Direct evidence of ferromagnetism without net magnetization observed by x-ray magnetic circular dichroism

We have performed x-ray magnetic circular dichroism experiments to study the cancellation of spin and orbital magnetic moments in (Sm,Gd)Al₂, a ferromagnet without net magnetization at a certain compensation temperature, Tcomp. We verified the existence of long-range order for both spin and orbital magnetic moments at Tcomp. The spin and orbital magnetic moments of the Sm ion are found always antiparallel coupled and the magnitude of its orbital magnetic moment is always larger than that of spin one, so the cancellation of magnetic moments cannot be achieved by only Sm $4f$ electrons. We show that the addition of spin magnetic moments of Gd ions and conduction electrons, which are ferromagnetically coupled with the spin magnetic moment of Sm ions, cancels out the surplus orbital magnetic moments in Sm ions completely and results in the zero magnetization at Tcomp. All our experimental results can be reproduced well by atomic multiplet calculations.