Adiabatic rise-time effects in pulsed magnetic resonance

Abstract

Theoretical treatments of pulsed magnetic resonance experiments, including EPR and NMR, free induction decay, and spin-echo measurements, have generally assumed that no significant spin motion occurs during the pulse rise and fall times. Hence it has been assumed that, as the rf field, B, , in the Larmor frame is swept up and B,B, the effective field, rotates from the z direction toward B1, the spin motion is completely nonadiabatic. The following examples indicate that significant rise-time effects will sometimes occur: (i) Commercial pulsed NMR spectrometers used at VHF frequencies to study magnetically ordered solids have typical rise times of about 0.2 ps. Since short pulses (6 1 ps) are generally used the pulse shape often approximates triangular rather than rectangular. (ii) In the first (1) gamma-radiation detected pulsed NMR experiments on oriented radioactive nuclei (NMRON) effects of complex spin motion but not of coherent precession were observed. When the experiments were repeated with the rise tilme reduced from 300 to 40 ns, coherent precession was observed for the shorter pulse widths (2). (iii) A new resonance technique involving multitum ramp pulses has recently been introduced (3). Here adiabatic spin rotations through up to 90°C occur deliberately during the rise time 7,; these offer the advantage of producing rotations which are relatively insensitive to rf inhomogeneous broadening. Consider an ensemble of free spins with resonant frequencies distant AU from the rf frequency subject to pulses with significant rise and fall times. The rotation of the axis of precession from the z axis during 7, is determined by the adiabatic parameter A = Aw2/[dW;/dt] = Aw27,/wI where w is the instantaneous value of yB, during the rise time and wI is the maximum value reached at the end of the rise time. Note the mverted roles of Aw and w1 to those in conventional single passage experiments (4). For A + 1 there will be no significant spin motion during 7, or during the fall time 7f and the usual theoretical treatments in terms of precession about Berr during each pulse will be applicable. On the other hand, when A % 1 the spins will remain parallel with B,tf during both 7, and Tf so that, after each pulse, they will have returned to the