Starting with Version 1.25, the static code supports tight-binding calculations for collinear spin-polarized systems. Basically, the tight-binding parameter set is doubled, with one set of parameters for the up spin channel and another set for the down spin channel. A brief description of the method is found in Physica B 296, 125 (2001). (For the complete citation, see the Publications page.) Tight-binding parameters for most of the magnetic elements are available from the Tight-Binding parameters page.

In this example we will find the equation of state of anti-ferromagnetic iron. As with ferromagnets, we must compile a spin-polarized version of the static code:

• Set the mspin parameter in the P1 parameter file to 2, and
• recompile.

In our case we'll use the spin-polarized parameters fe_ferro_par, available under iron on the Tight-Binding parameters page. Save these parameters in the working directory. Note that the first line of these parameters contains the string:

NM00000

The "M" parameter shows that this is a set of spin-polarized parameters. Note that the parameter list is twice as long as it is for, e.g. paramagnetic iron.

For our calculation we'll look at anti-ferromagnetic bcc iron. This almost surely does not exist^*, but is simple to set up. The simplest version of anti-ferromagnetic iron is the Cesium Chloride (B2) structure, with the Cs atoms representing spin up and the Cl atoms representing spin down. From the above like we can pick up the spcgrp file. The SKIN file is somewhat different than in the Example XVII:

Mode=1
0.005   100
fe_ferro_par
Anti-Ferromagnetic bcc (B2) iron
 4.500
 0.00                (No extra electrons in the unit cell)
4
 4.500           lattice constant a
0                   Strain parameter type
2               Atoms in the unit cell
4 4 4             search limits
FT                           No additional displacements
1  0.000  0.000  0.000  0 0 0   1
1  0.500  0.500  0.500  0 0 0   2
NEWSYM=T                (Construct new k-point mesh)
LATTIC=2
spcgrp
ILAT=F                (Cartesian coordinate space group file)
    0
lspec=f,linfok=f
    8    8    8

The first few lines are the same as in any other calculation. Since the CsCl structure has a simple cubic lattice, the lattice type is 4. The first new feature is on the line

FT                           No additional displacements

The F is standard, but the T tells static that at least some of the spins in the atom list are going to be flipped. The next two lines show how:

1  0.000  0.000  0.000  0 0 0   1
1  0.500  0.500  0.500  0 0 0   2

The first atom, which we assume is spin up, is on the (1a) (0,0,0) site of the CsCl crystal. The new numeral 1 at the end of the line tells the code this. The second atom in the CsCl crystal, which we assume is spin down, is on the (1b) (½,½,½) site. The 2 at the end of the line indicates this. Note that if this 2 were changed to a 1, then both spins would be up, the calculation would be ferromagnetic, and the resulting calculation would be identical to Example XVII, except that the unit cell size and volume would be doubled.

The remainder of the SKIN file is identical to the above block, except that we use the NEWSYM=F flag, indicating that we're using the same k-point mesh, and change the lattice constant. The complete working directory thus looks like this:

$ ls -l
-rw-r--r-- 1  4604 Aug 30 16:27 SKIN
-r--r--r-- 1 13217 Sep  1 17:02 fe_ferro_par
-r--r--r-- 1 10003 Jul 29 14:17 spcgrp

After compiling the code and running static, we find

$ ls -l
-rw-r--r--    1  1144 Aug 30 16:28 SKENG
-rw-r--r--    1  4604 Aug 30 16:27 SKIN
-rw-r--r--    1 33423 Aug 30 16:28 SKOUT
-r--r--r--    1 13217 Sep  1 17:02 fe_ferro_par
-rw-r--r--    1 31257 Aug 30 16:28 output
-r--r--r--    1 10003 Jul 29 14:17 spcgrp

Let's examine the SKENG file:

 4.500    91.125000    0.368161801    0.559783329    0.561444613  0.000000
 4.600    97.336000    0.328006039    0.444079638    0.446651589  0.000000
 4.700   103.823000    0.297110047    0.351398015    0.353627119  0.000000
 4.800   110.592000    0.272720928    0.279273167    0.281037081  0.000000
 4.900   117.649000    0.253109476    0.225622942    0.227297723  0.000000
 5.000   125.000000    0.236719971    0.187243535    0.189108430  0.000000
 5.100   132.651000    0.222840679    0.161002710    0.163191575  0.000000
 5.200   140.608000    0.211170378    0.144115367    0.146635993  0.000000
 5.300   148.877000    0.201404203    0.134234257    0.136973196  0.000000
 5.400   157.464000    0.193235264    0.129576082    0.132381554  0.000000
 5.500   166.375000    0.186459389    0.128795388    0.131564750  0.000000
 5.600   175.616000    0.180907567    0.130868042    0.133574263  0.000000
 5.700   185.193000    0.176348687    0.135062769    0.137748619  0.000000

The first five columns are, as usual, a label (here the bcc lattice constant), the unit cell volume, the Fermi level, the total energy, and the pressure. The sixth column is the spin polarization of the system, in other words the excess of majority spin electrons over minority spin electrons. Here, though, we have as many spin up as spin down electrons, so the total magnetization is zero.

For more details of the calculation, you can look at the SKOUT file.

An additional exercise, here left for the reader, would be to compare the energy per atom for this case to that of ferromagnetic iron.

Look at more examples

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Current URL: http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/bind/static/example18/index.html

^*To see why anti-ferromagnetic iron does not exist, use these parameters to compute the elastic constants. (back to text)