Hadith: The wife of Thābit ibn Qays was separated from her husband by a Khul‘ during the time of the Prophet (may Allah's peace and blessings be upon him). So the Prophet (may Allah's peace and blessings be upon him) ordered her to observe a waiting period of one menstrual cycle

عن ابن عباس رضي الله عنهما «أن امرأة ثابت بن قيس اخْتَلَعَت من زوجها على عهد النبي صلى الله عليه وسلم فأمرها النبي صلى الله عليه وسلم أن تَعْتَدَّ بحَيْضَة».
[صحيح] - [رواه أبو داود والترمذي]

Ibn ‘Abbās (may Allah be pleased with him) reported: The wife of Thābit ibn Qays was separated from her husband by a Khul‘ during the time of the Prophet (may Allah's peace and blessings be upon him). So the Prophet (may Allah's peace and blessings be upon him) ordered her to observe a waiting period of one menstrual cycle.
[Authentic hadith] - [Narrated by At-Termedhy - Narrated by Abu Daoud]

Explanation

This Hadīth relates to the story of the separation through a Khul‘ that occurred between Thābit ibn Qays (may Allah be pleased with him) and his wife. This narration indicates that after Thābit had divorced his wife, the Prophet (may Allah's peace and blessings be upon him) ordered the woman to observe a waiting period of one, rather than three, menstrual cycles. The rationale of this judgment is that a divorced woman is given a longer waiting time (three menstrual cycles); perhaps the husband might regret the divorce and restore his wife. So there is a chance for him to get his wife back during this long duration. On the contrary, in the case of a Khul‘, the separation is by mutual consent, and it is irrevocable. So one menstrual cycle is enough to make sure that the woman is not pregnant. This Hadīth, for many scholars, indicates that the Khul‘ represents a dissolution of marriage rather than a divorce, for the divorce entails a waiting period of three menstrual cycles.