enclosure, or hedged enclosure
Haia, sometimes rendered as hay, is translated as both 'enclosure' and 'hedged enclosure' in the Phillimore edition. The term is first recorded in Domesday Book
The haia was an enclosure formed by a hedge of trees, designed to trap or corral wild animals, usually deer, during the hunt. A number of Domesday entries refer to the enclosures 'where wild animals were caught' (eg, WOR 18,4), others to enclosures where the animals were kept (HEF 29,11).
Large numbers of enclosures are recorded in Domesday Book, all but one (which may be an error) in circuit 5, the majority of these in Cheshire and Shropshire. In part, this is no doubt another example of the eccentricities of the Domesday commissioners since hunting enclosures certainly existed elsewhere. However, it is noticeable that a high proportion of enclosures are associated with Domesday waste, which was extensive along the Welsh march. It may be that this waste had encouraged the creation of disproportionate numbers of enclosures.
For more detail, see H.C. Darby, Domesday England (1977); and Frank Barlow, William Rufus (new edition, 2000).