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The magnetocrystalline anisotropy (MCA) of bulk and thick films of FePt is calculated from a 'first-principles' theory. The starting point is a description from electronic density functional theory for systems of interacting electrons moving in lattices of ions. Relativistic effects such as spin–orbit coupling are included. FePt readily transforms into a CuAu-type (L 10) ordered phase and this coincides with the material's high anisotropy. Here we describe how to calculate the MCA of a partially ordered alloy and to extract its dependence on the long range chemical order parameter η. We present calculations of the MCA of FePt as a function of η and find excellent agreement with the experimental data of Okamoto et al (2002 Phys. Rev. B 66 024413) and others with respect to the magnetic easy axis, the magnitude of the MCA and its trend with decreasing η. We also study the paramagnetic phase of the ordered alloy using the 'disordered local moment' picture of metallic magnetism at finite temperatures. We calculate a Curie temperature of 935 K in reasonable agreement with experiment (710 K) and find the easy axis for the onset of ferromagnetic order to coincide with the magnetic easy axis found at low temperatures.

The electronic structure of invar alloys (i.e. materials in which the near absence of thermal expansion is observed) has been the focus of much study, owing both to the technological applications of these materials and interest in the fundamental mechanism that is responsible for the effect. Here, calculations of the magnetic Compton profiles are presented for ordered and disordered Fe3Pt alloys. Using linear muffin-tin orbital and KKR methods, the latter incorporating the coherent potential approximation to describe the substitutional disorder, the electronic band structure and measurable quantities such as the Fermi surface topology are presented.

The magnetic properties of FePt samples, potential materials for high density recording media, depend sharply on the degree of chemical ordering produced during their preparation. This has prompted our investigation of the chemical order in both paramagnetic (P) and ferromagnetic (F) phases of a Fe0.5Pt0.5 solid solution and its effect upon the magnetocrystalline anisotropy (MAE) of the latter phase. Our “first-principles” theory uses density functional electronic structure calculations and a mean field treatment of both compositional and magnetic “local moment” fluctuations. We find both phases to be unstable to L10 (CuAu)-type order below temperatures of 1975 K (P) and 1565 K (F) which compares well with that found experimentally (≈1600 K) and our estimate of the Curie temperature as 575 K is also in fair agreement (710 K). For L10 order the calculated MAE is uniaxial with a simple form, υL10c(0,0,1)2 sin2 θ, where the coefficient υL10=9.7×108 erg/cm3, c(0,0,1) is the degree of order (between 0 and 0.5)...

A theory is presented for describing the effects of annealing magnetic alloys in magnetic fields. It has an ab initio spin-polarized relativistic Korringa–Kohn– Rostoker coherent potential approximation (KKR-CPA) electronic structure basis and uses the framework of concentration waves. Alloys which would otherwise be soft magnets are found experimentally to develop directional chemical order and significant uniaxial anisotropy when annealed in magnetic fields. Our approach is able to provide a quantitative description of these effects together with the underlying electronic mechanisms. We describe applications to the soft magnetic alloys permalloy and FeCo.

We study the magnetocrystalline anisotropy of Fe0.5Pd0.5 alloy using the first-principles spin-polarized relativistic Korringa–Kohn–Rostoker coherentpotential approximation. We investigate the effect of long-ranged chemical order on the magnitude as well as the direction of easy magnetization. We find that in this alloy, the chemical order enhances the magnitude of the magnetocrystalline anisotropy energy as well as altering the easy axis. In particular, for the L10 ordered alloy the easy axis is perpendicular to the alternating layers of Fe and Pd with quite large magnetocrystalline anisotropy energy 124 µeV. These observations are in very good agreement with experiments. We also find that it is the electronic structure in the vicinity of the Fermi surface that is responsible for this effect.

We discuss the peculiarities of the CuPd phase diagram in relation with the Fermi surface of the random alloys, on the basis of first-principle calculations. In particular we study the Fermi surface nesting vectors as functions of the concentration and along a tetragonal Bain path. It turns out that the nesting vectors that can be associated with the experimentally observed ordering transitions towards the B2 phase and L12 phases are commensurate with the lattice only at non-stoichiometric concentrations. The competition between this frustration effect and the electrostatic gain obtained by chemical ordering determines the critical concentrations for the transitions. We argue that the inclusion of these Fermi surface frustration effects is necessary to obtain agreement between theory and experiment on the determination of the phase diagram.

