Ab initioelectron theory for magnetism in Fe:  Pressure dependence of spin-wave energies, exchange parameters, and Curie temperature

Abstract

The spin-wave spectra for bcc Fe at various lattice constants are calculated by the ab initio density functional electron theory for various lattice constants, and the exchange parameters of a Heisenberg model are determined from the data. The spin-wave energies increase with decreasing lattice constant, and the behavior of the exchange parameters can by no means be described by the Bethe-Slater curve for an effective nearest-neighbor Heisenberg model. From the spin-wave frequencies the pressure dependence of the Curie temperature is derived in mean-field and random-phase approximation, yielding ‫ץ‬T c MF /‫ץ‬pϷ1.6 K/kbar and ‫ץ‬T c RPA /‫ץ‬p Ϸ1.8 K/kbar, in contrast to the experimental result ‫ץ‬T c /‫ץ‬pϷ0. Possible reasons for this discrepancy are discussed. The exchange interactions in 3d transition metals and their compounds are often discussed within the framework of an effective nearest-neighbor Heisenberg model and the Bethe-Slater curve ͑see, e.g., Ref. 1͒ which represents a conjecture on the variation of the nearest-neighbor exchange parameter J(R) with the interatomic spacing R. According to this curve, J(R) increases with decreasing R for Co and Ni, whereas it decreases for Fe and changes sign from positive to negative for small R. As an example for the application of the Bethe-Slater curve, the temperature dependence of the magnetization of an amorphous ferromagnet was explained 2 by a mean-field approach with spatial fluctuations of J estimated by use of this curve. If this simple nearest-neighbor Bethe-Slater model was correct, then the critical temperature T c of body-centered-cubic Fe as calculated in mean-field theory would be expected to decrease strongly when pressure is exerted on the sample. Experimentally, however, nearly no change of T c was found 3 at pressures up to the structural transition from body-centered to face-centered.Indeed, calculations based on the ab initio densityfunctional electron theory have revealed ͑Table I͒ that the simple nearest-neighbor Heisenberg model fails badly for Fe. Instead, an effective Heisenberg model with long-range pair interaction parameters J i j is proposed,where e i and e j are the unit vectors pointing in directions of the local magnetic moments at sites (i, j), respectively. The exchange parameters remain non-negligible over a very long range, and they oscillate in sign ͑Table I͒. It is the objective of this paper to calculate, by ab initio density-functional theory, the change of the spin-wave spectrum with decreasing lattice constant. From this information we then obtain related modifications of J i j , and predictions of the meanfield theory and random-phase approximation for the pressure dependence of T c . For the determination of the spin-wave spectra we use the method of Grotheer et al., 10 which is an alternative to the so-called frozen-magnon method introduced by Halilov et al. 11 Thereby, a spiral external field is applied, which for a monatomic unit cell has the formwhere q is the wave vector of the spiral and T denotes the translation...

Exchange interaction function for spin-lattice coupling in bcc iron

“…7͑a͒, we plot J ij ef f as functions of the lattice constant from the 1NN to the ninth NN. 53 however, there is no cross over between J 1 ef f and J 2 ef f in our GGA results.…”

Revisited Stress-Dependent Curie-Temperature in BCC Iron: LSDA+U Cleansing of Magnon Ambiguities

“…Leger and Loriers-Susse (1972) reported the independence of T c and stress; they showed that the magnetic phase transition remained at a given temperature, even when under stress. However, Morán et al (2003) produced inconsistent results, concluding that the Heisenberg model might not correctly describe this phenomenon. Later, Körmann et al (2009) reported good consistency between their calculated and experimental results.…”

“…Theoretically, Morán et al (2003) and Körmann et al (2009) used nearly identical methodologies, but obtained different results. Both calculated T c by integrating magnon energy along a high symmetry path in the Brillouin zone (the so-called 'frozen magnon' approach) (Halilov et al, 1998).…”

“…Later, Körmann et al (2009) reported good consistency between their calculated and experimental results. Thus, density functional theory (DFT) calculations appeared to clearly describe the independence of stress, although why their results improved upon Morán et al (2003) has not been clarified.…”

Competition of lattice and spin excitations in the temperature dependence of spin-wave properties

“…For Fe, they show very good agreement with experimental Curie temperatures. The exchange interactions are strongly simplified, assuming a 1/r 3 functional dependence obtained from fitting two sets of calculated exchange integrals [3,23]. These exchange integrals are truncated to second-nearest neighbors, and do not take into account the detailed and oscillatory behavior of the exchange further out, which is relevant in many different magnetic materials.…”