Estimate of inhomogeneous line broadening in steady-state magnetic resonance

Abstract

We have established relationships between the experimental and theoretical absorption and dispersion line parameters for steady-state magnetic resonance, allowing us to determine both the field characteristics (amplitude of the a.c. magnetic field) and the relaxation characteristics (longitudinal and transverse relaxation times) of the object under study.Keywords: magnetic resonance spectroscopy, absorption and dispersion line parameters, detuning from resonance, rf field amplitude, relaxation time, inhomogeneous broadening of a spectral line.Introduction. Coherent magnetic spectroscopy of quantum systems are currently widely used in studying the structure and properties of the condensed state of matter. It is subdivided into steady-state and non-steady-state spectroscopy. Steady-state spectroscopy is based on the action of a continuous electromagnetic field on a quantum transition, where the dispersion and absorption signals act as the observable quantities [1, 2]. Non-steady state spectroscopy is based on study of the dynamics of quantum transitions after two-pulse action of coherent electromagnetic radiation on a sample. The observable quantity in this case is the "echo signal" generated at a certain instant of time after the end of the exciting pulse [3]. Among coherent magnetic spectroscopy methods, the most widely used are nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), and optical resonance. Most often non-steady-state effects are studied under exact resonance conditions, when the carrier frequency of the pulse matches the central frequency of the quantum transition. Until recently, it was assumed that nonresonant excitation leads to a trivial consequence, namely a reduced effect. However, in addition to this fact, under nonresonant excitation conditions in magnetic materials, as shown in [3], an interesting phenomenon has been observed: the appearance of multiple structure in the nuclear spin echo signal. Nonresonant excitation conditions in the theory [4] were described by dividing the parameter Δ into two terms: Δ → (Δ -δ), where Δ corresponds to the spread in the frequencies of the spin packets of the inhomogeneously broadened line, δ = ω n -ω 0 is the detuning from resonance, ω n is the carrier frequency of the electromagnetic field, ω 0 is the central frequency of the quantum transition.A similar situation also arises in steady-state magnetic resonance, when the dispersion u and absorption υ signals have the form: