Structure determination of monolayer-by-monolayer grown ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ thin films and the onset of magnetoresistance

Surface x-ray diffraction was used to determine the atomic structures of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ thin films, grown monolayer by monolayer on ${\mathrm{SrTiO}}_3$ by pulsed laser deposition. Structures for one-, two-, three-, four-, six-, and nine-monolayer-thick films were solved using the Coherent Bragg rod analysis phase-retrieval method and subsequent structural refinement. Four important results were found. First, the out-of-plane lattice constant is elongated across the substrate-film interface. Second, the transition from substrate to film is not abrupt, but proceeds gradually over approximately three unit cells. Third, Sr segregates towards the topmost monolayer of the film: we determined a Sr-segregation enthalpy of $-15\mathrm{kJ}∕\mathrm{mol}$ from the occupation parameters. Finally, the electronic bandwidth $W$ was used to explain the onset of magnetoresistance for films of nine or more monolayers thickness. Resistivity measurements of the nine monolayer-thick film confirm magnetoresistance and the presence of a dead layer with mostly insulating properties.

Figure 1

(Color online) COBRA results for LSMO 4. (a) The electron density (ED) map obtained by the COBRA phasing method, showing the plane along $z$ containing the La, Sr, and $\mathrm{O}2$ atoms. (b) The cumulative displacement $\mathrm{\Delta }z$ of the atoms from the reference frame of bulk STO (top), the distances $d$ between neighboring atoms of the same element across the substrate-film interface (middle), and the integrated electron densities of the Gaussian-like features in the ED maps (bottom). Uncertainties in $\mathrm{\Delta }z$ and $d$ are estimated to be $\pm 0.03\mathrm{\AA }$, while the electron densities are accurate to $\pm 5\%$.

Figure 2

(Color online) Top: Resistivity curves of LSMO 9 without magnetic field (solid black) and at $B=5\mathrm{T}$ (dashed red). Bottom: Magnetoresistance ratio $\mathrm{\Delta }R∕R_B=(R_B-R_0)∕R_B$. The dashed line is a guide to the eye and indicates zero magnetoresistance. Only every second error bar is drawn to improve the readability.

Figure 3

(Color online) Sets of SXRD data (black) and calculated intensities (red) for different film thicknesses as labeled. For representation, three rods of the data files were selected: $\left(11l\right)$ top, $\left(22l\right)$ middle, and $\left(32l\right)$ bottom.

Figure 4

(Color online) The cumulative displacements $\mathrm{\Delta }z$ of the atoms from the reference frame of the positions for bulk STO. The zero position in $z$ represents the top ${\mathrm{TiO}}_2$ layer of bulk STO with the nominal interface indicated by the dashed line. Color and symbol code: $\mathrm{Sr}∕\mathrm{La}$=black $•$, $\mathrm{Ti}∕\mathrm{Mn}$=red $◼$, $\mathrm{O}1$=green $◆$, $\mathrm{O}2$=blue $▴$. All film thicknesses show an elongation of the out-of-plane lattice constant at the interface. Results for metallic sites are estimated to be accurate to $\pm 0.03\mathrm{\AA }$, with the caveat that the positions in the topmost ML of the thinnest films (1–3 MLs) are likely to have significantly larger uncertainties, as are the oxygen displacements. Thinner films exhibit a more pronounced increase in the lattice constant than thicker films. The dotted line for LSMO 9 has a slope of $\mathrm{\Delta }z=-0.09z+0.4$ and indicates the LSMO lattice constant for strained bulk above $z\ge 3$ MLs, as detailed in the text.

Figure 5

(Color online) Occupancies across the substrate-film interface (dashed line) for different film thicknesses. The change in stoichiometry takes place over approximately three unit cells. Sr=black $•$, La=red $◼$, Ti=green $◆$, Mn=blue $▴$.

Figure 6

(Color online) Evolution of the stoichiometries for an idealized film of 9-ML thickness. Sr=black $•$, La=red $◼$, Ti=green $◆$, Mn=blue $▴$. The dotted lines are guides to the eye.

Figure 7

Electronic bandwidth according to Eq. (4) for different film thicknesses based on the refined structure data: (a) $W$ as a function of $z$ calculated ML for ML with the size of the circles representing the weight of this particular data point; or (b) averaged and weighted for each film thickness. The dashed lines indicate bulk LSMO.