnetic semiconductors (DMS). Owing to the p–d exchange interaction, ferromagnetic ordering of localized spins (red

arrows) leads to spin splitting of the sp valence band. The redistribution of the carriers between

the spin sub-bands lowers the energy of the holes which can overcompensate an increase of the

free energy associated with a decrease in Mn entropy. (Reprinted with permission from [1.123].

© 2006 Elsevier)



26



1 Introduction and Some Physical Principles



Fig. 1.28 Spin transport across a GaAs/ZnSe junction at ambient temperature. Kerr rotation

detects coherent spins in ZnSe generated in GaAs and transferred to the ZnSe layer. The spin

precession is observed in a magnetic field B = 0T (purple), 0.025T (pink), and 0.25T (black)).

(Reprinted with permission from [1.126]. © 2001 AAAS)



DMS (see Fig. 1.27). A more detailed quantum mechanical treatment indicates that

the sign of the interaction between the localized spins oscillates with their distance

according to the Ruderman–Kittel–Kasuya–Yosida (RKKY) model.

For the development of semiconductor-based spintronics the understanding of

spin transport and spin relaxation times is of importance. For information storage

purposes spin polarization should be maintained over long times whereas rapid spin

relaxation may be advantageous for fast switching [1.124]. Spin relaxation times

can be at present manipulated from picoseconds to many milliseconds [1.113].

Long-time spin polarization can be experimentally observed by the spin precession

in a magnetic field (see Fig. 1.28).

For application of dilute magnetic semiconductors ferromagnetic behavior at

ambient temperature is desirable. In the case of (Zn, Cr) Te, ferromagnetism persists up to 300 K [1.122] whereas in (Ga, Mn) As, Mn-rich (Mn, Ga) As nanocrystals

[1.127] account for the high apparent Tc of 360 K. In quantum wires of Mn-doped

GaN with a diameter down to 40 nm and lengths of 20 μm, ferromagnetic behavior

has been shown at ambient temperature [1.128].



1.4.3 Spin Hall Effect

In the spin Hall effect, which was postulated more than 30 years ago (see [1.129]),

a voltage on a specimen – as in the normal Hall effect – gives not only rise to a

current in field direction but also to a spin current js = σsH E transverse to the field

direction (see Fig. 1.29) where σ sH is the spin Hall conductivity. In contrast to the

normal Hall effect this is not due to an external magnetic field but rather due to

spin–orbit scattering. Therefore, the spin Hall current is a pure spin current where

no charge is transported. The spin Hall effect was demonstrated experimentally in

ZnSe [1.130] by making use of a Kerr rotation microscope with a spatial resolution

of 1 μm scanning the spin polarization profile over a distance of 100 μm. Due to

the large ZnSe band gap and the long spin coherence time the effect can also be

detected at ambient temperature.



1.5



Self-Assembly



27



Fig. 1.29 In the extrinsic

spin Hall effect (spindependent electron scattering

at defects) electrons with

differing spin polarization are

scattered asymmetrically

which gives rise to an

unbalance perpendicular to

the charge current and

thereby to a spin polarization

at the specimen fringes.

(Reprinted with permission

from [1.129]. © 2006

Wiley-VCH)



1.5 Self-Assembly

On a atomic or molecular scale, the application of interatomic or intermolecular forces can lead to new and previously unachievable nanostructures. This is

why molecular self-assembly is a highly topical and promising field of research

in nanoscience [1.131]. The term self-assembly implies spontaneity, a structure

builds itself from modular construction units, an ordered pattern forms from a disordered state. The self that drives the assembly is the interaction among building

blocks rather than the generally stronger bonding force within them [1.132]. The

forces governing self-assembly include hydrogen bonding, electrostatic and magnetic interaction, hydrophobic interaction, and van der Waals forces (see [1.131]). To

self-assemble building blocks into well-organized constructs depends on the ability

to control their size, shape, surface properties precisely (e.g., charge, hydrophobicity, hydrophilicity, functionality, see also Sect. 3.2). A prime goal, therefore,

is to gain control over the attractive and repulsive forces between the building blocks to allow them to assemble spontaneously over multiple length scales

[1.133] to create an integrated chemical, physical, or biological system with new

functionality.

In the absence of external influences, building block static self-assembly is driven

by energy minimization to form static equilibrium structures. Under outside influences, a dynamically self-assembling system may prevail that can adjust to the

surrounding environment, by residing on an energetic minimum which is caused

by the influx of energy into the system – once the energy flow stops, the minimum disappears, and the system disassembles. Any living organism is a perfect

example of dynamic self-assembly. It reduces entropy by absorbing energy from



28



1 Introduction and Some Physical Principles



the environment (see [1.132]). Once that flux ceases, the organism disassembles.

Self-assembly forms the basis for many natural processes including protein folding, DNA transcribing and hybridization, and the formation of cell membranes (see

[1.131]).

In the following a few examples of static self-assembly will be discussed,

including self-assembly via Friedel oscillations [1.134], via strains [1.135] and via

molecular interaction for the formation of a Kagomé lattice [1.136] or of selfassembled monolayers (SAMs) [1.131]. In addition, self-assembly gives rise to

colloidal superstructures in a magnetic field [1.137] or to complex nanostructures

making use of DNA [1.138, 1.139].



