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因此现在磁矩是平行于SAXIS矢量。这样有两种方式去旋转自旋到任意方向，即通过改变初始的磁矩MAGMOM或改变SAXIS。为了给计算赋予平行于一个选定的矢量 (x,y,z)的初始磁矩，可以通过设定（假定是单原子原胞）： MAGMOM = x y z !局域磁矩x y z SAXIS = 0 0 1 ! 量子轴平行于z轴 或者 MAGMOM = 0 0 total_magnetic_moment ! 局域磁矩平行于SAXIS SAXIS = x y z ! 量子轴平行于矢量(x,y,z) 两种设置都必须在相同能量的标准/辐射（原则、根源）场，但是要实现第二种方法，通常更加精确。第二种方法，也允许读入之前存在的WAVECAR文件（由线性计算还是非线性计算产生的都可以），然后继续用一个不同的自旋方向计算。当读入一个非线性WAVECAR文件，自旋假定平行于SAXIS（因此VASP将仅仅输出一个z轴方向的磁矩）。推荐计算磁各项异性的步骤如下： 先做线性计算，得到一个WAVECAR和CHGCAR文件。 加入以下参数： LSORBIT = .TRUE. ICHARG = 11 ! 非自洽计算, 读入 CHGCAR LMAXMIX = 4 ! 对于d电子元素设置 LMAXMIX=4, f电子元素设置 LMAXMIX = 6 ! 在线性计算中，需要设置LMAXMIX SAXIS = x y z ! 磁场的方向 NBANDS = 2 * 线性计算能带数 GGA_COMPAT = .FALSE. ! 在梯度场中应用球面截断能 VASP读入WAVECAR和 CHGCAR文件，将自旋量子轴对齐SAXIS矢量，这意味着现在磁场平行于SAXIS矢量，执行非线性计算。通过比较不同方向的能量，可以确定磁各向异性。请记住，原则上，在VASP中一个完全地自洽计算(ICHARG=1)也是有可能的，但是这种情况将会允许自旋波函数从它们的初始值旋转到平行于SAXIS矢量，直到获得正确的基态，也就是，直到磁矩平行于易磁化轴。实际操作中，这种旋转非常缓慢，直到自旋获得少量能量重新定位。因此，如果收敛标准太精确，完全地自洽计算可以得到一个比较合理的结果（我们实验过的几种自洽计算都没有问题。） 要非常小心对称性。我们建议选择计算自旋轨道耦合时，完全关掉对称性(ISYM=0)。通常会从一个自旋方向到另一个自旋方向k点的设置会发生改变，进而恶化转换的结果（如果k点改变WAVECAR将不会被正确地重新读取）。GGA_COMPAT 通常需要，应该被设置，因为磁各向异性能量通常需要精确到亚meV数量级。 当计算自旋轨道耦合，特别是磁各向异性时通常需要非常小心：能量差异非常小，k点的收敛冗长而且缓慢，需要耗费大量的计算时间。此外，这一特征--尽管长期存在于VASP中--在最新的版本中依然存在，你可以尝试频繁地升级发现这一点。不敢保证，你的结果是有用的！此处根据README文件做了一个小小的总结： 20.11.2003: 提出的GGA程序轻微的破坏了非正交体系晶胞的对称型。球面截断能应用于梯度及互逆空间中的所有中间结果。GGA引起的轻微的改变（通常每个原子0.1 meV），却对磁各项异性很重要。 05.12.2003: 继续...现在VASP.4.6默认旧的行为GGA_COMPAT=.TRUE.，新的行为将可以通过在INACR中设置GGA_COMPAT=.FALSE.得到。 12.08.2003: 主要的错误出现在symmetry.F 和paw.F：非线性计算的对称性例程没有正确的执行。 如果你阅读了以上内容，就会意识到在VASP.4.6和VASP.5.2版本中进行非线性计算推荐设置GGA_COMPAT=.FALSE.，这样可以提升GGA计算的数值精度。 VASP: Non-collinear calculations and spin orbit coupling : Spinors旋量 were included by Georg Kresse in the VASP code. The code required for the treatment处理 of non-collinear magnetic structures was written by David Hobbs, and spin-orbit coupling was implemented实施、执行 by Olivier Lebacq and Georg Kresse. Spinors are only supported as of VASP.4.5. Subsections：分段、子章节、下一级栏目 LNONCOLLINEAR-tag Supported支持 as of VASP.4.5.

