The easy axis of the magnetic response of the conduction electrons of yttrium and rare earths

We describe a scheme for first-principles calculations of the static, paramagnetic, spin susceptibility of metals with relativistic effects such as spin-orbit coupling included. This gives the direction for an applied modulated magnetic field to maximise its response. This easy axis depends on the modulation's wave-vector q. For h.c.p. yttrium we find the peak response at a q= (0,0,0.57)pi/c, coincident with a Fermi surface nesting vector, to have an easy axis perpendicular to q. This is consistent with the {\it helical} anti-ferromagnetic order found in many dilute rare earth-Yalloys. Conversely, the easy axis for the response to a uniform magnetic field lies along the c-axis. The conduction electrons' role in the canting of magnetic moments in Gd-Y alloys and other rare earth materials is mooted.