The competition between crystalline, liquid, and superfluid states in two-dimensional correlated fermion systems is at the frontier of research on a diverse set of platforms including semiconductor quantum wells, 3He films on surfaces, fermionic atoms in pancake optical traps, and transition metal oxides with quasi-two-dimensional electronic structure. Artificial superlattices (SLs) of d- and f-electron compounds have recently opened up the possibility to prepare dense, strongly interacting electron systems in two dimensions . Tuning the electronic dimensionality through the active layer thickness, and the strength and anisotropy of the interactions through epitaxial strain, affords novel insight into the mechanisms that control the competition between different electronic ground states.
Nickel oxides of composition RNiO3 (with R = rare earth other than La) have been of long-standing interest, because the crystallization of the conduction electrons into a charge-ordered state leads to sharp metal-insulator transitions (MIT). Non-collinear magnetic order of the Ni spins appears at temperatures TN < TMIT . TMIT decreases and TN increases when the single-electron bandwidth is enhanced with increasing size of the R anion, and both transitions coincide for R = Nd, Pr. The compound with the largest anion (R = La) and the largest bandwidth remains metallic and paramagnetic at all temperatures. Recent experiments on nickel-oxide thin films and SLs have demonstrated control of the MIT through dimensionality and epitaxial strain [1,2]. Stimulated in part by these results, theoretical research has begun to reassess the traditional interpretation of the charge-ordered state in terms of disproportionation of the Ni3+ valence state into Ni3+δ and Ni3–δ configurations that are stabilized by Hund's rule interactions. One set of models has invoked an unusual electron-phonon interaction that modulates the covalency of the Ni-O bond. According to another model, the MIT for R = Nd and Pr is caused by spin density density wave formation, with charge order as a secondary order parameter in some (but not all) lattice structures .
Experimental tests of these predictions remain challenging especially for thin films and SLs, where diffraction methods are difficult to apply because of the small scattering signal originating from the atomically thin active layers. Whereas resonant x-ray scattering (RXS) has successfully detected magnetic order in epitaxially strained nickelate SLs and ultrathin films , direct evidence of charge order has not yet been reported in such systems. Prior Raman scattering work on thick films has identified phonon anomalies characteristic of charge ordering, but in fully strained overlayers of ≈10 nm thickness, the signal from these modes is drowned out by the much more intense Raman spectrum of the substrate. Here we show that this background can be greatly reduced in a carefully aligned confocal Raman spectroscopy setup with polarized, visible laser light. We apply this technique to thin films of PrNiO3 (PNO), the compound with the lowest TMIT in the RNiO3 series, and to SLs of PNO and the wide-band-gap insulator PrAlO3 (PAO). Combined with RXS experiments on the same samples, the results indicate that the theoretically predicted  spin density wave phase is realized in PNO-PAO SLs.
Figure 1 shows the Raman spectra of 12 nm thick PNO films on tensile and compressive strain obtained in this way, together with the electrical resistivity and the intensity of the RXS Bragg reflection characteristic of the antiferromagnetic order parameter measured on the same samples as a function of temperature. The film under tensile strain shows a MIT with significant hysteresis in the temperature range 80–130 K, which is indicative of a first-order transition (Fig. 1(a)). The onset of magnetic order determined by RXS coincides approximately with the MIT, as it does in bulk PNO. By contrast, the compressively strained PNO film remains metallic and paramagnetic down to lowest temperatures (Fig. 1(b)).
The Raman spectra displayed in Figs. 1(c),(d) supply complementary information about charge ordering, which modifies the lattice structure and hence the phonon spectrum. At high temperatures, the Raman-active phonons reflect the pseudocubic perovskite structure, with uniform Ni valence. Upon cooling below TMIT, the spectrum of PNO under tensile strain exhibits two additional modes at 375 cm–1 and 425 cm–1 (Fig. 1(c)), consistent with a superstructure of two differently sized NiO6 octahedra, which in the bulk leads to a loss of the b mirror symmetry of Pbnm and to the monoclinic space group P21/n. The association with charge ordering is supported by the absence, at low temperature, of additional phonons in the compressively strained PNO film, which does not exhibit a MIT (Fig. 1(d)). Polarization-resolved data in different light-field configurations (indicated in Figs. 1(c),(d)) as arrows relative to the pseudocubic unit cell of PNO) determine the symmetry of the displacement patterns as Ag and B1g for the modes at 375 cm–1 and 425 cm–1, respectively.
Figure 2(a) shows the integrated intensity of the anomalous mode at 375 cm–1 characteristic of charge ordering obtained in this way. Its temperature dependence exhibits behavior characteristic of the order parameter of a continuous (or weakly first-order) phase transition with critical temperature ≈»80 K. In contrast, the regular phonons in the compressively strained PNO film exhibit standard anharmonic behavior, without anomalies.
