Itinerancy-dependent non-collinear spin textures in SrFeO3, CaFeO3, and CaFeO3/SrFeO3 heterostructures probed via resonant x-ray scattering

TL;DR

This study investigates how electron itinerancy influences the formation of complex multi-q spin textures in epitaxial films of SrFeO3 and CaFeO3, revealing metallicity's key role in stabilizing multi-q states.

Contribution

It demonstrates the impact of electron itinerancy on non-collinear spin textures, contrasting metallic SrFeO3 with insulating CaFeO3, and explores their behavior in heterostructures using resonant x-ray scattering.

Findings

SrFeO3 exhibits multi-q spin structures with asymmetric magnetic Bragg peaks.

CaFeO3 shows simple single-q helical order with symmetric peaks.

Electron itinerancy is crucial for stabilizing multi-q spin textures.

Abstract

Non-collinear, multi-q spin textures can give rise to exotic, topologically protected spin structures such as skyrmions, but the reason for their formation over simple single-q structures is not well understood. While lattice frustration and the Dzyaloshinskii-Moriya interaction are known to produce non-collinear spin textures, the role of electron itinerancy in multi-q formation is much less studied. Here we investigated the non-collinear, helical spin structures in epitaxial films of the perovskite oxides SrFeO3 and CaFeO3 using magnetotransport and resonant soft x-ray magnetic diffraction. Metallic SrFeO3 exhibits features in its magnetoresistance that are consistent with its recently proposed multi-q structure. Additionally, the magnetic Bragg peak of SrFeO3 measured at the Fe L edge resonance energy asymmetrically broadens with decreasing temperature in its multi-q state. In contrast, insulating CaFeO3 has a symmetric scattering peak with an intensity 10x weaker than SrFeO3. Enhanced magnetic scattering at O K edge prepeak energies demonstrates the role of a negative charge transfer energy and the resulting oxygen ligand holes in the magnetic ordering of these ferrates. By measuring magnetic diffraction of CaFeO3/SrFeO3 superlattices with thick CaFeO3 layers, we find that the CaFeO3 helical ordering is coherent across 1 unit cell-thick SrFeO3 layers but not 6 unit cell-thick layers. We conclude that insulating CaFeO3 supports only a simple single-q helical structure in contrast to metallic SrFeO3 that hosts multi-q structures. Our results provide important insight into the role of electron itinerancy in the formation of multi-q spin structures.

Full text

.1 Introduction

Non-collinear spin textures provide a platform for the study of magnetic ordering and exchange interactions beyond conventional ferro and antiferromagnets, as well as have potential application in electronic devices and data storage Fert et al. (2017); Hellman et al. (2017). Of particular recent interest are materials that support multi-q non-collinear spin structures, where the spin structure is a superposition of multiple non-collinear orderings, denoted by ordering wavevectors, $q$, along different crystallographic directions, which can lead to topologically non-trivial spin textures, such as skyrmions Rößler et al. (2006); Mühlbauer et al. (2009); Nagaosa and Tokura (2013). Such multi-q states are known to arise from lattice distortions that result in a non-zero Dzyaloshinskii-Moriya (DM) interaction Dzyaloshinsky (1958); Moriya (1960); Bak and Jensen (1980) or from frustration on triangular lattices Okubo et al. (2012); Batista et al. (2016). However, some materials have neither a DM interaction nor a frustrated lattice, yet still exhibit multi-q spin textures. These include elemental Nd Forgan et al. (1989), actinide monopnictides such as USb Rossat-Mignod et al. (1980); Normile et al. (2002), and, as very recently demonstrated, the cubic perovskite SrFeO3 Ishiwata et al. (2018). The underlying source of the multi-q behavior in these materials is unclear but is critical to understand in order to tune the properties of multi-q spin textures. Previous theoretical studies, however, point to a third consideration–electron itinerancy–such that coupling between itinerant and localized electrons leads to multi-q structures over single-q structures Martin and Batista (2008); Ozawa et al. (2016); Hayami and Motome (2014); Hayami et al. (2017, 2014); Kakehashi et al. (2018).

