Fallen Angel

A Fallen Angel (堕天使) is a concept that is typically synonymous with a wicked or rebellious angel. In the world of Toaru Majutsu no Index, all fallen angels are automatically referred to as a Demon (悪魔).

Principles
Vento of the Front explains that Angels in the magic side have no free will of their own and that they are meant to be God's perfect tools, and are often referred as messengers of God to humanity. However, when an angel malfunctions, they become a Fallen Angel. Tsuchimikado Motoharu explains that angels are like remote-controlled cars of God. If one of the cars couldn't receive the commands because of some failure, or if the command received was wrong, this is when they become demons, known as Fallen Angels.

Lucifer
Perhaps the most famous example of a fallen angel, according to Vento of the Front, is the machine known as Lucifer was dragged into malfunction, causing chaos to one-third of all angels deployed in heaven, which resulted into war. He was later defeated by Archangel Michael.

Grigori
The Grigori (グリゴリ) are a group of fallen angels, led by Satanail. They are referred to in Toaru Majutsu no Index as the ones who gave knowledge to humans on how God created Man from clay before the time of Noah. However, Man couldn't understand the Holy language, and the Fallen Angels could not pass their words to them correctly. With this, the life created by Man can only be puppets of mud. Thus, Man gave birth to the golem.