Magnetism and Spintronics in Carbon and Carbon Nanostructured Materials

By Sekhar Chandra Ray

Magnetism and Spintronics in Carbon and Carbon Nanostructured Materials offers coverage of electronic structure, magnetic properties and their spin injection, and the transport properties of DLC, graphene, graphene oxide, carbon nanotubes, fullerenes, and their different composite materials. This book is a valuable resource for those doing research or working with carbon and carbon-related nanostructured materials for electronic and magnetic devices.

Carbon-based nanomaterials are promising for spintronic applications because their weak spin-orbit (SO) coupling and hyperfine interaction in carbon atoms entail exceptionally long spin diffusion lengths (~100µm) in carbon nanotubes and graphene. The exceptional electronic and transport features of carbon nanomaterials could be exploited to build multifunctional spintronic devices. However, a large spin diffusion length comes at the price of small SO coupling, which limits the possibility of manipulating electrons via an external applied field.

• Assesses the relative utility of a variety of carbon-based nanomaterials for spintronics applications
• Analyzes the specific properties that make carbon and carbon nanostructured materials optimal for spintronics and magnetic applications
• Discusses the major challenges to using carbon nanostructured materials as magnetic agents on a mass scale

• Language: English
• Publisher: Elsevier Science
• Release date: Jan 15, 2020
• ISBN: 9780128176818

Sekhar Chandra Ray

Sekhar Chandra Ray is Professor of Physics at the University of South Africa, specializing in Experimental Condensed Matter Physics. His research focuses on carbon nanostructure materials on bio-imaging processes and photovoltaic materials. He has published 78 peer-reviewed research articles, with more than 1100 citations in internationally recognised journals.

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The fundamental aspects of spintronics

Abstract

Spintronics, or spin electronics, involve the study of active control and manipulation of spin degrees of freedom in solid-state systems. Electrons have a charge and spin associated with them. While the conventional semiconductor electronics make use of the charge, property of the electron only, the spintronic devices make use of the spin property of an electron. The use of magnetic materials in spintronic devices helps in storing information, to provide nonvolatility and an endurance that is unmatched by other memory technologies such as resistive or phase-change memory. Making use of the spin nature of electrons provides new and effective ways to control the motion of electrons, which helps in writing and reading information. As a result, these memory devices have a huge potential. The aim of this chapter is about the fundamental aspects of the spintronics: spin coherence, spin entanglement, generation of carrier-spin polarization, control spin and charge dynamics, spin injection, spin-polarized transport, etc.

Keywords

Spintronics; spin transport; spin polarization

1.1 Introduction

Information technology is one of the important issues in the 21st century. As the Moore law gradually loses its effect, conventional charge-based electronics will come to an end in the near future. Developing alternative high-speed and low-energy-consuming information technology is urgently needed. Many new methodologies have been proposed, such as molecular electronics, nano-electronics, spintronics, and quantum information techniques, among which spintronics is one of the most promising ones. Spintronics is a field of research exploiting the influence of the electron spin on electrical conduction. It is mainly known for the giant magnetoresistance (GMR) (Baibich et al., 1998; Binash et al., 1989) and the large increase of the hard disk capacity obtained with the read heads based on GMR. But the research on spintronics has also revealed many other interesting effects and is now developing along promising novel directions. Compared to other methodologies, spintronics is compatible with conventional electronics, thus many techniques used in conventional electronics can be directly extended to spintronics. "Spintronics, known as spin electronics, involves the study of active control and manipulation of the intrinsic spin of the electrical charge of electron and its associated magnetic moment in solid-state system. The approach in the field of electronics is based on the up- or downspin of the carriers rather than on electrons or holes as in traditional semiconductor electronics. It is different from conventional electronics, which uses the electron’s charge degree of freedom for information processing; spintronics is devoted to incorporating the electron’s spin degree of freedom. In an ideal situation, there will purely be spin current and no charge current in the spintronics circuit, thus no heat will be created and wasted. There has been a great deal of recent interest in the concept of spintronics (Prinz, 1995, 1998). Spintronics is a multidisciplinary field whose central theme is the active manipulation of spin degree of freedom in solid-state system. Controlling and probing spin-polarized charge carrier (or manipulation of electron spin) in semiconductors and/or metals via electrical means, an attractive route toward the development of practical semiconductor/metal spintronic devices, which are expected to have a strong impact on future information processing and storage technologies. It is the use of a fundamental property of particles known as spin for information processing. It carries information in both the charge and spin of an electron, potentially offers devices with a great diversity of functionality in solid-state devices and other devices that exploit spin properties. In the case of the electron, the spin can in fact assume only the values +1/2 or −1/2: an eloquent invitation to use it to encode information, in analogy to bits 0 and 1" of the binary code (Fig. 1–1). In ferromagnetic materials, the spin of the electrons can be modified from the outside, applying a magnetic field. When the magnetic field is removed, the new spin values are retained, that is, the encoded information remains firmly stored without need for power and without the risk of demagnetization.

