  A search for radiative decay of $B^0_s$ mesons to orbitally excited $K^+K^-$
states is performed using proton proton collisions recorded by the
\mbox{LHCb}\xspace experiment, corresponding to an integrated luminosity of
9~fb$^{-1}$. The dikaon spectrum in the mass range
$m_{KK}<2400$~{\ensuremath{\,\text{Me\kern -0.1em V\!/}c^2}\xspace} is
dominated by the $\phi(1020)$ resonance that accounts for almost 70$\%$ of the
decay rate. Considering the possible contributions of $f_2{(1270)}$,
$f'_2{(1525)}$ and $f_2{(2010)}$ meson states, the overall tensor contribution
to the amplitude is measured to be \begin{equation}
  {\cal F}_{\{f_2\}}=16.8\pm
0.5\mathrm{~(stat.)}\pm0.7\mathrm{~(syst.)}\%,\nonumber \end{equation} mostly
dominated by the $f'_2(1525)$ state. Several statistically equivalent solutions
are obtained for the detailed resonant structure depending on whether the
smaller amplitudes interfere destructively or constructively with the dominant
amplitude. The preferred solution that corresponds to the lowest values of the
fit fractions along with constructive interference leads to the relative
branching ratio measurement \begin{equation}
  \frac{{\cal B}(B^0_s\to f'_2\gamma)}{{\cal B}(B^0_s\to\phi\gamma)}=
19.4^{+0.9}_{-0.8}\mathrm{~(stat.)}{}^{+1.4}_{-0.5}\mathrm{~(syst.)}\pm0.5\mathrm{~(\cal{B})}\%\nonumber,
\end{equation} where the last uncertainty is due to the ratio of measured
branching fractions to the $K^+K^-$ final state. This result represents the
first observation of the radiative $B^0_s\to f'_2(1525)\gamma$ decay, which is
the second radiative transition observed in the $B^0_s$ sector.
