Electron spin polarisation

The secondary electron spin-polarisation spectroscopy (SESPS).112... 

Various experimental methods have been developed for investigating the magnetoelastic properties of thin films and nanoscale magnetic systems. In the following subsections, we discuss the most important ones (i) the magnetoelastic cantilever, (ii) strain induced anisotropy, (iii) magnetostriction in spin valves, (iv) strain modulated ferromagnetic resonance, (v) secondary-electron spin-polarisation, and (vi) strain-induced anisotropy due to the spontaneous strains. 

Optical electron spin polarisation (OEP) is the term used to describe a non-Boltzmann distribution of the populations of the three zero-field or Zeeman components of an optically-excited triplet state. This non-thermal equilibrium can be a stationary or a non-stationary state. The optical excitation, that is e.g. the UV excitation, must be neither narrow-band nor polarised, and at low temperatures, OEP is the normal case for most triplet states in organic tt-electron systems. The OEP is... 

The total electron density is just the sum of the densities for the two types of electron. The exchange-correlation functional is typically different for the two cases, leading to a set of spin-polarised Kohn-Sham equations ... 

Perhaps the most important conclusion to be drawn from results for metal atoms in groups such as 7SiL3 or -PL3+ is undetectably small (70,71). Indeed, the R2C- moiety displays hyperfine interaction with H and 13C that suggest normal planarity at carbon with essentially unit spin-density thereon, and coupling to the metal atom (specifically, 31P) is small and probably negative. This implies that spin-density is acquired by spin-polarisation of the C-M o-electrons and not by p -d delocalisation, as is so often... 

In the past, electron energy calculations have failed dramatically for magnetic elements since spin polarisation was not included. However, this can now be taken into account quite extensively (Moruzzi and Marcus 1988b, 1990, Asada and Terakura 1993) and calculations can reproduce the correct groimd states for the magnetic elements. 

It should be emphasised that it is the rule rather than the exception for p to change markedly with crystal structure (Table 8.2). It is therefore unwise to assume that various metastable allotropes can be given the same value of P for the stable structure. In some cases values of p can be extrapolated from stable or metastable alloys with the requisite crystal structure, but in others this is not possible. A significant development is that it is now possible to include spin polarisation in electron energy calculations (Moruzzi and Marcus 1988, 1990a,b, Asada and Terakura 1995). This allows a calculation of the equilibrium value of to be made in any desired crystal structure. More importantly, such values are in good accord with known values for equilibrium phases (Table 8.2). It has also been shown that magnetic orbital contributions play a relatively minor role (Eriksson et al. 1990), so calculated values of P for metastable phases should be reasonably reliable. 

Since the heroic early mechanistic investigations, there have been two developments of major significance in radical chemistry. The first was the advent of electron spin resonance (ESR) spectroscopy (and the associated technique of chemically induced dynamic nuclear polarisation, CIDNP) [24], which provided structural as well as kinetic information the second is the more recent development of a wide range of synthetically useful radical reactions [20]. Another recent development, the combination of the pulse radiolysis and laser-flash photolysis techniques, is enormously powerful for the study of radicals but beyond the scope of this book. 

The spin is an inherent property of an electron. Since the photo- or Auger electrons are ejected in a certain direction in space, for an ensemble of these electrons a spin polarisation vector P can be defined which gives the excess of individual spin components measured in three orthogonal directions (see Section 9.2.1). In Fig. 1.5 the components of P are shown for a convenient decomposition into one longitudinal, Plong, and two transverse components, P,ranS and PtransX, respectively. The measurement of these components requires an electron detector which is sensitive to spin. An example of the spectrometry of photoelectrons with spin-analysis will be described in Section 5.4. 

These agree rather well with the experimental values listed above, suggesting that the ionic model is a good one. On the other hand, the negative Fermi contact constant can only arise through polarisation of the electron spins in a covalent bond between the two atoms. The electric dipole moment also seems to be inconsistent with a purely ionic model, yet the quadrupole coupling constant eq0Q is very close to that of the ionic molecule LiF. 

