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Spherical harmonics are related to ORBITAL angular momentum, and not to the SPIN angular momentum.
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Spin spherical harmonics are related to TOTAL angular momentum. They are eigenfunctions of J, J
z and L, defined as sums of products of orbital and spin wavefunctions:
Ψ
jℓm(θ,φ) = ∑ (ℓ m ½ μ | ℓ ½ j m) Y
ℓm(θ,φ) χ
μ
where ( ... | ) are Clebsch-Gordan coefficients and χ
μ, μ = ±½ are spin states.