The orbital magnetic moment at each atomic site is calculated as default
in the non-collinear DFT. Since the orbital magnetic moment
appears as a manifestation of spin-orbit coupling (SOC),
the calculated values become finite when the SOC is included [79,80].
As an example, a non-collinear LDA+U (U=5 eV) calculation of iron
monoxide bulk is illustrated using an input file 'FeO_NC.dat'
in the directory 'work'. As for the LDA+U calculation, see the Section
'LDA+U'. The calculated orbital and spin magnetic moments
at the Fe site are listed in Table 4. Also, you can find the orientation
of the (decomposed) orbital moment in '*System.Name*.out', where '*System.Name*' means
'System.Name'
as follows:

*********************************************************** *********************************************************** Orbital moments *********************************************************** *********************************************************** Total Orbital Moment (muB) 0.000001885 Angles (Deg) 126.954120326 185.681623854 Orbital moment (muB) theta (Deg) phi (Deg) 1 Fe 0.76440 131.30039 51.57082 2 Fe 0.76440 48.69972 231.57071 3 O 0.00000 40.68612 210.48405 4 O 0.00000 48.18387 222.72367 Decomposed Orbital Moments 1 Fe Orbital Moment(muB) Angles (Deg) multiple s 0 0.000000000 90.0000 0.0000 sum over m 0.000000000 90.0000 0.0000 s 1 0.000000000 90.0000 0.0000 sum over m 0.000000000 90.0000 0.0000 px 0 0.000055764 42.7669 270.0000 py 0 0.000046795 28.9750 180.0000 pz 0 0.000044132 90.0000 239.0920 sum over m 0.000120390 47.1503 239.0920 px 1 0.001838092 10.8128 -90.0000 py 1 0.001809013 3.5933 180.0000 pz 1 0.000362989 90.0000 251.7994 sum over m 0.003683170 11.3678 251.7994 d3z^2-r^2 0 0.043435663 90.0000 224.2874 dx^2-y^2 0 0.066105902 24.3591 229.7056 dxy 0 0.361874370 80.4206 50.6465 dxz 0 0.397108491 144.2572 -12.7324 dyz 0 0.427070801 138.9995 100.0151 sum over m 0.776513038 132.4577 51.6984 d3z^2-r^2 1 0.000144144 90.0000 196.4795 dx^2-y^2 1 0.000270422 31.2673 224.0799 dxy 1 0.003006770 85.5910 50.2117 dxz 1 0.002952926 139.3539 -4.1301 dyz 1 0.003222374 134.0513 95.9246 sum over m 0.006795789 126.2536 52.1993 f5z^2-3r^2 0 0.001903274 90.0000 33.4663 f5xz^2-xr^2 0 0.005186342 14.5594 118.0868 f5yz^2-yr^2 0 0.005258572 17.3323 -35.0807 fzx^2-zy^2 0 0.005477755 29.3372 224.9067 fxyz 0 0.004851020 10.1407 249.0607 fx^3-3*xy^2 0 0.002029489 84.1842 -81.2087 f3yx^2-y^3 0 0.001611593 82.6686 176.3172 sum over m 0.020307129 9.9551 249.3739 ..... ...

As shown in Table 5, OpenMX gives a good agreement for both the
spin and orbital magnetic moments of a series of -transition
metal oxides with other calculation results.
However, it is noted that the absolute value of orbital magnetic moment
seems to be significantly influenced by calculation conditions
such as basis functions and on-site 'U' in the LDA+U method,
while the spin magnetic moment is relatively insensitive to
the calculation conditions, and that a rather rich basis set including
polarization functions will be needed for convergent calculations of
the orbital magnetic moment.

Compound | OpenMX | Other calc. | OpenMX | Other calc. | Expt. in total |

MnO | 4.519 | 4.49 | 0.004 | 0.00 | 4.79,4.58 |

FeO | 3.653 | 3.54 | 0.764 | 1.01 | 3.32 |

CoO | 2.714 | 2.53 | 1.269 | 1.19 | 3.35,3.8 |

NiO | 1.687 | 1.53 | 0.247 | 0.27 | 1.77,1.64,1.90 |

2016-04-03