deletions | additions       diff --git a/subsection_Varying_the_Magnetic_Polarization__1.tex b/subsection_Varying_the_Magnetic_Polarization__1.tex  index b39b4ce..c1d1c5d 100644  --- a/subsection_Varying_the_Magnetic_Polarization__1.tex  +++ b/subsection_Varying_the_Magnetic_Polarization__1.tex 
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\subsection{Varying the Magnetic Polarization}   The relationship described in Eq. \ref{eq:growthrate} can not be applied to the degree of polarization or magnetization. In order to determinewhether  the relationship between magnetic field and  degree of polarization depends on the strength of magnetic field, magnetization,  we have to vary varied  the saturation magnetization values $M_{\infty}$ as a function of polarizing applied magnetic  field.\textbf{correct?}  When varying the current, for electronic systems, magnetic field,  the fractional populations are affected by the g-factor or the spectroscopic splitting factor. The fractional populations can be described by the lower and upper states-- $N_1$ represents the lower state and $N_2$ represents the upper state. The difference between these two states multiplied by the magnetic moment describes the magnetization of the field. The following relationship, the Brillouin function, can be expressed in the equation below \cite{Kittel_1953}, \begin{equation}   \label{eq:tanh}  M=(N_1-N_2)\mu= N\mu\cdot\frac{e^x-e^{-x}}{e^x+e^{-x}}=N\mu \tanh{x} 
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