This is an idea I've been meaning to write up for awhile. The two Paths of the Barbarian class are cool, and the Totem Barbarian can be a lot of different things... like a really good melee ranger, thanks to some really stylish options. I'm sorry, rangers. Your lives are pain. Anyway, this class is a pretty dark take on barbarians, but "tribes get up to some pretty dark stuff" is a minor trope of D&D, when it isn't doubling down on Noble Savage tropes.
Demonscarred Path (Barbarian)
Among the darkest and most savage tribes of the wilds, demons supplant the gods and spirits of the old faiths. The demons turn these tribes from harmony to conquest, and goad them into violence against their neighbors. In other cases, pushed to desperation by a few seasons of scarce game or the pressures of stronger neighbors, a tribe may seek out the patronage of a demon. In exchange for their service, these demonic patrons grant extraordinary power. Just as the totemic barbarians gain traits of beasts, the demonscarred gain traits from the Abyssal legions. There are also those who simply lived too long in places tainted by the power of the Abyss, and found that the totemic spirits of the earth could no longer bear their presence; such individuals make the best of a difficult situation and often wield their powers against the Abyss.
The DC for abilities granted by this Path that require a saving throw is 8 + your Constitution bonus + your proficiency bonus.
Blood and Souls
Starting at third level when you choose this path, you learn to speak Abyssal, typically in a series of nightmares. Further, when you reduce an enemy to 0 hit points and inflict lethal damage, you gain temporary hit points equal to 1d6 + your target's Constitution modifier. (This ability still functions if your target receives one or more death saving throws before dying.)
Lesser Demonic Aspect
Starting at sixth level, you take on a trait of one of the lower orders of demons, choosing one of the following abilities. At your option, you might gain a minor physical or spiritual trait associated with that type of demon; that trait often appears only while you are raging.
Barlgura. You gain advantage on all Strength (Athletics) checks to initiate or escape a grapple. When an opponent attempts to escape a grapple with you and fails, the opponent takes bludgeoning damage equal to 1d4 + your Strength modifier.
Shadow Demon. While raging, you gain damage resistance to all damage types except radiant, and vulnerability to radiant damage.
Vrock. You gain a stunning screech similar to that used by a vrock. As an action, you force each non-demon creature within 10 feet of you to make a Constitution saving throw; on a failure the creature is stunned until the end of your next turn. Once you use this ability, you may not do so again until you complete a long rest.
Hezrou. You can emit a debilitating stench similar to that of a hezrou. As a reaction when you fall below half of your maximum hit point value, you may force all creatures within 10 feet of you to roll a Constitution saving throw; a creature that fails this saving throw is poisoned until the end of its next turn. Once you use this ability, you may not do so again until you complete a long rest.
Glabrezu. While raging, you manifest a spectral pincer similar to that of a glabrezu. The spectral pincer is attached to your body at your shoulder. Pincer. Melee Weapon Attack (finesse): reach 10 ft.; one target. Hit: 1d6 + ability modifier bludgeoning damage.
Starting at tenth level, you can cast planar binding. When you do so, you cast this spell as if you had spent a 5th-level spell slot. Once you have cast this spell, you may not do so again for one week. Constitution is your spellcasting ability for this spell.
Greater Demonic Aspect
Starting at fourteenth level, you take on a trait of one of the higher orders of demons, choosing one of the following abilities. At your option, you might gain a minor physical or spiritual trait associated with that type of demon, perhaps only when you are raging.
Nalfeshnee. When you initiate a rage, you inspire despair in your enemies. As part of the bonus action you spend to enter a rage, each enemy within 20 feet of you must make a Charisma saving throw. Creatures that are immune to the frightened condition gain advantage on this saving throw. On a failed saving throw, targets suffer a bane effect. This effect ends in one minute and does not require Concentration. Affected creatures may attempt a new saving throw once per round when they deal damage to you. Once a creature makes a successful saving throw against this ability, you cannot affect it with this ability again for 24 hours.
Marilith. While raging, you may choose to grow two additional arms, suffering 10 damage that you may not reduce through any means. You may wield a weapon or shield in these arms, but no character can use more than one shield. As a bonus action, you may make one attack with a weapon wielded in your additional arms.
Goristo. While raging, you may make a charge attack. If you move at least 15 feet straight toward a target and hit the target with a melee weapon or unarmed attack on the same turn, the target takes an additional 2d10 damage. You may additionally force it to make a Strength saving throw; on a failure, the target is pushed twenty feet away along the line of your charge.
Balor. While raging and at or below half your maximum hit point value, you gain the effect of a fire shield spell. You can dismiss this effect as a free action, but if you do so, you do not automatically regain the effect when you are at or below half of your maximum hit point value until you complete a short or long rest.
Mechanically, this is a remix of Berserker, Totem Warrior, and toned-down versions of demonic abilities. Not all demons have something obviously convenient to use, so I had to stretch in a few places.
Blood and Souls, other than being a blatant Moorcock ripoff, is also a toned-down version of the Fiend Patron warlock's first-level ability. I felt that toning it down a bit would avoid stealing the warlock's cool thing, and the barbarian's d12 HD just doesn't need that much help with mitigation.
I'm taking a risk with just about all of the demonic aspect abilities. The shadow demon aspect sounds kind of crazy, but it's actually the one most like something found in one of the existing paths - the Bear Totem, to be precise. PCs receive radiant damage less often than psychic damage, so I gave them vulnerability to sharpen the drawback. The glabrezu and marilith aspects are intended as indirect parallels of Frenzy, without the crushing drawback of exhaustion.
I'm not sure if barbarians will care to use planar binding all that often, but I felt that being able to cast it once a week was tolerably similar to commune with nature as a ritual.