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\begin_body

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


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\backslash
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newcommand{
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\begin_layout Plain Layout


\backslash
newcommand{
\backslash
MI}[1]{
\backslash
texttt{
\backslash
textcolor{olive}{#1}}}
\end_layout

\end_inset


\end_layout

\begin_layout Title
dHvA
\end_layout

\begin_layout Author
Klaus Koepernik
\end_layout

\begin_layout Standard
We will walk you through a basic setup of a dHvA calculation.
 The module is discussed in depth in a section of 
\family typewriter
FPLO
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

/DOC/MANUAL/doc.pdf
\family default
.
\end_layout

\begin_layout Standard
The solutions are to be found in the 
\family typewriter
solution
\family default
 directory and you will work in 
\family typewriter
task
\family default
.
\end_layout

\begin_layout Standard
dHvA has two stages.
 The first calculates the Fermi surface and the second calculates the dHvA
 spectrum.
 The first stage saves the data in the file 
\family typewriter
+isoergcache
\family default
.
 This cache file is designed for re-use.
 If you want to increase the accuracy of the Fermi surface you can change
 the settings accordingly and simply re-run fplo.
 It will read the cache data and only calculates data, which are not yet
 present in the file.
 Consequently, a fresh calculation would require to delete this file.
 Consult 
\family typewriter
doc.pdf
\family default
 for more details as mentioned above.
\end_layout

\begin_layout Itemize
Go into the directory 
\family typewriter
task
\family default
.
\end_layout

\begin_layout Itemize
Let's start by setting up stage one: the creation of the Fermi surface.
 Open fedit and go to the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{dHvA}
\end_layout

\end_inset

 submenu (hotkeys 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{space d}
\end_layout

\end_inset

).
 Switch on 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Iso Surface Run}
\end_layout

\end_inset

, set 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{initial subdivision}
\end_layout

\end_inset

 to 
\family typewriter
6,,
\family default
 and leave 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bisections}
\end_layout

\end_inset

 at zero.
 Leave the submenu and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Quit/Save}
\end_layout

\end_inset

 fedit.
 
\end_layout

\begin_layout Itemize
Run 
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\end_deeper
\begin_layout Itemize
Have a look at the relevant output
\end_layout

\begin_deeper
\begin_layout LyX-Code
grep ISO: out|less 
\end_layout

\begin_layout Standard
In contrast to other modules this module determines the Fermi surface in
 a adaptive way.
 It will find a minimal reciprocal cell which is printed after 
\end_layout

\begin_layout Standard

\family typewriter
ISO: Reciprocal iso cell vectors/(2*pi): 
\family default
 
\end_layout

\begin_layout Standard
subdivide it according to 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{subdivision}
\end_layout

\end_inset

 in the fedit submenu and prints a suggestion, which subdivision ratios
 are optimal in the line
\end_layout

\begin_layout Standard

\family typewriter
ISO: Most homogenous initial subdivision would be: 6 6 5 or multiples of
 these.
 
\end_layout

\begin_layout Standard
On this initial grid all cells containing the Fermi surface will be determined.
 This means that very tiny parts might be missed if the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{subdivision}
\end_layout

\end_inset

 is too course.
 (If in doubt use xfplo to get an idea which sheets must exist.) 
\end_layout

\begin_layout Standard
After this initial step the resulting non-empy cells will be subdivided
 into 8 equal parts of which agian the cells which contain the Fermi surface
 will be registerd.
 These subdivision steps are repeated up to 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bisection}
\end_layout

\end_inset

 times (zero means no bisetion at all --- just the orignal mesh is used).
 At the end we have a set of cells, which finely wraps around the Fermi
 surfaces.
 The resulting Fermi surfaces are extracted sheet-wise (sheet = band number)
 and part-wise (disconnected sheets) and written to files called e.g.
 
\family typewriter
+iso_b00011_p0001_spin1
\family default
 (b=band number, p=part number).
\end_layout

\end_deeper
\begin_layout Itemize
Check the files
\end_layout

\begin_deeper
\begin_layout LyX-Code
ls -l +iso_*
\end_layout

\begin_layout Standard
You will find one part of band number 11 and 6 parts of band number 12.
 (That there are 6 parts is an artifact of the low resolution, which results
 in disconnected parts).
\end_layout

\end_deeper
\begin_layout Itemize
Let's visualize the result
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo -raw +iso_* # the underscore matters!
\end_layout

\begin_layout Standard
Use 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Ctrl-R r}
\end_layout

\end_inset

 to re-scale the sceene and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{left click + mouse move}
\end_layout

\end_inset

 to rotated the picture.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bisec0.jpg
	lyxscale 30
	width 50col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-first-approximation"

\end_inset

The first approximation of the Fermi surfaces.
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Standard
Later you will find that the little blobs in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-first-approximation"

\end_inset

 belong to the two ring-like sheets.
\end_layout

\end_deeper
\begin_layout Itemize
Note, the size of 
\family typewriter
+isoergcache
\end_layout

