Angel's Tear

The Angel's Tear (天使の涙) is a spiritual item introduced in the Toaru Majutsu no Index PSP game said to be able to allow the user to speak to angels if used properly, but falls upon the user if it fails.

Principles
It is a jewel with a story behind it. It's composition resembles that of sapphire and ruby. Wholly, it has a transparent appearance, with the center portion shining gold. It's internal crystal structure is "something different from ruby and sapphire," and is believed have been incorporated into it to gain such a color scheme, but it is currently unknown how and cannot be understood scientifically.

Toaru Majutsu no Index (PSP game)
At the start of Sasha Kreutzev's story in the game, the jewel is held in Academy City for its academic value. Sasha, who suffers from an unexplained angel power that dwells inside her, decides to obtain it and infiltrates Academy City along with Oriana Thomson, hired by the Russian Orthodox Church. However, members of the Anglican Church face-off against them in battle, as they believe "the jewel was to be protected from the magic side".

The jewel has apparently been already analyzed by Academy City, and is able to create an artificial replication of it. According to Kihara Amata regarding its use, the effect is "that through the use of light stimulation the spirit of humans can be turned into something like an eraser to neutralize "monsters" by creating a vessel to hold them." In other words, there was a possibility of artificially creating somebody of the same constitution as Sasha. Kihara Amata tried using Last Order as a vessel, though failed because of Sasha's efforts. However, because the gathering of AIM was not able to fit in the vessel, Fuse Kazakiri descended temporarily.