Quadrupolar ALCR in

Copper

Fitting exercise for TSI 2011 Data Analysis workshops

In about 1982, theorists McMullen & Zaremba suggested that there should be enhanced relaxation in copper at a field of about 80 Oe, where the electric quadrupole frequency of Cu nuclei matches the Zeeman frequency of the µ⁺. The first experiments looked for this effect in TF and found nothing.

In 1985 it dawned on us that the effect would be most noticeable in LF, where it would permit "flip-flop" relaxation of the muon and the Cu in a regime where the muon spin was otherwise strongly decoupled from local fields, and therefore static. So the experiment was repeated in LF; this time it worked.

The Experiment

Subsequent developments used time-integral (TI)-µSR to investigate ALCR more efficiently, but the original discovery used ordinary time-differential (TD)-µSR to acquire A(t) = (B-F)/(B+F) asymmetry spectra in LF, fit them to a stretched exponential decay, and plot the relaxation rate as a function of LF. Later on, after Moreno Celio has calculated the true G_zz(t) for the quantum system of a µ⁺ in an octahedral site surrounded by six nearest neighbor Cu ions, better data were taken and fit to that tabulated function. Now you can rediscover that famous resonance.

The Exercise

Visit the TRIUMF µSR runs database at http://musr.ca/mud/runSel.html and search for Experiment 286 in 1985.

Click on the run-number button for run 5687 and investigate the run header information, especially the names and ordering of the data histograms. Select various Spectrum types and look at the entire time range with (let us say) 300 ns bins. Eventually choose Spectrum type 2, Histograms 1,2 to plot some nice ASY spectra for that series of runs at 20 K.

When you have these runs selected, 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.

Use musrgui or (on bnqrexp.triumf.ca) physica ['t0', 'bkgd' and 'early' commands] to verify the correctness of the t = 0 bin, background bin range and good data bin range. Checking one run should be sufficient. Notice that there are additional histograms with no counts; these can be ignored. Prepare your fit-control template file, for either musrfit (.msr) or msrfit (.i), starting from another such file. Fit to a single stretched-exponential relaxing signal in each case. You can construct a global fit with common values of the initial asymmetry and the ALPHA parameter if you like, but this is not essential. Should you choose to try global fits, here are some templates for use with msrfit: cu_zlf_45k-GKT.IGL and cu_zlf_45k.IGL; both of these cover only the ZF to low LF region (well below the qALCR) and so address only the question of the muon hop rate at 45 K. They will not show you the resonance at higher LF. They use two different tables to look up the dynamic G_zz(t) corresponding to the fitting model.

Do You See the Resonance?

Plot your fitted relaxation rate versus LF, using the calibration B [Oe] = 0.07605314*(DAC - 17.7) to convert the magnet control Digital-to-Analog Converter settings into the magnetic field.

If you are keen to "do it right", you can make a global fit of the series of runs taken under Experiment 336 in 1985 on Cu with <110> || B at 45 K (where the muon is most static in the Cu lattice) to a "dynamicized" version of Celio's theoretical G_zz(t) using the table td_cu_110_lf.tbl which Jess will show you where to find.

If you do it this way, you will find it difficult to plot your fit results in a manner that looks like a resonance. Why?

Jess H. Brewer

Last modified: Mon Aug 15 19:46:10 PDT 2011