Kleinman, Bylander, and Morrison Reply: We [1] have recently argued that because of the nonlinear nature of the local spin-density approximation (LSDA) for exchange and correlation (XC) potentials, an unphysical diminution of the XC interaction between valence electrons is present in the core region. We then performed a pseudopotential [2] calculation for a nine layer Rh(OOl) film in which all the electrons see a Hartree-Fock potential from the core electrons and an LSDA potential from the valence electrons. We found [1] that the first two layers of the film are ferromagnetic with \.Sju B per surface unit cell. To mimic our XC potential Weinert, Bliigel, and Johnson [3] constructed their all-electron VLSDA potential and essentially reproduced our results. Using the LSDA they found that the Rh(OOl) surface is paramagnetic. They found that the VLSDA resulted in an unrealistically large moment for Fe whereas the LSDA moment is in close agreement with experiment. They also invoked the Stoner model to determine that the VLSDA results in a susceptibility for Rh which is too large by a factor between 4 and 6. From these two facts they conclude that although the LSDA is not defect free, in this case its results are to be believed and the Rh(OOl) surface is paramagnetic. Although we think their model may have overestimated the VLSDA susceptibility error and underestimated the LSDA susceptibility error, we are in general agreement with their results.We do not believe that there can be any dispute over the fact that the core charge density reduces the LSDA exchange interaction between valence electrons in the core region by a factor of j (pvai/pcore) 2/3 and that this is unphysical. Correlation should result in a large reduction of the exchange splitting which both the LSDA and VLSDA correlation terms fail to do. It is the cancellation of these errors which allows the LSDA to work as well as it does, although we should not forget that it fails to predict the correct ground state of iron. Furthermore, Moruzzi and Marcus [4] have just shown that the LDA yields accurate bulk moduli for the nonmagnetic 3d and 4d transition metals. The error for Ni is actually increased while for Co and Fe it is decreased when the LSDA is used, but in all three cases it remains large. Thus it is clear that although the LSDA yields accurate spin polarizations for these metals, it fails to predict their magnetic energies. It was, and is, our feeling that because the Ad electrons of Rh are more free-electron-like than the 3d's of Fe, the error in their LSDA correlation should be smaller. Whether the LSDA or VLSDA better predict the surface properties of Rh will be decided by experiment. We have been informed [5] that Jona et ai, using spin polarized photoemission, have found a weak spin polarization (0.1 to 0.3/us) of the Rh(00l) surface. These data were taken at room temperature. If the usual linear temperature dependence of two dimensional ferromagnetism holds, a much larger polarization may be found at He temperatures.
The crystalline and magnetic structures of the YCo 3 -H͑D͒ system have been investigated by means of x-ray and neutron diffraction with the objective of understanding the complex magnetic changes that are observed in this system as hydrogen is added. Synchrotron x-ray diffraction ͑XRD͒ patterns were first refined to yield the lattice parameters and coordination of Y and Co atoms in the metal and two -hydride phases while XRD was used for the ␥ phase. In situ neutron powder diffraction measurements of YCo 3 D x were then made in all four phases to determine the deuterium site occupancies and magnetic structures. The site occupancies were also rationalized using the Westlake geometric model. The highest hydrogen concentration measured was YCo 3 H 4.6 . Using the Westlake model, we conclude that the saturated hydrogen content would be YCo 3 H 5 . Our results reported here and in Part I ͓Phys. Rev. B 76, 184443 ͑2007͔͒ have enabled us to rationalize the changes in the magnetic structures in terms of changes in the cobalt-cobalt distance caused by the addition of hydrogen. In particular, in the antiferromagnetic ␥ phase, we observe Co atomic displacements that enable the structure to adopt a particular antiferromagnetic structure in a manner that is reminiscent of a Peierls distortion as observed in transitions from the conducting to nonconducting hydrides on addition of hydrogen in YH 3 .
VOLUME 47, NUMBER 11 15 MARCH 1993-I Brief ReportsBrief Reports are accounts of completed research which, while meeting the usual Physical Review standards of scientific quality, do not warrant regular articles A. Brief Report may be no longer than four printed pages and must be accompanied by an abstract Th. e same publication schedule as for regular articles is followed, and page proofs are sent to authors Nonlocal Chou has recently presented an approximation to the norm-conserving form of Vanderbilt's nonlocal Hermitian pseudopotential.We point out two minor shortcomings of the Chou approximation and also show that it is actually easier to construct the Vanderbilt pseudopotential than to construct Chou's approximation to it. The all-electron silver d-electron logarithmic derivative is compared over a range of energies with that obtained from a Vanderbilt pseudopotential which is exact at two energies and with Chou's approximate pseudopotential.The agreement with the former is excellent and with the latter is only fair. 476728
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