Stoner Theory Research Articles

A systematic analysis of the ferromagnetism in the itinerant electron model

Abstract The susceptibility is studied by the inversion method, which advances the Stoner theory systematically. This is because the method is a kind of perturbation theory and its first order calculation reproduces the mean-field theory. The second order of the inversion method is applied for the concrete model for the first time. It is possible to realize the Curie-Weiss law and the lowering of the critical temperature.

From the Hubbard model to classical spin-fluctuation theory.

In this paper we develop a microscopic foundation for the Murata-Doniach model of spin fluctuations which has been widely used in connection with band-structure calculations. The main result of the paper is the formulation of the partition function of an itinerant system as a functional integral over magnetization modes, and an explicit formula for the energy functional appearing in the exponent of the Boltzmann factor. Such a derivation is made since former theoretical investigations focus on the interaction part of the parition function Z/${\mathit{Z}}_{0}$, whereas the Murata-Doniach model is formulated in terms of a functional integral for the complete partition function Z. We start with an approximate description of magnetic excitations of noninteracting fermions with collective modes, and derive a bosonlike partition function for these magnetization modes. This is combined with the well-known result for the interaction part of the partition function in the Hubbard model obtained by functional-integral theory. The leading term of the energy functional appearing in the exponent of the parition function agrees with that of the Ginzburg-Landau expansion for the energy of a classical magnetization field. In the course of the transformation to a bosonlike system we predict that the cutoff wave vector ${\mathit{q}}_{\mathit{c}}$ which must be introduced in the classical model is temperature dependent with ${\mathit{q}}_{\mathit{c}}$\ensuremath{\sim}${\mathit{T}}^{1/3}$. It is shown that the frequencies of the collective modes are reduced by the Stoner enhancement factor compared with the one-particle excitation energies of Stoner theory.

Ferromagnetism in FeCu metastable alloys

We present linearized augmented-plane-wave calculations for FeCu fcc and bcc metastable phases using the local-density approximation (LDA) as well as the local-spin-density approximation (LSDA). The nonpolarized density of states calculated within the framework of LDA together with the reformulated Stoner theory provide results in excellent agreement with those obtained from LSDA calculations. The magnetization is calculated for several alloy compositions---the magnetic moment per Fe atom is almost constant over a wide range of Fe content---in good agreement with recent experiments.

A calculation of the temperature-dependent susceptibility of Pd and dilute Pd1-xAgx and PdHx alloys

The temperature dependence of the magnetic properties of itinerant electron systems is mainly due to the excitation of spin fluctuations. We calculate the susceptibilities of Pd, Pd1-xAgx, and PdHx (0<or=x<or=0.03) with an extension of the classical Murata-Doniach model for spin fluctuations, which treats the energy functional without a Landau expansion of the magnetization-dependent ground state energy. To obtain this energy ASW (augmented spherical wave) and KKR-CPA bandstructure calculations are performed. In agreement with experiment the KKR-CPA method yields a maximum of chi (T) for Pd, which disappears with increasing Ag concentration. In the ASW calculations, low Ag and H concentrations are simulated by the supercells Pd31Ag and Pd32H. In addition the alloy PdHx is simulated by calculations for pure Pd, with the valence electron concentration increased suitably. Calculations of the susceptibility of Pd within the framework of the Stoner theory and the spin fluctuation theory based upon the rigid-band model are presented. The role of the electron interaction in both theories is examined and the reason for the maximum of chi (T) for Pd is investigated. We find the different scaling of the temperature axis in the Stoner and spin fluctuation theories to have its origin in a different treatment of the electron interaction.

Electronic structure, ferromagnetism, and EELS spectra of crystalline alloys FenB and NinB (n=1,2,3): Aspects of universal behavior.

