First-principles relativistic theory of the magnetic response of paramagnetic metals: Application to yttrium and scandium

We describe a first-principles theoretical formalism for the magnetic response of paramagnetic metals in which all relativistic effects such as spin-orbit coupling are included. In particular, the easy axis and dependence upon wave vector q of the paramagnetic spin susceptibility x(q) can be calculated. To illustrate we apply the method to two transition metals, yttrium and scandium. In each case we findx(q) to peak at a wave vector q5(0,0,0.57) p/c, coincident with a Fermi surface nesting vector, and to have an easy axis perpendicular to q. Since x(q) plays a key role in determining the interaction between magnetic impurities in these metals, these results are consistent with the helical antiferromagnetic order found in many dilute rare-earth Y alloys. Conversely, the easy axis for the response to a uniform magnetic field, q50, lies along the c axis.