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[Stefaan Cottenier <Stefaan.Cottenier@ugent.be>]

Dear Matthieu,

This reply does not concern abinit itself, and the methods that are 
described take a pragmatic rather than a rigorously theoretical point of 
view -- so far the disclaimer ;-)  :

> I am using LDA+U with the latest (pre-release) abinit 5.7,
> on ifort 9.1/itanium/mpi (tests pass fine), trying to do
> calculations in LDA+U of alloys of d and f metals (which I
> cannot name for confidentiality reasons).

I refer to two papers of our previous work that deal with isolated 
lanthanide and actinide impurities in bcc Fe, which can be considered as 
a dilute d-f alloy (albeit with the difference that the space available 
for the f-atom is much smaller than in a typical d-f alloy). There is a 
lot of information in these papers along different story lines. You 
might find something there that is relevant for you:

Hyperfine interactions at lanthanide impurities in Fe
D. Torumba, V. Vanhoof, M. Rots, and S. Cottenier, Phys. Rev. B 74, 
014409 (2006),
DOI:10.1103/PhysRevB.74.014409
http://link.aps.org/doi/10.1103/PhysRevB.74.014409

Hybrid exchange-correlation functionals applied to hyperfine 
interactions at lanthanide and actinide impurities in Fe
D. Torumba, P. Novak, and S. Cottenier, Phys. Rev. B 77, 155101 (2008), 
DOI:10.1103/PhysRevB.77.155101
http://link.aps.org/doi/10.1103/PhysRevB.77.155101

The 2006 paper deals with LDA+U on lanthanides in Fe exclusively. The 
2008 paper has LDA+U on actinides in Fe, as well as B3PW91 (hybrid 
functional) for lanthanides and actinides in Fe.

> For pure f metals
> I have reference values of U and J, and the f states are at
> the correct position,

You might check this against the internally consistent procedure to 
determine U for lanthanides (Fig. 5 of the 2006 paper). In my 
experience, lanthanides in whatever environment can be described by such 
a value for U. For actinides, the value of U is more dependent on the 
environment. (Your confidentiallity concern does not allow to guess 
whether you are interested in 4f or 5f... ;-) ).

> but in mixed systems the f states tend
> to alloy, broaden, and end up just below the Fermi level
> (2 eV instead of 10 eV below), and are relatively insensitive
> to U. This makes sense if the states are less localized, but
> still it's strange: experimentally the f peak in these systems
> is still found at -10 eV... So:

I'll send a slide to your private email, where you see a plot of the DOS 
for Er in Fe -- LDA+U (upper) and LDA (lower). The horizontal scale is 
in eV, and the Fermi energy is at zero. The broad (itinerant) LDA-peaks 
get more structured due to LDA+U, and are shifted downwards by about 2 
eV for a filled spin channel and are heavily split for a partially 
filled spin channel.

> 1) is this hybridization physical?
> 2) has anyone seen this before?

To 1) and 2) :  In our experience, the hybridization between 4f and 3d 
is -- even in this case with small Fe-lanthanide distances -- by far not 
as large as is given e.g. by LDA. Still, hybridisation is there and can 
be described by crystal-field splitting. It also depends quite a bit on 
the flavour of LDA+U (can you use a different one, and does that alter 
your results?)

> 3) is there evidence that U for a surface is different from U for a bulk?

Yes. I have unpublished work on this, which I never tried to pour into a 
paper because the comparison with experiment was getting too tricky. It 
was for isolated Fe atoms on a Ag surface. Pragmatic ways to estimate 
the U clearly showed an increase towards the surface. And that's not too 
strange: surface atoms are 'halfway' between bulk and isolated atoms, 
hence more tendency towards localization and a larger value of U is needed.

> 4) is there a way to increase U or something, to force the band to 
the "correct" position?

In the two papers quoted above, we ran into a similar problem as you 
probably have: LDA+U does not give the type of solutions that on 
physical grounds would be expected. We had to 'force' it into the 
'proper' solution. See section B.2 of the 2006 paper for 'constrained 
density matrix' calculations. Perhaps you could use something like that.

Best,
Stefaan

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Stefaan Cottenier
Center for Molecular Modeling
Ghent University
Proeftuinstraat 86
BE-9000 Gent
Belgium

http://molmod.Ugent.be
email: Stefaan . Cottenier /at/ UGent . be <===== NEW EMAIL ===