Figure 1–1 Manipulation of electron movement (electron spin): spin-up (anticlockwise) and spin-down (clockwise).

Spin transport and spin relaxation in semiconductors and metals are important solid-state physics issues that are included in the fundamental research along with new technology being implemented in the electronic storage technology. Spintronics helped in creating a prototype device that is used in the industry as a read head, and a memory-storage cell is the giant-magnetoresistive (GMR) sandwich structure, which consists of alternating ferromagnetic and nonmagnetic metal layers. Depending on the relative orientation of the magnetizations in the magnetic layers, the device resistance changes from small (parallel magnetizations) to large (antiparallel magnetizations). This change in resistance (also called magnetoresistance) is used to sense changes in magnetic fields. Electron spin can be identified as a magnetic field having one or two positions, known as up and down. This gives an extra two binary states to the conventional high and low-logic values, which are represented by simple currents. When the spin state is added to the mix, a bit can have four possible states, which can be called up-high, up-low, down-high, and down-low. These four states represent quantum bits or qubits.

Why do we need spintronics?

• Failure of Moore’s law

• Low power consumption

• Less electric current required

• Faster devices

• Larger storage capacity

• Smaller devices

• Less heat dissipation

• Spintronic memory is nonvolatile

• Spin manipulation is faster, hence greater reading and writing speed

Metallic spintronics has already delivered functional devices (GMR read heads in large-capacity hard disk drives), and magnetic random access memory (RAM) (MRAM), of insulator spintronics [magnetic tunnel junctions (MTJs)]. The basic spin valve has evolved to a related thin-layered structure—MTJ—that displays giant tunneling magnetoresistance (TMR), a phenomenon where electrons tunnel through a thin insulator. This means the TMR signal is much larger than that from a GMR spin valve: indeed, it is almost 100 times larger. TMR is also the basis of magnetic RAM (MRAM), a nonvolatile memory that uses magnetic moments to retain data instead of electrical charges.

However, the current basic physics research is mostly focused on semiconductor spintronics. Although creation of inhomogeneous spin distribution does not require energy penalty (in contrast to charge distributions of conventional electronics), spin is not conserved whereas charge is. Thus efforts in semiconductor spintronics research are focused on basic problems, such as coherent manipulation of electron spin at a given location, transporting spins between different locations within conventional semiconductor environment, all-electrical spin control via spin–orbit interactions, diluted magnetic semiconductors, and fixed or mobile spin qubits for quantum computing. Other possible applications of spintronics include high-speed magnetic filters, sensors, quantum transistors, and spin qubits for quantum computers (Steane, 1998; Loss et al., 1998; Burkard et al., 1999). Moreover, these spintronic devices might lead to quantum computer and quantum communication based on electronic solid-state devices, thus changing the perspective of information technology in the 21st century. More fundamental research will, however, be needed before a practical spintronic device can be demonstrated, as much remains to be understood about spin coherence, spin entanglement, spin dynamics, spin relaxation, spin transports, etc.—the different fundamental aspects of spintronics.

