Second-Scale <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msup><mml:mi/><mml:mn>9</mml:mn></mml:msup></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>Be</mml:mi></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math> Spin Coherence in a Compact Penning Trap

We report microwave spectroscopy of co-trapped ${}^{9}$$\mathrm{Be}$${}^{+}$ and ${}^{40}$$\mathrm{Ca}$${}^{+}$ ions within a compact permanent-magnet-based Penning ion trap. The trap is constructed with a reconfigurable array of $\mathrm{Nd}$-$\mathrm{Fe}$-$\mathrm{B}$ rings providing a 0.654-T magnetic field that is near the 0.6774-T magnetic-field-insensitive hyperfine transition in ${}^{9}$$\mathrm{Be}$${}^{+}$. Performing Ramsey spectroscopy on this hyperfine transition, we demonstrate nuclear spin coherence with a contrast decay time of &gt;1 s. The ${}^{9}$$\mathrm{Be}$${}^{+}$ is sympathetically cooled by a Coulomb crystal of ${}^{40}$$\mathrm{Ca}$${}^{+}$, which minimizes ${}^{9}$$\mathrm{Be}$${}^{+}$ illumination and thus mitigates reactive loss. Introducing a unique high-magnetic-field optical-detection scheme for ${}^{40}$$\mathrm{Ca}$${}^{+}$, we perform spin-state readout without a 729-nm shelving laser. We record a fractional trap magnetic field instability below 20 ppb (13 nT) at 43 s of averaging time with no magnetic shielding and only passive thermal isolation. We discuss potential applications of this compact reconfigurable Penning trap.