Ab initiocalculation of the giant magnetostriction in terbium and erbium

The single-ion $4f$ contributions to the components λ₂^α,2, λ^γ,2, and λ₁^α,2 of the giant magnetostriction tensor of Tb and Er are calculated ab initio by a constrained density-functional theory in the local spin-density approximation and the full-potential linear-muffin-tin-orbital method. The data exhibit the expected change in sign when going from Tb with an oblate $4f$ charge density to Er with a prolate $4f$ charge density. The satisfactory agreement with experimental results shows that the giant magnetostriction in Tb and Er is dominated by the single-ion $4f$ contribution.