Fig. 1.
Aspects of the ESR spectroscopy. (A) Free precession of the magnetization M of an ensemble of isolated electrons around the static magnetic field B0 with Larmor angular frequency ω0 = γB0, γ being the magnetogyric ratio. The transverse magnetization oscillates at the same frequency. (B) In condensed matter, the electrons exchange energy with the surroundings. A rotating microwave field B1(t) ⊥ B0 with angular frequency ω forces the precession of the magnetization around B0 with the same angular frequency. When ω ≈ ω0, an absorption resonance occurs. (C) The magnetic dipoles m of immobile spin probes in a frozen liquid have different ω0 values because of their different orientations with respect to B0, thus resulting in a broad line with width Δω0 (black line), usually referred to as rigid-limit or powder lineshape. (D) If the spin probe undergoes rotation (sketched as instantaneous clockwise jumps at random times), ω0 fluctuates. When the rotational rate 1/τ is larger than the width of the ω0 distribution Δω0, the different precession frequencies become indistinguishable and an average value is seen, i.e., the ESR lineshape coalesces (motional narrowing).