We apply a recently developed first-principles asymptotic approach to the problem of the oscillatory exchange coupling ~OEC! in the Co/Cu(12x)Nix /Co trilayer system for all ~100!, ~110!, and ~111! directions of growth. We compare results of the asymptotic analysis with full calculations. Our results are consistent with the available experimental data and give strong evidence for the existence of the exponential decay in the asymptotic form of the OEC for x.0.04. Moreover, we discover a caliper vector of the alloy Fermi surface Q(100) (3) which did not exist in the case of pure Cu, but contributes to the OEC significantly for x>0.11.

We describe our theoretical formalism and computational scheme for making ab initio calculations of the dynamic paramagnetic spin susceptibilities of metals and alloys at finite temperatures. Its basis is timedependent density functional theory within an electronic multiple scattering, imaginary time Green function formalism. Results receive a natural interpretation in terms of overdamped oscillator systems making them suitable for incorporation into spin fluctuation theories. For illustration we apply our method to the nearly ferromagnetic metal Pd and the nearly antiferromagnetic chromium alloy Cr95V5. We compare and contrast the spin dynamics of these two metals and in each case identify those fluctuations with relaxation times much longer than typical electronic ‘‘hopping times.’’ There is renewed interest in spin fluctuations in materials close to magnetic order. This is due in part to a realization that nearly critical magnetic fluctuations may be important factors governing the nonconventional properties of a wide range of materials which include the high-Tc ~HTC! superconducting cuprates and heavy fermion systems. 1 The strongly correlated electrons in many of these systems, however, have meant that most theoretical work has concentrated on parametrized models in which the electronic motion is treated rather simply. Another complementary approach is to use an ab initio theory such as time-dependent density functional theory ~TDDFT !~ Ref. 2! but apply it to materials where it can be expected to work, i.e., where the effects of electron correlations are not so important, but which otherwise have important similarities to the systems in question. For example, with its perovskite structure containing transition metal ~TM!-oxygen planes Sr2RuO4 has several aspects in common with the HTC materials. But the presence of the 4d TM Ru rather than the narrower band 3d TM Cu means that electron correlation effects are smaller and therefore DFT-based calculations can provide a valuable starting point. Moreover, its exotic superconductivity at low temperature seems likely to be affected by spin fluctuations. 3‐5 Concerning another example, the transition temperature separating paramagnetic and magnetically ordered phases of the cubic transition metal compound MnSi, which has the B20 crystal structure, is driven down to zero temperature upon the application of pressure. In the vicinity of the critical pressure for this quantum phase transition the system exhibits

We have identified the pieces of the Fermi surface responsible for the long period oscillations of magnetic coupling across Cr and Cr(1 x)Vx alloy spacers in metallic multilayers. Analysing experiments and results of KKR-CPA calculations we find that the periods are determined by the extremal wave vectors of the hole pockets centered on the N-point in the Brillouin zone.

The cubic lattice symmetry of ferromagnetic homogeneously disordered alloys is broken when a compositional modulation is imposed. This can have a profound influence on the magnetocrystalline anisotropy energy (MAE). We describe our ab initio theory of this effect and use the framework of concentration waves with the electronic structure described within the spin-polarized relativistic Korringa-Kohn-Rostoker coherent-potential approximation. We find that ordering produces a 2 order of magnitude increase in the MAE as well as altering the equilibrium direction of magnetization. Using the same theoretical framework we also examine directional compositional order produced by magnetic annealing with an explicit study of permalloy. [S0031-9007(99)09484-3]

