  The magnetization, crystal structure, and thermal expansion of a nearly
stoichiometric Sr$_{1.04(3)}$Er$_{2.09(6)}$O$_{4.00(1)}$ single crystal have
been studied by PPMS measurements and in-house and high-resolution synchrotron
X-ray powder diffraction. No evidence was detected for any structural phase
transitions even up to 500 K. The average thermal expansions of lattice
constants and unit-cell volume are consistent with the first-order Gr\"uneisen
approximations taking into account only the phonon contributions for an
insulator, displaying an anisotropic character along the crystallographic
\emph{a}, \emph{b}, and \emph{c} axes. Our magnetization measurements indicate
that obvious magnetic frustration appears below $\sim$15 K, and
antiferromagnetic correlations may persist up to 300 K.
