Path of the Lumberjack

The barbarians who grow up in the forests learn to live in harmony with the forest.

Will of the Wild

When you choose this path at 3rd level, you retain a sense of self while you rage. You gain a bonus to your Charisma saving throws equal to your rage bonus as long as you are raging. 

Axe Adept

Also at 3rd level, you master the use of the axe. When you roll a 1 or 2 on a damage die for an attack you make with an axe, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2.

Additionally, when you use an axe to damage a plant creature, you roll another of the weapon's damage die and add it to your damage.

Woodsman's Quarry

Beginning at 6th level, you retain a sense of purpose while raging. When you rage, you cast the hunter's mark spell at its lowest level without using a spell slot and you can maintain concentration on it while raging. The spell ends when your rage ends or when you lose concentration on it as normal. 

Axe Mastery

At 10th level, you learn to throw even the largest of axes as an attack. An axe weapon wielded by you gains the thrown property with a range equal to five times your Strength modifier.

Additionally, while you are raging, you can use a bonus action to cause any weapon you've thrown that turn to return to your hand.

Roots and Vines

At 14th level, the power of the forest emanates from you. When you enter a rage, you cause the ground around you to magically writhe with roots and vines to a radius of 10 feet. This area is difficult terrain for everyone except you, and moves as you move.

Additionally, when a hostile creature enters this area you can use your reaction to cause the creature to make a Dexterity saving throw with a DC equal to 8 + your proficiency bonus + your Constitution modifier. On a failed save, the creature loses all its remaining movement and takes piercing damage equal to your Barbarian level.