Spherical harmonics are related to ORBITAL angular momentum, and not to the SPIN angular momentum.

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 ClebschGordan coefficients and χ
_{μ}, μ = ±½ are spin states.