A biomagnetic recording was a type of data pattern used by the Federation in Project Atlas. Transmutation beams converted matter into biomagnetic recordings, which were stored in crystals or tapes.
In 2267, after testing the technology on a schnauzer, the Federation converted the endangered population of Styra into biomagnetic recordings, which were stored in a handheld sphere. The USS Enterprise was assigned to transport the recordings to a new location, but they were stolen by Allura, who delivered it to her mad brother Anzar, who sought to ransom them. Anzar was captured and the recordings were recovered when Spock used Atlas technology to deploy Captain James T. Kirk and a security team into Anzar's base, allowing them to capture him. (TOS comic: "The Hijacked Planet")