Elastic Signature of the High-Spin to Low-Spin Transition in Magnesiow\"{u}stite*

It has been reported that the high to low-spin spin transition in ferrous iron in magnesiow\"{u}stite (Mw) under pressure is accompanied by considerable volume reduction and changes in elastic properties. Using an LDA+U method with consistently calculated U, we investigate the elastic signature of this transition. We confirm that there is large contrast in elasticity across this transition. However, this contrast is temperature sensitive. We address the geophysical signature of this phenomenon.