We have performed an extensive study of the electronic structure, optical properties, and electron-energy-loss spectra (EELS) for the series of the ${\mathit{M}}_{3}$B, ${\mathit{M}}_{2}$B, and MB (M=Fe, Ni) crystalline alloys. The electron density of states (DOS) of iron and nickel borides of the same composition have almost the same shape in spite of some minor differences in actual atomic structures. The Fermi level in nickel borides is shifted upwards in comparison with its position in iron borides, away from the main DOS peak formed by the nonbonding M d states. This behavior provides insight into the ``marginal'' stability of the nickel magnetic moment upon dilution by nonmagnetic atoms. As a result of competitive interaction between d-d metallic bonding and d-p M-metalloid covalent bonding the magnetic moment on the Fe atom gradually decreases with increasing boron content. This tendency is in accordance with the results of a simple generalized Stoner theory, which is capable of describing the ferromagnetic behavior in detail with good accuracy for the estimated magnetic moments. In spite of some differences in actual crystal structure and a high degree of crystalline anisotropy, the calculated EELS spectra are practically identical for all iron compounds studied. The spectra are dominated by a giant peak at about 20 eV, with some fine structure at lower energies (at about 10 eV) relevant to B p--M d transitions. The d-d transitions appear to be very strong in the low-energy region (0--10 eV) leaving the usual Drude term effective only at energies below 1.5 eV. These transitions suppress the low-energy plasmons both in para- and ferromagnetic phases and make just small differences in the calculated EELS spectra, in accordance with the available experimental data. The implications of the present results for the amorphous systems are discussed.

Magnetic properties of the neutral MX chain systems

Both local density-functional (LDF) Stoner theory and spin-polarized LDF, each in conjunction with the scalar relativistic linear muffin-tin orbital technique, are used to study the magnetic properties of the neutral halogen-bridged transition-metal linear chains, denoted by MX (MNi or Pt, and XCl, Br, or I). Both approaches show the Ni-based compounds are antiferomagnetic, whereas the Pt-based compounds are paramagnetic. Besides these calculations, we have also studied the magnetism of the MX chain systems using the new density functional, which takes orbital polarization into account and uses a Hubbard interaction instead of the Stoner parameter. Despite the additional sophistication of this approach, very similar results are obtained.

Electronic structure of palladium monolayers: effects of crystalline orientation

The electronic structure of unsupported Pd monolayers is calculated within the multi-orbital tight-binding model. Three crystalline orientations, namely fcc (100), fcc (110) and fcc (111), are considered. In each case the stability of the paramagnetic state is investigated on the basis of Stoner theory.

Ab initio calculation of molecular field interactions in rare-earth transition-metal intermetallics (invited)

The interaction, KRM, between the rare-earth 4f moment and the transition-metal 3d moments in rare-earth transition-metal intermetallics is shown to depend upon the R-5d moment, which is due to 3d–5d hybridization, and local 4f–5d exchange integrals. Both the R-5d moment and KRM may be calculated ab initio from the local spin-density approximation to density functional theory in self-consistent energy-band calculations with the localized 4f-moments fixed at their Russel–Saunders values. Detailed examples are given for the RFe2 (R=Gd−Yb) series. The exchange integrals are similar to those entering into the density functional version of Stoner theory and their energy dependence must be treated carefully. The calculated local exchange integrals are shown to be related to the molecular fields derived from spin Hamiltonians, hence to the spin-wave spectra. Reasonable agreement with values of the molecular fields extracted from inelastic neutron scattering and high field susceptibility measurements is obtained.

Electronic-structure calculations for amorphous solids using the recursion method and linear muffin-tin orbitals: Application toFe80B20

We describe a method for performing density-functional calculations for topologically disordered condensed matter. This method combines the recursion and the linear-muffin-tin-orbital (LMTO) methods, and uses the tight-binding representation. In the present version, the LMTO matrix elements are evaluated in the atomic-sphere approximation (ASA). Various levels of approximation for the ASA Hamiltonian, such as the two-center tight-binding one, are systematically derived and tested. The method is applied to crystalline bcc Fe and to amorphous ${\mathrm{Fe}}_{80}$${\mathrm{B}}_{20}$. Charge self-consistency is only treated for the average Fe and the average B atoms. The Fe-B bonding is found to be covalent. A Stoner theory is derived and used to describe the ferromagnetism. The structures of our density of states for ferromagnetic ${\mathrm{Fe}}_{80}$${\mathrm{B}}_{20}$ agree in detail with reliable photoemission data.