For the case of a purely electrostatic external potential, P = (F , 0), the complete proof of the relativistic HK-theorem can be repeated using just the zeroth component f (x) of the four current (in the following often denoted by the more familiar n x)), i.e. the structure of the external potential determines the minimum set of basic variables for a DFT approach. As a consequence the ground state and all observables, in this case, can be understood as unique functionals of the density n only. This does, however, not imply that the spatial components of the current vanish, but rather that j(jc) = < o[w]liWI oM) has to be interpreted as a functional of n(x). Thus for standard electronic structure problems one can choose between a four current DFT description and a formulation solely in terms of n x), although one might expect the former approach to be more useful in applications to systems with j x) 0 as soon as approximations are involved. This situation is similar to the nonrelativistic case where for a spin-polarised system not subject to an external magnetic field B both the 0 limit of spin-density functional theory as well as the original pure density functional theory can be used. While the former leads in practice to more accurate results for actual spin-polarised systems (as one additional symmetry of the system is take into account explicitly), both approaches coincide for unpolarized systems. 

In 1960 s, CIDEP was less popular than CIDNP because CIDEP did need much faster measuring techniques than CIDNP. This is due to much faster relaxation times (usually less than 1 /r s) of polarised electron spins than those (usually a few second for protons) of nuclear spins. In 1968, Smaller et al. [2] observed a population inversion for the cyclopentyl radical with a 2-MHz ESR apparatus coupled with a 15 MeV electron beam with pulse duration of 0.5 -4.0 /z s. The response time of the system corresponded to a time constant of 1.6/z s. In 1970, Atkins et al. [3] obtained the photo-CIDEP for the ketyl radical from benzophenone in paraffin solvents with a 2-MHz ESR apparatus coupled with a 20-ns laser flash. Under favorable chemical conditions, Wong and Wan [4] demonstrated that the photo-CIDEP for some semiquinone radicals in alcohol solvents could be observed with a commercial ESR spectrometer having a 100-kHz modulation unit and a custom-designed rotating sector giving light pulses. 

An ensemble of electrons is said to be polarised if there is a preferential orientation of the electron spins. If there are N- electrons with spins parallel to a particular direction or axis of quantisation and N[ with spins antiparallel to that direction, then the component of the electron polarisation vector P = (Px,Py,Pz) in that direction is defined by... 

McClelland, Kelley and Celotta (1986) were the first to measure superelastic scattering in the configuration where the spins of both the incoming electron and target atom were polarised, ensuring that the transitions studied are transitions between well-characterised pure quantum states. In particular they studied the superelastic scattering of spin polarised electrons from the mp = 3 and mp = —3 states of Na 3 P3/2 atoms (or the m/ = +1 and m/ = — 1 states on making the conventional assumption... 

In conventional collision experiments the strong Coulomb interaction generally masks the much weaker relativistic spin-dependent interactions. The role of the spin-dependent interactions, such as the exchange and spin—orbit interactions, has also been clarified by sophisticated measurements with spin-polarised electrons and/or spin-polarised targets, sometimes employing spin analysis after the collision process (Kessler, 1985, 1991 Hanne, 1983). 

Such measurements were first applied with considerable success to elastic scattering. Indeed one was able to discuss experiments which would determine all the theoretically calculable amplitudes (Bederson, 1970). For inelastic processes, such measurements necessitate the simultaneous application of spin selection techniques and the alignment and orientation measurements discussed in the previous chapter. The experiments have become feasible with the advancement of experimental techniques. The first successful differential electron impact excitation study with spin-polarised electrons and alignment and orientation measurements was performed by Goeke et al. (1983) for the e—Hg case. McClelland, Kelley and Celotta (1985, 1986) carried out a systematic study for superelastic scattering of polarised electrons from polarised laser-excited Na (3 P) atoms. This system is essentially a two-electron collision system in which spin exchange is the dominant spin-dependent interaction. It thus allows one to obtain... 

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