The relatively soft layer of the upper mantle is called the asthenosphere
Its asthenosphere!
The partially molten layer of the mantle is called the asthenosphere. This zone is partially molten and allows tectonic plates to move on top of it.
The layer of the Earth that contains both the crust and upper mantle is called the Lithosphere.
The mantle or perhaps you are referring to the asthenosphere, the upper layer of the earth's mantle, below the lithosphere, in which there is relatively low resistance to plastic flow and convection is thought to occur.
lithosphere
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upper mantle
The uppermost layer of the mantle is called the lithosphere. It is a rigid outer layer that includes the crust and a small part of the upper mantle. The lithosphere is divided into tectonic plates that float on the semi-fluid asthenosphere below.
Together the crust and upper mantle make the lithosphere.
The lithosphere is also called the Earth's crust. It includes the outermost layer of the Earth, consisting of the crust and the upper part of the mantle. This layer is solid and relatively rigid compared to the underlying layers of the Earth.
The plates are part of the crust, the upper layer of the Earth. The plates are moved by currents in the upper mantle. The plates and flexible upper mantle are referred to collectively as the lithosphere and sit atop the mantle layer called the aesthenosphere.