How do memory controllers allocate a page?

Question

The memory controller allows the OS to access physical memory.

If the OS needs to read an address, it sends the address to the memory controller and then receives the data. However, I am not sure what happens during a page fault or how the memory controller is invoked.

From what I understand, the following steps are involved in handling a page fault caused by a missing page:

1. The MMU raises an interrupt.
2. The OS begins to handle the interrupt.
3. The OS determines which page needs to be allocated.
4. ??

What happens once the OS decides which page to allocate? Are there specific commands to ask the memory controller to allocate a physical page?

Can someone please explain this process more thoroughly or provide me with some good resources for studying?