  The process $e^+ e^- \to \phi \Lambda \bar{\Lambda}$ is studied using data
samples collected with the BESIII detector at the BEPCII collider at
center-of-mass energies $\sqrt{s}$ ranging from $3.51$ to $4.60~{\rm GeV}$ . An
intermediate resonance structure is observed near the threshold of $\Lambda
\bar{\Lambda}$. It has a mass of $(2262 \pm 4 \pm 28)~{\rm{MeV}}/c^{2}$ and a
width of $(72 \pm 5 \pm 43)~\rm{MeV}$, where the quoted uncertainties are
statistical and systematic, respectively. The $J^{PC}$ quantum numbers of
$0^{-+}$ and $0^{++}$ are rejected, while other $J^{PC}$ hypotheses are
possible, according to the helicity angle study. The energy-dependent cross
section of the $e^+ e^- \to \phi \Lambda \bar{\Lambda}$ process is measured for
the first time in this energy region, and contributions from excited $\psi$
states and vector charmonium-like $Y$-states are investigated.
