Aggregate Frequency Width, Nuclear Hyperfine Coupling and Jahn-Teller Effect of $C{u}^{2+}$ Impurity Ion ESR in $SrLaAl{O}_4$ Dielectric Resonator at $20$ Millikelvin

Abstract

The impurity paramagnetic ion, $C{u}^{2+}$ substitutes $Al$ in the $SrLaAl{O}_4$ single crystal lattice, this results in a $Cu{O}_6$ 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 $SrLaAl{O}_4$ at $20$ millikelvin. Measured parallel hyperfine constants, $A_{\parallel Cu}$, were determined to be $-155.7\times 10^{-4}c{m}^{-1},-163.0\times 10^{-4}c{m}^{-1},-178.3\times 10^{-4}c{m}^{-1}$ and$-211.1\times 10^{-4}c{m}^{-1}$ at $9.072GHz(WG{H}_{4,1,1})$ 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, $\sim (\frac{spin-orbitcoupling}{10D_q}{)}^2$, is significant and can not be disregarded, with the local strain dominating over the observed Zeeman-anisotropy-energy difference. The Bohr electron magneton, ${\hat{I}}^2=9.23\times 10^{-24}J{T}^{-1}$, (within $-0.43\%$ so-called experimental error) has been found using the measured spin-Hamiltonian parameters. Measured nuclear dipolar hyperfine structure parameter $P_{\parallel }=12.3\times 10^{-4}c{m}^{-1}$ shows that the mean inverse third power of the electron distance from the nucleus is $⟨r_q^{-3}⟩\simeq 5.23$ a.u. for $C{u}^{2+}$ ion in the substituted $A{l}^{3+}$ ion site assuming nuclear electric quadruple moment $Q=-0.211$ barn.