Multiple Frequencies in
Transverse Field
FFT exercise for TSI 2011 Data Analysis workshops
More often than not, when a material with large paramagnetic moments
is studied in high transverse field (HTF) with µSR,
several frequencies of µ+
precession are observed.
This is conventionally interpreted as evidence for several muon sites
in a magnetically ordered crystal lattice;
however, this interpretation is hard to accept when the sample
is not magnetically ordered.
Then the usual explanation is multiple magnetically inequivalent sites
with different (frequently quite large) Knight shifts,
another "stretch" of plausibility.
Some think the µ+ may drive
a region around the muon into a magnetically ordered state
(an alarming proposition for those who like to think
of the µ+ as a "gentle probe");
others claim that the µ+ is
bound to a pre-existing "magnetic polaron"
(a species prdicted by de Gennes over half a century ago).
This is a controversial topic, so it behooves anyone
wishing to study magnetic materials with µSR
to be familiar with using the fast Fourier transform (FFT)
to display these frequency spectra as a function of T.
A good first attempt at producing the desired FFTs
for TRIUMF µSR runs
can be achieved on any Web browser using the MUD Runs Database at
http://musr.ca/mud/,
but a publication-quality 3D-like plot is best produced using the
fft3d program on bnqrexp.triumf.ca
(unfortunately this version is not available on the Hennings workstations).
This program is based on the same msrfft program
used by the Web utility, but interfaced to the TRIUMF GPLOT
graphics library, which can make editable plots in EDGR format.
The Experiment
Muons were stopped in a spherical ball pressed from a powder
of the magnetic semiconductor samarium sulphide (SmS)
in the HiTime spectrometer running in Sample/Reference (S/R) mode
in various high transverse fields (HTF) at various temperatures (up to 875 K).
Two distinct oscillation frequencies are observed in the Sample Spectrum.
The Exercise
Visit the TRIUMF µSR runs database at
http://musr.ca/mud/runSel.html
and search for all runs with "SmS%3T" in the title.
Click on the run-number button for the high-temperature run 1152
and investigate the run header information,
especially the names and ordering of the data histograms.
Select various Spectrum types and look at the range
from 0 to 0.1 µs with 0.2 ns bins.
Eventually choose Spectrum type 4 (Histograms 1,3,2,4) with a RRF frequency of 406 MHz
and a packed bin size of 0.05 µs to display the whole time range in the RRF.
Now click on "Plot FFT" and adjust the FFT parameters and options
until you get a sharp, symmetric line in the FFT,
plotting the Real part of the amplitude.
(Allow pop-ups in your browser!)
Do this for type 4 spectra which histograms 1,3,2,4 for the Sample signal;
then repeat with histograms 5,7,6,8 to see the Reference signal.
Then click on a few other runs at different Ts and see if their
FFTs look different.
If you like, you can move on to the
Advanced Fitting Exercise
on this dataset.
Jess H. Brewer
Last modified: Sun Aug 14 22:56:47 PDT 2011