What density-functional theory can tell us about the spin-density wave in Cr

Abstract

The energy-versus-volume curve of the spin-density wave (SDW) in body-centred-cubic Cr is calculated with the density functional theory/full-potential linearized augmented plane wave (DFT/FLAPW) method using the generalized gradient approximation (GGA). The predicted ground state is not the SDW, in contrast to an earlier FLAPW calculation. A conjecture is formulated that the widely varying results of the local density approximation (LDA) and GGA - and of different solution methods - can be scaled by the size of the calculated moment. As a consequence, experimentally relevant properties of the SDW can be calculated by tuning the moment. The implications of these results for the ability of DFT to describe Cr are discussed.

Spin-density wave in Cr: Nesting versus low-lying thermal excitations

“…For GGA the antiferromagnetic state exists at an equilibrium lattice constant of 2.87 Å, which is rather close to the experimental value, but the corresponding magnetic moment of 1.02 B is almost twice as large as the experimental one. In principle these lattice constants and magnetic moments should not be comparable to the experimental values since the SDW is known to be the experimental ground state, but previous calculations 21 have shown that the values for simple antiferromagnetic and SDW calculations do not differ too much, justifying the comparison. We can summarize by saying that LDA finds the experimental magnetic moment in the neighborhood of the experimental lattice constant but not at its own equilibrium, while GGA gives a lattice constant comparable with the experimental value but with a magnetic moment that is twice too large: none of both therefore gives a satisfactory description of Cr.…”

“…For LDA as well as GGA the nonmagnetic and the antiferromagnetic energy-versus-volume curves 8,9,18,21 behave qualitatively identical ͑Fig. 1͒, with a magnetic moment that goes asymptotically to zero for low volumes and a splitting of the two curves at higher volumes, with the antiferromagnetic curve lowest in energy.…”

“…8,9,21 We will summarize these deficiencies in the present section and use this as a basis to propose LDA+ U as a useful pragmatic alternative. In this part, we limit ourselves to the nonmagnetic and simple antiferromagnetic states, which are computationally much easier to treat and are sufficient to highlight the main features of the various functionals.…”

“…It prompted several ab initio investigations of SDW Cr and attempts to reconcile theory and experiment. [7][8][9][10][14][15][16][17][18][19][20][21] Some time ago, a remarkable solution to the conflict was put forward by Uzdin and Demangeat 22 based on a model Hamiltonian study ͓periodic Anderson model ͑PAM͔͒. It builds further upon ideas that were in an embryonic form formulated in the work of Hafner et al 8,9 Their argument goes as follows.…”

First-principles study of point defects in an fcc Fe-10Ni-20Cr model alloy

“…Cr has a bcc crystal structure and exhibits an incommensurate spin-density wave at low temperatures, which is not trivial to properly capture in DFT. [24][25][26] Ni is fcc and displays a ferromagnetic (FM) ordering at low temperatures. This large difference between the properties of the pure elements is responsible for the wide variety of magnetic phases in the ternary phase diagram.…”