Electron Spin Resonance

Sara Lim & Elizabeth Ann Pollock

University of Rochester

PHY 243: Advanced Lab

Professor Regina Demina

External Magnetic Field

Zeeman Effect Energy Splitting:

Landé Factor:

Apply an external magnetic field

For a Spin ½ system with a free electron (and zero angular momentum), g= 2

Spin in an External Magnetic FieldIn an external magnetic field, the spin is either parallel or anti-parallel to applied magnetic field

m = +1/2,-1/2

the energy levels: or

ResonanceAn electromagnetic field can induce magnetic dipole moment transitions if its frequency is near the energy difference:

When the levels have spacing ΔE||H the oscillatory magnetic field exerts a torque on the dipoles some of them reverse orientation, ie, they change energy levels: RESONANCE

Precessing

Set-up

Set-up

Samples

Differences in samples

Valance electron acts analogously to H atom which has a free electron, so applying a magnetic field and sweeping allows observance of resonance

It is harder to observe resonance by sweeping magnetic field because ‘subshell’ of molecule is filled, so only a few electrons are free in copper sulfate complex. They are held closer to the complex, so they alternate spin up/down given the relaxation time. The inverse of the relaxation time- the time to reach equilibrium in spin states- is the width of the absorption peak.

DPPHCalculations (in cgs units)

Values obtained in lab (via gaussmeter and wavemeter)

Errors/Uncertainty

Error in B-field- study with function generator- Imperfect B-field

Problems- Oscilloscope dials- Do not apply more than 20 amps when sweeping the applied B field because the fuse will blow!