Laser cooling and hyperfine measurements of Ra + 225 ions

²²⁵Ra⁺ ions (nuclear spin $I=1/2$) have transitions that are first-order insensitive to magnetic field noise, which is advantageous for optical clocks and quantum information science. We report on laser cooling and trapping of ²²⁵Ra⁺ ions and hyperfine splitting measurements of the ion's 7s ²S1/2, 7p ²P1/2, and 6d ²D3/2 states. We measured the ground state hyperfine constant, A(S1/2) = $-27.684511052(5)$ GHz, and the quadratic Zeeman coefficient, C₂ = $142.3(1.0)$ Hz\ G⁻², of the ²S1/2 (F=0, mF = 0) ↔~²S1/2 (F=1, mF = 0) transition. Our result addresses a discrepancy in the literature for the ground state hyperfine splitting. We measured the hyperfine constants of the ²P1/2 state, A(P1/2) = $-5.447(4)$ GHz, and the ²D3/2 state, A(D3/2) = $-619.7(1.1)$ MHz. We also performed state preparation and measurement using the ground state hyperfine levels and realized a fidelity of $0.9951(9)$.