Spintronics faces a number of challenges, including spin generation and injection, long distance spin transport, and manipulation and detection of spin orientation. In solving these issues, new concepts and spintronics materials were proposed one after another, such as half metals, spin-gapless semiconductors, and bipolar magnetic semiconductors. Topological insulators can also be viewed as a special class of spintronics materials, with their surface states used for pure spin generation and transportation. In designing these spintronics materials, first-principles calculations play a very important role. In this section, we attempt to give a brief discussion on the basic principles and theoretical design of these materials. Meanwhile, we also give some attention to antiferromagnetic (AFM) spintronics, which is mainly based on antiferromagnets and has aroused much interest in recent years.

1.2 Fundamental aspects of spintronics

The fundamental aspects of spintronics are underlying the generation of carrier-spin polarization, spin coherence, spin entanglement, control spin and charge dynamics, spin injection, and spin-polarized transport in semiconducting/metallic electronic materials.

1.2.1 Spin polarization

Spin polarization is the degree to which the spin, that is, the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in ferromagnetic materials giving rise to spin-polarized currents. Spin polarization, not only of electrons, but also of holes, nuclei, and the excitations, can be defined as PX=XS/X; where the ratio of the difference XS=Xλ−X−λ and the sum X=Xλ+X−λ of the spin-resolved λ components for a particular quantity X. To avoid ambiguity as to what precisely is meant by spin polarization, both the choices of the spin-resolved components and the relevant physical quantity X need to be specified. Conventionally, λ is taken to be ↑ or + (numerical value +1) for spin-up, and ↓ or − (numerical value −1) for spin-down, with respect to the chosen axis of quantization (along the spin angular momentum, applied magnetic field, magnetization, or direction of light propagation). In ferromagnetic metals (FMs), it is customary to refer to ↑ (↓) as carriers with magnetic moment parallel (antiparallel) to the magnetization or, equivalently, as carriers with majority or minority spin (Tedrow et al., 1973). In semiconductors the terms majority and minority usually refer to relative populations of the carriers while ↑ or + and ↓ or − correspond to the quantum numbers mj with respect to the z axis taken along the direction of the light propagation or along the applied magnetic field (Meier and Zakharchenya, 1984; Jonker et al., 2003).

1.2.2 Spin relaxation

Having established that one can generate spin-polarized earners, the most important issue is to determine how long these electrons remember their spin orientation. This is especially important for electronic applications, because if the spins relax too rapidly, the distances traversed by the spin-polarized current in a device will be too short to serve any practical purpose (, the transverse component of the magnetization vector, exponentially decays toward its equilibrium value in nuclear magnetic resonance (NMR) and magnetic resonance imaging. It is characterized by the spin–spin relaxation time, known as T2, a time constant characterizing the signal decay. It is named in contrast to T1, the spin–lattice relaxation time. It is the time it takes for the magnetic resonance signal to irreversibly decay (37% i.e., 1/e. T2 relaxation generally proceeds more rapidly than T1 recovery and different materials have different T2. When excited nuclear spins, lying partially in the transverse plane, interact with each other by the local magnetic field in-homogeneities on the micro- and nanoscales, their respective accumulated phases deviate from expected values. While the slow- or nonvarying component of this deviation is reversible, some net signal will inevitably be lost due to short-lived interactions, such as collisions and diffusion, through heterogeneous space. T2 decay does not occur due to the tilting of the magnetization vector away from the transverse plane.

Spin relaxation is very sensitive to the electronic band structure. Spins of conduction electrons decay because of the spin–orbit interaction and momentum scattering. At low temperatures (T≤20K), spin relaxation is caused by impurity scattering and is temperature independent. At higher temperatures, electrons lose spin coherence by colliding with phonons (phonons can induce a spin flip because in the presence of a spin–orbit coupling, electronic Bloch states are not spin Eigen states). Spin relaxation rate 1/T1 increases as temperature increases, with the growth becoming linear above the Debye temperature. This mechanism (Elliott, 1954; Yafet, 1963) is the most important spin relaxation mechanism in metals and semiconductors with inversion symmetry.