In order to investigate the role of itinerancy in multi-q spin structures, we synthesized epitaxial films of SrFeO3 and CaFeO3 and probed their magnetic structure using magnetotransport and resonant soft x-ray magnetic diffraction. While both materials exhibit incommensurate, non-collinear helical spin structures along $\langle 111\rangle$ (see Fig. 1(a)) Takeda et al. (1972); Adler et al. (2006); Reehuis et al. (2012); Mostovoy (2005); Ishiwata et al. (2011); Chakraverty et al. (2013); Woodward et al. (2000); Kawasaki et al. (1998), SrFeO3 is metallic whereas CaFeO3 is insulating (CaFeO3 exhibits an electronic phase transition ${\sim}$170 K above its Néel temperature) MacChesney et al. (1965); Matsuno et al. (2002). We demonstrate that the SrFeO3 film exhibits the same complex magnetic phase diagram with distinct helical structures as measured in bulk samples, while further finding that transition temperatures between the magnetic phases more closely resembles Co-doped SrFeO3, which we attribute to the moderate tensile strain induced by the substrate. Via resonant soft x-ray magnetic diffraction (RXMD), we show that the magnetic Bragg peaks of CaFeO3 and SrFeO3 exhibit significantly different behavior as a function of temperature. We discuss the SrFeO3 results in context of the recently proposed multi-q structures Ishiwata et al. (2018), and from this we conclude that our results are consistent with insulating CaFeO3 supporting a simple multi-domain, single-q structure. By synthesizing CaFeO3/SrFeO3 superlattices with different SrFeO3 layer thicknesses, we find the CaFeO3 helical structure is coherent through a single unit cell-thick SrFeO3 layer but is not coherent when the SrFeO3 layer is increased to 6 unit cells, even though both compounds support helical magnetic structures albeit with slightly different wavevector magnitudes. This result further suggests that the differences in the helical structures of SrFeO3 and CaFeO3 are more significant than a simple change to the magnitude of a single q wavevector. Our findings point to the importance of carrier itinerancy in multi-q spin structures and provide insight into the effect of heterostructuring dissimilar helical structures.

.2 Film Results

Epitaxial, (001)-oriented SrFeO3 and CaFeO3 films were deposited by oxygen-assisted molecular beam epitaxy at ${\sim}$650 ∘C with an oxygen partial pressure of 8x$10^{-6}$ Torr (base pressure 4x$10^{-10}$ Torr). The as-grown films were subsequently annealed in the deposition chamber by heating to ${\sim}$600 ∘C in oxygen plasma (200 Watts, 1x$10^{-5}$ Torr chamber pressure) and then cooled in oxygen plasma by progressively turning down the heater to zero output power over approximately one hour, followed by continued exposure to the plasma for another hour to ensure complete cooling to room temperature Rogge et al. (2018a, b). Because ferrates are known to lose oxygen over time, prior to all measurements the films were re-annealed in oxygen plasma by the same post-growth process to mitigate oxygen deficiency.

SrFeO3 was deposited on single crystal (La0.18Sr0.82)(Al0.59Ta0.41)O3 (LSAT, +0.5% strain). CaFeO3 was deposited on LaAlO3 (+0.2% strain), as were superlattices of SrFeO3/CaFeO3. X-ray diffraction of the monolithic films is shown in Fig. 1(b). The simulated diffraction intensity of an ideal epitaxial film exhibits good agreement with measured data. Analysis of thickness fringes from x-ray reflectivity measurements shown in Fig. 1(c) indicate that the SrFeO3 film is 14.2 nm thick (37 unit cells) and the CaFeO3 film is 15.8 nm thick (42 pseudocubic unit cells), values that approximately match those obtained from the simulated diffraction data. Electrical transport, measured with Ag paint contacts in the van der Pauw geometry, further confirms the high-quality nature of the films. As seen in Fig. 1(d), CaFeO3 exhibits a metal-insulator transition near 270 K, and both SrFeO3 and CaFeO3 have a 300 K resistivity comparable to bulk samples MacChesney et al. (1965); Matsuno et al. (2002). The electrical transport confirms that CaFeO3 is insulating below its Néel temperature, whereas SrFeO3 is metallic.

The electrical transport and magnetoresistance of SrFeO3 is known to exhibit rich features due to its helical magnetic ordering. Electrical transport, shown in Fig. 2(a), exhibits three anomalies as identified by the derivative of the resistivity with temperature (cooling). The first at 117 K is attributed to the onset of magnetic ordering, and a second and third anomaly occur at 110 K and 83 K, respectively. Additionally, the electrical resistivity exhibits hysteresis with temperature. These anomalies and hysteresis are consistent with previous measurements of bulk SrFeO3, although a resistivity anomaly at the onset of helical ordering was not observed previously Lebon et al. (2004); Ishiwata et al. (2011); Long et al. (2012); Chakraverty et al. (2013). We adopt the previously used nomenclature and label the regions as Phases I, II, and III Ishiwata et al. (2011), as shown in Fig. 2(a). No such anomalies are observed in the CaFeO3 electrical transport SI_ .

Magnetoresistance [MR $=(\rho(\textrm{H})-\rho(\textrm{H=0}))/\rho(\textrm{H=0})$] measurements out to 9 T on SrFeO3 are shown in Fig. 2(b) and further confirm the distinct nature of the three identified magnetic phases. The transition from a negative slope (e.g., between 155 K – 120 K) to a positive slope (e.g., 100 K) is consistent with the onset of helical ordering below 117 K Ishiwata et al. (2011). At lower temperatures, the slope of the MR changes sign as the field increases, and a small degree of hysteresis is observed. This change in slope has been attributed to a transition to a field-induced fan- or cone-like helical state (Phases IV and V) Ishiwata et al. (2011). Interestingly, this inflection point occurs at lower applied fields compared to previous measurements of both bulk and thin film samples of SrFeO3, and instead is more comparable to Co-doped SrFeO3 Long et al. (2012); Chakraverty et al. (2013).