A scheme for making ab initio calculations of the dynamic paramagnetic spin susceptibilities of solids at finite temperatures is described. It is based on time-dependent density functional theory and employs an electronic multiple scattering formalism. Incommensurate and commensurate antiferromagnetic spin fluctuations in paramagnetic Cr and compositionally disordered Cr 95V5 and Cr95Re5 alloys are studied together with the connection with the nesting of their Fermi surfaces. We find that the spin fluctuations can be described rather simply in terms of an overdamped oscillator model. Good agreement with inelastic neutron scattering data is obtained. [S0031-9007(99)08949-8] PACS numbers: 75.40.Gb, 71.15.Mb, 75.10.Lp, 75.20.En Chromium is the archetypal itinerant antiferromagnet (AF) whose famous incommensurate spin density wave (SDW) ground state is determined by the nesting wave vectors qnest identified in the Fermi surface [1]. Chromium alloys also have varied AF properties [1] and their paramagnetic states have recently attracted attention owing, in part, to analogies drawn with the high temperature superconducting cuprates especially sLacSr12cd2CuO4. The incommensurate SDW fluctuations in these materials [2] are rather similar to those seen in the paramagnetic phase of Cr close to TN . Moreover “parent” materials La 2CuO4, in the one instance, and Cr95Mn5 or Cr95Re5, in the other, are simple commensurate AF materials which on lowering the electron concentration by suitable doping develop incommensurate spin fluctuations which may be promoted by imperfectly nested Fermi surfaces. Here we examine the nature of damped diffusive spin fluctuations in chromium above the Neel temperature TN which are precursory to the SDW ground state. We also study dilute chromium alloys, Cr95Re5 and Cr95V5, and obtain good agreement with experimental data. For example, recent inelastic neutron scattering experiments [1,3] have measured incommensurate AF “paramagnons,” persisting up to high frequencies in the latter system. We explore the temperature dependence, the variation with dopant concentration, and the evolution of the spin fluctuations in these systems from incommensurability to commensurability with increasing frequency and provide the first ab initio description of these effects. To this end we describe a new scheme for calculating the wave vector and frequency dependent dynamic spin susceptibility of metals which is based on the time-dependent density functional theory (TDDFT) of Gross et al. [4] and as such is an allelectron theory. For the first time the temperature dependent dynamic spin susceptibility of metals and alloys is calculated from this basis. There have been several simple parametrized models to describe the magnetic properties of Cr and its alloys [5]. All of these have concentrated on the approximately nested electron “jack” and slightly larger octahedral hole pieces of the Fermi surface [1] and, at best, have included only the effects of all the remaining electrons via an electron reservoir. We find similarities between our results and results from such models but show that a complete picture is obtained only when an electronic band-filling effect which favors a simple AF ordering at low temperature is also considered. We also find that the spin fluctuations are given an accurate description as over

We present a theory to study the relation between compositional order and magnetocrystalline anisotropy of ferromagnetic alloys. The ordering phenomenon is represented by static concentration waves. The electronic part is described within the spin-polarized relativistic Korringa-Kohn-Rostoker coherent-potential approximation. This scheme can be used to investigate the change in the magnitude as well as the direction of magnetic anisotropy in an alloy at the onset of ordering. The same framework can also be used to study directional chemical order produced by magnetic annealing. We have calculated the magnetocrystalline anisotropy energy of ordered fcc-Co0.5Pt0.5 alloy using this method. We find that the magnetocrystalline anisotropy energy of the ordered phase is two orders of magnitude larger than that of the disordered phase. Also, that the direction of ‘easy’ magnetization in the ordered phase depends on the type of ordering. These results are in good agreement with the experimental observations.

The deviations from linearity in the concentration dependence of lattice spacings in AgcPd1-c have been recently related to the topology changes shown by the Fermi Surface, or Electronic Topological Transitions (ETTs), of this alloy. Using an extension of the ETTs theory to finite-temperature and impurity scattering case, and in terms of a simple Rigid Band Model, we study such deviations and interpret them as the results of the filling of the hole pocket centered at theX point of the Brillouin Zone, remarking the role of the finiteness of the quasi-particle lifetime of the relevant states. We also show howab initio calculations based on the Coherent Potential Approximation underestimate these lifetimes.

We present some algorithms for improvements of band theory calculations based on the Korringa-Kohn-Rostoker method and on the coherent potential approximation, in the cases of ordered metals and random alloys. The purpose of our work was to develop a code flexible enough to deal on equal footing with any lattice geometry. The algorithms proposed are designed to achieve an arbitrary accuracy and to minimize the required computational efforts. In particular, we describe (i) an efficient and accurate method for the calculation of the KKR structure constants, and (ii) an adaptive method for the Brillouin zone integration. These algorithms have been tested for a free-electron Green{close_quote}s function and by explicit calculations for a number of systems and, when possible, discussed in comparison with other methods. {ital Ab initio} calculations for hexagonal close packed and face centered cubic Ti and for Cu{sub 0.75}-Pt{sub 0.25} random alloys are presented. {copyright} {ital 1997} {ital The American Physical Society}

We report an experimental and theoretical study of angle-resolved photoemission from the (1 1 1) surface of the ordered alloy CuAu I () structure. The aim of the work is to test the predictions of first-principle band structure calculations by examining the fine details of the electronic structure as probed by photoemission. We compare theory with the experimental measurements not by determining an `experimental' band structure, but rather by calculating theoretical photocurrent spectra using site potential functions determined from first-principle electronic structure calculations. We show that the one-particle theory is sufficient to explain the origin of the most important features in the experimental spectra.

