  We show that, when connected with monopoles, the flat $D$-flat direction
breaking the local $U(1)_{B-L}$ symmetry as an extension of the minimal
supersymmetric standard model can be responsible for the signal of a stochastic
gravitational wave background recently reported by NANOGrav collaborations,
while naturally satisfying constraints at high frequency band. Thanks to the
flatness of the direction, a phase of thermal inflation arises naturally. The
reheating temperature is quite low, and suppresses signals at frequencies
higher than the characteristic frequency set by the reheating temperature.
Notably, forthcoming spaced-based experiments such as LISA can probe the cutoff
frequency, providing an indirect clue of the scale of soft SUSY-breaking mass
parameter.