The results of our experiments now allow us to compare data generated by two microscopic probes of magnetic and charge order, respectively. The fact that the former persists to ≈120 K upon heating (Fig. 1(a)), while the latter vanishes at ≈80 K (Fig. 2(a)), suggests that the two order parameters are only weakly coupled, and that the sublattice magnetization is the primary order parameter. This is consistent with the theoretically predicted spin density wave phase .
We now turn to the measurements on PNO–PAO superlattices grown under the same strain conditions as the PNO films. In contrast to the film grown under compressive strain, the spatial confinement of the superlattice induces antiferromagnetic order with TN ≈ 100 K, (Fig. 3(b)) in a manner similar to SLs based on LaNiO3,  but already at an active layer thickness of four (rather than two) unit cells. The resistivity upturn upon cooling below TN of the compressively strained PNO–PAO SL is much more subtle than in the PNO films and in the SL under tensile strain, and the SL remains highly conductive even below TN. Combined with the RXS data that demonstrate similar magnetic order parameters in both samples, this suggests that differences in charge order may be responsible for the different transport properties.
The Raman spectra of the SLs provide direct insight into the influence of spatial confinement and strain on charge ordering. Figure 3(c),(d) presents polarized spectra of the PNO-PAO SLs, in a manner parallel to those of the films (Fig. 1(c),(d)).
Whereas only regular modes appear in the spectrum of the SL under compressive strain, anomalous modes closely similar to those in the film under tensile strain (Fig. 1(c)) also appear in the SL under tensile strain at 375 cm–1 in Ag and at 445 cm–1 in B1g configurations, respectively (shaded areas in Fig. 3(c)). The energy of the B1g mode is ≈20 cm–1 higher than the one of the corresponding PNO film, and both Ag and B1g phonons are significantly broader in the SLs (mirroring the broadening of the regular modes), but their overall integrated intensities are similar to those of the film. The onset temperature of the anomalous modes (Fig. 2(b)) coincides with TMIT within the experimental error, once again strengthening the association with charge order. Their absence in the spectra of the SL under compressive strain (Fig. 3d) therefore implies that the amplitude of charge modulation is either absent or much smaller than in the SL under tensile strain.
In summary, we have used two complementary, microscopic probes to elucidate the influence of temperature, epitaxial strain, and spatial confinement on charge and spin order in PrNiO3. The RXS data show that both SLs have identical magnetic ground states, while our Raman scattering data imply that the amplitude of the charge order differs greatly in both systems. This is consistent with the prediction by Balents and coworkers  that the spin density modulation is the primary order parameter, whereas a charge density modulation may or may not accompany the spin density as a secondary order parameter, depending on the specific lattice symmetry.
We have thus identified three different states, only two of which were observed before in bulk RNiO3: an insulating state with robust spin and charge order in films and superlattices under tensile strain, and a metallic state with neither form of order in films under compressive strain. In superlattices under compressive strain, a weakly metallic state with fully developed spin order but no (or very weak) charge order is realized. Further evidence of decoupling of spin and charge order comes from films under tensile strain, where we showed that superheating of magnetic order persists over a much larger temperature range than charge ordering. In contrast, we find no evidence for a charge-ordered "spin liquid'' state with converse combination of both order parameters.
Our data thus directly confirm theoretical predictions for a spin density wave phase with charge order as a secondary order parameter . The mechanism invoked by these predictions, Fermi surface nesting, is enhanced by spatial confinement, in accord with our data on PNO films and PNO–PAO SLs under the same (compressive) strain conditions. Spin density waves have been directly observed and characterized only in few bulk metals, including elemental chromium and its alloys, organic charge-transfer salts, and most recently the iron pnictides. The separate control of magnetic and charge order we have reported here for the nickelates opens up new opportunities for device applications, including designs in which metallic antiferromagnets serve as active elements. In addition, our determination of the energies and symmetries of the vibrational modes characteristic of charge ordering, as well as their dependence on strain and spatial confinement, provides specific input for models of charge ordering and electron-phonon interactions in the nickelates and related transition metal oxides.
Finally, we have demonstrated that confocal Raman spectroscopy with visible laser light is a powerful alternative to ultraviolet Raman spectroscopy for the investigation of lattice vibrations in epitaxially strained thin films and superlattices. We have also shown that the technique is accurate enough to resolve phonon anomalies associated with electronic phase transitions in thin films and heterostructures. We thus foresee manifold applications in the determination of the structural and electronic phase behavior of oxide heterostructures.