Amplitude Of Local Moment Research Articles

First-Principles Momentum Dependent Local Ansatz Approach to the Ground-State Properties of Iron-Group Transition Metals

The ground-state properties of iron-group transition metals from Sc to Cu have been investigated on the basis of the first-principles momentum dependent local ansatz (MLA) theory. Correlation energy gain is found to show large values for Mn and Fe: 0.090 Ry (Mn) and 0.094 Ry (Fe). The Hund-rule coupling energies are found to be 3000 K (Fe), 1400 K (Co), and 300 K (Ni). It is sugested that these values can resolve the inconsistency in magnetic energy between the density functional theory and the first-principles dynamical coherent potential approximation theory at finite temperatures. Charge fluctuations are shown to be suppressed by the intra-orbital correlations and inter-orbital charge-charge correlations, so that they show nearly constant values from V to Fe: 1.57 (V and Cr), 1.52 (Mn), and 1.44 (Fe), which are roughly twice as large as those obtained by the $d$ band model. The amplitudes of local moments are enhanced by the intra-orbital and inter-orbital spin-spin correlations and show large values for Mn and Fe: 2.87 (Mn) and 2.58 (Fe). These values are in good agreement with the experimental values estimated from the effective Bohr magneton number and the inner core photoemission data.

First-Principles Dynamical Coherent-Potential Approximation Approach to the Ferromagnetism of Fe, Co, and Ni

Magnetic properties of Fe, Co, and Ni at finite temperatures have been investigated on the basis of the first-principles dynamical CPA (Coherent Potential Approximation) combined with the LDA (Local Density Approximation) + $U$ Hamiltonian in the Tight-Binding Linear Muffintin Orbital (TB-LMTO) representation. The Hamiltonian includes the transverse spin fluctuation terms. Numerical calculations have been performed within the harmonic approximation with 4th-order dynamical corrections. Calculated single-particle densities of states in the ferromagnetic state indicate that the dynamical effects reduce the exchange splitting, suppress the band width of the quasi-particle state, and causes incoherent excitations corresponding the 6 eV satellites. Results of the magnetization vs temperature curves, paramagnetic spin susceptibilities, and the amplitudes of local moments are presented. Calculated Curie temperatures ($T_{\rm C}$) are reported to be 1930K for Fe, 2550K for Co, and 620K for Ni; $T_{\rm C}$ for Fe and Co are overestimated by a factor of 1.8, while $T_{\rm C}$ in Ni agrees with the experimental result. Effective Bohr magneton numbers calculated from the inverse susceptibilities are 3.0 $\mu_{\rm B}$ (Fe), 3.0 $\mu_{\rm B}$ (Co), and 1.6 $\mu_{\rm B}$ (Ni), being in agreement with the experimental ones. Overestimate of $T_{\rm C}$ in Fe and Co is attributed to the neglects of the higher-order dynamical effects as well as the magnetic short range order.

Molecular-Dynamics Approach to the Magnetic Structure of Competing Magnetic Alloys: Fe-Cr Alloys

A molecular dynamics (MD) approach which determines automatically the complex magnetic structures in itinerant electron systems is applied to Fe-Cr alloys with use of 250 atoms in a MD unit cell (5×5×5 bcc lattice). It is demonstrated that the Fe-Cr alloys show various complex magnetic structures due to competing interactions: the collinear ferromagnetism (F) of matrix Fe with antiparallel Cr moments beyond 80 at.% Fe, the coexistence of non-collinear structure of Cr and collinear F of Fe between 50 and 75 at.% Fe, the coexistence of broken antiferromagnetism (AF) of Cr and the F of Fe between 25 and 45 at.% Fe, the coexistence of F of Fe and antiferromagnetic long-range order of Cr around 20 at.% Fe, the AF of Cr matrix with non-collinear Fe moments (spin-glass like structure) between 5 and 15 at.% Fe, and the AF below 5 at.% Fe. In the concentration region between 5 and 20 at.% Fe, ferromagnetic Fe pairs which are stabilized with different amplitudes of local moments are found. The magnetic phase diagram and calculated magnetic moments are shown to be consistent with the neutron, Mossbauer, and photoemission experiments.

Finite-temperature theory of local environment effects in amorphous and liquid magnetic alloys.

A finite-temperature theory of magnetism that takes into account the fluctuations of local magnetic moments due to structural disorder is presented on the basis of the functional-integral method and the method of the distribution function. The theory describes qualitatively or semiquantitatively the finite-temperature magnetism of liquid and amorphous metals and alloys as well as the substitutional alloys in a wide range of electron-electron interaction strength from metal to insulator. The results of numerical calculations are presented for amorphous iron. The local environment effects on the density of states, local magnetic moment, susceptibility, and amplitude of local moment are examined. It is found that amorphous iron forms an itinerant-electron spin glass at low temperatures because of the nonlinear magnetic coupling between Fe local moments and the local environment effect on the amplitude of the Fe local moment due to the structural disorder. The calculated spin-glass temperature (100 K) is in good agreement with the value extrapolated from experimental data on Fe-rich amorphous alloys.

