What is the term for the breakdown of organic sediment into inorganic phosphorous?

This might refer to the phosphorus cycle.

Phosphorus cycle is a biogeochemical cycle that observes how phosphorus move through minerals, soil, water, and organisms. Typically, plants absorb phosphorus from the soil. And animals get phosphorus from the eaten plants. When these organisms dies, they decay and the phosphorus returns to the soil and inorganic matter.