Resonant inelastic x-ray scattering study of bond order and spin excitations in nickelate thin-film structures

We used high-resolution resonant inelastic x-ray scattering (RIXS) at the Ni $L_3$ edge to simultaneously investigate high-energy interband transitions characteristic of Ni-O bond ordering and low-energy collective excitations of the Ni spins in the rare-earth nickelates $R{\mathrm{NiO}}_3$ ($R=\mathrm{Nd}$, Pr, La) with pseudocubic perovskite structure. With the support of calculations based on a double-cluster model we quantify bond order (BO) amplitudes for different thin films and heterostructures and discriminate short-range BO fluctuations from long-range static order. Moreover we investigate magnetic order and exchange interactions in spatially confined $R{\mathrm{NiO}}_3$ slabs by probing dispersive magnon excitations. While our study of superlattices (SLs) grown in the (001) direction of the perovskite structure reveals a robust noncollinear spin spiral magnetic order with dispersive magnon excitations that are essentially unperturbed by BO modulations and spatial confinement, we find magnons with flat dispersions and strongly reduced energies in SLs grown in the ${\left(111\right)}_{\text{pc}}$ direction that exhibit collinear magnetic order. These results give insight into the interplay of different collective ordering phenomena in a prototypical $3d$ transition metal oxide and establish RIXS as a powerful tool to quantitatively study several order parameters and the corresponding collective excitations within one experiment.

Figure 1

Overview of calculated XAS and RIXS spectra within the double-cluster model. Panel (a) gives the theoretical XAS at the Ni $L_3$ edge calculated with (blue) and without (red) bond disproportionation and defines the incident energies: peak A and B. (b) Scattering geometry for the RIXS experiment. (c) and (e): RIXS spectrum with incident photon energy tuned to peak A, as defined in panel (a). (d) and (f): RIXS spectrum with incident energy tuned to peak B. Spectra in panels (c) and (d) [(e) and (f)] were calculated with (without) bond disproportionation. The spectrum for the low-temperature bond-ordered state is the sum of the spectra corresponding to LB (green) and SB (purple) octahedra. The sketches in panels (d) and (f) illustrate the BO below and above the MIT transition. For clarity, the octahedral rotations are omitted.

Figure 2

(a) XAS spectra for all investigated samples. The big symbol indicates the incident energy for the RIXS experiment, i.e. the peak A. For the LNO-LAO SL we subtracted the La $M_4$ line. (b) RIXS spectra for two ${\mathrm{PrNiO}}_3$-based superlattices with different stacking periodicities. The SL with 2/4 stacking is offset for clarity. (c) Double-cluster calculation for the PNO-PAO SLs. (d) RIXS spectra for the ${\mathrm{NdNiO}}_3-{\mathrm{NdGaO}}_3$ SL with the corresponding double-cluster calculation in (e). For both SLs we find a bond disproportionation of $\delta d=0.01\AA$. (f) Experimental and (g) calculated spectra for a ${\mathrm{NdNiO}}_3$ reference thin film. Panels (f) and (g) are reproduced from Ref. [17].

Figure 3

(a) RIXS spectra for a LNO-LAO SL. (b) Calculation without bond disproportionation $\delta d$ and adjusted intercluster mixing $V_{\text{I}}$. (c) Calculation with small bond disproportionation. The spectra calculated with finite $\delta d$ reproduce the experiment much better. $V_{\text{I}}$ is kept the same as in the PNO and NNO-based samples.

Figure 4

Dispersive magnetic excitations in PNO-based heterostructures after removal of elastic contribution and subtraction of high-temperature data, along the lines of Ref. [17]. (a) PNO-PAO ($2\mathrm{u}.\mathrm{c}./2\mathrm{u}$.c.) SL on LSAO. (b) PNO-PAO ($2\mathrm{u}.\mathrm{c}./4\mathrm{u}$.c.) SL on LSAT. (c) NNO-NGO ($3\mathrm{u}.\mathrm{c}./2\mathrm{u}$.c.) SL on NGO ${\left(111\right)}_{\text{pc}}$.

Figure 5

Magnon dispersion of PNO-based superlattices compared to the one from the NNO-NGO ${\left(111\right)}_{\text{pc}}$ superlattice (extracted from Fig. 4). In addition we show the magnon dispersion for a NNO thin film which is taken from Ref. [17].

Figure 6

Linear spin-wave theory for a collinear magnetic structure. The magnetic supercell comprises 8 ML NNO separated by nonmagnetic NGO. Orange lines show the low-energy eigenmodes of the system. The purple diamonds represent the measured data, while the gray box indicates the resolution limit in the RIXS experiment. Gray lines indicate the calculated dispersion of magnons in the spiral state of a bulklike NNO film for Ref. [17].

Figure 7

(a) Azimuthal dependence. (b) Sketch of collinear magnetic order (best fit) and spin spiral. (c) Temperature dependence of magnetic REXS signal.

Figure 8

(a) and (b): PNO-PAO SL with 2/4 stacking grown on LSAT. (a) L scan around the (001) reflection. (b) Reciprocal space map around (103). The SL is partially relaxed. (c) PNO-PAO SL with 2/2 stacking grown on LSAO. L scan around (004). (d) LNO-LAO SL with 2/2 stacking grown on LSAO. L scan around (004).