# Orbital magnetic moment

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 [118,119]. 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:

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Orbital moments
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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 6, 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