I’m pretty sure this varies state-to-state.
“Common law” is the court-made law historically developed in England and exported to most (all?) English colonies. These courts came up with the principle of mitigating certain homicides to manslaughter, including in the case of the murderous husband. It’s possible that the reasoning behind the very first use of the principle may have been something like the ad hoc lowering of the sentence in Yvain’s example. (It’s also possible that some of the early judges may have stated their reasoning differently and in a way that is in conflict with modern values; one thread that runs through some of the early murderous husband authority is that the husband is partially justified in the killing because he is protecting his “property” from “trespass.”) As courts continued to apply the reasoning, this principle became a well-established part of the “common law.”
As both of my comments suggested, there are likely variations in the current state of the law among jurisdictions. This is true even among common law jurisdictions, that is, among other countries with a common law background and among the states with such background (Louisiana has a civil law background). I believe that no states currently rely on the common law for homicide law, but instead all states have enacted statutes defining the various degrees of homicide, that is, defining murder in various degrees, manslaughter (voluntary/involuntary), negligent homicide, etc. (States have taken somewhat different approaches here; per the same book I quoted previously, “reform of the common law has taken three separate paths,” including a version dividing homicide into three offenses, murder, manslaughter, and negligent homicide, which I believe is similar to what jimrandomh was describing. But further discussion of those paths in this comment seems like too much of a detour.)
At any rate, in most states, the definitions in the penal code draw strongly from the original common law definitions as well as from later adaptations of the common law. Therefore, while there is indeed variation from state to state, it is quite likely that some version of this principle still exists in most states. To be sure what the law is in any given state, one would indeed have to look at the individual state’s penal code. But given that this comment is not intended to be legal advice to any potential murderous husbands who may be reading, further discussion seems unnecessary.