Variational approach to finite-temperature magnetism in the degenerate-band Hubbard model.

The variational approach (VA), which goes beyond the static approximation to the functional-integral method by taking into account the local electron correlations of the Gutzwiller type, has been extended to the degenerate bands for the purpose of a more realistic description of the finite-temperature magnetism in narrow-band systems. The magnetic properties of Fe, Co, and Ni are investigated numerically within a single-site approximation to the VA. The magnetization-versus-temperature curve, susceptibility, specific heat, the amplitude of local moment, and the charge fluctuations are calculated. The results are compared with those in the static approximation and the experimental data. The Curie temperatures ${T}_{C}$ in the VA are found to be between the observed values ${T}_{C}$(obs) and 2${T}_{C}$(obs). It is shown that ${T}_{C}$ in Fe and Ni are reduced by a factor of 2 because of electron correlations even in the degenerate-band case. The other strong-correlation effects at finite temperatures are found in particular in Ni; the sign of \ensuremath{\partial}${T}_{C}$/\ensuremath{\partial}P is changed, and the temperature-independent charge fluctuation is suppressed by a factor of 3.

Magnetic and thermodynamical properties of the simple-cubic Hubbard model.

Magnetic and thermodynamical properties of the half-filled Hubbard model on the simple-cubic lattice have been investigated by using the two analytical theories for band magnetism: the single-site spin fluctuation (SSF) theory proposed independently by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) developed by Kakehashi and Fulde. We have calculated, as a function of the temperature T and the electron-electron interaction U, the sublattice magnetization, amplitude of local moments, susceptibilities, energy, and entropy, from which the U-T phase diagram is obtained. Our ground-state results, particularly of the VA, are in good agreement with those obtained in the variational Monte Carlo calculations performed by Yokoyama and Shiba. Our finite-temperature calculations are compared with those in the recent Monte Carlo (MC) simulations made by Hirsch. It is shown that, as far as local quantities such as the amplitude of local moments and the Curie constants are concerned, our results are consistent with the MC results. It is realized, however, that the antiferromagnetic correlation is much overestimated in a small 4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4 cluster in Hirsch's MC simulation, yielding N\'eel temperatures, ${T}_{N}$, about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.

Variational approach to finite-temperature magnetism. II. Antiferromagnetism.

The overall features of a variational theory for finite-temperature magnetism, which has recently been proposed, are investigated numerically for a half-filled Hubbard model. The phase diagram, sublattice magnetization, staggered susceptibility, amplitude of local moments, charge fluctuations, and electronic contributions to the internal energy, entropy, and the thermal expansion are calculated as functions of temperature T and the Coulomb interaction U. It is found that the local electron correlations, which cannot be described by the static approximation to the functional integral, act so as to reduce the effective Coulomb interaction for the magnetization, the N\'eel temperature, the internal energy, the specific heat, and the entropy, while they enhance the atomic character for the amplitude of local moments, the charge fluctuation, and the reduced-magnetization-- versus--temperature curves. Electron correlations reduce the thermal expansion, in contrast to the case of ferromagnets.

Wave vector-dependent spin susceptibility of iron above the Curie temperature

Microscopic calculations are given of the wavevector- and temperature-dependent spin susceptibility, chi (q), of itinerant-electron magnets by generalising the approach initiated by Hubbard and Hasegawa (1979-1983). The expressions for chi (q) in the limit of q=0 and q=Q (the antiferromagnetic wavevector) are shown to reduce to the results obtained previously by the present author. Detailed calculations of chi (q) of paramagnetic iron are made using the density of states generated by the recursion method. The amplitude of local moments evaluated by summing chi (q) over the BCC Brillouin zone using the classical fluctuation-dissipation theorem is nearly in agreement with effective moments deduced from the susceptibility chi (0). The equal-time and spatial spin-spin correlation functions are also calculated, and discussed with reference to recent neutron diffraction experiments.

A spin fluctuation theory of degenerate narrow bands-finite-temperature magnetism of iron

A previously developed theory of itinerant-electron magnetism at finite temperatures is generalised to include the effect of degenerate multi-bands with t2g and eg symmetry by adopting the static functional integral method and the coherent potential approximation (CPA). Numerical calculations of the Curie temperature, the magnetisation curve, the amplitude of local moments and the susceptibility are made for iron by using the detailed density of states generated by the recursion method for the tight-binding model. Calculated results are shown to account for finite-temperature properties of iron. In particular, the calculation explains the observed very weak temperature dependence in the spin-density asphericity, which cannot be explained by the Stoner theory. The authors' results are compared with those obtained by alternative approaches in which the five sub-bands are taken to be equivalent.