Different spin relaxation processes have been found to be important in solids:

• Elliot–Yafet

• D’yakonov–Perel’

• Bir–Aronov–Pikus

• Hyperfine interaction

Nonequilibrium distribution of spins caused by interfaces or spin injections is brought back into equilibrium by these mechanisms, which can be obstacles for spintronics. Usually, suppressions of these effects are important issues in research and development though, sometimes, the relaxation would help fast device action.

1.2.3 Spin injection

Spin injection in a nonmagnetic material is, in most cases, achieved by the creation of a nonequilibrium spin population (called spin accumulation) at the interface with a magnetic electrode. The rate of spin injection depends on the spin relaxation and dephasing mechanisms in the nonmagnetic material, which tends to restore the equilibrium in the accumulated spin population; the relatively long lifetimes of nonequilibrium electronic spins in semiconductors and metals, of about 1 ns, are essential for spintronic devices. The spin lifetimes can however increase to hundreds of nanoseconds in confined semiconductor heterostructures, which imply transport of coherent spin packets over hundreds of μm.

1.2.4 Ohmic injection

In an FM the electrical conductivity of the majority-spin (spin-up) electrons differs substantially from minority spin (spin-down), resulting in a spin-polarized electric current. The most straightforward approach to spin injection is the formation of an ohmic contact between an FM and a semiconductor, anticipating a spin-polarized current in the semiconductor. However, typical metal–semiconductor ohmic contacts result from heavily doping the semiconductor surface, leading to spin–flip scattering and loss of the spin polarization. Following up on earlier studies (Johnson et al., 1987; Van Son et al., 1987; Valet et al., 1993; HershÞeld et al., 1997) of diffusive spin transport, a recent work by Schmidt et al. (2000) has pointed out a fundamental problem regarding ohmic spin injection across ideal FM–nonferromagnet (NFM) interfaces. The effectiveness of the spin injection depends on the ratio of the (spin-dependent) conductivities of the FM and NFM electrodes, σF and σN, respectively. When σF≤σN, as in the case of a typical metal, then efficient and substantial spin injection can occur, but when the NFM electrode is a semiconductor, σF σN, and the spin-injection efficiency will be very low. Only for a ferromagnet where the conduction electrons are nearly 100% spin polarized can efficient spin injection be expected in the diffusive transport. A large number of materials apparently have such half-metal-ferromagnetic properties (De Grot et al., 1983; Kamper et al., 1988). Johnson et al. have proposed and pursued (Johnson 1998, 2001; Hammar et al., 1999, 2000a,b) an approach that may overcome this obstacle to spin injection by taking advantage of the splitting of the spin degeneracy of electrons confined in a semiconductor two-dimensional (2D) quantum well structure. The splitting is due to the spin–orbit effect that can arise from an asymmetry in the confining potential (Bychkov et al., 1994). The result can be an inducement of a nonequilibrium spin polarization if the 2D electron gas is carrying a current (Vorob’ev et al., 1979). However, as in the ohmic contact experiments, the small percentage change in device resistance, that is observed with changes in ferromagnet orientation, has led to suggestions of an alternative, local-Hall-effect explanation for the data and to other questions regarding this approach (Monzon et al., 2000; Wees, 2000; Hammar et al., 2000a,b).

1.2.5 Tunnel injection

Alvarado and Renaud (Alvarado et al., 1992), using a scanning tunneling microscope (STM) with a ferromagnetic tip, showed that a vacuum tunneling process can effectively inject spins into a semiconductor. A recent extension of this has examined the effect of surface structure on spin-dependent STM tunneling (LaBella et al., 2001). The development of FM-insulator–FM-tunnel junctions with high magnetoresistance has also demonstrated that tunnel barriers can result in the conservation of the spin polarization during tunneling, suggesting that tunneling may be a much more effective means for achieving spin injection than diffusive transport. Theoretical work by Rashba (2000) has quantitatively developed the understanding of the potential effectiveness of tunnel injection. If the impedance of a barrier at an interface is sufficiently high, then the transport across that interface will be determined by the (spin-dependent) density of the electronic states of the two electrodes that are involved in the tunneling process. The current passing through the barrier is then sufficiently small enough for the electrodes to remain in equilibrium and the relative (spin-dependent) conductivities of the electrodes play no substantial role in defining or limiting the spin-dependent transport across the interface. Thus either a metal–insulator semiconductor tunnel diode or a metal–semiconductor Schottky barrier diode that uses an FM electrode can be expected to be an effective means for injecting spins into a semiconductor system.

