Search for $8.4$-keV solar axions emitted in the $M1$ transition in $^{169}$Tm nuclei

Axions with an energy of $8.4$ keV emitted in the $M1$ transition in $^{169}$Tm nuclei in the Sun are sought in the $A +{^{169}\mathrm{Tm}} \rightarrow {^{169}\mathrm{Tm}^*} \rightarrow {^{169}\mathrm{Tm}} + (\gamma, e)$ ($8.4$ keV) reaction of resonant absorption by $^{169}$Tm nuclei on the Earth using a $\mathrm{Tm}_3\mathrm{Al}_5\mathrm{O}_{12}$ thulium garnet crystal as a bolometric detector. The flux of monochromatic $8.4$-keV axions has been calculated. New constraints on the axion-nucleon coupling constants have been obtained and, as a result, new upper bounds on the axion mass $m_A^{\mathrm{KSVZ}} \leq 141$ eV and $m_A^{\mathrm{DFSZ}} \leq \rm{244}$ eV have been obtained at $90\%$ C.L. in the KSVZ and DFSZ models, respectively.