Magnetization plots

Edit and compile if you like:

% Author: Izaak Neutelings (Februari, 2020)

\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \dfrac
\usepackage{physics,siunitx}
\usepackage{tikz,pgfplots}
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\usetikzlibrary{decorations.markings}
\tikzset{>=latex} % for LaTeX arrow head
\usepackage{xcolor}
\colorlet{Rcol}{green!60!black}
\colorlet{myblue}{blue!70!black}
\colorlet{myred}{red!70!black}
\colorlet{Ecol}{orange!90!black}
\tikzstyle{Rline}=[Rcol,thick]
\tikzstyle{gline}=[Rcol,thick]
\tikzstyle{bline}=[myblue,thick]
\tikzstyle{rline}=[myred,thick]
\def\xmax{4.0}
\def\ymax{2.2}
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.03*\ymax) --++ (#2-180:0.06*\ymax)}
\newcommand\EMF{\mathcal{E}} %\varepsilon}

\begin{document}

% MAGNETIZATION vs. Bext
\begin{tikzpicture}
\def\a{1.75} % amplitude
\def\c{0.90}
\def\t{1.00} % slope
\coordinate (O) at (0,0);
\coordinate (X) at (\xmax,0);
\coordinate (Y) at (0,\ymax);
\coordinate (Q) at (0,\a);
\coordinate (T) at (\t,\a);
\coordinate (Tx) at (\t,0);

% AXIS
\draw[<->,thick]
(X) node[below] {$B_\text{ext}$} -- (O) -- (Y) node[left] {$M$};
\tick{Q}{0} node[left] {$M_\mathrm{S}$};
%\tick{Tx}{90} node[below] {$\tau = RC$};

% PLOT
\draw[dashed] (Q) --++ (0.98*\xmax,0);
%\draw[dashed] (Tx) -- (T);
%\draw[dashed] (O) -- (T);
\draw[dashed,samples=100,smooth,variable=\x,domain=0:0.28*\xmax]
plot(\x,{\a*\t*\x/sqrt(\c))});
\draw[rline,samples=100,smooth,variable=\x,domain=0:0.98*\xmax]
plot(\x,{\a*sinh(\t*\x)/sqrt(sinh(\t*\x)^2+\c)});

\end{tikzpicture}

% MAGNETIZATION vs. kT
\begin{tikzpicture}
\def\a{1.3}
\coordinate (O) at (0,0);
\coordinate (X) at (\xmax,0);
\coordinate (Y) at (0,\ymax);

% AXIS
\draw[<->,thick]
(X) node[below] {$k_\mathrm{B}T$} -- (O) -- (Y) node[left] {$M$};

% PLOT
\draw[rline,samples=100,smooth,variable=\x,domain={1.1*\a/\ymax}:0.95*\xmax]
plot(\x,\a/\x);
%\node[above right] at (1.4,1.8) {$E \sim \dfrac{1}{T}$};

\end{tikzpicture}

\end{document}