1.2.6 Ballistic electron injection

An alternative to tunnel injection is spin injection across ferromagnet–semiconductor interfaces in the ballistic regime, with the difference between the two spin conduction subbands of the FM and the conduction band of the semiconductor determining the spin-dependent interfacial ballistic electron transmission probability. It is generally assumed that the transverse momentum of an incident electron is conserved, and this determines the ballistic transmission and reflection probabilities of the interface (Kirczenow, 2001; Grundler, 2001). Also, once a spin-polarized electron enters the semiconductor electrode, the probability that it will be elastically scattered back into the ferromagnetic injector must be very small. If the device design also involves, for example, the spin-dependent capture of an injected carrier by another ferromagnetic electrode, then transport through the semiconductor region must be fully ballistic. However, if the objective is simply efficient spin injection, a three-dimensional ballistic point contact between a ferromagnet and a semiconductor should be effective. Recent experiments with point contacts formed between ferromagnetic and non-FMs have demonstrated the ballistic point-contact injection of high (>40%) spin-polarized currents into the NFM (Upadhyay et al., 1998, 1999).

1.2.7 Hot electron injection

Another spin technique involves the use of polarized hot electrons injection, having energies that are much greater than EFEF (Monsma et al., 1995; Jansen et al., 2001; Rippard et al., 2000). As the majority-spin and minority-spin electrons have much different inelastic mean free paths, hot electron passage through, for example, a 3-nm Co layer, is sufficient to result in a ballistic electron current that is more than 90% polarized (Rippard et al., 2000). This highly polarized hot electron current can then continue on to an underlying metal–semiconductor interface where a portion of the beam will enter the semiconductor, with the transmission probability being determined by energy and momentum constraints imposed by the band structure difference between the semiconductor and metal at the interface. If there is no substantial spin–flip scattering at the interface, the ballistic electron current entering the semiconductor will also be very highly polarized (>90%), and the injection energy, relative to the bottom of the semiconductor conduction band, will be tunable through the tunnel injection bias. The disadvantage of hot electron injection is that the overall efficiency is low.

1.2.8 Spin transport

Particular interest to the spin transport theory in semiconductor systems has been the question as to whether the quasiindependent electron model can adequately account for the experimental results, or whether many-body or correlated electron processes are important. The presence of spin-polarized carriers gives rise to both modified charge transport and intrinsic spin transport, absent in the unpolarized case. Each of these aspects provides information about the degree of spin polarization, which can be utilized in spintronics. Spin-polarized transport will occur naturally in any material for which there is an imbalance of the spin populations at the Fermi level. This imbalance commonly occurs in FMs because the density of states available to spin-up and spin-down electrons is often nearly identical, but the states are shifted in energy with respect to each other (Fig. 1–2). This shift results in an unequal filling of the bands, which is the source of the net magnetic moment for the materials, but it can also cause the spin-up and spin-down carriers at the Fermi level to be unequal in number, character, and mobility. This inequality can produce a net spin polarization in a transport measurement, but the sign and magnitude of that polarization depends on the specific measurement being made. For example, an FM may be used as a source of spin-polarized carriers injected into a semiconductor, a superconductor, or a normal metal or can be used to tunnel through an insulating barrier. The nature of the specific spin-polarized carriers and the electronic energy states associated with each material must be identified in each case. The most dramatic effects are generally seen for the most highly polarized currents; therefore there are continuing efforts to find 100% spin-polarized conducting materials. These are materials that have only one occupied spin band at the Fermi level. Materials that are only partially polarized such as Fe, Co, Ni, and their alloys, which have a polarization P of 40%–50% (Soulen et al., 1998), are, however, adequate to develop technologically useful devices. Here the polarization P is defined in terms of the number of carriers n that have spin-up (n↑) or spin-down (n↓), as