So my question is about whether mail (aka chainmail in pop culture) from 1000 - 1250 was made from iron or steel?
The other answers I got from searching all talk armour from the later periods. I know that Alan William's The Knight and the Blast Furnace takes shows most plate armour from the late middle ages (1350 - 1500) to be made from steel, but he also states the armours pre 1350 in areas other than Milan were made from iron. Are there any other sources that describe the earlier armour pieces?
Both iron and steel were used for mail in the late Medieval and post-Medieval period. Of the Medieval and post-Medieval mail links examined in
Williams, Alan. (1980). The Manufacture of Mail in Medieval Europe: A technical note. Gladius. XV. 105-134. 10.3989/gladius.1980.135.
Edwin Wood, David Edge, Alan Williams 2013, A note on the construction and metallurgy of mail armour exhibited in The Wallace Collection, Acta Militaria Mediaevalia IX: 203-229
Béla Török, Péter Barkóczy, Árpád Kovács, Balázs Major & Zsolt Vágner (2017) Arrowheads and chainmail fragments from the Crusader Al-Marqab Citadel (Syria): First archeometallurgical approach, Materials and Manufacturing Processes, 32:7-8, 916-925, https://doi.org/10.1080/10426914.2016.1269914
Smith, C. (1959). Methods of Making Chain Mail (14th to 18th Centuries): A Metallographic Note. Technology and Culture, 1(1), 60-67. doi:10.2307/3100788
20 were iron, 6 low-carbon steel (carbon content too low for significant hardening), 12 high-carbon steel (some hardened), and 4 copper alloys. Two links date to your period of interest; both were iron. In addition, the studies included 1 Roman link, also iron.
Generally, there appears to be a trend towards more use of steel in mail, but even into the 16th century, iron was common. It's a safe assumption that most mail in the 11th to 13th centuries was wrought iron.