Space-partitioning indexes are widely used for managing multi-dimensional data, but their throughput is often memory-bottlenecked. Processing-in-memory (PIM), an emerging architectural paradigm, mitigates memory bottlenecks by embedding processing cores directly within memory modules, allowing computation to be offloaded to these PIM cores. In this paper, we present PIM-zd-tree, the first space-partitioning index specifically designed for real-world PIM systems. PIM-zd-tree employs a tunable multi-layer structure, with each layer adopting distinct data layouts, partitioning schemes, and caching strategies. Its design is theoretically grounded to achieve load balance, minimal memory-channel communication, and low space overhead. To bridge theory and practice, we incorporate implementation techniques such as practical chunking and lazy counters. Evaluation on a real-world PIM system shows that PIM-zd-tree’s throughput is up to 4.25$ imes$ and 99$ imes$ higher than two state-of-the-art shared-memory baselines.