Ferromagnetism and crystal lattice stability of bcc and fcc iron

The Stoner theory of itinerant ferromagnetism was used in calculating the magnetic properties of iron within the self-consistent linear muffin-tin orbital approach. The Stoner exchange parameter, I, was found from the linear-response theory as a function of volume and then adjusted by a constant enhancement factor determined by fitting the equilibrium atomic volume of the ferromagnetic (FM) bcc phase. No other adjustments of any quantities were performed. The calculations revealed a somewhat unusual behavior of phases. The nonmagnetic (NM) bcc phase is unstable with respect to spontaneous magnetization. Moreover, the enthalpy of the NM phase exhibits a monotonic decrease with c/a along the so-called Bain deformation path, the bcc modification being unstable with respect to the shear deformation. Ferromagnetism stabilizes the bcc phase. However, the FM fcc phase is unstable with respect to the shear deformation. The enthalpy curve along the deformation path has a cusp corresponding to a first-order phase transition between FM and NM states. The FM contributions to the energy versus atomic volume for different c/a valves are tabulated.

The relativistic equation of state of actinide metals and compounds

Abstract The effect of spin-orbit coupling upon the calculated pressure-volume relationship is summarized. It is shown that the main effect is to increase the lattice constant, especially in Pu systems. The both measured and calculated pronounced minimum in the lattice constants of the Anlr2 laves phase compounds at Nplr2 is also discussed. One influence of spin-orbit coupling upon the magnetic equation of state is shown to be suppression of magnetism. Again the effects are particularly large in Pu systems. The foregoing is illustrated by a relativistic Stoner theory which explains well the absence of magnetism in Np metal and in several Pu compounds.

Energetics of bcc-fcc lattice deformation in iron.

The energetics of homogeneous bcc-fcc lattice deformation in iron at 0 K has been investigated along the tetragonal ``Bain'' deformation path. The total energy (as a function of volume), the enthalpy (as a function of pressure), the pressure-volume relations---both for nonmagnetic (NM) and ferromagnetic (FM) states---were calculated using the linear muffin-tin-orbital (LMTO) method. The ground-state magnetic properties (ferromagnetic contributions to the total energy and magnetic moments) were found by making use of the Stoner theory of itinerant ferromagnetism, rather than spin-polarized calculations. This circumvents the difficulties of using the traditional local-spin-density approximation which fails to describe correctly the energetics of iron phases. The Stoner exchange parameter I was calculated from the linear-response theory for each axial ratio c/a as a function of volume and then adjusted by a constant enhancement factor \ensuremath{\beta}, determined by fitting the equilibrium atomic volume of the FM bcc phase. No other adjustments of any quantities were performed. The calculations revealed a somewhat unusual behavior of enthalpy along the deformation path.The enthalpy of the NM phase exhibits a monotonic decrease with c/a, the bcc modification being unstable with respect to the shear deformation. Moreover, up to a certain c/a (depending on pressure), the NM bcc phase is also unstable with respect to spontaneous magnetization. Ferromagnetism stabilizes the bcc phase. However, the FM fcc phase is unstable with respect to shear deformation. The enthalphy curve along the deformation path then has a cusp corresponding to a first-order phase transition between FM and NM states accompanied by an appreciable volume discontinuity. For the FM bcc, the calculated bulk modulus (1.689 mbar) and the magnetic moment (2.223${\ensuremath{\mu}}_{B}$/atom) as well as the fcc-bcc enthalpy difference at zero pressure (6.947 kJ/mol) are in good agreement with available experimental data. A fcc-bcc lattice-deformation enthalpy barrier at the equilibrium pressure ${P}_{0}$=145 kbar is found to be 12.762 kJ/mol. The NM fcc lattice loses mechanical stability at a fcc-bcc enthalpy difference of -14.072 kJ/mol. As an aid to the development of improved interatomic potentials for iron, plots of FM contributions to the energy versus Wigner-Seitz radius for different c/a are also presented.

Electronic structure of the actinide-Rh3 systems and the 5f localization in UPd3.

