Because Christ also suffered for sins once, the righteous for the unrighteous, that he might bring you to God; being put to death in the flesh, but made alive in the spirit;
The reference must be to His own divine nature by which He was restored to life after He was crucified. At the point of death, Jesus committed His spirit to God; in that His spirit moved into a new sphere of existence, He was "made alive in the spirit." It seems a reasonable conclusion that the reference is not directly to the Holy Spirit but rather to the divine nature of Christ Himself. This conclusion accords with John 10:17-18 : "I lay down my life, that I may take it again. I have power to lay it down, and I have power to take it again." No mere human can do this; Christ could and did! As a human He was put to death; as the Son of God, He was made alive again by the power of His own divine spirit. In the flesh and in the spirit locate the spheres in which these things occurred. The sphere of death was in the flesh; the sphere in which He was made alive was in the spirit.