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Dear fellow matter modelers, I am trying to model the zig-zag antiferromagnetic material $\alpha$-RuCl$_3$ using QUANTUM ESPRESSO. My end goal is to include DFT + U + SOC, however, including too many of these things together seems to hurt convergence. I am using a supercell with 8 Ru atoms and 32 Cl atoms to accommodate the zig-zag magnetic structure as reported in Phys. Rev. B 92, 235119. I have succeeded in getting the zig-zag magnetic structure to converge without SOC or DFT by first converging for colinear magnetism, then using that as the charge density input for the noncolinear calculation as described in this tutorial. However, when adding a Hubbard_U term to the Ru atoms, the SCF error does not decrease beyond roughly 0.05 Ry. I have tried modifying mixing_beta, different types of smearing, different k_point grids, and fixing the total magnetization. Any help or advice with this would be appreciated.

Cheers!

My input file is below:

 &CONTROL
   calculation     =  'scf'
   outdir          =  '.'
   prefix          =  'rucl3'
   pseudo_dir      =  '.'
   restart_mode    =  'from_scratch'
 /

 &SYSTEM
   A               =  5.97620
   Hubbard_U(2)    =  4.8
   Hubbard_U(3)    =  4.8
   degauss         =  0.005
   ecutrho         =  200
   ecutwfc         =  50
   ibrav           =  0
   lda_plus_u      =  .TRUE.
   nat             =  32
   nspin           =  2
   ntyp            =  3
   occupations     =  'smearing'
   smearing        =  'gauss'
   starting_magnetization(2) =  1
   starting_magnetization(3) =  -1
 /

 &ELECTRONS
   conv_thr        =  1e-6
   mixing_beta     =  0.1
 /

ATOMIC_SPECIES 
  Cl    35.453   Cl.pbe.ONCVPSP.fr.upf 
  Ru1    101.07   Ru.pbe.ONCVPSP.fr.upf 
  Ru2    101.07   Ru.pbe.ONCVPSP.fr.upf 


CELL_PARAMETERS alat
    1.0000000000000000   0.0000000000000000   0.0000000000000000
    0.0000000000000000   1.7305311067233360   0.0000000000000000
   -0.6508271189589490   0.0000000000000000   1.9041632824171890

ATOMIC_POSITIONS crystal
  Ru1      0.000000000000   0.334410000000   0.000000000000
  Ru2      0.000000000000   0.665590000000   0.000000000000
  Ru2      0.500000000000   0.834410000000   0.000000000000
  Ru1      0.500000000000   0.165590000000   0.000000000000
  Ru1      0.000000000000   0.334410000000   0.500000000000
  Ru2      0.000000000000   0.665590000000   0.500000000000
  Ru2      0.500000000000   0.834410000000   0.500000000000
  Ru1      0.500000000000   0.165590000000   0.500000000000
  Cl       0.751380000000   0.173500000000   0.383095000000
  Cl       0.248620000000   0.173500000000   0.116905000000
  Cl       0.248620000000   0.826500000000   0.116905000000
  Cl       0.748620000000   0.673500000000   0.116905000000
  Cl       0.748620000000   0.326500000000   0.116905000000
  Cl       0.751380000000   0.826500000000   0.383095000000
  Cl       0.251380000000   0.673500000000   0.383095000000
  Cl       0.251380000000   0.326500000000   0.383095000000
  Cl       0.751380000000   0.173500000000   0.883095000000
  Cl       0.248620000000   0.173500000000   0.616905000000
  Cl       0.248620000000   0.826500000000   0.616905000000
  Cl       0.748620000000   0.673500000000   0.616905000000
  Cl       0.748620000000   0.326500000000   0.616905000000
  Cl       0.751380000000   0.826500000000   0.883095000000
  Cl       0.251380000000   0.673500000000   0.883095000000
  Cl       0.251380000000   0.326500000000   0.883095000000
  Cl       0.730230000000   0.000000000000   0.119475000000
  Cl       0.269770000000   0.000000000000   0.380525000000
  Cl       0.769770000000   0.500000000000   0.380525000000
  Cl       0.230230000000   0.500000000000   0.119475000000
  Cl       0.730230000000   0.000000000000   0.619475000000
  Cl       0.269770000000   0.000000000000   0.880525000000
  Cl       0.769770000000   0.500000000000   0.880525000000
  Cl       0.230230000000   0.500000000000   0.619475000000

K_POINTS automatic
  5   5   5   1   1   1 
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  • $\begingroup$ +1 and welcome to our new community! Thank you for contributing your question here and we hope to see much more of you!!! It look nicer if you can use hyperlinks for the URL links. $\endgroup$ Jul 21, 2022 at 0:19

1 Answer 1

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As a solution, you should check if convergence is difficult due to the magnitude of your Ru U correction. Try smaller corrections and see if that helps. You can also try applying a correction to the Cl p orbitals. Something like linear response will allow you to calculate a proper number to use, although some other methods such as the method used in the Cedar paper can alternatively be used.

I have also seen cases where the U needs to be "ramped" from a small value to a larger value while saving charge density and wavefunctions. You start from 0, then move to 0.5, then to 1 and so on. This helps to find a solution, but obviously can cost a bit of computational time.

I am surprised you are adding a U correction to Ru. How did you determine you need this? I can't say that its unreasonable but I feel I have never seen it applied to Ru before. The method used to determine it (was it just taken from the paper) might be useful to include in your question because it might highlight if the correction is way too large for some reason.

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  • $\begingroup$ Thank you very much for your reply! I will definitely try all the tips that you have given. The source for the calculation details is Sci Rep 6, 39544 (2016), where they use U = 4.5 eV. I calculated the U value using QE (perhaps incorrectly) and obtained a value of 4.8 eV, in reasonable agreement with their method. With respect to the Cl p orbitals, I am still using QE 7.0 (due to GPU support), which does not support the new orbital notation for U. Do you know how to implement this in the old way? $\endgroup$ Jul 21, 2022 at 16:29
  • 1
    $\begingroup$ I don't actually use QE often sadly, so I am unsure. I assume it would apply it to the Cl p orbitals by default though. Hopefully another suggestion will work. $\endgroup$ Jul 21, 2022 at 22:01
  • $\begingroup$ I did succeed in ramping up U from 0 to 4.8 using colinear spin! Thank you very much for that tip. I also succeeded in doing colinear spin at U = 0. Unfortunately, any attempt at going from colinear to noncolinear with U$\neq$0 did not work, terminating with the error Error in routine c_bands (1): too many bands are not converged $\endgroup$ Jul 22, 2022 at 23:04

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