Setting LNONCOLLINEAR=.TRUE. in the INCAR file allows to perform fully non-collinear magnetic structure calculations. VASP is capable有能力的 of reading WAVECAR and CHGCAR files from previous之前的 non-magnetic非磁 or collinear线性 calculations, it is however not possible to rotate旋转、转动 the magnetic field locally on selected atoms. Hence因此, in practice在实践中, we recommend推荐 to perform non-collinear calculations in two steps: First, calculate the non magnetic groundstate基态 and generate a WAVECAR and CHGCAR file. Second, read the WAVECAR and CHGCAR file, and supply提供 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 0 Initialises赋初值 the magnetic moment on the first atom in the x-direction, and on the second atom in the y direction. 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. LSORBIT=.TRUE. Switches接通、开启 on spin-orbit coupling and automatically sets LNONCOLLINEAR= .TRUE.. This option选项、选择 works only for PAW potentials and is not supported for ultrasoft pseudopotentials. If spin-orbit coupling is not included, the energy does not depend on依赖 the direction of the magnetic moment, i.e.也就是说 rotating旋转 all magnetic moments磁矩 by the same angle results exactly in the same energy. Hence因此 there is no need to define the spin quantization axis自旋量子化坐标轴, as long as只要 spin-orbit coupling is not included. Spin-orbit coupling, however, couples一对、一双 the spin to the crystal structure. Spin orbit coupling is switched on开启 by selecting LSORBIT = .TRUE. SAXIS = s_x s_y s_z (quantisation axis for spin自旋量子化轴) GGA_COMPAT = .FALSE. ! apply spherical球面 cutoff截断能 on gradient field梯度场 where the default for SAXIS= (0+,0,1)(the notation符号 0+ implies意味着 an infinitesimal无穷小 small positive number in ? direction). The flag GGA_COMPAT (see Sec. 6.42) is optional选项 and should be set when small energy differences in the xsub副、下标 meV regime体制、状态 need to be calculated (often the case for magnetic anisotropy calculations磁各向异性计算). All magnetic moments are now given with respect to关于 the axis坐标轴 (Sx,Sy,Sz), where we have adopted应用 the convention惯例 that all magnetic moments and spinor-like quantities written or read by VASP are given with respect to this axis. This includes the MAGMOM line in the INCAR file, the total and local magnetizations in the OUTCAR and PROCAR file, the spinor自旋量-like orbitals in the WAVECAR file, and the magnetization density in the CHGCAR file. With respect to the cartesian笛卡尔 lattice vectors the components组件、部分 of the magnetization are (internally内部地、内在的) given by axisaxismx?cos(?)cos(?)mx?sin(?)my?sin(?)*cos(?)mzaxisaxismy?cos(?)sin(?)mx?cos(?)my?sin(?)sin(?)mzaxisaxismz??sin(?)mx?cos(?)mzaxis Where maxis is the externally外部地 visible可得到的，现有的，可见的 magnetic moment. Here, α is the angle between the SAXIS vector (sx, sy, sz) and the cartesian vector ?, and β is the angle between the vector SAXIS and the cartesian vector z?: x??atansysx,??atan22|sx?sy| szThe inverse倒转、翻转 transformation转化、转换 is given by maxis?cos(?)cos(?)mx?cos(?)sin(?)my?sin(?)mzxmaxis??sin(?)mx?cos(?)myymaxis?sin(?)cos(?)mx?sin(?)sin(?)my?cos(?)mzz It is easy to see that for the default (sx, sy, sz) = (0+,0,1), both angles are zero, i.e. β=0 and α=0. In this case, the internal representation is simply equivalent to the external representation: m?maxis,m?maxis,m?maxis xxyyzzaxisaxisThe second important case, is mx?0and my?0. In this case

22mx?sin(?)*cos(?)mzaxis?mzaxissz/s2x?sy?szmy?axis22mz?cos(?)mx?mzaxissz/sx?sy?sz2 Hence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 = 0 0 1 ! quantisation axis parallel to z or MAGMOM = 0 0 total_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 WAVECAR 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 WAVECAR 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 WAVECAR 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 by 0.1 meV per atom), but is important for magnetic anisotropies. 05.12.2003: continue... Now VASP.4.6 defaults 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_COMPAT=.FALSE. for non collinear calculations in VASP.4.6 and VASP.5.2, since this improves the numerical precision of GGA calculations. degree: BSc：Bachelor of Science理科学士 MD MS：master硕士 PhD： Doctor of Philosophy 博士学位 AA Associate degree of Arts大 专 文 科 学 位 AAS Associate degree of Arts and Science大 专 文 理 科 学 位 AS Associate degree of Science大 专 理 科 学 位 BA Bachelor of Arts 文 科 本 科 学 位 BS Bachelor of Science理 科 本 科 学 位 MA Master of Arts 文 科 硕 士 MBA Master of Business Administration 商 学 硕 士 MS Master of Science理 科 硕 士 Ph.D. Doctor of Phiolosphy 哲 学(通 才)博 士 JD Doctor of Journalism 新 闻 博 士 MD Doctor of Medicine 医 学 博 士 DVM Doctor of Veterinry 兽 医 博 士 Call to ZHEGV failed Error EDDDAV: Call to ZHEGV failed. Returncode = 13 1 8 The earlier solution suggested by admin（DOS操作系统中，超级管理员。行政、管理） (suppressing制止的 the line #define USE_ZHEEVX in davidson.F, subrot.F, and wavpre_noio.F and recompiling VASP) does not work, i.e. the same error messages, and the same indication迹象、表示 of ZHEGV failure, still appear出现. I may add now that the problem appears both with the lapack which comes with VASP and with a system-native lapack library. The warnings given suggest that the problem actually appears at an earlier stage阶段, in which a matrix is generated with inadequate不适当的 values which make it nonhermitian, and consequently ZHEGV fails even if working correctly; the solution thus would not be to avoid using ZHEGV, but to avoid an incorrect generation of the said matrix. Can someone give an idea to really solve the problem? 答：Please try if it works by adding \对策：grep LSCALAPACK OUTCAR 空 设置： LSCALAPACK = .FALSE 问：No; adding \问：I was successful to fix this problem解决此问题 by using IALGO=48 instead of IALGO=Default。 unfortunately, when i set IALGO=48, the new warning is： WARNING in EDDRMM: call to ZHEGV failed, returncode = 6 3 14 how to solve this problem? what does \对策：grep IALGO OUTCAR IALGO = 68 algorithm （INCAR ALGO=Fast） 设置： IALGO=48 please try one of the following: 1) choose a different algorithm for ionic optimization (IBRION=1) 采用准牛顿算法来优化原子位置 2) set ADDGRID=.True. in INCAR (only for vasp releases发布管理、释放、豁免 4.4.5 and newer)