\begin_deeper
\begin_layout LyX-Code
ls -lh +isoergcache
\end_layout

\begin_layout Standard
It has 328KB.
\end_layout

\end_deeper
\begin_layout Itemize
Open fedit and in the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{dHvA}
\end_layout

\end_inset

 submenu increase the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bisection}
\end_layout

\end_inset

 to 2 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{quit/save}
\end_layout

\end_inset

 fedit.
\end_layout

\begin_layout Itemize
Re-run fplo
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\end_deeper
\begin_layout Itemize
and visualize
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo -raw +iso_* # the underscore matters!
\end_layout

\begin_layout Standard
to get Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-two-bisections-approximation"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bisec2.jpg
	lyxscale 30
	width 50col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-two-bisections-approximation"

\end_inset

The two-bisections approximation of the Fermi surfaces.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We still have 6 parts of sheet 12.
 If you type
\end_layout

\begin_layout LyX-Code
ls -lh +iso* # no underscore
\end_layout

\begin_layout Standard
you will find out that 
\family typewriter
+isoergcache
\family default
 now has 7MB and that all but part 1 and 2 are very smaller.
 Let's load an isolated part
\end_layout

\begin_layout LyX-Code
xfplo -raw +iso_b00012_p0003_spin1
\end_layout

\begin_layout Standard
You will not see much: this tiny part is a little spec at the end of the
 arms of the ring like sheeets, which got separated due to the finite resolution.
 It is basically un-important.
\end_layout

\end_deeper
\begin_layout Standard
Our approximation is still not very good, but for teaching purpose let's
 continue to the second stage: the dHvA spectrum.
\end_layout

\begin_layout Itemize
Open fedit and in the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{dHvA}
\end_layout

\end_inset

 submenu put the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Number of fields}
\end_layout

\end_inset

 to 4.
 Edit the fields to look like this
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Graphics
	filename pics/fields.png
	width 60col%

\end_inset


\end_layout

\begin_layout Standard
Set 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Parts}
\end_layout

\end_inset

 (hotkey 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{t}
\end_layout

\end_inset

) to 1.
 This will ignore all but the first part of each sheet.
 This makes sense since band 12 has two symmetry related parts and sheet
 11 has only one part.
 Note, that the number and the numbering of parts can change depending in
 the value for 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bisections}
\end_layout

\end_inset

.
 Hence, it is always a good idea to check the 
\family typewriter
+iso_*
\family default
 files.
\end_layout

\end_deeper
\begin_layout Itemize
Now, run 
\end_layout

\begin_deeper
\begin_layout LyX-Code
fdhva
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout Standard
When done, have a look at the files created:
\end_layout

\begin_layout LyX-Code
ls -ltr
\end_layout

\begin_layout Standard
We have a 
\family typewriter
dHvAdata
\family default
 directory, 
\family typewriter
+area
\family default
 and 
\family typewriter
+mass
\family default
 files for parts 1 of both sheets and an xfbp script 
\family typewriter
area_vs_angle.cmd
\family default
 which we will use now
\end_layout

\begin_layout LyX-Code
xfbp area_vs_angle.cmd
\end_layout

\begin_layout Standard
Open the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Edit 
\backslash
RA{} World 
\backslash
RA{} properties}
\end_layout

\end_inset

 dialog and set 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{Y-max}
\end_layout

\end_inset

 to 1000.
\end_layout

\begin_layout Standard
You see Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Our-first-dHvA"

\end_inset

.
 It is quite a mess.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/area2_30_100.png
	lyxscale 10
	width 80col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Our-first-dHvA"

\end_inset

Our first dHvA spectrum.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We will not explain the details of the algorithm here.
 For this we strongly encourage to read the dHvA section in 
\family typewriter
doc.pdf
\family default
.
 We will however increase the accuracy.
\end_layout

\end_deeper
\begin_layout Itemize
In the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{dHvA}
\end_layout

\end_inset

 submenu of fedit change the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{angle subdiv}
\end_layout

\end_inset

 to 60 and the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{No of planes}
\end_layout

\end_inset

 to 200.
\end_layout

\begin_layout Itemize
Re-run 
\end_layout

\begin_deeper
\begin_layout LyX-Code
fdhva
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout Standard
Have a look at the result
\end_layout

\begin_layout LyX-Code
xfbp area_vs_angle.cmd
\end_layout

\begin_layout Standard
It is a bit better in that there are more lines and less isolated symbols.
 However, there seem to be doublings of lines.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/areas_2_60_200.png
	lyxscale 10
	width 80col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:A-better-dHvA"

\end_inset

A better dHvA spectrum.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
We cannot do much better here, since most of the trouble comes from the
 crude Fremi surface Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-two-bisections-approximation"

\end_inset

.
\end_layout

\begin_layout Itemize
Open fedit and in the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{dHvA}
\end_layout

\end_inset

 submenu increase the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bisection}
\end_layout

\end_inset

 to 4 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{quit/save}
\end_layout

\end_inset

 fedit.
\end_layout

\begin_layout Itemize
Re-run fplo
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\begin_layout Standard
After some time (1min) we can visualize the Fermi surfaces
\end_layout

\begin_layout LyX-Code
xfplo -raw +iso_*
\end_layout

\begin_layout Standard
Now that is much better
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bisec4.jpg
	lyxscale 10
	width 50col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Bisection-4."

