Spin polarisation

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 ... 

This result is remarkably simple as compared to the usual methods. For a spin-polarised potential V, Kraft, Oppeneer, Antonov and Eschrig (1995) used the elimination method and found the corrections as a sum of 9 terms, which is equivalent to our Eq.(ll). They notice that three terms of their sum have a known physical meaning (spin-orbit, Darwin and mass-velocity corrections), but the other terms have no special name . 

Spin-polarised scanning tunnelling microscopy (SP-STM) Magnetic force scanning tunnelling microscopy (MF-STM)... 

Another technique is spin polarised EELS, or SPEELS, which can provide information on phenomena such as magnetic coupling and exchange excitation processes, but SPEELS will not be discussed further here. 

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. 

Transitions from a localized to an itinerant state of an unfilled shell are not a special property of actinides they can, for instance, be induced by pressure as they rue in Ce and in other lanthanides or heavy actinides under pressure (see Chap. C). The uniqueness for the actinide metals series lies in the fact that the transition occurs naturally almost as a pure consequence of the increase of the magnetic moment due to unpaired spins, which is maximum at the half-filled shell. The concept has resulted in re-writing the Periodic Chart in such a way as to make the onset of an atomic magnetic moment the ordering rule (see Fig. 1 of Chap. E). Whether the spin-polarisation model is the only way to explain the transition remains an open question. In a very recent article by Harrison an Ander-... 

The Stoner product of UN (see Chaps. A and D) is greater than one, in agreement with the antiferromagnetic behaviour of this solid. The antiferromagnetism was attributed to itinerant band magnetism (as in some d-metals and compounds but unlike light actinide metals). In fact, cohesive properties of this solid have been well explained in a pure spin-polarised picture and Fournier et al. have shown that the magnetic uranium sublattice moment and the Neel temperature have a similar pressure dependence. Discrepancies existed, however, between calculations and experiments ... 

I-spin polarisation remains observable under all conditions.26... 

Poluektov et al. used high-frequency time-resolved spin-polarised EPR spectroscopy of radical pairs to characterise quantitatively isotopically labelled quinine exchange in the PS I reaction centre of proteins.91 Intra-subunit interactions in the Fe-S cluster of PS I of Synechocystis sp. PCC 6803 were studied by using mutations and following the changes in stabilisation of the cluster by EPR spectroscopy.92... 

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. 

Short Tj (spin lattice) NMR relaxation time, since spin polarisation may be readily transferred on to the metal centre. 

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. 

Many techniques in SS NMR make use of dipolar couplings in order to transfer spin polarisation between adjacent spins. The usefulness of this type of experiments is due to the fact that value of dipolar coupling Rdip depends only on the distance between spins and is expressed by the simple equation ... 

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. 

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