Spin structure and first-order transition ofGdIn3: Near-surface magnetism, buried amplitude-modulated phase, and interface delocalization

Abstract

A resonant x-ray magnetic diffraction study was performed for pure and (Cd,Ga)-doped $\mathrm{Gd}{\mathrm{In}}_{3}$ single crystals with cubic structure. All studied samples show an equal-magnitude antiferromagnetic spin structure with propagation vector $\stackrel{P\vec}{\ensuremath{\tau}}=[\frac{1}{2},\frac{1}{2},0]$ at low temperatures, corresponding to a parallel spin propagation along the $\stackrel{P\vec}{c}$ direction (normal to the studied surfaces) and antiparallel propagation along $\stackrel{P\vec}{a}$ and $\stackrel{P\vec}{b}$. A complex magnetic behavior in the submicrometric near-surface region (NSR) was found close to ${T}_{N}^{\mathit{\text{bulk}}}\ensuremath{\sim}44\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. For both pure and substituted samples, a fairly strong signal from the equal-magnitude magnetic phase was found to survive above ${T}_{N}^{\mathit{\text{bulk}}}$ and abruptly disappears at ${T}_{N}^{\mathit{NSR}}\ensuremath{\sim}{T}_{N}^{\mathit{\text{bulk}}}+0.7\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, indicating that the NSR may show a larger ${T}_{N}$ than the bulk for all studied samples. For the pure compound only, satellite peaks consistent with an amplitude-modulated magnetic phase with a wavelength of $380\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ were found between ${T}_{N}^{\mathit{\text{bulk}}}$ and ${T}_{N}^{\mathit{NSR}}$. A successful fit of the scattering profile around several magnetic Bragg positions and photon energies, using a simple phase coexistence model, confirmed that the amplitude-modulated phase develops underneath the most superficial region showing the equal magnitude structure. The evolution of the magnetic scattering profile on cooling indicates that the interface between equal-magnitude and amplitude-modulated phases diverges towards the bulk as $T\ensuremath{\rightarrow}{T}_{N}^{\mathit{\text{bulk}}}$ from above. A detailed analysis of the magnetic scattering, as well as the existence of a single bulk transition within the experimental sensitivity of our specific heat and magnetic susceptibility measurements, in contrast to the rich behavior shown by the near-surface region, indicates that the amplitude-modulated phase is not bulk representative, being actually sandwiched between the bulk paramagnetic and the equal-magnitude phases. Depth-temperature phase diagrams for pure and (Ga,Cd)-doped $\mathrm{Gd}{\mathrm{In}}_{3}$ are drawn on the basis of our results, which are discussed in terms of a three-phase coexistence scenario theoretically proposed for first-order transitions in the NSR.