just correct something, Long memory models in fact incorporate both stationary and nonstationary process that is , when d=0 or d=1. Depend on the values you estimate.
Again, long memory is not just for long time dependent. In fact, when you have mixed data like mixed unit root and stationary data, long memory will play an important role in it. For example, monthly inflation data,output growth data, daily stock index data exchange rate data. Sometimes, even for most unit root test, it may misspecify the long memory process as unit root process.