Modulation Broadening of NMR and ESR Line Shapes

Abstract

An analysis is made of the phase sensitive detection of magnetic resonances at various harmonics of the modulation frequency. The results are applicable to any experiment in which phase sensitive detection is employed. A mathematical treatment of modulation broadening is developed. Unlike the Taylor expansion method this is applicable in all practical cases. Signal amplitude and line shape of Lorentz and Gaussian resonances are calculated for the first three harmonics as functions of the modulation amplitude. Expressions which relate the Fourier coefficients of a modulation-broadened resonance line shape to those of the true integrated line shape are derived. The use of these expressions in correcting observed line shapes for modulation broadening is compared with that of another method involving the summation of a convergent series.

Pseudo field modulation in EPR spectroscopy

“…See, for example, the citations in Poole's treatise [1]. Berger and Gª [2] give an early analysis, and Wilson [3] arrives at equivalent results using a somewhat different approach. The modern computer greatly facilitates the ease with which Fourier transitions can be obtained, compared with the years when [2] and [3] were written.…”

“…Berger and Gª [2] give an early analysis, and Wilson [3] arrives at equivalent results using a somewhat different approach. The modern computer greatly facilitates the ease with which Fourier transitions can be obtained, compared with the years when [2] and [3] were written. Based on this observation, we introduce the subject of this paper by developing an alternative derivation to those presented in these two papers.…”

“…(4), they obtained Eq.(5). Wilson's paper on modulation effects [3] is frequently quoted. Like Berger and Gª [2], he starts from Eq.…”

Test studies of some conventional CW EPR spectrometer settings

“…In the case when H m > 91 the linear proportionality disappears [5,[12][13][14] and the line becomes broader due to the overmodulation. Keeping in mind these restrictions the possible regions for investigating the influence of magnetic field modulation amplitudes on the lpp was up to 4 G for pyrolized sucrose and up to 187 G for MnSO4.2.9H20.…”

Theory of Temperature Modulation Studies of Ferromagnetic Materials

“…If larger values are used, so that the signal leads to modulation-broadened curves, instead Xl(T) of equation (5) should be replaced by a Fourier integral (Wilson 1963). In the AC experiments the temperature modulated sample is used as the core of an AC transformer operating at a carrier frequency We ~ w. If the amplitude of magnetic field produced by the primary coil is Ho, the sample magnetization becomes (8) and the Taylor expansion leads to (9) Neglecting the contribution 110 dH/dt, which is not modulated, the secondary voltage is given by…”