\end_inset

Bisection 4.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
To convince youself that the cache-file works re-run 
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 | tee out
\end_layout

\begin_layout Standard
It basically does not take any time.
\end_layout

\end_deeper
\begin_layout Itemize
Let's check the files: 
\end_layout

\begin_deeper
\begin_layout LyX-Code
ls -lh +iso* # no underscore
\end_layout

\begin_layout Standard
We now have only 3 
\family typewriter
+iso_
\family default
 files: band 11 part 1 and parts 1 and 2 of sheet 12.
 You will notice that the older 
\family typewriter
+iso_
\family default
 files have vanished.
 This was triggered by the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{delete old files}
\end_layout

\end_inset

 option in the fedit submenu.
 It is for your convenience in order to avoid outdated files from previous
 runs.
 
\end_layout

\begin_layout Standard
Furthermore, you will notice that the cache has 111MB.
 The size of the Fermi surface data is growing exponentially with the number
 of bisections.
 (Well, who would have thought that 
\begin_inset Formula $2^{n}$
\end_inset

 is an exponential.
 But seriously, keep this in mind.
 At any state, the next higher bisection could flood all your RAM and make
 the system swap.)
\end_layout

\begin_layout Standard
We approximate from our three calculations that the size grows as 
\begin_inset Formula $\mathrm{mem}=0.3\cdot4.8^{n}$
\end_inset

, which gives 760 MB for bisection 5.
 Indeed we get 440MB, so the estimate is rough.
 Moreover, the cache data is not all.
 The RAM actually used for bisection 5 was 700MB.
 So, be cautious.
 
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Box Boxed
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "70col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
The intel MKL library has a bug on some machines, which makes the memory
 grow.
 If you see such behaviour compile without it.
\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Let's proceed to the dHvA spectrum.
 Re-run 
\end_layout

\begin_deeper
\begin_layout LyX-Code
fdhva
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\end_layout

\begin_layout Standard
When done have a look at the result
\end_layout

\begin_layout LyX-Code
xfbp area_vs_angle.cmd
\end_layout

\begin_layout Standard
This is the best we can show in such a tutorial.
 We could increase the bisections to 6 to obtain the results shown in 
\family typewriter
doc.pdf
\family default
.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/area_4_60_200.png
	lyxscale 10
	width 80col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Our-final-result"

\end_inset

Our final result for this tutorial.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Finally, we will display the extremal orbits.
 Execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp area_vs_angle.cmd
\end_layout

\end_deeper
\begin_layout Itemize
Set the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{world ymax}
\end_layout

\end_inset

 to 1000.
 In the viewport 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{right click}
\end_layout

\end_inset

 close to the yellow parabolic curve (bottom 250T, angle at minimum 50)
 to get this
\end_layout

\begin_deeper
\begin_layout Standard
\noindent
\align center
\begin_inset Graphics
	filename pics/yellowcurve.png
	width 70col%

\end_inset


\end_layout

\begin_layout Standard
It tells you that this curve belongs to sheet 12 part 1 chain21.
\end_layout

\begin_layout Standard
We use this information to load the extremal orbits belonging to this curve.
\end_layout

\end_deeper
\begin_layout Itemize
Execute the following command.
 Hint: use tab-completion to avoid typing.
\end_layout

\begin_deeper
\begin_layout LyX-Code

\size footnotesize
xfplo -raw +iso_b00012_p0001_spin1 dHvAdata/b00012_p0001_spin1/extrorbit_chain00
021_*
\end_layout

\begin_layout Standard
We changed the color of the sheet to get this picture
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/extr.jpg
	lyxscale 10
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Extremal-orbits-of"

\end_inset

Extremal orbits of chain 21
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Of course there are more files like this.
 In a real application you might be interested to check them out.
 
\end_layout

\end_deeper
\begin_layout Itemize
As a final exercise we load 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo +iso_* # without the raw option
\end_layout

\begin_layout Standard
which loads the sheets and backfolds them into the boundary.
 We changed the boundary a bit to obtain this final picture.
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/tree.jpg
	lyxscale 10
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-ZrFe2-tree."

\end_inset

The ZrFe
\begin_inset Formula $_{2}$
\end_inset

 tree.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Standard
A remark on file sizes.
 It is possible to reduce the size of the cache file by using the following
 options in the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
MI{bandplot}
\end_layout

\end_inset

 submenu: set 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Lower energy bound}
\end_layout

\end_inset

 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Upper energy bound}
\end_layout

\end_inset

 and switch on 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Restrict bands to window}
\end_layout

\end_inset

.
\end_layout

\end_body
\end_document
