Sleipnir

From MangaHelpers:

"The Sixth Dimension Experiment." This experiment, in attempting to open one of the eleven dimensions in our reality, the sixth dimension (Secht), resulted in a catastrophic explosion that killed 110 million people and left 12 countries in ruins. The originator of this experiment, Himeka Yuki, bearing the total responsibility for the failure of this experiment, has been banished from reality for eternity. In response to this event, the world leaders in sciences formed a monitoring agency known as "Zeien" to keep control of all scientists and technology in order to prevent another Sixth Dimension Experiment.

10 years have passed since the incident. Takaomi Yuki, the younger brother of Himeka, notices a change in the "Time Machine Destination" that his sister has given him before her banishment. Suddenly, the device summons a lively girl armored with metals he has never seen. "Takaomi-san! To save Earth, pull out your lance and ride me!" To uncover the truth, the two will begin an adventure that crosses time and space. [DrCoke]