Can I use SGGA+U Exchange-correlation potential for transport calculation?

[clark]

I calculated transmission spectrum of fe/mgo/fe magnetic tunnel junction using the SGGA+U Exchange-correlation potential for Mg, but the result seems wrong:

 energy (eV)      T(up)         T(down)
 -2.000000e+00   7.359234e-02   1.575396e-02
 -1.900000e+00   4.752671e-02   3.328986e-02
 -1.800000e+00   3.876577e-02   3.769258e-02
 -1.700000e+00   5.075683e-02   7.200586e-02
 -1.600000e+00   4.783458e-02   7.238770e-02
 -1.500000e+00   6.749334e-02   8.836559e-02
 -1.400000e+00   1.207360e-01   1.279868e-01
 -1.300000e+00   1.755151e-01   1.565134e-01
 -1.200000e+00   2.025906e-01   1.246247e-01
 -1.100000e+00   2.976305e-01   1.338918e-01
 -1.000000e+00   2.001293e-01   1.287574e-01
 -9.000000e-01   2.268985e-01   1.274554e-01
 -8.000000e-01   1.548494e-01   7.139636e-02
 -7.000000e-01   1.446821e-01   1.005546e-01
 -6.000000e-01   1.072199e-01   5.061934e-02
 -5.000000e-01   8.161175e-02   4.926054e-02
 -4.000000e-01   7.442812e-02   1.562091e-02
 -3.000000e-01   6.174792e-02   8.025265e-03
 -2.000000e-01   3.476308e-02   2.165560e-03
 -1.000000e-01   3.328062e-02   2.250245e-03
  0.000000e+00   1.576522e-02   1.952985e-03
  1.000000e-01   2.109151e-02   3.575160e-04
  2.000000e-01   7.334028e-03   8.772420e-04
  3.000000e-01   4.601747e-03   8.120860e-06
  4.000000e-01   1.030548e-02   1.016774e-05
  5.000000e-01   1.381889e-02   3.465895e-05
  6.000000e-01   8.526817e-03   9.408154e-05
  7.000000e-01   1.546726e-03   6.761147e-08
  8.000000e-01   1.867503e-04   1.264305e-08
  9.000000e-01   4.622378e-05   3.432443e-09
  1.000000e+00   1.525821e-05   1.059971e-09
  1.100000e+00   5.868977e-06   3.507419e-10
  1.200000e+00   2.477182e-06   1.242672e-10
  1.300000e+00   1.109999e-06   5.010421e-11
  1.400000e+00   5.169824e-07   2.574732e-11
  1.500000e+00   2.465086e-07   1.854089e-11
  1.600000e+00   1.189180e-07   1.671491e-10
  1.700000e+00   5.748862e-08   3.517107e-11
  1.800000e+00   2.766303e-08   8.078225e-10
  1.900000e+00   1.323612e-08   6.729046e-09
  2.000000e+00   6.379466e-09   2.075338e-08

and the calculated transmission spectrum without hubbard u is:

energy  ( eV)     T(up)         T(down)
 -2.000000e+00   2.192314e-13   2.699950e-11
 -1.900000e+00   1.159918e-13   2.312347e-10
 -1.800000e+00   1.909143e-13   4.977940e-11
 -1.700000e+00   6.634284e-14   4.964251e-11
 -1.600000e+00   8.036492e-14   2.968821e-11
 -1.500000e+00   4.031784e-13   1.144877e-11
 -1.400000e+00   1.754009e-12   5.143252e-09
 -1.300000e+00   1.335622e-10   6.444458e-12
 -1.200000e+00   1.250935e-07   7.796190e-12
 -1.100000e+00   3.064643e-09   8.962319e-12
 -1.000000e+00   4.067027e-09   9.051339e-12
 -9.000000e-01   7.235466e-09   9.229104e-12
 -8.000000e-01   1.032260e-08   1.355638e-11
 -7.000000e-01   1.056395e-08   7.930413e-12
 -6.000000e-01   1.125172e-08   7.050996e-12
 -5.000000e-01   1.320135e-08   1.051105e-11
 -4.000000e-01   1.669488e-08   9.097804e-12
 -3.000000e-01   2.235478e-08   1.680387e-12
 -2.000000e-01   3.144456e-08   1.079387e-12
 -1.000000e-01   4.618436e-08   1.181674e-12
  0.000000e+00   7.052900e-08   3.071133e-12
  1.000000e-01   1.119533e-07   1.215069e-11
  2.000000e-01   1.835724e-07   6.310866e-11
  3.000000e-01   3.138680e-07   3.397042e-10
  4.000000e-01   5.625070e-07   1.690368e-09
  5.000000e-01   1.067489e-06   7.922923e-09
  6.000000e-01   2.176246e-06   3.772807e-08
  7.000000e-01   4.871430e-06   2.208804e-07
  8.000000e-01   1.241580e-05   2.541869e-06
  9.000000e-01   3.863144e-05   1.034904e-03
  1.000000e+00   1.739469e-04   6.224177e-03
  1.100000e+00   1.886715e-03   5.034524e-03
  1.200000e+00   6.564475e-03   3.269805e-03
  1.300000e+00   8.198202e-03   2.480162e-03
  1.400000e+00   9.490935e-03   3.637451e-03
  1.500000e+00   1.284054e-02   3.401341e-03
  1.600000e+00   1.978573e-02   3.150266e-03
  1.700000e+00   2.558336e-02   2.134390e-03
  1.800000e+00   2.911208e-02   4.348823e-03
  1.900000e+00   3.081802e-02   7.713965e-03
  2.000000e+00   3.414162e-02   1.059903e-02