We have calculated the Fermi surfaces of ${\mathrm{Ag}}_{\mathit{c}}$${\mathrm{Pd}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$ vs Ag atomic concentration, within the fully relativistic Korringa-Kohn-Rostoker--coherent-potential-approximation framework. The Fermi surfaces of these alloys change, on varying the concentration, from the Pd- to the Ag-like topology. This implies that a number of electronic topological transitions (ETT's) occur on changing the e/a ratio, as a consequence of the fact that the Fermi level moves away from the d states towards the sp states. It is well known that such changes in connectivity of the Fermi surfaces affect transport coefficients; however, as we have shown in Paper I, equilibrium properties such as equilibrium volume, specific heat, enthalpy of mixing, etc., also display anomalies at the same concentrations where such topological changes occur. In particular we have found 5 ETT's in correspondence to the deviations from Vegard's law of the lattice parameter shown in Paper I. Another unexpected result of this study is that, in the range of atomic concentration beteen 0.55 and 0.69, this alloy Fermi surface is simply connected, although nonspherical, as for a simple metal. Moreover, we show that a fully relativistic study is necessary for AgPd Fermi surfaces, because the spin-orbit interaction is responsible for the fact that the two hole pockets at X close at different concentrations.

We describe an ordering mechanism that arises due to coupling between electronic states at van Hove singularities. This novel mechanism, which naturally leads to ordered structures with small unit cells, couples states near the Fermi energy which are localized at high-symmetry points in {bold k} space, in contrast to the conventional mechanism which relies on large parallel sheets of Fermi surface. Using first-principles calculations of the electronic structure of ordered and disordered alloys, we show that this mechanism drives the unusual short- and long-range order found in fcc CuPt.

Notwithstanding the substitutional disorder, the Fermi surface of metallic alloys can be measured and computed. We show that, from the theoretical point of view, it is defined as the locus of the peaks of the Bloch Spectral Function (BSF). Such Fermi surfaces, on varying the atomic concentrations, may undergo changes of their topology, known as Electronic Topological Transitions (ETT). Thus, for instance, pockets of electrons or holes may appear or disappear, necks may open or close. ETTs cause anomalous behaviours of thermodynamic, transport and elastic properties of metals and constitute a fascinating field in the study of Fermi liquid systems. Although ETTs could be studied on pure systems as a function of the thermodynamic variables, nevertheless such a study would often require extreme conditions, and would lead to experimental difficulties. On the other hand, it is possible to explore the variations of atomic concentration, i.e. the valence electron per atom ratio, in metallic solid solutions with a relative experimental ease. In this paper we review the theoretical techniques for the determination of Fermi surfaces in metallic solid solutions and discuss some examples of ETTs, namely LiMg, ZrNb, NbMo, MoRe, AgPd, CdMg, NiW and NiTi alloys, also in connection with experimental data as thermoelectric power, resistivity, elastic constants and electron-phonon coupling and with the determinations of the electron momentum distribution function from Compton scattering and positron annihilation experiments. We show that the ab initio calculations of the electronic structure for the quoted systems, together with a careful determination of the BSF, are able to predict quantitatively ETTs at those concentrations where physical quantities display anomalies, so confirming directly ETT theory. Although it is not the purpose of the present review to give a full account of electronic structure calculation schemes, however, we briefly discuss the ideas and the main physical approximations underlying theories of substitutional disorder in alloys. We shall pay some more attention to the Coherent Potential Approximation (CPA) in the Korringa-Kohn-Rostoker (KKR) multiple scattering framework and the Hohenberg and Kohn Density Functional Theory in the Local Density Approximation (LDA) for the exchange-correlation potential. The above choice is supported by the numerical versatility of the LDAKKRCPA theory, and, more important, by the a fortiori evidence that essentially equivalent results are obtained from different theoretical frameworks, provided the same basic physical approximations are used. Accordingly, when convenient, we present new LDAKKRCPA determinations of the Fermi surfaces, as for the ZrNbMoRe series.

We have calculated the electronic structures of the valence bands in a series of [alpha]-phase (disordered fcc) Ag-Mg alloys over the range 0--30 at. % Mg using the Korringa-Kohn-Rostoker method within the coherent potential approximation (KKR-CPA). We find that the variation of the equilibrium lattice constant with composition is in good agreement with experimental measurements. The bandwidth of the Ag-related [ital d] states decreases with the addition of Mg although the position of the bottom of the band remains roughly fixed in energy with respect to the Fermi level; an observation that is consistent with photoemission measurements. The electronic spectral densities are very sharply peaked at the Fermi energy with widths that are [lt]1% of the Brillouin zone dimension and so the Fermi surfaces of the alloys are well defined throughout the zone. The radius of the neck at the [ital L] point and the belly radii in the [Gamma][ital X] and [Gamma][ital K] direction increases approximately linearly with increasing Mg content. Taking into account some previous work on the origin of the short range order in Ag-rich alloys, we conclude that the local-density approximation KKR-CPA method provides a realistic description of the electronic structure in [alpha]-phase [ital Ag]-Mg alloys.

