When and under what circumstances did Charlemagne’s empire split?

In the 9th century, Charles’ empire was the most powerful in western Europe. We can say that it then reached its peak. However, after the death of Charlemagne, the situation began to change. Soon, the empire was divided into three parts between the heirs. This happened as a result of the signing of the Treaty of Verdun in 843. True, this also became the reason for the beginning of feudal wars, which led to even greater fragmentation.