Let
$A\,:=\,-\,\left( \nabla \,-\,i\overrightarrow{a} \right)\,.\,\left( \nabla \,-\,i\overrightarrow{a} \right)\,+\,V$
be a magnetic Schrödinger operator on
${{\mathbb{R}}^{n}}$
, where
$$\vec{a}:=\left( {{a}_{1}},...,{{a}_{n}} \right)\in L_{\text{loc}}^{2}\left( {{\mathbb{R}}^{n}},{{\mathbb{R}}^{n}} \right)\operatorname{and}0\le V\in L_{\text{loc}}^{1}\left( {{\mathbb{R}}^{n}} \right)$$
satisfy some reverse Hölder conditions. Let
$\phi :\,{{\mathbb{R}}^{n}}\,\times \,[0,\,\infty )\,\to \,[0,\,\infty )$
be such that
$\phi \left( x,\,. \right)$
for any given
$x\,\in \,{{\mathbb{R}}^{n}}$
is an Orlicz function,
$\phi \left( ^{.}\,,\,t \right)\,\in \,{{\mathbb{A}}_{\infty }}\left( {{\mathbb{R}}^{n}} \right)$
for all
$t\,\in \,\left( 0,\,\infty \right)$
(the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index
$I\left( \phi \right)\,\in \,(0,\,1]$
. In this article, the authors prove that second-order Riesz transforms
$V{{A}^{-1}}$
and
${{\left( \nabla \,-\,i\overrightarrow{a} \right)}^{2}}{{A}^{-1}}$
are bounded from the Musielak–Orlicz–Hardy space
${{H}_{\phi ,\,A}}\left( {{\mathbb{R}}^{n}} \right)$
, associated with
$A$
, to theMusielak–Orlicz space
${{L}^{\phi }}\left( {{\mathbb{R}}^{n}} \right)$
. Moreover, we establish the boundedness of
$V{{A}^{-1}}$
on
${{H}_{\phi ,\,A}}\left( {{\mathbb{R}}^{n}} \right)$
. As applications, some maximal inequalities associated with
$A$
in the scale of
${{H}_{\phi ,\,A}}\left( {{\mathbb{R}}^{n}} \right)$
are obtained.