In recent years, DRAM-based main memories have become susceptible to the Row Hammer (RH) problem, which causes bits to flip in a row without accessing them directly. Frequent activation of a row, called an aggressor row, causes its adjacent rows' (victim) bits to flip. The state-of-The-Art solution is to refresh the victim rows explicitly to prevent bit flipping. There have been several proposals made to detect RH attacks. These include both probabilistic as well as deterministic counter-based methods. The technique of handling RH attacks, however, remains the same. In this work, we propose an efficient technique for handling the RH problem. We show that the mechanism is agnostic of the detection mechanism. Our RH handling technique omits the necessity of refreshing the victim rows. Instead, we use a small non-volatile Spin-Transfer Torque Magnetic Random Access Memory (STTRAM) that ensures no unnecessary refreshes of the victim rows on the DRAM device and thus allowing more time for normal applications in the same DRAM device. Our model relies on the migration of the aggressor rows. This accounts for removing blocking of the DRAM operations due to the refreshing of victim rows incurred in the previous solution. After extensive evaluation, we found that, compared to the conventional RH mitigation techniques, our model minimizes the blocking time of the memory that is imposed due to explicit refreshing by an average of 80.72% in the worst-case scenario and provides energy savings of about 15.82% on average, across different types of RH-based workloads. A lookup table is necessary to pinpoint the location of a particular row, which, when combined with the STTMRAM, limits the storage overhead to 0.39% of a 2 GB DRAM. Our proposed model prevents repeated refreshing of the same victim rows in different refreshing windows on the DRAM device and leads to an efficient RH handling technique. © 2021 ACM.