  We employ the eigen microstate approach to explore the self-organized
criticality (SOC) in two celebrated sandpile models, namely, the BTW model and
the Manna model. In both models, phase transitions from the absorbing-state to
the critical state can be understood by the emergence of dominant eigen
microstates with significantly increased weights. Spatial eigen microstates of
avalanches can be uniformly characterized by a linear system size rescaling.
The first temporal eigen microstates reveal scaling relations in both models.
Furthermore, by finite-size scaling analysis of the first eigen microstate, we
numerically estimate critical exponents i.e., $\sqrt{\sigma_0
w_1}/\tilde{v}_{1} \propto L^D$ and $\tilde{v}_{1} \propto L^{D(1-\tau_s)/2}$.
Our findings could provide profound insights into eigen states of the
universality and phase transition in non-equilibrium complex systems governed
by self-organized criticality.
