Storage Class Memory (SCM) is a novel class of memory technologies that promise to revolutionize database architectures. SCM is byte-addressable and exhibits latencies similar to those of DRAM, while being non-volatile. Hence, SCM could replace both main memory and storage, enabling a novel single-level database architecture without the traditional I/O bottleneck. Fail-safe persistent SCM allocation can be considered conditio sine qua non for enabling this novel architecture paradigm for database management systems. In this paper we present PAllocator, a fail-safe persistent SCM allocator whose design emphasizes high concurrency and capacity scalability. Contrary to previous works, PAllocator thoroughly addresses the important challenge of persistent memory fragmentation by implementing an efficient defragmentation algorithm. We show that PAllocator outperforms state-of-the-art persistent allocators by up to one order of magnitude, both in operation throughput and recovery time, and enables up to 2.39x higher operation throughput on a persistent B-Tree.