Some numerical methods for the solution of KKR-CPA equations are discussed and tested. New, efficient, computational algorithms are proposed, allowing a remarkable reduction of computing time and a good reliability in evaluating special quantities.

The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing non-perturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. By taking advantage of a coarse grained formulation of the density functional theory [Bruno et al., Phys. Rev. B 77, 155108 (2008)] we develop a MonteCarlo technique, based on an ab initio Hamiltonian, that allows for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and Ni$_3$V support that our theory provides an appropriate description of order-disorder phase transitions., Comment: 4 pages, 4 figures

Self-consistent ‘band theory’, based on density functional theory, is a useful approach to describing the electron glue which holds solids together. However, its powerful group theoretic and numerical techniques cannot be deployed for disordered states of matter. The self-consistent KKR-CPA is an analogous method which is able to deal with some of these interesting cases. In particular, we show how it describes random metallic alloys, treating all the classic Hume-Rothery factors: size-effect, electronegativity and electrons per atom ratio ( e:a ) on more or less equal footing and from first principles. Moreover, we use the KKR-CPA framework to analyse the instability of the disorder state to compositional ordering processes and hence provide a first principle description of the forces which drive order-disorder transformations.

The question, of whether the lattice mismatch between Cr (1− x ) Mo x alloy and Fe in Fe/Cr (1− x ) Mo x /Fe sandwich structures is the explanation for the failure of the rigid band model to explain the strong decline with Mo concentration of the oscillation period in the oscillatory exchange coupling for (1 1 0) growth direction across Cr (1− x ) Mo x alloy spacers, is discussed in quantitative detail.

Diffuse scattering of X-rays, electrons and neutrons from binary alloys provide detailed information about the state of compositional short-range order. Angle-resolved photoemission spectroscopy may be used to probe the corresponding electronic structure. Thus in principle these experiments together can shed light on the electronic causes of ordering. In order to facilitate the interpretation of both kinds of experiment from this point of view we develop a first-principles theory for each. Both theories are based on the self-consistent Korringa-Kohn-Rostoker coherent-potential approximation description of the electronic structure and are fully relativistic. To illustrate the power of such an approach we present explicit calculations for the Cu0·75Au0·25 system and comment on some recent experiments on this classic example of ordering alloys.

For many years the Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA) has been widely used to describe the electronic structure of disordered systems based upon a first-principles description of the crystal potential. However, as a single-site theory the KKR-CPA is unable to account for important environmental effects such as short-range order (SRO) in alloys and spin fluctuations in magnets, amongst others. Using the recently devised KKR-NLCPA (where NL stands for nonlocal), we show how to remedy this by presenting explicit calculations for the effects of SRO on the electronic structure of the bcc Cu_{50}Zn_{50} solid solution., 8 pages, 6 figures, Revised version

A comprehensive investigation of the Fermi surface topologies of a series of Cr1-xVx and Cr1-xMox alloys highlights the role of nesting in determining the periods of the oscillatory exchange coupling observed in multilayer systems. The long-standing controversy over the origin of the long-period oscillations across Cr and Cr-based alloys is resolved, with the evolution of one dimension of the N-hole ellipsoid Fermi surface sheet being directly associated with the evolution of the period.

Using the fully relativistic spin-polarized Korringa-Kohn-Rostoker method, we study the prototypical soft magnet, bcc iron. We investigate how its magnetic anisotropy (MAE) varies as a function of volume, band filling, and tetragonal distortions of the crystal lattice. We follow the trends of the linear magnetostriction and magnetic permeability. We find that a slight reduction in band filling and modest lattice expansion produces a significant magnetic softening of this model system. We explore whether this situation can be realized by doping bcc Fe with vanadium. Treating the compositional disorder with the coherent potential approximation, we calculate the magnetic anisotropy and magnetostriction trends of iron-rich ${\mathrm{Fe}}_{1\ensuremath{-}c}{\mathrm{V}}_{c}$ disordered alloys and find the behavior to accord with the predictions from the bcc Fe model. In particular we find that for $c\ensuremath{\approx}0.1$ the MAE is very small and the linear magnetostriction is zero. We propose ${\mathrm{Fe}}_{0.9}{\mathrm{V}}_{0.1}$ as a high permeability material. Fair agreement with experimental values for the MAE and magnetostriction of both Fe and FeV is found.

