NICKEL COMPOSITE HYDROXIDE, METHOD FOR PRODUCING NICKEL COMPOSITE HYDROXIDE, POSITIVE ELECTRODE ACTIVE MATERIAL FOR LITHIUM ION SECONDARY BATTERY, METHOD FOR PRODUCING POSITIVE ELECTRODE ACTIVE MATERIAL FOR LITHIUM ION SECONDARY BATTERY, AND LITHIUM ION SECONDARY BATTERY

A nickel composite hydroxide includes nickel, cobalt, manganese, and an element M with an atomic ratio of Ni:Co:Mn:M=1−x1−y1−z1:x1:y1:z1 (wherein M is at least one element selected from a group consisting of a transition metal element other than Ni, Co, Mn, a II group element, and a XIII group element, 0.15≤0.25, 0.15≤y1≤0.25, 0≤z1≤0.1), the nickel composite hydroxide having a cobalt or manganese rich layer from a surface of a particle of the secondary particles toward an inside of the secondary particles and a layered low-density layer between the cobalt or manganese rich layer and a center of the particle of the secondary particles, and a thickness of the cobalt or manganese rich layer and low-density layer is 1% or more and 10% or less to a diameter of the secondary particles.