  We search for stochastic gravitational wave background (SGWB) generated by
domain wall networks in the Data Release-2 of Parkes Pulsar Timing Array and
find that the observed strong common power-law process can be explained by
domain wall networks for the wall tension $\sigma_{\textrm{DW}}\sim
(29-414~\textrm{TeV})^3$ and the wall-decay temperature $T_d\sim
20-257~\textrm{MeV}$ at $68\%$ Credible Level. Interestingly, the same
parameter region can largely alleviate the Hubble tension, if the free
particles generated from domain wall networks further decay into dark
radiation. This coincidence that a domain wall network can simultaneously
account for the nano-Hertz SGWB and Hubble tension is robust, independent of
domain wall parameters and applicable to observations by other pulsar timing
array collaborations in general. On the other hand, assuming that the common
power-law process is not due to domain wall networks, we can put stringent
constraints on the wall tension and decay temperature.
