Diamagnetic correction to the $\mathrm{<msup><mrow></mrow><mn\; mathvariant="bold">9</mn></msup>}$Be$\mathrm{<msup><mrow></mrow><mo\; mathvariant="bold-italic">+</mo></msup>}$ ground-state hyperfine constant

We report an experimental determination of the diamagnetic correction to the ${}^9$Be${}^{+}$ ground state hyperfine constant $A$. We measured $A$ = $-625008837.371(11)$ Hz at a magnetic field $B$ of 4.4609 T. Comparison with previous results, obtained at lower values of $B$ (0.68 T and 0.82 T), yields the diamagnetic shift coefficient $k$ = $2.63(18)\times {10}^{-11}$ T${}^{-2}$, where $A(B)=A_0\times (1+k{B}^2)$. The zero-field hyperfine constant $A_0$ is determined to be $-625008837.044(12)$ Hz. The $g$-factor ratio ${g_I}^{\mathrm{\prime }}\mathrm{/}{g}_J$ is determined to be $2.1347798527(10)\times {10}^{-4}$, which is equal to the value measured at lower $B$ to within experimental error. Upper limits are placed on some other corrections to the Breit-Rabi formula. The measured value of $k$ agrees with theoretical estimates.