My two cents concerning this problem:

What moments do you consider to be zero, Reggad? With Ni being a METAL I would claim that the electron spin moment is the one to inspect. Certainely you (or the authors you read) do not propose to set the electron spin to zero?

Remember that DFT calculates the situation at T=0. Simulating paramagnetism at high temperature by forcing the spin-polarization to zero may work for some purposes, but will be bad if you are interested in magnetic properties: With zero moments nothing will happen if you switch on a magnetic field!

With 4f-electrons there is a good chance that one can consider the whole 4f-shell as a quantum system of its own, instead of the single electrons. Then each lattice site carrys some moment. The paramgnetic phase of such an ensemble is by definition the one where the expectation value of the total magnetization vanishes due to incoherent random fluctuations of the 4f-moments. imho, the view of this phase as all the moments pointing in random directions has its merits, but one should not over-interprete the picture. Such a state is most probably not even an eigenstate of the Hamiltonian, let alone the ground state that DFT is concerned with.



---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564


Am 26.11.2016 22:30, schrieb Abderrahmane Reggad:
Thank you Prof Blaha for your quick answer.

The Ni atom is 3d transition metal . But my question is about the
simulation of the paramagnetic state. There are many people that
considere that the paramagnetic state is the non-spin polarierd one
and the magnetic moment is zero, but you say no and the magnetic
moments exist in arbitrary directions and my quoting is about that.

I have given 2 examples for that discrepancy with your statement.

Best regards--

Mr:
A.Reggad                                          

Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret

Algerie


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