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33845983640
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Only one specific antiferromagnetic (AF) configuration was considered: The B2 (CsCl type) magnetic ordering on the A2 crystal structure where the cube center sites take a local moment opposite that of the cube corner sites. This gave rise to three AF results with non-vanishing local moments (as defined by integrating the spin density over the Voronoi polyhedron), namely for Co, Cr, and Fe. In the case of Co and Fe, this AF configuration was higher in enthalpy than the ferromagnetic A2 result, while for Cr the difference in energy was less than the rounding error in Table 3. The calculation of the enthalpy difference between A2 ferromagnetic and B2 antiferromagnetic Cr required a larger number of k-points than was used elsewhere. There are countless other magnetic orderings possible, where the crystal symmetry is broken, even for the simplest underlying crystal structures such as A1 and A2. It is not expected that these other magnetic orderings will substantially change the enthalpy differences listed in Table 3, and they will almost certainly be much less than other errors inherent in the current calculations. For that reason, and because such magnetic orderings break the symmetry of the crystal structure, they are not further considered here.
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For Al and Mn, the extrapolation to an infinite number of k-points was considered by repeating calculations for the simplest structures with 8 times and 64 times more k-points in the first Brillouin zone. It was concluded that inaccuracies associated with the k-point sampling were about 0.22 kJ/mol for Al, and about 0.06 kJ/mol for Mn. These inaccuries are a small fraction of typical structural enthalpy differences.
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It is prudent to mention that removal of symmetry elements, say by using supercells that are non-standard multiples of the unit cell, might affect the robustness under structural optimization. Performing calculations using multiples of the unit cell is required for examining antiferromagnetic states. In Nature also, symmetry elements are continuously challenged by fluctuations such as lattice vibrations. Therefore, the imposition of symmetry in ab initio calculations during structural optimizations is somewhat artificial.
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