(U, Pr)S: Magnetic Susceptibility

Abstract

This note is written for experimentalists of the condensed matter physics, who want to know the fundamental physics of the AC magnetic susceptibility. Experimentally, in recent days one can easily measure the AC magnetic susceptibility of various magnetic systems, using the SQUID magnetometer (such as the equipment from Quantum Design). However, it is sometime hard even for many professional researchers to figure out the physics of the magnetic behavior. We have been studying the magnetic phase transitions of low-dimensional magnetism, including spin glasses for many years. This note is based on our experience. In spite of many reviews on the AC magnetic susceptibility, it seems that there are few reviews on the physics of the AC magnetic susceptibility on the magnetic system such as random spin systems (spin glasses, superspin glasses, superparamagnets, quasi 2D ferromagnets, and so on). It is hoped that this note will be useful for experimentalists and students to understand the physics of magnetism. In order to investigate the magnetism of the matters, it is important to observe directly the magnetic response of the magnetic systems by the application of external magnetic field. Immediately after the application of the magnetic field, the state of the system remains unchanged. After some characteristic times, the state of the system will reach a new state in thermal equilibrium, leading to the new magnetization. This is called as a magnetic relaxation phenomenon. In order to examine the mechanism, we need to know the magnetization in thermal equilibrium and also need to know the information concerning the relaxation process into the state in thermal equilibrium. The dynamic magnetization measurement is required for one to understand the time dependence of magnetic correlations. There are many methods for this purpose, including the inelastic magnetic neutron scattering, the relaxation rate measurement of the zero-field-cooled susceptibility, and the AC magnetic susceptibility. The most suitable dynamic methods should be chosen, depending on the properties of the systems (spin glasses, ferromagnetism, superspin glass, superparamagnetism), the condition of the observation, and the physical quantities derived. In this note, we present the physics on the AC magnetic susceptibility and the magnetic neutron scattering. Contents 1. Simple theory of AC magnetic susceptibility 2. Debye relaxation with a single relaxation time 3. Relaxation with a distribution of relaxation times 4. Yoshimitsu-Matsubara method 5. Kramers-Kronig relation