The Hypnosis crystal, not to be confused with the hypno crystal, was used in Calling All Domos to help Junko calm down from his excruciatingly painful toothache. It is green coloured and dangles from a string.
To activate the crystal, it needs to be swayed back and forth. This swaying motion causes the victim to be "hypnotized", therefore causing them to fall asleep. The effects of the hypnosis crystal wear off with time.