Multi-function material integrated with nanofibers.
This is Heavenly Maiden's secondary line of defense and offense next to her Chinese Straight Sword . Though it appears to be an ordinary piece of cloth, it is actually a high-tech fabric that is imbued with nanofibres, allowing it to bend and reshape itself. Through some unknown control process, (possibly cybernetic or hidden within her long sleeves), Mikoto is able to make the shawl move and flatten itself to defend against incoming projectile attacks or slash forward with a keen edge to cut like a knife. It can also deflect some energy attacks. Due to the fact that she is the president of a vintage textiles company, it is very likely that the shawl is a product of its fabrication line. In her civilian clothes, the haori takes the form of the ribbon she wears to tie up her hair.
The shawl proves instrumental during her fight with IS-KA as it saves her life by deflecting his lightsaber's blade. This could suggest that it has an automatic function to defend her. It is also used in combination with Mikoto's sword to form her Killer Move.