Is it reliable using SGGA+U Exchange-correlation potential for transport calculation?

[Anders Blom]

How did you determine the value of U for MgO?

[clark]

I added the U value of 23 eV to the Mg 3s shell, so I can get the band gap of MgO about 7.7eV

[Anders Blom]

23 eV sounds a bit extreme; at very high U the band structure can get distorted. I haven't tried this for MgO myself precisely.

Btw, which version of ATK/VNL did you use? We just discovered a bug in VNL, if you set U to 1 eV, it writes 1 Hartree to the file, i.e. 27.2 eV - not what you wanted. So double-check the actual Python code, to make sure it didn't use 23*27.2 eV for U!

However, even 23 eV is large, very large...

[zh]

I doubt the validity of the LDA+U on MgO. Anyway, there is one paper on this topic and the U is applied on the p orbital of oxygen:
Michael Nolan, Graeme W. Watson, The electronic structure of alkali doped alkaline earth metal oxides: Li doping of MgO studied with DFT-GGA and GGA + U, Surface Science, Volume 586, Issues 1-3, 20 July 2005, Pages 25-37


For the determination of U, a possible technique is the line-response method, as implemented in the Quantum-espresso.

[Anders Blom]

Also for TiO2, the U is applied to oxygen to get the band gap right (Phys. Rev. B 82, 115109 (2010)) plus the Ti 3d orbitals, but Mg doesn't have those. It could be an idea to use the HGH pseudopotential with semicore states (the whole 2-shell in the valence) included in ATK 11.8, then you can add U to 2p. See the new mini-tutorial on vanadium regarding how to use the HGH potentials; the name of the basis set is Magnesium_HGH_10_XXX (where XXX is DoubleZetaPolarized etc, as usual).

Using LDA+U is a little bit of an art.

[clark]

I used the latest version atk-11.8.1 with a trial license, I have checked the band structure of MgO carefully, I found I can get correct band gap of 7.7 eV for MgO when I applied 23 eV of U value to the Mg DZP 3s orbitals(including split and polarization orbitals), which is different from the Tutorial "Bandgap of MgO with LDA+U", where need only about 10 eV can get correct band gap. If I use the value of 10 eV , I only get the band gap about 6.4 eV.

My doubt is it is reliable using SGGA+U Exchange-correlation potential for transport calculation?  e.g. for fe/mgo/fe mtj. because the correct band gap is important for device simulating. It seems validity for bulk calculation.

thanks!

[zh]

What is fundamental reason why you apply the U on the 2s orbital of O?  The LDA+U method may be  suitable for the transition metal oxides with strongly correlations such as NiO, FeO, and so on, but it may be not suitable for the MgO. 

[clark]

What is fundamental reason why you apply the U on the 2s orbital of O?  The LDA+U method may be  suitable for the transition metal oxides with strongly correlations such as NiO, FeO, and so on, but it may be not suitable for the MgO. 

Sorry, I applied the U on the Mg 3s orbital, I made a slip of the pen. What I did is followed the Tutorial "Bandgap of MgO with LDA+U: Tutorial how to fit LDA+U to an experimental band gap", published online by QuantumWise, but i can't find it now.