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

TL;DR

This paper presents a first-principles method to determine the preferred magnetic response direction of conduction electrons in yttrium and rare earth metals, revealing how the easy axis depends on wave-vector and relates to magnetic ordering.

Contribution

It introduces a relativistic first-principles scheme to calculate the static spin susceptibility and easy axis of magnetic response, accounting for wave-vector dependence and Fermi surface features.

Findings

Peak response at specific wave-vector q in yttrium aligns with Fermi surface nesting.

Easy axis for modulated magnetic field response is perpendicular to q.

Uniform magnetic field response easy axis is along the c-axis.

Abstract

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.