J-dependent SOC in LDA+U

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J-dependent SOC in LDA+U

Postby umklapp » Fri Sep 21, 2018 3:18 pm

J-dependent SOC in LDA+U
I am using Liechtenstein LDA+U to calculate the full relativistic energy (and also the magnetic anisotropy) of Co-doped Cr2O3 when the spin quantization is along the different directions. The non-relativistic spin-collinear state is firstly obtained within LDA+U. Then start from the previously converged WAVECAR, I perform the self-consistent relativistic calculation with spin-orbit coupling included. (LSORBIT = .TRUE. ; LNONCOLLINEAR = .TRUE.)
Firstly, I got a weird J-dependent anisotropy energy (K), and anisotropy of the spin-orbit energy (Kso). According to https://www.sciencedirect.com/science/a ... 9814002476, K~Kso if the perturbation theory is valid. However, this relationship is sustained at J= 0 eV, however, diverges strikingly at elevated J. (see the first figure and the following inputs).
For the case when spin quantization axis is along x direction, we constrain the direction of local moment on Co (small moment) to various in-plane direction (in the xy plane), starting from x direction. At the same time, the other spins on Cr are fully relaxed.
We found the energy is not variational:
Using the constrained DFT, the energy minimal corresponds to \theta_Co ~0 deg. However, in full spin relaxation calculations (without any constrain), the spin canting on Co is quite sizable, circled using the purple sphere in the second figure.

I appreciate any comments for this bizarre behavior.

Best,
Sai Mu

INPUTS:
[INCAR]
# ISTART = 0
# ICHARG = 2
LPLANE = F
LSCALU = F
ISYM = -1
IALGO = 38
LDIAG = T
NBANDS = 320
LREAL = F
NELM =160
EDIFF = 1E-7
PREC = Accurate
ENCUT = 520
ADDGRID = T
LMAXMIX = 4
ISMEAR = -5

ISPIN = 2
# MAGMOM = 2 -5 5 -5 5 -5 5 -5 5 -5 5 -5 18*0
VOSKOWN = 1
LSORBIT = T
SAXIS = 0 0 1
LORBMOM = T

EDIFFG = -0.005
NSW = 0
ISIF = 0
IBRION = -1

LWAVE = T
LCHARG = T
LORBIT = 11

LDAU = T
LDAUTYPE = 1
LDAUL =2 2 -1
LDAUU =4.0 4.0 0.0
LDAUJ =0.58 0.58 0.0
LDAUPRINT =2
LASPH = T
[POSCAR]
Cr2O3 bulk hex
1.00000000000000
4.2604182062427478 -2.4597535944258353 0.0000000000000000
-0.0000000032985165 4.9195071945648685 0.0000000000000000
0.0000000000000000 0.0000000000000000 13.4891869077699180
Co Cr O
1 11 18
Direct
0.9999999442629957 0.9999998307240787 1.0022063338743374
0.6666666222206317 0.3333332093609158 0.0277157637037803
0.3333333063286332 0.6666667471633119 0.1627744491989426
0.9999999545615665 0.0000000995503839 0.1934053020818036
0.6666666282294642 0.3333334961138519 0.3324500473090360
0.3333332867116638 0.6666668069946198 0.3601355940430158
0.9999999487524036 0.9999999669479607 0.5005894804122863
0.6666666798330638 0.3333333144574766 0.5286526039225763
0.3333334382116178 0.6666666654539100 0.6685381111213635
0.0000000830738074 0.9999999830268393 0.6971949308857917
0.6666667686589207 0.3333333164653638 0.8359937515197047
0.3333334051860604 0.6666666075117220 0.8657891333965974
0.7005943535993655 0.7031467273508103 0.0937704944650421
1.0025523455901206 0.2994055415662850 0.0937705013000653
0.2968530746259528 -0.0025524719959222 0.0937704543595587
0.6364950244164128 0.9728156412587917 0.2616504318192971
0.3363203902999755 0.3635051185055144 0.2616504347753041
0.0271845056680021 0.6636797422970405 0.2616504663513756
0.3607013115646883 0.0274917225374889 0.4302980230348061
0.6667901696350990 0.6392986624597665 0.4302980589056466
0.9725082809976960 0.3332096909649291 0.4302979997218279
0.3055421880188490 0.3051696503023983 0.5986489722775825
-0.0003724057526492 0.6944577988206985 0.5986489614811557
0.6948303618365493 1.0003724407709877 0.5986489589194430
0.0277962735781988 0.3628117735164492 0.7664858204126442
0.3350156899882810 0.9722038583763161 0.7664858193671801
0.6371883936739935 0.6649844638885947 0.7664858542111229
0.9720055170125338 0.6500897036667536 0.9335302325564095
0.6780843767151151 0.0279943895895442 0.9335302279112080
0.3499100825010020 0.3219155023531120 0.9335302012654504

[KPOINTS]
bulk
0
G
4 4 2
0 0 0
umklapp
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