Multiple Frequencies in

Zero Field

FFT exercise for TSI 2011 Data Analysis workshops

It is often the case that, below some critical temperature, the polarization of muons in magnetic samples will oscillate [The term "precess" is inappropriate here. Why?] at well-defined frequencies in zero applied magnetic field (ZF). More often than not, several different frequencies are present simultaneously. This is conventionally interpreted as evidence for several muon sites in a magnetically ordered crystal lattice. Therefore one of the most common applications of the fast Fourier transform (FFT) is the display of 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 BaFe₂As in ZF at temperatures from about 2 K to above the magnetic transition around 135 K. Two distinct oscillation frequencies are observed.

The Exercise

Visit the TRIUMF µSR runs database at http://musr.ca/mud/runSel.html and search for Experiment 1118 in 2008 with "BaFe2As2" in the title.

Click on the run-number button for one of these runs 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 0.02 to 0.3 µs with 3 ns bins. Eventually choose Spectrum type 2 (Histograms 1,2) and make ASY plots of various ZF runs on a pleasing time range.

Now click on "Plot FFT" and adjust the FFT parameters and options until you can see two lines in the FFT, around 7 and 28 MHz for the low-T runs. (Allow pop-ups in your browser!) See if you can plot the Real part of the amplitude for both peaks simultaneously. Select a few other runs at different Ts and see if their FFTs look different.

When you know which runs you want to fit, click Zip & Download Runs at the bottom of the Run List window to bring the selected runs into your computer; then unzip the download into the directory where you want to fit them.

If you are working on bnqrexp.triumf.ca, the zip/unzip step is not required, as all runs are directly accessible in the /data/<beamline>/<year>/ directories on that host; unfortunately this is not available on the workstations in Hennings.

After you have mastered the art of displaying nice FFT spectra in your Web browser, you can feed the script fft3d-BaFe2As2_ZF.cmd into fft3d (only on bnqrexp.triumf.ca) by starting up fft3d and entering "@fft3d-BaFe2As2_ZF.cmd". Try some of the formatting commands (like "view") in DOPL3D. The resultant plot can be saved to an EDGR file using the edgr command in DOPL3D. Play with this script to see how it works.

Can You Find T_N?

Where do you conclude that the frequencies go to zero? Is it the same temperature for both frequencies? Do both frequencies scale the same way with T?

Jess H. Brewer