We study Ni80Fe20-based permalloys with the relativistic spin-polarized Korringa-Kohn-Rostoker electronic structure method. Treating the compositional disorder with the coherent potential approximation, we investigate how the magnetocrystalline anisotropy, K, and magnetostriction, lambda, of Ni-rich Ni-Fe alloys vary with the addition of small amounts of non-magnetic transition metals, Cu and Mo. From our calculations we follow the trends in K and lambda and find the compositions of Ni-Fe-Cu and Ni-Fe-Mo where both are near zero. These high permeability compositions of Ni-Fe-Cu and Ni-Fe-Mo match well with those discovered experimentally. We monitor the connection of the magnetic anisotropy with the number of minority spin electrons, Nmin. By raising Nmin via artificially increasing the band-filling of Ni80Fe20, we are able to reproduce the key features that underpin the magnetic softening we find in the ternary alloys. The effect of band-filling on the dependence of magnetocrystalline anisotropy on atomic short-range order in Ni80Fe20 is also studied. Our calculations, based on a static concentration wave theory, indicate that the susceptibility of the high permeability of the Ni-Fe-Cu and Ni-Fe-Mo alloys to their annealing conditions is also strongly dependent on the alloys' compositions. An ideal soft magnet appears from these calculations., Comment: 20 pages, 6 figures

We present ab initio calculations of the static paramagnetic spin susceptibility for hcp iron at finite temperatures and for a range of pressures. The dominant magnetic fluctuations in hcp Fe are found to be incommensurate antiferromagnetic, characterized by the wave vector ${\mathbf{q}}_{\mathrm{inc}}=(0.56,0.22,0).$ We show that ${\mathbf{q}}_{\mathrm{inc}}$ is linked to a Fermi-surface nesting feature. For the lowest pressure $\ensuremath{\sim}16\mathrm{GPa}$ at which hcp Fe forms, we find that these modes become unstable below a N\'eel temperature ${(T}_{N})$ of 69 K. ${T}_{N}$ rapidly diminishes with increasing pressure. We therefore predict that hcp Fe will be found to have an incommensurate spin-density-wave-ordered state over a small pressure range starting with the onset of hcp phase. We note the coincidence with the superconductivity recently found in this material.

We describe a first-principles theoretical formalism for the magnetic response of paramagnetic metals in which all relativistic effects such as spin-orbit coupling are included. In particular, the easy axis and dependence upon wave vector q of the paramagnetic spin susceptibility x(q) can be calculated. To illustrate we apply the method to two transition metals, yttrium and scandium. In each case we findx(q) to peak at a wave vector q5(0,0,0.57) p/c, coincident with a Fermi surface nesting vector, and to have an easy axis perpendicular to q. Since x(q) plays a key role in determining the interaction between magnetic impurities in these metals, these results are consistent with the helical antiferromagnetic order found in many dilute rare-earth Y alloys. Conversely, the easy axis for the response to a uniform magnetic field, q50, lies along the c axis.

tions, we study the conditions that, for ZrZn 2, determine the proximity to this magnetic instability. More specifically, we discuss the role played by the geometrical arrangement of the lattice, the hybridization effects, and the presence of disorder, as well as the application of external pressure. These circumstances influence the width of the relevant Zr d bands whose narrowing, due to the reduction of the effective number of neighbors or to an increase of the cell volume, causes an enhancement of the density of states at the Fermi level. Finally, we highlight some general features that may aid the design of other materials close to magnetic instabilities.

Nature or Physics laws rule everything occurs within the Universe and on the Earth, including economical activities and social processes. Opposite to human laws, Physics laws cannot be transgressed, therefore environmental and economic sustainability can be pursued only through economy development models coherent with them, and it is insanity to think that politics and economy can preferentially respect free market laws. The first and the second Thermodynamics principles have a great economic and social relevance, because they imply that all human activities are transformations (nothing is created, nothing is destroyed, everything is transformed) with efficiency less than 100%, whose scrap is directly related to the environment pollution. This holds for economical activities too. In fact companies, in order to produce, need raw materials and energy, make wastes and run into debt; consumers, in order to consume, need energy, make wastes and run into debt; governments, in order to provide infrastructures and services for production and consumptions, need energy, make wastes and run into debt. The inputs of such process are then the planet resources while the outputs are debt and wastes that, in turn, require more energy and other resources to be treated. Because of the narrowness of the natural resources this model might get unstable and lead to the economical crisis and to consumption and degradation of the resources, as striking prescription of Thermodynamics laws. Any alternative model must realize that, since the pollution is unavoidable, it is wise to pollute as least as possible and as slowly as possible. Again the second Thermodynamics principle, not ideology, states that this is possible only through an ordered, fair and jointly liable access to the common assets, opposite to the predatory access onto which free market is based.

