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Dear admin,

We are trying to find out how VASP calculates the orbital magnetic moment. In the discussions about the orbital magnetic we find, people are concerned with the keywords to use or with convergence issues and the like. But we are interested is knowing the expression that is used to calculate for these calculations. An analysis of the results we obtain in the case of U3O8 seems to indicate that it is not the expectation value of the operator L that is reported in the OUTCAR file.

A point that called our attention in this regard is the following. U3O8 is a complicated antiferromagnetic system (6 U and 16 O atoms in the unit cell), with magnetism arising from the localized U 5f electrons. But two of the U ions in the unit cell have zero spin magnetic moment and zero orbital magnetic moment. This is not surprising as these ions are expected to be depleted of 5f electrons. The zero magnetic moment atoms are labelled 1 and 2 in the OUTCAR file attached, and you can verify that the moments of these two ions are zero in all three directions. But as you can verify in the same OUTCAR file, the 5f charge of theses ions is 2.287. The questions is, how can the magnetic moment be zero if there is charge in the f orbitals? This is why we would like to know what expression is used in VASP to calculate the orbital moment.

We are attaching the INCAR file used as well.

Hi,

If possible, could you please also provide the POSCAR file?

Sure, here it goes ...

U3O8 mZ1 ex Amm2 AFM
1.00000000000000
8.3022003174000005 0.0000000000000000 0.0000000000000000
0.0000000000000000 6.8652820587000001 0.0000000000000000
0.0000000000000000 -3.5897825328000001 5.8519705325000002
U O
6 16
Direct
0.0000000000000000 0.9664389027457470 0.9664389027457470
0.5000000000000000 0.9664389471523165 0.9664389471523165
0.0000000000000000 0.3286532590021660 0.6781864277755693
0.0000000000000000 0.6781864277755693 0.3286532590021660
0.5000000000000000 0.3286533196225132 0.6781864596779651
0.5000000000000000 0.6781864596779651 0.3286533196225132
0.2500000028539968 0.9600968246225248 0.9600968246225248
0.7499999971460034 0.9600968246225248 0.9600968246225248
0.2499999663622994 0.3267897986026854 0.6838777249877708
0.7500000336377005 0.6838777249877708 0.3267897986026854
0.7500000336377005 0.3267897986026854 0.6838777249877708
0.2499999663622994 0.6838777249877708 0.3267897986026854
0.0000000000000000 0.6007958476143651 0.6007958476143651
0.5000000000000000 0.6007958223865432 0.6007958223865432
0.0000000000000000 0.3132456558685029 0.0709589423818977
0.0000000000000000 0.0709589423818977 0.3132456558685029
0.5000000000000000 0.3132456745785000 0.0709589637910524
0.5000000000000000 0.0709589637910524 0.3132456745785000
0.0000000000000000 0.6647334863753513 0.9974229685689160
0.0000000000000000 0.9974229685689161 0.6647334863753513
0.5000000000000000 0.6647335370830942 0.9974230189495410
0.5000000000000000 0.9974230189495410 0.6647335370830942

Best regards,
Rolando

The orbital moment is calculated in the subroutine CALC_ORBITAL_MOMENT in LDApU.F using the L-operator. You may find some details in https://doi.org/10.1088/1361-648X/aae80a.

Regarding U3O8, atoms 1 and 2 have indeed zero spin and orbital moments, despite they have a total f-charge similar to the other U atoms. That means that for these two U atoms, the occupation of the f-orbitals is such that the occupations of the plus and minus m_s characters are the same (and similar for m_l).