630 – Yaʿlā ibn Umayyah (may Allah be pleased with him) said, “The Messenger of Allah ﷺ performed ṭawāf with his right shoulder exposed (muḍṭabiʿ) while wrapped in a green mantle.” The Five compilers narrated it except al-Nasāʾī, and al-Tirmidhī declared it authentic. (1)

Degree of authenticity
The ḥadīth is ḥasan (sound).
Al-Muntaqā states: It was reported by Aḥmad, Abū Dāwūd, Ibn Mājah, and al-Tirmidhī, who graded it authentic.
Al-Shawkānī said: Al-Tirmidhī judged the ḥadīth of Yaʿlā ibn Umayyah authentic; Abū Dāwūd and al-Mundhirī recorded it without comment, and al-Nawawī also declared it authentic.

Glossary
• muḍṭabiʿan: iḍṭibāʿ is derived from ḍabʿ (with a silent bāʾ), meaning the upper arm or shoulder; with a ḍamma it refers to the hyena. Iḍṭibāʿ is to place the middle of one’s upper garment beneath the right armpit and throw both ends over the left shoulder, thus exposing the right shoulder.
• burd: with ḍamma on the bāʾ and sukūn on the rāʾ. Al-Muʿjam al-Wasīṭ defines a burd as a striped cloak used as a wrap; its plurals are abrād, abrud, and burūd.

Points derived from the ḥadīth
1 – Iḍṭibāʿ is recommended exclusively for the ṭawāf of arrival (ṭawāf al-qudūm); there is no evidence for it in any other form of ṭawāf.