1.5.1 Self-Assembly of Ni Nanoclusters on Rh (111) via Friedel

Oscillations

When a Rh (111) substrate is covered by 0.8 monolayers (ML) of Ni, hollow crystallographic Ni nanoclusters with predominantly 12 atoms (see Fig. 1.30a) are formed

on the Ni adislands. Surface Friedel oscillations of electrons can generate standing waves (SWs) which modify the electron local density of states (LDOS) at the

surface and can be imaged by scanning tunneling microscopy (STM). Friedel oscillations modify the adsorption properties of the surface. A maximum in the variation

LDOS of the LDOS due to the Friedel oscillations is a potential well and a suitable atomic adsorption site. The map of the LDOS (Fig. 1.30b) calculated by a

simple model [1.134] for a 12-atom cluster can be directly compared with the STM

image in Fig. 1.30a and suggests that the Friedel oscillations are responsible for the

formation of the triangular clusters. A model for the likely sites of adsorption for a

cluster of 12 atoms is shown in Fig. 1.30c.



Fig. 1.30 (a) Scanning tunneling micrograph (STM) of a hollow Ni nanocluster with 12 atoms on

a Ni adisland deposited on a Rh (111) substrate. (b) Variation LDOS map of the electron local

density of states (LDOS) obtained by linear combination of the single patterns produced by each

interfering adatom. (c) Model of the likely sites of adsorption for a cluster of 12 atoms. Light blue

corresponds to the Ni adisland layer while red represents the adatoms of the cluster. (Reprinted

with permission from [1.134]. © 2008 American Physical Society)



1.5



Self-Assembly



29



1.5.2 Self-Assembly of Fe Nanoparticles by Strain Patterns

Self-assembly of nanoparticles can be induced by strain fields [1.135]. In bilayers

of two thin films of metals as, e.g., Cu/Pt (111), with different lattice parameters,

the lattice misfit is compensated by a regular network of surface-near dislocations,

which can be detected by STM due to their strain fields. The strain fields are

repulsive toward diffusing Fe adatoms so that the Fe atoms regularly agglomerate

between the dislocations with exactly one island or agglomerate per network unit

cell (Fig. 1.31). The islands exhibit a narrow size distribution.

Fig. 1.31 Scanning

tunneling micrograph (STM)

of a periodic array of Fe

islands nucleated on a

dislocation network of a

Cu/Pt (111) bilayer at 250 K.

(Reprinted with permission

from [1.135]. © 1998 Nature

Publishing Group)



1.5.3 Chiral Kagomé Lattice from Molecular Bricks

Long-range periodic nanonetworks can be formed on a surface atomic lattice using

simple linear molecular bricks. Making use of, e.g., dicarbonitrile-pentaphenyl NCPh5 -CN (Fig. 1.32a) a uniform tiling forms (Fig. 1.32b) where two triangles and

two hexagons join each vertex, which is known in natural science as “Kagomé”

lattice (see [1.136]). The molecular networks are commensurate with the underlying Ag (111) surface, with the terminal benzonitrile group of the NC-Ph5 -CN

molecule showing a rotation of 20◦ around the molecular axis (Fig. 1.32c–f) as

determined by near-edge x-ray absorption fine structure spectroscopy (NEXAFS;

see [1.136]) and supported by extended Hückel theory calculations. This suggests

that the terminal Ph–CN groups are rotated to form a CN π-bond instead of a CN–

H linkage, demonstrating the interplay between substrate epitaxial fit, non-covalent

lateral interactions, and the molecules’ conformational flexibility.



30



1 Introduction and Some Physical Principles



Fig. 1.32 Kagomé lattice formed by dicarbonitrile–pentaphenyl NC–Ph5 –CN molecules selfassembled on a Ag (111) surface. (a) Structure model of the NC–Ph5 –CN building block. (b)

High-resolution scanning tunneling micrograph identifying two different types of nodes in the

Kagomé lattice. (c, d) 3D representations of structural models of two specific non-planar nodal

geometries associated with molecular flexure. (e, f) The corresponding charge density contour

plots mimic the main features of the experimental data. (Reprinted with permission from [1.136].

© 2008 American Chemical Society)



1.5.4 Self-Assembled Monolayers (SAMs)

For SAMs, synthetic chemistry is used only to construct the constituent molecules,

such as thiols and silanes, and weaker van der Waals interactions are involved in

arranging and binding the constituents together into a structure. The weak bonding makes solution, and hence reversible processing



√ of SAMs, possible. A typical

alkanethiol (Fig. 1.33) monolayer forms a ( 3 × 3) R 30◦ structure (see [1.131])



Fig. 1.33 Schematic diagram

of a thiol molecule for

building a self-assembled

monolayer. The sulfur group

links the molecule to the gold

surface. The head group can

be designed to provide

virtually any surface

chemistry or binding

capacity. (Reprinted with

permission from [1.131].

© 2006 Sigma-Aldrich)



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