Described systems, apparatuses, and methods relate to volatile memories that are refreshed to maintain data integrity, such as dynamic random-access memory (DRAM) and synchronous DRAM (SDRAM). A memory device includes multiple dies, with each die having a memory array to be refreshed. The multiple dies may be interconnected via at least one inter-die bus of the memory device. A memory controller sends a command to the memory device to enter a self-refresh mode. In response, a die of the multiple dies can enter the self-refresh mode and initiate or otherwise coordinate refresh operations of the other dies. To do so, the die may transmit at least one refresh-related command to at least one other die using the inter-die bus. Multiple different signaling schemes and timing approaches are disclosed. The described inter-die refresh control principles may be implemented in energy-efficient applications, such as in low-power double data rate (LPDDR) SDRAM.