The Gemara in Masechet Shabbat (27) records a debate among the Amora’im as to which garments require Sisit on the level of Torah obligation. (Of course, we are dealing specifically with four-cornered garments; garments that do not have four corners do not require Sisit.) Rav Nahman claimed that since the Torah uses the word "Beged" ("garment") in the context of the Misva of Sisit, it refers specifically to the kinds of garment to which the Torah refers elsewhere with the term "Beged." In its discussion of Tum’at Sara’at – the laws of the Sara’at discoloration – the Torah addresses the situation of "Sara’at Ha’beged" – discolorations on a garment. In that context, the Torah specifies "Beged Semer" and "Beged Pishtim," meaning, wool and linen garments. Accordingly, Rav Nahman maintained, the term "Beged" used in the context of Sisit also refers specifically to garments made from wool or linen, and thus only these kinds of garments are included in the Torah obligation of Sisit.
Rava, however, disagreed, and held that all four-cornered garments require Sisit on the level of Torah obligation.
The Shulhan Aruch (Orah Haim 9; listen to audio recording for precise citation) codifies the ruling of Rav Nahman, and rules that one fulfills the Torah obligation of Sisit only by wearing wool or linen garments. Garments made from other materials require Sisit only on the level of Rabbinic enactment. The Rama (Rabbi Moshe Isserles of Cracow, 1525-1572), who wrote the Halachot for the Ashkenazim, cited Rava’s opinion, that all garments require Sisit on the level of Torah obligation, and he writes that this is the final Halacha. Therefore, according to Ashkenazic tradition, one fulfills the Misva of Sisit with any type of four-cornered garment, regardless of whether it’s made from wool, cotton, silk or any other material.
Sepharadim, however, who have accepted the rulings of Maran (author of Shulhan Aruch), should make every effort to wear specifically a woolen Tallit Katan so they can fulfill the Torah obligation of Sisit according to the Shulhan Aruch’s opinion. It is proper to endeavor to fulfill the Misva on the level of Torah law, as opposed to the level of Mi’de’rabbanan (Rabbinic enactment). Sepharadim should therefore make a point of wearing wool Sisit even during the summer months, when woolen Sisit may be less comfortable than cotton or silk Sisit. The Mishna in Pirkeh Abot famously exhorts, "Le’fum Sa’ara Agra" – the reward we receive is proportional to the exertion and discomfort entailed. We should therefore be prepared to endure the mild discomfort of wearing wool Sisit in order to receive immense reward for fulfilling the Torah obligation of Sisit. It should be emphasized that according to some authorities, one fulfills the Misva of Sisit every moment he wears them; certainly, then, it is worthwhile to observe this Misva at the highest level.
If, however, a person suffers considerable discomfort wearing woolen Sisit, due to the heat or because it causes his skin to itch, he may wear cotton or silk Sisit.
It should be noted that despite the fact that, technically speaking, the Misva of Sisit applies only if a person chooses to wear a four-cornered garment, it is proper to make a point of wearing a four-cornered Tallit Katan in order to fulfill the Misva. This Misva is especially easy to fulfill; once a person puts on his Tallit Katan, he fulfills a Misva the entire day without even thinking about it. One should therefore ensure to wear a Tallit Katan the entire day in order to fulfill this special misva.
Summary: Sepharadim should make a point of wearing specifically a woolen Tallit Katan, unless this causes him considerable discomfort, in which case one may wear Sisit from other materials, such as cotton and silk.
