Introduction to Magnetic Relaxation

Relaxation is the process involved when a system in an equilibrium state is perturbed and moves to a new equilibrium state. The time between the two equilibrium states is called the relaxation time. In a magnetic relaxation, the perturbation is a change in the magnetic field. 

Magnetic relaxation time x, is the parameter that describes the magnetic relaxation process, during which the magnetization Mt will reach a new equilibrium value Mq after a change of the magnetic field from H to H + AH, as shown in Equation 9.5  

Alternating current susceptibility [100,101] (AC susceptibility), xac, is the most widely used parameter to characterize the dynamic behavior of the relaxation system. The AC susceptibility is a function of the frequency of the alternating field, where the static field (which may be zero) is parallel to the AC field. ac is a complex value, combined from two parts, in-phase and out-of-phase. 

Ho is a constant (which may be zero) on behalf of the static field h is the amplitude of the oscillating field 

Any harmonic function with the form A(t) = acos(cot- -a) can be rewritten in a complex form A(t) = ae + which can be expanded as A t) = acos(cot -E a) -E Msin(cof -E a). So the complex form of the oscillating field can be written as  

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