Why is neodymium the most paramagnetic lanthanide?
This is from Shriver and Atkins' Inorganic Chemistry (p.586, 2009 ed) :


  The magnetic moment of many d-metal ions can be calculated by using the spin-only approximation because the strong ligand field quenches the orbital contribution. But, for the lanthanoids, where the spin orbital coupling is strong, the orbital angular momentum contributes to the magnetic moment, and the ions behave like almost free atoms. Therefore, the magnetic moment must be expressed in terms of the total angular momentum quantum number J:
  $$\mu = g_J{\{J(J+1)\}}^{1/2}\mu_B
$$
  where the Landé g-factor is
  $$g_J=1+\frac{S(S+1)-L(L+1)+J(J+1)}{2J(J+1)}
$$
  and $\mu_B$ is the Bohr Magneton.


Being a high school student, the only thing of matter for you is the key point at the top of the page:


  The magnetic moments of lanthanoid compounds arise from both spin and orbital
  contributions.