Figure 3: Magnetic critical behaviour of the three strain states and XRD of the oxygen octahedral rotations in the ETO on LSAT.

(a) The temperature dependence of the XRMS Eu L_II amplitudes for all three strain states, STO—unstrained, LSAT—0.9% compressive and DSO—1.1% tensile. The solid lines are fits of the critical behaviour ‹m›²~I=I₀(1−T/T_C)^2β, where ‹m› is the magnetic moment, I is the magnetic scattered intensity, T is the sample temperature, T_C is the magnetic transition temperature and β is the critical order exponent. Both the G-AFM order in the unstrained (STO) and FM order of tensile (DSO) films show typical three-dimensional Heisenberg behaviour while the compressively strained (LSAT) film shows significant suppression, a classic indicator of local magnetic competition. Inset—top, presents a log–log plot showing the near transition region. Inset bottom illustrates the multiple coexisting magnetic interactions between the first, second and third NN Eu ions. (b) The symmetry response of the ETO film to the biaxial compressive tetragonal distortion imposed by the LSAT (001) substrate. Both the (1/2 5/2 1/2)_ETO and (1/2 1/2 5/2)_ETO reflections at 300 K are presented. The occurrence of half-order Bragg peaks show the presence of long-range AFD rotations in the film. The combination of H=L allowed and H=K forbidden reflections indicate I4/mcm symmetry with the oxygen octahedral pattern (a⁰a⁰c⁻) in Glazer notation³², illustrated in the bottom inset. Again the LSAT substrate generates substantial background from the anti-phase boundary half-order reflections. The top inset indicates the relative position of the (002)_ETO reciprocal position with respect to the substrate (002)_LSAT.