Magnetic Moments units when spin spin-orbit

[Emanuele Bosoni]

Using Siesta-4.1-b2/b3

The moment printed by the routine moments.F (reported in the output file under "moments: Atomic and Orbital Populations and Magnetic Moments:") seems to me to have a factor of two difference respect to the same quantity in the collinear case. Is it a choice or a bug??

I'm comparing for the same system the "mulliken: Atomic and Orbital Populations:" in the collinear case with "moments: Atomic and Orbital Populations and Magnetic Moments:" of the non collinear case

mulliken: Spin UP Species: Fe
Atom Qatom Qorb
               4s 4s 3dxy 3dyz 3dz2 3dxz 3dx2-y2 3dxy
               3dyz 3dz2 3dxz 3dx2-y2 4Ppy 4Ppz 4Ppx
   1 3.902 -0.027 0.349 0.643 0.643 0.665 0.643 0.665 -0.013
             -0.013 -0.044 -0.013 -0.044 0.149 0.149 0.149
mulliken: Spin DOWN Species: Fe
Atom Qatom Qorb
               4s 4s 3dxy 3dyz 3dz2 3dxz 3dx2-y2 3dxy
               3dyz 3dz2 3dxz 3dx2-y2 4Ppy 4Ppz 4Ppx
   1 4.163 -0.025 0.359 0.747 0.747 0.614 0.747 0.614 -0.014
             -0.014 -0.045 -0.014 -0.045 0.163 0.163 0.163
Need to do UP-DOWN to get the moment (in units of mu_b if I'm correct), so for example the atomic moment here is -0.261

moments: Atomic and Orbital Populations and Magnetic Moments:
Species: Fe
Atom Orb Charge sqrt(<S>^2) <(Sx,Sy,Sz)> sqrt(<L>^2) <(Lx,Ly,Lz)>
----------------------------------------------------------------------------------------------------
   1 1 4s -0.0553 -0.000 0.000 -0.001 0.000 0.000 0.000
   1 2 4s 0.7096 0.000 0.000 -0.005 0.000 0.000 0.000
   1 3 3dxy 1.3892 0.000 0.000 -0.052 0.000 0.000 -0.003
   1 4 3dyz 1.3893 0.000 0.000 -0.052 0.000 0.000 -0.001
   1 5 3dz2 1.2792 0.000 0.000 0.025 0.000 0.000 0.000
   1 6 3dxz 1.3893 0.000 0.000 -0.052 0.000 0.000 -0.001
   1 7 3dx2-y2 1.2793 0.000 0.000 0.025 0.000 0.000 -0.003
   1 8 3dxy -0.0260 -0.000 0.000 0.000 -0.000 -0.000 -0.000
   1 9 3dyz -0.0260 -0.000 0.000 0.000 0.000 -0.000 -0.000
   1 10 3dz2 -0.0882 -0.000 -0.000 0.000 0.000 0.000 0.000
   1 11 3dxz -0.0260 0.000 0.000 0.000 -0.000 0.000 -0.000
   1 12 3dx2-y2 -0.0882 -0.000 -0.000 0.000 -0.000 0.000 -0.000
   1 13 4Ppy 0.3125 0.000 0.000 -0.007 -0.000 0.000 0.000
   1 14 4Ppz 0.3124 0.000 0.000 -0.007 -0.000 -0.000 0.000
   1 15 4Ppx 0.3125 0.000 0.000 -0.007 0.000 -0.000 0.000
----------------------------------------------------------------------------------------------------
   1 Total 8.0638 0.130 0.000 0.000 -0.130 0.014 0.000 0.000 -0.014
Atomic moment here is -0.130