关注：

1) 铁磁性、反铁磁性计算

2) VASP的自带算例分析

参考handsonIV手册、Wiki算例

引子:

Besides, we canevaluate the spin and orbital contribution to the magnetic moment (μ_s and μ_l).

In our calculations,we constrain the direction of the magnetic moments along z-axis in LDA and LDA +U.

In LDA +U +SOC,instead, the magnetic moments are automatically set to be noncollinear.

However, in the finalself-consistent solution, they result again all aligned along the z-axis.

For the sake of the computation efficiencyof so many calculation models,we decide to leave the 3-k structure outside of scope for our present calculations. Therefore, only the results ofthe collinear 1-k AFM configurations related to the (100) lattice directions are discussed.

参考handsonIV手册、Wiki算例、百度12算例

手册参考：

MAGMOM-tag：      http://cms.mpi.univie.ac.at/vasp/vasp/MAGMOM_tag.html 

LNONCOLLINEAR:    http://cms.mpi.univie.ac.at/vasp/vasp/LNONCOLLINEAR_tag.html

LSORBIT-tag：          http://cms.mpi.univie.ac.at/vasp/vasp/LSORBIT_tag.html  

手册学习：

LNONCOLLINEAR-tag

Supported as of VASP.4.5.

Setting LNONCOLLINEAR=.TRUE. in the INCAR file allows to perform fully  non-collinear magnetic structure calculations.

VASP is capable of reading WAVECAR and CHGCAR  files from previous  non-magnetic or collinear  calculations, it is however not possible to rotate the magnetic field locally on selected atoms.

Hence, in practice, we recommend to perform non collinear calculations in two steps:

• First, calculate the non magnetic groundstate and generate a WAVECAR and CHGCAR file.

  
  

• Second, read the WAVECAR and CHGCAR file, and supply initial  magnetic moments by means of the MAGMOM tag (compare Sec. 6.13).

  For a non-collinear setup, three values must be supplied for each ion in the MAGMOM line.

  The  three entries correspond to the initial local magnetic moment for each ion in x, y and z direction respectively. The line  MAGMOM = 1 0 0   0 1 0initialises the magnetic moment on the first atom in the x-direction, and on the second atom in the y direction【每个原子都只有一个方向有磁矩，有磁矩的方向也可以各不相同？】.
  

  
  

  Mind, that the MAGMOM line supplies initial magnetic moments only if ICHARG=2, or if the CHGCAR file contains only charge but no magnetisation density.
  

Wiki 算例

http://cms.mpi.univie.ac.at/wiki/index.php/VASP_example_calculations#Magnetism

Magnetism

fcc Ni (revisited)

NiO

NiO LSDA+U

Spin-orbit coupling in a Fe monolayer

Spin-orbit coupling in a Ni monolayer

constraining local magnetic moments

（1） 铁磁性计算，Ni

Description: spin polarized fcc Ni, a ferromagnet.

• INCAR

SYSTEM  = Ni fcc bulk

ISTART  = 0

ISPIN   = 2

MAGMOM  = 1.0  【一个原子，不分方向，设置一个总的磁矩？】

ISMEAR  = -5

VOSKOWN = 1

LORBIT  = 11

• KPOINTS

k-points

0

Gamma

11 11 11

 0  0  0

• POSCAR

fcc:          

 -10.93    

0.5 0.5 0.0

0.0 0.5 0.5

0.5 0.0 0.5  

1  

Cartesian

0 0 0

(2) 反铁磁计算，NiO 【反铁磁就是没有磁性？】

Description: NiO, an antiferromagnet.

SYSTEM   = NiO

ISTART   = 0

ISPIN    = 2

MAGMOM   = 2.0 -2.0 2*0 【只有Ni是磁性原子，O不是？】

ENMAX    = 250.0

EDIFF    = 1E-3

ISMEAR   = -5

AMIX     = 0.2      【便于收敛？】

BMIX     = 0.00001  【便于收敛？】

AMIX_MAG = 0.8   【便于收敛？】

BMIX_MAG = 0.00001  【便于收敛？】

LORBIT   = 11  

• KPOINTS

k-points

0

gamma

4  4  4

0  0  0

• POSCAR

AFM  NiO

4.17

1.0 0.5 0.5

0.5 1.0 0.5

0.5 0.5 1.0

2  2

Cartesian

0.0 0.0 0.0

1.0 1.0 1.0

0.5 0.5 0.5

1.5 1.5 1.5

（3）基于LSDA+U的反铁磁计算

Description: antiferromagnetic NiO in the LSDA+U (Dudarev's approach).

