[Wannier] How to calculate orbital magnetization by the integration in irreducible Brillouin zone?

[Wanxiang Feng]

Dear all,

I have great interest in the calculation of orbital magnetization (OM) implemented in Wannier formalism [Lopez et al., PRB 85, 014435 (2012)]. Indeed, I can repeat all results of bcc Fe in this paper, by following the example19 in the tutorial. In example19, the integration is adopted in full Brillouin zone (BZ). Thus, the computational cost is not too much because only 18 Wannier functions in Fe and the convergence of OM with respect to k-mesh can be easily reached. However, the irreducible BZ integration must be adopted if a system contains more than hundreds of orbitals or the convergence is difficult .

For this purpose, I fist test the irreducible BZ integrations of OM in bcc Fe, by setting the tag "wanint_kpoint_file = true” in the win file and providing the irreducible k-points and their weights in file “kpoint.dat”. I have read the code in berry.F90 and other related subroutines, and I guess that the k-points are given in relative coordinates of the reciprocal lattice and the sum of weights equals to one. The irreducible k-points are generated by using the “pw.x”. The calculated OMs are very different between the full and irreducible BZ integrations.

For example, if I use full BZ integration with the k-mesh of 50x50x50, the result is:

 M_orb (bohr magn/cell)        x          y          z
 ======================
    Local circulation :     -0.0000    -0.0000     0.0935
 Itinerant circulation:      0.0000    -0.0000    -0.0187
 --------------------------------------------------------
                     Total   :      0.0000    -0.0000     0.0749


This value is identical to the paper PRB 2012. On the other hand, if use the irreducible BZ integration with 102 k-points (the file “kpoint.dat" is attached), the result is


 M_orb (bohr magn/cell)        x          y          z
 ======================
    Local circulation :     -0.0153     0.0040     0.0932
 Itinerant circulation:      0.0030     0.0027    -0.0163
 --------------------------------------------------------
                     Total   :     -0.0123     0.0066     0.0768

Could anyone tell me what mistakes I have did? Please ask for other details I may forget to show. Any suggestions will be appreciated.

By the way, I noted that someone has asked that the DOS calculations with full and irreducible BZs are also different. He generated file “kpoint.dat” by both abinit and elk. 
http://mailman.qe-forge.org/pipermail/wannier/2014-December/000929.html

Wanxiang Feng
————————————————
School of Physics
Beijing Institute of Technology
Beijing 100081, China


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