Electron Spin Resonance

        Introduction

A free electron has spin ½, which means the stationary states in an applied magnetic field have components of spin angular momentum parallel to the field of ± ћ/2 . There is a corresponding magnetic moment μ= ± ½ gμ_B, where μ_B = ½ eћ/m is called the “Bohr magneton.” The energy of interaction of this magnetic moment with the magnetic field is then ΔE = ± μ B = ± ½ gμ_BB. Transitions between the “up” and “down” states can be induced by absorption or emission of photons satisfying the energy conservation (or resonance) condition:

hν = 2ΔE = gμ_BB, or

ν = g (e/4πm) B = g (13.99 GHz/Tesla) B .

For orbital motion the ratio of magnetic moment to angular momentum corresponds to g=1. For the electron spin, g=2.0023 (2 comes from Dirac relativistic quantum mechanics and the small correction from quantum electrodynamics). Some molecules and some solids have unpaired electrons which act like almost free spins. This can be modified to a small or a large degree by spin-orbit coupling and by local electric fields in a crystal. We will study DPPH, which has a very narrow resonance. This discussion based on energy considerations has ignored the dynamics of the spin in the magnetic field (precession). The dynamics are important in NMR experiments, but do not affect our ESR measurements.

        Equipment

• Pasco SE-9634 Electron Spin Resonance Apparatus, which includes:

•           Probe unit with base

•           3 RF probes and a DPPH sample in a vial

•           Passive resonant circuit

•           Current measuring lead

•           Pair of Helmholtz coils with bases

•           ESR adapter

•           Control unit

•          Instruction manual

• DC ammeter

• Oscilloscope

• Connecting wires

         Procedure

Set the Helmholtz coils at the proper spacing of ½ diameter (see datasheet). Connect the rf unit (“basic unit”) with the middle-sized rf coil, as well as the Helmholtz coils, to the “control unit” (per instruction sheet), and turn on both power switches. Watch the detector output on the scope. Adjust the tuning knob on top of the rf unit to get a frequency reading near the high end (say 60-70 MHz). Be sure the DPPH sample is in the coil.

  Three knobs on the control unit control the dc and ac current to the Helmholtz coils, and the phase shift of the signal sent to the scope (for convenience and viewing). Set a moderate ac level and adjust the dc current until you see indication of a resonance (somewhere near mid-range). This should show up as a dip in the somewhat noisy “Y” output from the detector each time the modulation takes the total field through resonance, the dip indicating a decrease in the level of oscillation due to absorption of power in the DPPH. Adjust the amplitude knob on the back of the rf unit for the best signal-to-noise ratio.

  Determine the magnetic field at resonance. This is the field due to the dc current, provided you adjust things so that the dip occurs at the zero crossing of the modulation. There are two good ways to do this: Adjust for symmetric dips in a time trace (“MTB”), or for a symmetric dip pattern with the scope in XY mode (“X-DEFL”). For the latter, reduce the modulation level until you see only half the dip; the phase shift may also be useful here. Check that the coil spacing is correct for the Helmholtz formula to be appropriate. Do this for a number of frequencies over as wide a range as possible.

  Determine the width of the resonance (in magnetic field units). Is it frequency dependent? If other samples are available, study them as well. A limitation of these relatively low-field measurements is that the intrinsic width must be quite small: at least smaller than the field used.

        References

       D. W. Preston and E. R. Dietz, The Art of Experimental Physics, Wiley, New York (1991).

       A. C. Melissinos, Experiments in Modern Physics, Academic Press, Orlando (1966).