When an external magnetic field B is applied to a sample, the magnetization M exponentially approaches the equilibrium magnetization. The magnetization does not assume the equilibrium value instantaneously. The relationship between the polarization time and the voltage is described by the growth rate. The growth rate of M(t) towards \(M_{\infty}\) is described by the following equation, \[\label{eq:growthrate} M(t)=M_{\infty}(1-e^\frac{t}{T_1})\]
In the equation above, \(M_{\infty}\) represents the equilibrium Curie value (Eq. \ref{eq:curielaw}). The time constant \(T_1\) is known as the spin-lattice relaxation time. In other words, \(T_1\) is the time it takes for the magnetization to exponentially approach \(M_{\infty}\). Eq. \ref{eq:growthrate} is used to describe the relationship between the voltage verses a changing polarization time.
The Curie law can derived using \(M=n\mu\left<cos\theta\right>\) where \(\left<cos\theta\right>\) represents the average value of \(cos\theta\), measuring the alignment between the magnetic moment and the external field B, for all magnetic moments in the sample. The calculation of \(\left<cos\theta\right>\) using classical thermodynamics results in the Curie law. The Curie value can be calculated using the following equation: \[\label{eq:curielaw}
M_o=\frac{n\mu^2B}{3kT}\] where \(\mu\) is the magnetic moment of each spin, n is the number of magnetic moments per unit volume, and B represents the magnetic field.