Study of Magnetism

In this chapter we provide examples of the use of the \(\mu \) SR technique for studies of magnetic materials. First, we discuss the various contributions to the local field that occur in magnetic materials. Starting from the muon-electron interaction, the concept of the hyperfine field in a solid and its components (contact field, dipolar field,…) are introduced. The so-called Lorentz construction (with associated Lorentz field and demagnetization fields) to calculate the local field experienced by the muon in a magnetic material is outlined and examples of its use to determine the hyperfine field are given. The determination of the magnetic fraction and the transition temperature of a sample by a weak transverse field technique is presented and applications to various magnetic systems are shown. Examples are given for the study of magnetic fluctuations and of critical phenomena. The \(\mu \) SR signal in incommensurate or short-range magnetic systems is discussed. The use of \(\mu \) SR to study complex dynamical systems is explained using the spin glass system as an example. The chapter continues with a presentation of the Knight shift, which represents the magnetic response in paramagnetic and diamagnetic materials. The Knight shift in materials without and with local magnetic materials is detailed, and its the use in measurements as a function of temperature or angle to determine the muon stopping site in crystals is presented. A classical calculation of the depolarization effects due to nuclear dipole moments in the zero field and transverse field cases is shown, and the influence of the quadrupolar interaction on the nuclear depolarization rate is briefly discussed.