  The impurity paramagnetic ion, $Cu^{2+}$ substitutes $Al$ in the $SrLaAlO_4$
single crystal lattice, this results in a $CuO_6$ elongated octahedron, the
resulting measured g-factors shows four-fold axes variation condition. The
aggregate frequency width of the electron spin resonance with the required
minimum level of impurity concentration has been evaluated in single crystal
$SrLaAlO_4$ at $20$ millikelvin. Measured parallel hyperfine constants,
$A_{\scriptscriptstyle\parallel Cu}$, were determined to be
$-155.7\times10^{-4}~cm^{-1},~ -163.0\times10^{-4}~cm^{-1},~
-178.3\times10^{-4}~cm^{-1} $ and$~-211.1\times10^{-4}~cm^{-1}$ at
$9.072~GHz~(WGH_{4,1,1})$ for the nuclear magnetic quantum number
$M_I=+\frac{3}{2},+\frac{1}{2},-\frac{1}{2}$,~and$-\frac{3}{2}$ respectively.
The anisotropy of the hyperfine structure reveals a characteristics of static
Jahn-Teller effect. The second-order-anisotropy-term, $\sim
(\frac{spin-orbit~coupling}{10D_q})^2$, is significant and can not be
disregarded, with the local strain dominating over the observed
Zeeman-anisotropy-energy difference. The Bohr electron magneton,
$\beta=9.23\times 10^{-24} JT^{-1}$, (within $-0.43\%$ so-called experimental
error) has been found using the measured spin-Hamiltonian parameters. Measured
nuclear dipolar hyperfine structure parameter
$P_{\scriptscriptstyle\parallel}=12.3\times10^{-4}~cm^{-1}$ shows that the mean
inverse third power of the electron distance from the nucleus is $\langle
r^{-3}_q\rangle\simeq 5.23$ a.u. for $Cu^{2+}$ ion in the substituted $Al^{3+}$
ion site assuming nuclear electric quadruple moment $Q=-0.211$ barn.
