Magnetic and structural properties of erbium films

The results of x-ray-scattering studies of the magnetic and structural properties of two erbium thin films $(\mathrm{thickness}>~1\mathrm{}\mathrm{\mu }\mathrm{m})$ grown epitaxially on Lu and Y substrates are presented. These substrates, respectively, compress or expand the erbium $a$-axis lattice constants and clamp them at the film-substrate interfaces, thereby introducing epitaxial strain. Detailed measurements of the temperature dependence of the $c$- and $a$-axis lattice constants, magnetic wave vectors, and magnetic order parameters of the films are reported. The qualitative features of the magnetic phase behavior mirror those of the bulk, including the scaling of the order-parameter critical exponents ${\beta }_n$ and the existence of lock-in transitions to bulk commensurate wave vectors. The magnetic phase transitions, however, exhibit marked hysteresis and the magnetic structures are characterized by multiphase coexistence and limited correlation lengths. The low-temperature phase of bulk erbium with magnetic wave vector $5/21$ is suppressed in both films, and is replaced in Er/Lu by two new phases with wave vectors near $6/25$ and $11/45.$ Qualitative $c$-axis strain profiles are deduced from the measurements and confirm that the Er/Y film is more distorted than the Er/Lu.