[Wien] quadrupolar-wien2k

[Yue Hai]

Dear wien2k users:
   Fellowing is my question, if something is wrong, please correct me.
   I have calculated an intermetallic system AB, where A is 4f element and 
B is  4d transitional-metal.The experiments have shown that the high 
temperature phase of it was cubic with CsCl structure. At T=16k, it 
undergoes a structure transition to a tetragonal phase, without magnetic 
ordering. At T=5k, a ferromagnetic phase transition occurs. For the 
structure phase transition at T=16k, two explanations have been proposed :
  1.it is the result of band Jahn-Teller effect due to the Jahn-teller 
theorem:"for a non-linear molecule in an electronically degenerate state, 
distortion must occur to lower the symmetry, remove the degeneracy, and 
lower the energy"
  2. it is the effect of the quadrupolar interactions. The effect includes 
two aspects: one is the magnetic-strain coupling and the other is 
quadrupole-quadrupole interaction.
 
 In order to study the structure phase, I have calculated the AB with two 
structure: Cubic CsCl structure and tetragonal structure , both with the 
experimental crystallography parameters. The result is as followings:
   1. for the nomagneitc calculation (run_lapw) and paramagnetic 
calculation (runsp_c_lapw)with LDA or GGA96: the 
E(cubic)<E(tetragonal).This means that the groud state should be cubic. 
Obviously, this is in contradicted with the experiment.
   2. from the DOS of 1 and 2, we did not find obvious difference between 
the cubic phase and tetragonal phase.  This means the Jahn-Teller effect is 
not the driving factor of the structure transition. 
  From these results, we expect that the sturcuture transition should be 
ascribed to the quadrupolar interactions. But I did not know if the 
quadrupolar interactions are included in the wien2k. In the papaer of V.I. 
Anisimov (Phys. Rev. B, vol 52, 5467), They have shown that with the LSDA+U 
method, the groud state of KCuF3 with quadrupolar distortion in the ab 
plane because of the orbital ordering  can be obtained(They have used the 
FP_LMTO method). Then I also calculated the system with LSDA+SIC and 
GGA+SIC. The result shows that :
  For LSDA+SIC , E(cubic)<E(tetragonal)
  for GGA+SIC , E(cubic)>E(tetragonal).
obvisouly, with GGA+SIC, we can get the tetragonal phase to be ground 
state.
(I remeber some days ago, a discussion about the GGA+SIC has been raised, 
some people believe that the orbital potential U can also be applied to GGA 
,while others believe that the U can only be applied to L(S)DA. Who is 
right? ). I do this because from the voluem optimization without SIC, I 
find the GGA is more appropriate than the L(S)DA.
  
  Furthermore, I also calculate the system of ferromagnetic phase with 
cubic and tetragonal structure respectively. The results are as fellowings:

   1. the runsp_lapw with LSDA or GGA , E(cubic)<E(tetragonal)
   2. the runsp_lapw+SIC with LSDA or GGA, E(cubic)>E(tetragonal)

 with the SIC U, we can get the ground state of the AB(obivous, the 
spin-orbital coupling should be taken into account in the ferromagnetic 
pahse but we have  neglected it at this time. in the final calclulation we 
will add it)

So my questions are:
  1,in the wien2k, can we discuss the effect of the quadrupolar 
interactions?
  2,and if can , how to do it ? with the U?

Best regards:
Hai

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