We present electronic-structure calculations for the isostructural (${\mathrm{AuCu}}_{3}$-structure) series of intermetallic compounds A${\mathrm{Rh}}_{3}$ (A=Ac, Th, Pa, U, Np, Pu, Am, and Cm). The calculations were performed using both the scalar relativistic and the fully relativistic linear muffin-tin orbital (LMTO) method. Calculated cohesive and magnetic properties are compared with available experimental data. The onset of magnetism is discussed by means of a relativistic Stoner theory. The influence of the ligand states on the uranium 5f electrons is studied for the U${M}_{3}$ (M=Mo, Tc, Ru, Rh, Pd, and Ag) series of compounds. The localization of the 5f electrons in ${\mathrm{UPd}}_{3}$ as opposed to the itinerant 5f behavior for the earlier compounds (${\mathrm{UMo}}_{3}$, ${\mathrm{UTc}}_{3}$ , ${\mathrm{URu}}_{3}$, and ${\mathrm{URh}}_{3}$) is explained in terms of the variation of the hybridization between 5f and ligand 4d states through the series.

Structural properties of BCC and FCC iron: LMTO-ASA-Stoner calculations

The LMTO-ASA (Linear Muffin-Tin Orbitals - Atomic Spheres Approximation) calculations of structural properties of BCC and FCC iron were performed. The ground-state magnetic properties: ferromagnetic contributions to the total energy and magnetic moments, were found by making use of the Stoner theory of itenerant ferromagnetism, rather than spin-polarized calculations. This enabled us to circumvent the difficulty resulting from using the traditional local spin-density approximation which is known to have failed predicting correctly the energetics of iron phases. The Stoner exchange parameter, I, was calculated from the linear response theory as a function of volume. Then a constant enhancement factor, β, was introduced and the new Stoner parameter, β βI, was used in all the calculations. The factor β was found by fitting the equilibrium atomic volume of the ferromagnetic BCC phase to its experimental value. No other adjustments of any quantities were performed. The calculations revealed that the nonmagnetic BCC modification was unstable with respect to the spontaneous magnetization. Ferromagnetism stabilizes the BCC phase. The calculated bulk moduli, magnetic moments and the BCC-FCC energy difference are in good agreement with the available experimental data.

Mean-field theories of the two-band model and the magnetism in high-Tc oxides.

The antiferromagnetic ground state of a two-band model Hamiltonian which ) and O(2${p}_{x(y)}$) orbitals within a ${\mathrm{CuO}}_{2}$ plane, a common structural unit of high-${T}_{c}$ superconducting oxides (HTSO), is studied by using a Hartree-Fock approximation (HFA) and the Gutzwiller ansatz (GA). Using the GA, a weak-coupling effective Stoner theory is derived in the low hole density limit. Compared to HFA, the Stoner parameter is strongly reduced, showing that correlations tend to weaken the magnetic instability in this limit. In the localized limit both the HFA and the GA converge to the same solution, corresponding to a classical Heisenberg system with the correct superexchange. We point out that the local spin-density approximation has intrinsic difficulties for the present problem. For intermediate d-hole densities numerical results are obtained and the magnetism of the HTSO is discussed. We argue that, in spite of its qualitative success, the model cannot account at the same time for the known magnetic and electronic properties of the HTSO.

Ferromagnetism in hexagonal-close-packed elements.

The Stoner theory of ferromagnetism has been applied to 3d transition metals in the hexagonal-close-packed (hcp) phase. The elements Co and Ni (and possibly Cr) are found to be ferromagnetic. A self-consistent calculation of the band structure of paramagnetic hcp Ni revealed the highest-known density of states at the Fermi level of any transition metal in any structure, providing strong evidence for ferromagnetism. A first-principles, spin-polarized band-structure calculation for hcp Ni yielded a stable magnetic moment of 0.76${\ensuremath{\mu}}_{B}$ per atom and an average spin splitting of 0.1 Ry.