• INCAR

SYSTEM   = NiO

ISTART   = 0

ISPIN    = 2

MAGMOM   = 2.0 -2.0 2*0 【反铁磁就是没有磁性？共线就是一个原子三个方向的磁矩共线？只需就每个原子设置一个总的磁矩】

ENMAX    = 250.0

EDIFF    = 1E-3

ISMEAR   = -5   【Why  -5】

AMIX     = 0.2

BMIX     = 0.00001

AMIX_MAG = 0.8

BMIX_MAG = 0.00001

LORBIT   = 11

LDAU      = .TRUE.

LDAUTYPE  = 2

LDAUL     = 2 -1

LDAUU     = 8.00 0.00

LDAUJ     = 0.95 0.00

LDAUPRINT = 2

LMAXMIX   = 4          ! Important: mix paw occupancies up to L=4

• KPOINTS

k-points

0

gamma

4  4  4  

0  0  0

• POSCAR

AFM  NiO

4.17

1.0 0.5 0.5

0.5 1.0 0.5

0.5 0.5 1.0

2 2

Cartesian

0.0 0.0 0.0

1.0 1.0 1.0

0.5 0.5 0.5

1.5 1.5 1.5

（4） Dr Ao算例

算例1. XO2 AFM relax

System=XO2-AFM  【8个X原子，4个O原子】
PREC=Accurate
ISPIN=2
MAGMOM=8*0 2*4 2*-4
VOSKOWN=1

LDAU=.TRUE.
LDAUTYPE=2
LDAUL=3 -1  
LDAUU=4.7 0
LDAUJ=0.7 0  
LDAUPRINT=2
LMAXMIX=6

ISTART=0
ICHARG=2
ISMEAR=0
SIGMA=0.1
NSW=500
IBRION=2
ISIF=3
ISYM=2
POTIM=0.2
EDIFF=1E-4
ENCUT=600.0

*POSCAR

XO2 AFM
1.0
       5.4500000000         0.0000000000         0.0000000000
       0.0000000000         5.4500000000         0.0000000000
       0.0000000000         0.0000000000         5.4500000000
   O   X
   8    4
Direct
    0.250000000         0.250000000         0.250000000
    0.750000000         0.750000000         0.250000000
    0.750000000         0.250000000         0.750000000
    0.250000000         0.750000000         0.750000000
    0.250000000         0.250000000         0.750000000
    0.750000000         0.750000000         0.750000000
    0.750000000         0.250000000         0.250000000
    0.250000000         0.750000000         0.250000000
    0.000000000         0.000000000         0.000000000
    0.000000000         0.500000000         0.500000000
    0.500000000         0.000000000         0.500000000
    0.500000000         0.500000000         0.000000000

*KPOINTS

k-points
0
Monhkhorst-Pack
12 12 12
0.0 0.0 0.0

算例1：static计算

System=XO2-AFM
PREC=Accurate
ISPIN=2
MAGMOM=8*0 4 -4 4 -4
GGA=PE
VOSKOWN=1

LDAU=.TRUE.
LDAUTYPE=2
LDAUL=-1 3  
LDAUU=0 4.7
LDAUJ=0 0.7  
LDAUPRINT=2
LMAXMIX=6

ISTART=1
ICHARG=11
LORBIT=11
EMAX=20
EMIN=-20
NBANDS=120
NEDOS=5000
ISMEAR=-5
EDIFF=1E-5
ENCUT=600.0
LWAVE=.FALSE.
LCHARGE=.FALSE.
LELF=.FALSE.

*KPOINTS

k-points
0
Monhkhorst-Pack
12 12 12
0.0 0.0 0.0

算例2：X4O8H-AFM relax

System=X4O8H-AFM 【8个O原子，1个H原子，4个X原子】
PREC=Accurate
ISPIN=2
MAGMOM=8*0 0 4 -4 4 -4
GGA=PE
VOSKOWN=1

LDAU=.TRUE.
LDAUTYPE=2
LDAUL=-1 -1 3  
LDAUU=0 0 4.7
LDAUJ=0 0 0.7  
LDAUPRINT=2
LMAXMIX=6

ISTART=0
ICHARG=2
ISMEAR=0
SIGMA=0.1
NSW=500
IBRION=2
ISIF=3
ISYM=2
POTIM=0.2
EDIFF=1E-4
ENCUT=500.0

*POSCAR

X4O8H AFM
1.0
       5.3963999748         0.0000000000         0.0000000000
       0.0000000000         5.3963999748         0.0000000000
       0.0000000000         0.0000000000         5.3963999748
   O  H  X
   8  1  4
Direct
    0.250000000         0.250000000         0.250000000
    0.750000000         0.750000000         0.250000000
    0.750000000         0.250000000         0.750000000
    0.250000000         0.750000000         0.750000000
    0.250000000         0.250000000         0.750000000
    0.750000000         0.750000000         0.750000000
    0.750000000         0.250000000         0.250000000
    0.250000000         0.750000000         0.250000000
    0.500000000         0.500000000         0.500000000
    0.000000000         0.000000000         0.000000000
    0.000000000         0.500000000         0.500000000
    0.500000000         0.000000000         0.500000000
    0.500000000         0.500000000         0.000000000

