VASP自旋轨道耦合计算错误汇总(3)

axis z

axis x z axis z

axis y x y axis z

axis y axis x x m m m m m m m m m m m )cos()sin()sin()sin()cos()sin()cos()cos(*)sin()sin()cos()cos(ββαβααβαβααβ+-=++=+-=Where m axis is the externally 外部地visible 可得到的，现有的，可见的magnetic moment.Here,αis the angle between the SAXIS vector (s x ,s y ,s z )and the cartesian vector x

?,and βis the angle between the vector SAXIS and the cartesian vector z ?:z

y x x y

s s s a s s a ||tan ,tan 22+==βαThe inverse 倒转、翻转transformation 转化、转换is given by

z y x axis y x axis z y x axis m m m m m m m m m m m z

y

x

)cos()sin()sin()cos()sin()cos()sin()sin()sin()cos()cos()cos(βαβαβααβαβαβ++=+-=++=It is easy to see that for the default (s x ,s y ,s z )=(0+,0,1),both angles are zero,i.e.β=0and α=0.In this case,the internal representation is simply equivalent to the external representation:

axis z z axis y y axis x x m m m m m m ===,,The second important case,is 0=axis x m and 0=axis y m .In this case

2

22222/)(cos /)cos(*)sin(z y x z axis z axis x z y z

y z axis z axis z x s s s s m m m m s s s s m m m x ++===

++==βαβHence 因此、今后now the magnetic moment is parallel to the vector SAXIS.Thus there are two ways to rotate the spins in an arbitrary 任意的direction,either by changing the initial magnetic moments MAGMOM or by changing SAXIS.

To initialise calculations with the magnetic moment parallel to a chosen vector (x,y,z),it is therefore 因此possible to either specify 指定(assuming 假定、假设a single atom in the cell)

MAGMOM =x y z

!local magnetic moment in x,y,z SAXIS =001

!quantisation axis parallel to z or

MAGMOM =00total_magnetic_moment

!local magnetic moment parallel to SAXIS SAXIS =x y z !quantisation axis parallel to vector (x,y,z)

Both setups should in principle yield exactly the same energy,but for implementation 实现reasons the second method is usually more precise 精确.The second method also allows to read a preexisting WAVECAR file (from a collinear or non collinear run),and to continue the calculation with a different spin orientation.When a non collinear WAVECAR file is read,the spin is

assumed 假定to be parallel to SAXIS (hence 因此VASP will initially report a magnetic moment in the z-direction only).

The recommended 被推荐的procedure 过程、步骤for the calculation of magnetic anisotropies is therefore 因而、表示结果(please check the section on LMAXMIX 6.63):

?

Start with a collinear calculation and calculate a WA VECAR and CHGCAR file.?Add the tags

LSORBIT =.TRUE.

ICHARG =11

!non selfconsistent run,read CHGCAR LMAXMIX =4!for d elements increase LMAXMIX to 4,f:LMAXMIX =6

!you need to set LMAXMIX already in the collinear calculation

SAXIS =x y z !direction of the magnetic field

NBANDS =2*number of bands of collinear run

GGA_COMPAT =.FALSE.!apply spherical cutoff on gradient field

VASP reads in the WA VECAR and CHGCAR files,aligns 排列the spin quantization axis parallel to SAXIS,which implies 意味着that the magnetic field is now parallel to SAXIS,and performs a non selfconsistent calculation.By comparing the energies for different orientations the magnetic anisotropy can be determined 确定.Please mind,that a completely selfconsistent calculation (ICHARG=1)is in principle 大体上、原则上also possible with VASP,but this would allow the the spinor wavefunctions to rotate from their initial orientation parallel to SAXIS until the correct groundstate is obtained,i.e.until the magnetic moment is parallel to the easy axis （?=the easy magnetic axis ）.In practice this rotation will be slow,since reorientation 再定位of the spin gains 获得little energy.Therefore if the convergence 收敛criterion 标准is not too tight,sensible 明智的results might be obtained even for fully selfconsistent calculations (in the few cases we have tried 可靠地，试验过的selfconsistentcy worked without problems).

Be very careful with symmetry.We recommend 建议to switch off 关掉symmetry (ISYM=0)altogether 完全地,when spin orbit coupling is selected.Often the k-point set changes from one to the other spin orientation,worsening 恶化the transferability of the results (also the WA VECAR file can not be reread properly 正确地if the number of k-points changes).The flag GGA_COMPAT is usually required and should be set,since magnetic anisotropy energies are often in the sub meV regime (see Sec.6.42).

Generally be extremely 非常careful,when using spin orbit coupling and,specifically 特别地,magnetic anisotropies:energy differences are tiny 微小的,k-point convergence 收敛is tedious 冗长乏味and slow,and the computer time might be huge.

Additionally此外,this feature这一特征--although long implemented应用in VASP--is still in a late beta stage,as you might deduce from推断，从...得出结论the frequent频繁的updates升级、更新.No promise允诺,that your results will be useful! Here is a small summary总结from the README file:

20.11.2003:The present提出GGA routine程序breaks the symmetry slightly轻微地for non orthorhombic正交晶系cells.A spherical球面的cutoff is now imposed on应用于the gradients and all intermediate中间的results in reciprocal互逆space.This changes the GGA results slightly(usually by0.1meV per atom),but is important for magnetic anisotropies.

05.12.2003:continue...Now VASP.4.6defaults to the old behavior GGA_COMPAT=.TRUE.,the new behavior can be obtained by setting GGA_COMPAT=.FALSE.in the INCAR file.

12.08.2003:MAJOR主要的BUG故障FIX固定in symmetry.F and paw.F:for non-collinear calculations the symmetry routines惯例did not work properly正确地

If you have read the previous lines,you will realize that it is recommended推荐to set GGA_COMPA T=.FALSE.for non collinear calculations in VASP.4.6and VASP.5.2,since this improves the numerical precision of GGA calculations.

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