Precision measurement of ${\mathrm{Mg}}^{+}$ ion $D_1$ and $D_2$ doublet transition frequencies plays a significant part in the study of space-time variation of fundamental physical constant $\alpha$. Here, we report a precision measurement of ${}^{25}\mathrm{Mg}^{+}$ ion $D_1$ and $D_2$ doublet transition frequencies using the decoherence-assisted spectroscopy method with the full use of spontaneous emission signals to improve the detection sensitivity. We obtain the $D_1\text{and}{D}_2$ transition frequencies of ${}^{25}\mathrm{Mg}^{+}$ with uncertainties of 0.12 and 0.24 MHz, respectively, which are one third of that in [A. Ozawa et al., Nat. Commun. 8, 44 (2017)]. Simultaneously, we obtain the experimental and theoretical values of the ${}^{25}\mathrm{Mg}^{+}$ hyperfine structure constants in this work. The differences between the measured magnetic dipole constants $A_{P_{1/2}}=-102.87\left(8\right)$ MHz, $A_{P_{3/2}}=-18.74\left(9\right)$ MHz and the theoretical values $A_{P_{1/2}}=-102.02\left(94\right)$ MHz, $A_{P_{3/2}}=-19.46\left(45\right)$ MHz are within $2\sigma$, while the measured electric quadrupole constant $B_{P_{3/2}}=24.54\left(45\right)$ MHz and the theoretical value of $B_{P_{3/2}}=22.67\left(32\right)$ MHz shows a difference of more than $2\sigma$, indicating that considerations of more physical effects in theoretical calculation, such as the possible capture of electron correlations, is required.

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• Atomic spectra
• Coherent control
• Cooling & trapping
• Fine & hyperfine structure
• Spontaneous emission
• Zeeman effect
• Diode lasers
• Ions
• Trapped ions
• Electric moment
• Magnetic moment
• Polarization
• Hartree-Fock methods