Ab initiocalculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni

Abstract

We have calculated Heisenberg exchange parameters for bcc-Fe, fcc-Co, and fcc-Ni using the non-relativistic spin-polarized Green function technique within the tight-binding linear muffin-tin orbital method and by employing the magnetic force theorem to calculate total energy changes associated with a local rotation of magnetization directions. We have also determined spinwave stiffness constants and found the dispersion curves for metals in question employing the Fourier transform of calculated Heisenberg exchange parameters. Detailed analysis of convergence properties of the underlying lattice sums was carried out and a regularization procedure for calculation of the spin-wave stiffness constant was suggested. Curie temperatures were calculated both in the mean-field approximation and within the Green function random phase approximation. The latter results were found to be in a better agreement with available experimental data.PACS numbers: 71.15.-m, 75.10.-b, 75.30.Ds of the relevant physical quantities such as spin-wave stiffness, Curie temperature T C , etc., for comparison with experimental data.It is therefore of a great importance to develop an ab initio, parameter-free, scheme for the description of ferromagnetic metals at T > 0 K. Such an approach must be able to go beyond the ground state and to take into account excited states, in particular the magnetic excitations responsible for the decrease of the magnetization with temperature and for the phase transition at T = T C . Although density functional theory can be formally extended to non-zero temperature, there exists at present no practical scheme allowing to implement it. One therefore has to rely on approximate approaches. The approximations to be performed must be chosen on the basis of physical arguments.In itinerant ferromagnets, it is well known that magnetic excitations are basically of two different types: (i) Stoner excitations, in which an electron is excited from an occupied state of the majority-spin band to an empty state of the minority-spin band and creates an electron-hole pair of triplet spin. They are associated with longitudinal fluctuations of the magnetization; (ii) the spin-waves or magnons, which correspond to collective transverse fluctuations of the direction of the magnetization. Near the bottom of the excitation spectrum, the density of states of magnons is considerably larger than that of corresponding Stoner excitations, so that the thermodynamics in the low-temperature regime is completely dominated by magnons and Stoner excitations can be neglected. Therefore it seems reasonable to extend this approximation up to the Curie temperature, and to estimate the latter by neglecting Stoner excitations. This is a good approximation for ferromagnets with a large exchange splitting such as Fe and Co, but it is less justified for Ni which has a small exchange splitting.The purpose of the present paper is to describe the spin-wave properties of transition metal itinerant ferromagnets at ab initio level. With thermodynamic propertie...

Exchange interactions in transition metal oxides: the role of oxygen spin polarization

“…If oxygen spin polarization is taken into account, the positive J Mn−O interaction reduces the effective exchange interactions as defined by (12) to J eff 1 (↑↑) = −0.2 meV, J eff 1 (↑↓) = −0.4 meV, and J eff 2 = −1.7 meV. Therefore, spin polarization on oxygen leads to considerable changes in the effective Mn-Mn exchange interactions.…”

“…[9][10][11] The MFT proved to be a powerful method for studying magnetic interactions from first principles. [12][13][14][15][16] The necessity of only a single magnetic state allows to study the applicability of the Heisenberg model by determining the dependence of the exchange interactions on the magnetic states.…”

Atomic forces at finite magnetic temperatures: Phonons in paramagnetic iron

“…This approach implicitly assumes that in each microstate "fast" atoms move in a "fixed" magnetic configuration. This assumption does not hold at high temperatures where the magnitude of typical magnetic excitations is higher in energy than vibronic excitations, implying a faster time scale for the magnetic degree of freedom [11,12,27]. A very recent theoretical approach by Leonov et al which takes magnetic correlations in force constant calculations within the framework of dynamical mean field theory into account, provides promising preliminary results for fcc iron [28].…”

Electronic Structure and Magnetic Properties of Solids

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“…Quantitative calculations demonstrating the sizeable reduction of T C due to spin waves in Fe in the framework of a Heisenberg model were performed in Ref. 41. This physics whereby the long wavelength fluctuations renormalize the critical temperature would be reintroduced in the DMFT by the use E-DMFT.…”