Precision measurement of the $^{43}$Ca$^{+}$ nuclear magnetic moment

We report precision measurements of the nuclear magnetic moment of \textsuperscript{43}Ca\textsuperscript{+}, made by microwave spectroscopy of the 4s $^2$S$_{1/2}$ $\left|F=4, M=0\right\rangle \rightarrow \left|F=3, M=1\right\rangle$ ground level hyperfine clock transition at a magnetic field of $\approx$ 146 G, using a single laser-cooled ion in a Paul trap. We measure a clock transition frequency of $f = 3199941076.920 \pm 0.046$ Hz, from which we determine $\mu_I / \mu_{\rm{N}} = -1.315350(9)(1)$, where the uncertainty (9) arises from uncertainty in the hyperfine $A$ constant, and the (1) arises from the uncertainty in our measurement. This measurement is not corrected for diamagnetic shielding due to the bound electrons. We make a second measurement which is less precise but agrees with the first. We use our $\mu_I$ value, in combination with previous NMR results, to extract the change in shielding constant of calcium ions due to solvation in D$_2$O: $\Delta \sigma = -0.00022(1)$.