We combine the first-principles, Korringa-Kohn-Rostoker coherent potential approximation based calculations of compositional fluctuations with a statistical mechanical ring approximation to study the temperature ~T! and composition ~c! dependence of the atomic short-range order ~SRO! in disordered, face-centred cubic, Cu-Pd alloys. The fourfold splitting of SRO peaks around the equivalent X(0,1,0) points in reciprocal space is obtained in a wide T-c region. Such splitting is shown to be an ‘‘energy’’ effect caused by the absolute minima of the Fourier transform of the effective atomic interactions and related previously to the existence of nested sheets of the disordered alloy’s Fermi surface. However, we find that the T dependence of the SRO peak position is mostly an ‘‘entropy’’ effect. Both the calculated T and c dependences of the SRO peaks position are in good correspondence with the experimental data. The real-space effective atomic interactions and SRO parameters indicate the tendency for longer-period structures with increasing Pd concentration, as observed.

The concentration-dependent position of the diffuse peaks in electron and x-ray diffraction patterns of Cu12xPdx alloys in the disordered state is attributed to Fermi surface nesting. We present the first experimentally determined Fermi surfaces of Cu0.72Pd0.28 and Cu0.6Pd0.4, and show that they do indeed possess significant flat areas capable of nesting. Moreover, the magnitudes of the nesting vectors are in excellent agreement with those deduced from electronic structure calculations and diffraction experiments. The shape of the Fermi surface (FS) often results in a variety of ordering phenomena in metals. These arise because of large areas of parallel or near-parallel sheets of FS which can “nest” with each other, resulting in a significant enhancement of those electronic excitations with a wave vector q which spans the parallel sections. Spin- and charge-density waves [1] are two examples of FS-driven orderings, where the periodicity of the modulation of the conduction electrons is determined by a nesting vector on the FS. The study of the short-range compositional order found in many binary metallic alloys above the order-disorder transition temperature (Tc provides valuable insight into the phase behavior of these systems [2,3]. The origin of the short-range order (SRO) often lies in a nestable FS, in a manner analogous to the way nesting may yield a paramagnetic state susceptible to magnetic order. Indeed, it was just this idea that led Moss to suggest that measurements of the diffuse scattering in x-ray and electron diffraction patterns could be used to make inferences about the FS topology of disordered alloys [4].

Recently, we outlined a scheme to investigate the effects of both short-ranged and long-ranged compositional order on the magnetocrystalline anisotropy of alloys from a first-principles electronic structure point of view [Phys. Rev. Lett. 82, 5369 (1999)] and showed that in the ${\mathrm{Co}}_{0.5}{\mathrm{Pt}}_{0.5}$ alloy compositional order enhances the magnitude of magnetocrystalline anisotropy energy (MAE) by some two orders of magnitude. Here we describe our scheme in detail and study some more transition metal alloys. In the ${\mathrm{Co}}_{0.25}{\mathrm{Pt}}_{0.75}$ alloy we find the perfect ${L1}_{2}$ structure to be magnetically soft whereas imposition of directional order greatly enhances its MAE. We also present the effect of lattice distortion (tetragonalization) on MAE on the same footing and find that in the ${\mathrm{Co}}_{0.5}{\mathrm{Pt}}_{0.5}$ alloy it accounts for only about 20% of the observed enhancement, thus confirming that compositional order is the major player in this effect. Tetragonalization of the lattice has also a modest effect on the MAE of the ${\mathrm{Fe}}_{0.5}{\mathrm{Co}}_{0.5}$ alloy. We also examine the electronic effects which underpin the directional chemical order that is produced by magnetic annealing of permalloy which we study within the same framework.

The Cu-Pd phase diagram shows two low-temperature ordered phases corresponding to B2 and L1 2 superlattices or, regardless of the site occupation, to bcc and fcc geometrical arrangements. We show how the phase equilibria between these intermetallic compounds can be understood by introducing a hypothetical bcc random-alloy phase and a three-step transformation from B2 to random bcc to random fcc to L1 2. The two order-disorder transformations, B2 to random bcc and random fcc to L1 2, analyzed in the framework of the concentration wave-functional theory, appear to be ruled by the sizes of the relevant Fermi surface ~FS! nesting vectors in the two random-alloy systems. The transformation between the bcc and fcc solid solution phase is studied by first-principles Korringa-Kohn-Rostoker and coherent-potential approximation calculations, and it is shown to be influenced by electronic topological transitions occurring in the same systems. Our analysis points out the preeminent role played by the lattice-incommensurate FS nesting vectors that in both the random-alloy systems, give rise to frustrated concentration waves. The location of the B2-L1 2 coexistence at T50 appears to be determined by the condition that the concentration waves of the fcc and bcc random alloys are equally frustrated.

