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To be fair to all gardeners worldwide, we must include information for all plants and trees. In reality, ANY plant has the capacity to become invasive, given the proper environment, so it is the sole responsibility as a responsible gardener to ensure that proper research is done before planting any plant in one's area.

For example, if we were to exclude any plants that have the capacity to become invasive in any part of the world, our website would not be able to contain much information.

This would be unfair to much of the world that can grow these trees to leave out the information to do so, when research should always be done before planting in one's area. In fact, planting blacklisted plants can lend to fines and jail time, making it even more important for each gardener to research applicable laws and regulations in the area before planting anything that one is unfamiliar with.

The best thing you can put under a tree is organic mulch such as wood chips. Plants only compete with the tree for nutrients and water. In addition, digging into the soil can damage the tree roots. The feeder roots are usually about 12 inches below the soil.

The downside of rocks as mulch is they can increase the heat around the tree and cause dryness problems. Here is more:

https://www.gardeningknowhow.com/garden-how-to/mulch/benefits-of-using-mulch.htm

https://www.gardeningknowhow.com/garden-how-to/mulch/using-inorganic-mulch-in-gardens.htm

Did you know Carrotwood trees are considered invasive because birds eat the seeds and leave their droppings in other areas where the seeded trees displace native species. Here is more:

https://sites.redlands.edu/trees/species-accounts/carrotwood/