*KPOINTS

k-points
0
Monhkhorst-Pack
9 9 9
0.0 0.0 0.0

!!! 算例2： static计算

System=X4O8H-AFM
PREC=Accurate
ISPIN=2
MAGMOM=8*0 0 4 -4 4 -4
GGA=PE
VOSKOWN=1

LDAU=.TRUE.
LDAUTYPE=2
LDAUL=-1 -1 3  
LDAUU=0 0 4.7
LDAUJ=0 0 0.7  
LDAUPRINT=2
LMAXMIX=6

ISTART=1
ICHARG=11
LORBIT=11

EMAX=20
EMIN=-20
NBANDS=120
NEDOS=5000
ISMEAR=-5
EDIFF=1E-4
ENCUT=500.0
LELF=.FALSE.
LWAVE=.FALSE.
LCHARGE=.FALSE.

*KPOINTS

k-points
0
Monhkhorst-Pack
9 9 9
0.0 0.0 0.0

(5) My 算例:XH3-FM

SYSTEM = XH3-FM- local optimisation
PREC = Accurate
ENCUT = 500.0
EDIFF = 1E-4
#EDIFFG = -1E-3
#SYMPREC=1e-3
IBRION = 2
POTIM = 0.2
ISIF = 3
NSW = 500

ISPIN=2
MAGMOM= 12*0 4*4  【12个H原子，4个X原子】
VOSKOWN=1

#LSDA-plus-U
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = -1  3
LDAUU = 0.00 4.70
LDAUJ = 0.0   0.7
LDAUPRINT = 2
LMAXMIX = 6

PSTRESS =0.001
ISMEAR = 1
SIGMA = 0.2

ISTART=0
ICHARG=2
ISYM=2

#ISYM=0
#LREAL = .FALSE.
LCHARG = FALSE
LWAVE = FALSE

*POSCAR

XH3-FM                    
  1.00000000000000    
    5.3387670005129664    0.0000000000000000    0.0000000000000000
    0.0000000000000000    5.3387670005129664    0.0000000000000000
    0.0000000000000000    0.0000000000000000    5.3387670005129664
  H    X
   12     4
Direct
 0.5000000000000000  0.5000000000000000  0.5000000000000000
 0.5000000000000000  0.0000000000000000  0.0000000000000000
 0.0000000000000000  0.5000000000000000  0.0000000000000000
 0.0000000000000000  0.0000000000000000  0.5000000000000000
 0.7500000000000000  0.2500000000000000  0.2500000000000000
 0.2500000000000000  0.7500000000000000  0.7500000000000000
 0.2500000000000000  0.7500000000000000  0.2500000000000000
 0.7500000000000000  0.2500000000000000  0.7500000000000000
 0.2500000000000000  0.2500000000000000  0.7500000000000000
 0.7500000000000000  0.7500000000000000  0.2500000000000000
 0.7500000000000000  0.7500000000000000  0.7500000000000000
 0.2500000000000000  0.2500000000000000  0.2500000000000000
 0.0000000000000000  0.0000000000000000  0.0000000000000000
 0.0000000000000000  0.5000000000000000  0.5000000000000000
 0.5000000000000000  0.0000000000000000  0.5000000000000000
 0.5000000000000000  0.5000000000000000  0.0000000000000000

参数解释：

1.  LORBIT

LORBIT = .TRUE. | .FALSE. (VASP.3.2)  
LORBIT =  0 | 1 | 2 | 5 | 10 | 11 | 12 (VASP.4.X and later)  

This flag determines, together with an appropriate RWIGS (see section 6.33), whether the PROCAR   or  PROOUT   files  (see section 5.21) are written.

The file PROCAR contains the spd- and site projected  wavefunction character of each band.

The wavefunction character is calculated, either by projecting the orbitals onto spherical harmonics that are non-zero within spheres of a radius RWIGS around each ion (LORBIT=1, 2),

or using a quick projection scheme relying that works only for the PAW method (LORBIT=10,11,12, see below).

If the LORBIT flag is not equal zero, the site and l-projected density  of states is also calculated.