Stoner theory of magnetic structure of alternate cubic phases of transition metals

Epitaxial growth of bcc Co on a (110) GaAs substrate has demonstrated the feasibility of producing thin films of transition metals with structures not usually stable at room temperature and pressure. Thus an entirely new group of magnetic materials may be possible with interesting and perhaps significant magnetic properties. In this paper the simple Stoner theory of ferromagnetism is employed, with exchange-correlation parameters obtained from Janak’s work and density of states at the Fermi level determined from self-consistent, paramagnetic energy-band calculations. The theory is applied to each of the 3d and 4d transition metals in both fcc and bcc phases. Ferromagnetism is obtained for bcc Fe, Co, and Mn and fcc Co and Ni, and strongly enhanced paramagnetism for bcc Sc, Ni, and Y and fcc Sc, Fe, and Pd. Comparisons are made with predictions of total energy and enhanced magnetic susceptibility calculations.

Specific-heat measurements of HoxY

We report on specific-heat measurements of (Ho/sub x/Y/sub 1/..sqrt../sub x/)Co/sub 2/ in the temperature range from 1.5 to 60 K. Sharp peaks at the Curie temperature T/sub C/ and the spin-reorientation temperature T/sub r/ characterize the temperature dependence for 0.5less than or equal toxless than or equal to1. For 0.2less than or equal toxless than or equal to0.4 the magnetic specific heat C/sub m/ indicates spin-glass-like behavior, which appears to be in agreement with freezing phenomena observed in magnetic measurements. From the analysis of the magnetic entropy S/sub m/, we deduce that the induced Co moment can be referred to as itinerant in the sense of the Stoner theory. In the dilute Ho-concentration range, various anomalies are observed as, e.g., an enhancement of the effective electronic specific heat ..gamma.. and the effective Debye temperature FTHETA/sub D/ (of about 400% and 100%, respectively) and significant upturns of the C/sub p/T versus T/sup 2/ graphs together with a pronounced reduction of the magnetic entropy. These anomalies are discussed in terms of spin fluctuations;the loss of the magnetic entropy for x<0.2 may point to an instability of the Ho moment

Energetics of Bcc-Fcc Lattice Deformation in Iron

AbstractThe lattice deformation of the BCC-FCC martensitic transformation in iron can be described as a continuous change of the c/a parameter of the body-centered tetragonal (BCT) lattice from c/a=1 (BCC) to c/a=√2 (FCC). Along this deformation path, the total energy (as a function of volume), the enthalpy (as a function of pressure), the pressure-volume relations--both for nonmagnetic (NM) and ferromagnetic (FM) states--were calculated using the ab initio LMTO method. The ground-state magnetic properties: ferromagnetic contributions to the total energy and magnetic moments, were found by making use of the Stoner theory of itinerant ferromagnetism, rather than spin-polarized calculations. This circumvents the difficulties of using the traditional local spin-density approximation which failes to describe correctly the energetics of iron phases. The Stoner exchange parameter, I, was calculated from the linear response theory for each c/a as a function of volume. Then a constant enhancement factor, β, was introduced and the new Stoner parameter, βl, as used in all the calculations. The factor β was found by fitting the equilibrium atomic volume of the FM BCC phase to its experimental value. No other adjustments of any quantities were performed. The calculations revealed a somewhat unusual behavior of enthalpy along the deformation path. Instead of a double-well curve with a barrier maximum somewhere at 1 &lt; c/a &lt; √2, the enthalpy of the NM phase exhibits a monotonic decrease with c/a, the BCC modification being unstable with respect to the shear deformation. Moreover, up to a certain c/a (depending on pressure), the nonmagnetic BCT phase is also unstable with respect to spontaneous magnetization. Ferromagnetism stabilizes the BCT phases. However, the FM FCC phase is unstable with respect to shear deformation. The enthalpy curve along the deformation path then has a cusp corresponding to a first-order phase transition between ferromagnetic and nonmagnetic states accompanied by an appreciable volume discontinuity. The bulk modulus, the magnetic moments and the BCC-FCC enthalpy differences are in good agreement with the available experimental data.

Electronic structure and magnetovolume effect of AFe2 compounds with C14 and C15 Laves structures

The density of states of d-electrons is calculated by the recursion method for AFe2 with the C14 and C15 structures in the para-, ferro- and antiferromagnetic states. The trends of the crystal structures are discussed. Magnetic moment and volume magnetostriction are calculated on the basis of the Stoner theory.