Electron Spin Resonance

We will observe the electron spin resonance in an organic sample of PHHP. In this sample the electron spin in a single hydrogen atom is aligned along an axial field B produced in a Helmholz coil. When a perpendicular RF field of energy E=hf is applied flipping of he electron spin is observed when the resonance condition is met.

                                                                 h f = g ub Bo

h is Planck's constant, ub is the Bohr magneton, B=Bo is peak field at the resonance condition.

We find the g-factor for an electron from a series of measurements of Bo at different frequencies.

Measurements and Apparatus

Before inserting the ESR probe the we want to calibrate the axial magnetic field vs VARIAC setting with a Hall Probe.

1) Zero the Hall probe as described on the back cover. Set the Hall probe to measure AC gauss. Insert the probe in to the center of the Helmholz coil. Take readings of AC-Gauss vs VARIAC setting.   THe peak field  Bo=sqrt(2) Brms!

VARIAC(V)	00	10	20	30	40	.......	140	150	160
B(AC-Gauss)

You will use the VARIAC to set the resonance condition for different RF frequencies f,

2) Remove the Hall probe and insert the ESR coil in to the center of the Helmholz coil. Power up the DC supply, Frequency meter, and ESR RF Module, and oscilloscope.

3) Note the two traces on the oscilloscope.
CH-1 Output of a pickup coil in the Helmholz magnet. V ~ B
CH-2 Outout of ESR RF Module. V ~ Power absorbed by sample.

4) Set f = 10 MHz on the ESR RF Module. You should observe a double peak 90deg out of phase with the Helmholz coil signal when B<Bo, Change the VARIAC setting until the rtwo peaks are just merged.. Overmerging will decrease overall amplitude.

  Undermerge                             Merge                                     Overmerge
        B>Bo                                 B=Bo                                       B<Bo

----      ----     ----                  ----         ----                             ----           -----
    -  -       -  -                             -     -                                           -      -
     --         --                                -  -                                                -
      -          -                                  -

Wiggle the VARIAC setting to estimate the error on Bo.

5) Continue the measurements.

f ( MHz )	10	12	14	.......	28	30
Brms (Tesla)
Bo (Tesla)

Remember that Bo=sqrt(2) Brms

Analysis

1) Calculate g for each resonance f . Treating them as independent measurements find the average <g> and err(<g>).

You may also find g by plotting  h f = g ub Bo   (h f vs Bo)  and fit to a straight line where the slope = g ub.  

2) Discuss the accuracy and uncertainty in your measurements in your lab rrepot.