2. Mixing tag

please rely on these defaults:

There are only a few other parameter combinitions which can be tried, if convergence turns out to be very slow.

 In particular, for slabs, magnetic systems and insulating systems   (e.g. molecules and clusters),  an initial ``linear mixing'' can result in faster convergence than  the Kerker model function.

One can therefore try to use the following setting

3. VOSKOWN-tag VOSKOWN = 0 | 1

Usually VASP uses the standard interpolation for the correlation part of the exchange correlation functional.

If VOSKOWN is set to 1 the interpolation formula according to Vosko, Wilk and Nusair[53] is used.

This usually enhances the magnetic moments and the magnetic energies.

Because the Vosko-Wilk-Nusair interpolation is the interpolation usually applied in the context of

gradient corrected functionals, it is desirable to use this interpolation whenever the PW91 functional is applied.

Setting this tag is not required for the PBE or PBEsol functional, since these functional strictly follow the original publications and disregard this flag entirely (this implicitly implies that the correlation energy is interpolated according to Vosko, Wilk and Nusair[53]).

4. ICHARG

ICHARG-tag

ICHARG= 0 | 1 | 2 | 4

This flag determines how to construct the 'initial' charge density. 0Calculate charge density from initial orbitals.

Mind: if ISTART is  internally reset due to an invalid WAVECAR-file the  parameter ICHARG will be set to ICHARG=2.

1  Read the charge density from file CHGCAR  

  and extrapolate from the old positions (on CHCGAR) to the new positions using a linear combination of atomic charge densities. In the PAW method, there is however one important point to keep in mind.

For the on-site densities (that is the densities within the PAW sphere)

only l-decomposed charge densities up to LMAXMIX are written.  Upon restart the energies might therefore differ slightly from  the fully converged energies.

The discrepancies can be large for the L(S)AD+U method. In this case, one might need to increase LMAXMIX  to 4 (d-elements) or even 6 (f-elements) (see Section  6.63).

2  Take superposition of atomic charge densities

4   up from VASP.5.1 only: read potential from file POT.

The local potential  on the file POT is written by the optimized effective potential  methods (OEP), if the flag LVTOT = .TRUE. is supplied  in the INCAR file.

+10  non-selfconsistent calculation

Adding ten to the value of ICHARG (e.g. using 11,12 or the less convenient value 10) means that the charge density will be kept constant during the whole electronic minimization.

There are several reasons why to use this flag:

• ICHARG=11:  To obtain the eigenvalues (for band structure plots) or the DOS for a given charge density read from CHGCAR. The selfconsistent CHGCAR file must be determined beforehand  doing by a fully selfconsistent calculation  with a k-point grid spanning the entire Brillouin zone.9.3.

  
  

• ICHARG=12: Non-selfconsistent calculations for a superposition of atomic charge densities. This is in the spirit of the  non-selfconsistent Harris-Foulkes functional. The stress and the forces calculated by VASP are correct, and it is absolutely possible to perform an ab-initio MD for the  non-selfconsistent Harris-Foulkes functional  (see section 7.3).

If ICHARG is set to 11 or 12, it is strongly recommened to set LMAXMIX to twice the maximum l-quantum number in the pseudpotentials. Thus for s and p elements LMAXMIX should be set to 2, for d elements LMAXMIX should be set to 4, and for f elements  LMAXMIX should be set to 6 (see section 6.63).

The initial charge density is of importance in the following cases:

• If ICHARG10 the charge density remains constant during the run.

• For all algorithms except IALGO=5X the initial charge density  is used to set up the initial Hamiltonian which is  used in the first few (NELMDL) non selfconsistent steps.

  
  

5. ISYM-tag and SYMPREC-tag

ISYM= -1 | 0 | 1  | 2  | 3

switch symmetry on (ISYM=1, 2 or 3) or off (ISYM=-1 or 0).

For ISYM=2 a more efficient, memory conserving symmetrisation of the charge density is used. This reduces memory requirements in particular for the parallel version.

6. What can one do when convergence is bad?

􀀀 Start from charge density of non-spin-polarized calculation, using
ISTART = 0 (or remove WAVECAR)
ICHARG = 1

􀀀 Linear mixing
BMIX = 0.0001 ; BMIX MAG = 0.0001

􀀀 Mix slowly, i.e., reduce AMIX and AMIX MAG

􀀀 Reduce MAXMIX, the number of steps stored in the Broyden mixer(default = 45)

􀀀 Restart from partly converged results
(stop a calculation after say 20 steps and restart from the WAVECAR)

􀀀 Use constraints to stabilize the magetic configuration

􀀀 Pray