In this paper, we discuss about the variations of the equilibrium lattice parameter versus the alloy concentration in AgPd fcc solid solutions. We interpret the experimentally observed deviations from Vegard’s rule in terms of the Electronic Topological Transition (ETT) related to the d band filling which occurs about the equiatomic concentration. Through simple Rigid Band Model (RBM) calculations, we show how the finiteness of quasi-particle lifetimes affects these deviations, namely reducing their amplitude. RBM calculations are also used to compare versus the experiment the predictions of ab initio Local Density Approximation, Korringa-Kohn-Rostoker Coherent Potential Approximation (LDA-KKR-CPA) calculations. On this basis we shall discuss the apparent underestimation of the relevant quasi-particle lifetime in the CPA theory.

Metallic random alloys can display Electronic Topological Transitions, i.e. changes of the Fermi Surface connectivity, on varying the atomic concentrations. We present a study of Ag-Pd and Cu-Pt Fermi Surfaces, based on the LDA-KKR-CPA theory, and argue that the different phase equilibria of such isoelectronic systems are related to the spectacular differences in their Fermi Surfaces.

Almost immediately after the discovery of quantum mechanics, physicists and metallurgist began the task of trying to understand the origins of alloy phase stability in terms of the underlying electronic structure. Hume-Rothery [1] used the chemical concepts of electronegativity and atomic size supplemented with the solid state physics notion of electron to atom ratio to formulate a set of rules that could be used to rationalize the complex array of phases that form when two elemental metals are mixed to form an alloy. The Hume-Rothery rulesand their progeny [2], [3] have proved very successful in providing metallurgists and alloy designers with a basis for understanding alloy phase stability.

A relativistic theory of photoemission is applied to calculate angle-, energy- and “spin”resolved photoemission spectra from the (1,0,0) surface of Cu3Au, both in the ordered and solid solution phases, in order to compare them with experimental data and learn what sort of informations could be achieved by such experiments about the “spin” structure of systems made up by “light” and “heavy” atomic species. Results show the interesting potentiality of the approach.

The alloy CuPt is one of the few that order into a L11 crystal structure, i.e. planes of copper and planes of platinum perpendicular to the > 111 < direction. For disordered CuPt, the calculated Warren-Cowley short-range order parameter indicates an instability to concentration fluctuations with a wave-vector of (½, ½, ½), consistent with L11 ordering. We show that this rare tendency is due to this ordering vector arising from the large joint density of states associated with L point and X point van-Hove singularities which He near the Fermi energy.

We discuss ways that first principles LDA methods can be adapted to take advantage of the computational power of massively parallel supercomputers. We discuss the need for new theoretical and computational strategies that circumvent the N 3 problem associated with standard LDA implementations limiting their extention to large systems. We propose a new, spatially local, multiple scattering theory algorithm that offers the possibility of producing a scalable O(N) method. As a first step, we use the method to calculate the self-consistent charge density for a large system.

We review, briefly, the arguments which gave rise to the current controversy concerning the origin of compositional order in NicPt(1-c) alloys. We note that strain fluctuations play an important role in determining the state of compositional order in this system and outline a theoretical framework that takes account of them.

We investigate the cause of compositional ordering in fcc ${\mathrm{Ni}}_{0.50}$${\mathrm{Pt}}_{0.50}$ on the basis of a first-principles theory of electronic structure and finite-temperature concentration fluctuations. We treat the size effect, electronegativity, and band filling on an equal footing and find that the first of these dominates, leading to L${1}_{0}$ ordering in agreement with experiment. An electronic origin is given for the metallurgical ``rule of thumb'' that alloys comprised of big atoms and little atoms tend to order into simple stuctures.

By applying a new method for solving the equations of the relativistic Korringa-Kohn-Rostoker-coherent-potential approximation. The authors have been able to study the electronic structure of compositionally disordered Pd-Pt alloys. This investigation was carried out, on the one hand, to test the reliability of the method itself and, on the other, to learn whether a 'rigid band' picture is appropriate for these alloys as suggested by an interpretation of residual resistivity measurements. They find that the method is numerically stable and can now be safely incorporated into a self-consistent-field local-density theory for alloys with heavy elements. Moreover, the electronic structure of Pd-Pt is found to be 'non-rigid-band' like and demonstrates some interesting new features arising from mass-velocity, Darwin and spin-orbit coupling effects.

We have developed a hybrid, parallel computer code for calculating the electronic structure of both ordered and substitutionally disordered materials. By using PVM3.3, we can integrate into our local computer environment multiple parallel and vector supercomputers as well as high performance workstations. Without this approach, calculations of materials properties of large systems would be otherwise untenable due to a lack of computer resources. For example, we have determined the short-range order intensity and its electronic origin for the Ag-Mg alloy system, including an estimate of the order-disorder (spinodal) temperature. >