  PdFe/Ir(111) has attracted tremendous attention for next-generation
spintronics devices due to existence of magnetic skyrmions with the external
magnetic field. Our density functional theoretical calculations in combination
with spin dynamics simulation suggest that the spin spiral phase in fcc stacked
PdFe/Ir(111) flips into the skyrmion lattice phase around B$_{ext} \sim$ 6 T.
This leads to the microscopic understanding of the thermodynamic and kinetic
behaviours affected by the intrinsic spin-lattice couplings (SLCs) in this
skyrmion material for magneto-mechanical properties. Here we calculate fully
relativistic SLC parameters from first principle computations and investigate
the effect of SLC on dynamical magnetic interactions in skyrmion multilayers
PdFe/Ir(111). The exchange interactions arising from next nearest-neighbors
(NN) in this material are highly frustrated and responsible for enhancing
skyrmion stability. We report the larger spin-lattice effect on both dynamical
Heisenberg exchanges and Dzyaloshinskii-Moriya interactions for next NN
compared to NN which is in contrast with recently observed spin-lattice effect
in bulk bcc Fe and CrI$_3$ monolayer. Based on our analysis, we find that the
effective measures of SLCs in fcc (hcp) stacking of PdFe/Ir(111) are $\sim 2.71
( \sim 2.36)$ and $\sim 14.71 ( \sim21.89)$ times stronger for NN and next NN
respectively, compared to bcc Fe. The linear regime of displacement for SLC
parameters is $\leq$ 0.02 {\AA} which is 0.72\% of the lattice constant for
PdFe/Ir(111). The microscopic understanding of SLCs provided by our current
study could help in designing spintronic devices based on thermodynamic
properties of skyrmion multilayers.
