N.M. Stat. § 77-16-3
When any trespassing shall have been done by any cattle, horses, sheep, goats, hogs or other livestock upon the cultivated or enclosed ground of any other person, when the same is fenced as provided by Section 77-16-1 NMSA 1978, but not otherwise, such person may recover any damage that he may sustain by reason thereof by suit in any court having jurisdiction and a person so damaged is hereby given a lien on all livestock of the same kind and brand, belonging to the owner of such trespassing animal or animals for security of his damages and costs; but in no case shall he have such lien nor shall he be entitled to recover any damages, under any circumstances, for such trespass, unless he has such lands and crops enclosed by a legal fence as provided by the preceding section [77-16-1 NMSA 1978].
NMS § 77-16-3