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Recently, upper bounds on the static time-reversal ($\mathcal{T}$) andspatial parity ($\mathcal{P}$)-violating electron electric dipole moment($e$EDM) and dimensionless constant characterizing the strength of the$\mathcal{T}$,$\mathcal{P}$-violating scalar-pseudoscalar nucleus-electroninteraction have been updated in the JILA experiment using the HfF$^+$ cations[T.S. Roussy et al, arxiv:2212.11841 (2022)]. We considered other two sourcesof the $\mathcal{T}$,$\mathcal{P}$,-violation in HfF$^+$ --axionlike-particle-mediated (ALP) scalar-pseudoscalar electron-electron andnucleus-electron interactions. To estimate the magnitude of effects, induced bysuch interactions in HfF$^+$ we have developed and applied a method whichimplies direct use of the ab-initio relativistic coupled cluster theory tocalculate molecular parameters that characterize the interactions. Using theseparameters, we showed that an order of magnitude updated laboratory constraintson the ALP-mediated electron-electron and nucleus-electron interactions can bederived from the experimental data on $\mathcal{T}$,$\mathcal{P}$-violatingeffects in HfF$^+$ for a wide range of ALP masses.

Updated constraints on $\mathcal{T}$,$\mathcal{P}$-violating  axionlike-particle-mediated electron-electron and electron-nucleus  interactions from HfF$^+$ experiment