In order to further distinguish Phase I and II, zero field cooling (ZFC) MR measurements were performed. After each measurement, the sample was heated to 150 K and then cooled with no applied field. The data are shown in Fig. 2(c) and reveal that the ZFC MR hysteresis is a strong function of temperature [hysteresis $=(\rho$ZFC(H=0) – $\rho$0T,9T,0T(H=0))/$\rho$ZFC(H=0)]. An onset of hysteresis is not observed until ${\sim}75$ K that then increases with decreasing temperature. The ZFC MR hysteresis reaches a maximum near 40 K and vanishes below 20 K (see Fig. 2(d)). These results are consistent with previous work that attributed the ZFC MR hysteresis to $H$-induced domain rotation, where Phase I exhibits hysteresis but Phase II, notably, does not Ishiwata et al. (2011). The onset of MR hysteresis here at ${\sim}75$ K approximately correlates with the transition from Phase II to Phase I as identified by electrical transport (83 K) in Fig. 2(a). Additionally, the reduction in hysteresis at lower temperatures suggests that the critical field for domain rotation increases with decreasing temperature below 40 K and is consistent with previous measurements that showed a critical field of ${\sim}$15 T at 4.2 K Ishiwata et al. (2011, 2018). Similar MR measurements for CaFeO3 were not possible due to its large resistivity below its Néel temperature (100 K). The main difference between these results and previous work is that the temperature range of Phase II is significantly smaller here (83 - 110 K) compared to bulk SrFeO3 (56 - 110 K) Ishiwata et al. (2011) and previous measurements of a SrFeO3 film (46 - 104 K) Chakraverty et al. (2013). Instead, the Phase II temperature range of our SrFeO3 film is comparable to Co-doped SrFeO3, approximately equivalent to 1% Co-doping (SrFe0.99Co0.01O3) in both bulk and thin-film samples Long et al. (2012); Chakraverty et al. (2013).

To gain further insight, we probed the magnetic ordering by measuring the resonant x-ray scattering at the Fe $L$ edge along $q_{H=K=L}$ for the CaFeO3 and SrFeO3 films. Measurements were performed at the REIXS beamline at the Canadian Light Source. The (001)-oriented samples were mounted on a ${\sim}$55 degree wedge in order to place the (111) planes in a symmetric scattering configuration. The scattered intensity measured as a function of temperature for the CaFeO3 and SrFeO3 films are shown in Figs. 3(a) and (b), respectively. Both films exhibit scattered intensity at values of $q$ slightly suppressed compared to bulk samples: qCaFeO3$\sim 0.459$ Å-1 (${\sim}1.37$ nm helical wavelength) (1% suppressed; bulk: qCaFeO3 = 0.465 Å-1 Woodward et al. (2000); Kawasaki et al. (1998)); qSrFeO3$\sim 0.356$ Å-1 (${\sim}1.76$ nm helical wavelength) (3% suppressed; bulk: qSrFeO3 = 0.367 Å-1 Reehuis et al. (2012)). The suppressed q vector for SrFeO3 is again equivalent to approximately 1% Co-doping Long et al. (2012). As seen in Fig. 3(a), the CaFeO3 peak grows uniformly in intensity with decreasing temperature. Integrating the peak area and plotting as a function of temperature in Fig. 3(c) reveals an onset of magnetic ordering at ${\sim}$100 K, which is slightly suppressed compared to bulk ($T_{N}=120$ K Kanamaru et al. (1970)). Repeating for the SrFeO3 film, we find an onset temperature of ${\sim}$115 K, which correlates with $T_{N3}=117$ K as determined from the electrical transport data, and is similarly suppressed compared to bulk ($T_{N3\textrm{,bulk}}=133$ K Reehuis et al. (2012)).

From the magnetic scattering data, the q vector as a function of temperature was extracted and is plotted in Fig. 3(d). Consistent with previous studies, the SrFeO3 q vector increases in magnitude with decreasing temperature Reehuis et al. (2012); Chakraverty et al. (2013), although here we additionally observe a small decrease below 80 K (Phase II$\rightarrow$I transition). In contrast, CaFeO3 exhibits the opposite behavior, where the q vector decreases with decreasing temperature followed by a small increase at the lowest temperatures. Additionally, the overall change in q for CaFeO3 is approximately 2x smaller than that exhibited by SrFeO3.

Comparing the peak shape evolution with temperature between CaFeO3 and SrFeO3 in Figs. 3(a) and 3(b), respectively, reveals three striking contrasts. First, SrFeO3 exhibits a significantly enhanced scattering intensity compared to CaFeO3. As seen in Fig. 3(c), the scattered intensity for SrFeO3 is over 10x greater than CaFeO3, which is unexpected given the same nominal film thickness, x-ray footprint, and detector settings (because the q vectors are different, the x-ray footprint for CaFeO3 is reduced by ${\sim}$25%, which does not sufficiently explain the 10x reduction in intensity). The second observable difference between SrFeO3 and CaFeO3 is whereas the CaFeO3 peak is initially broad and becomes more narrow with decreasing temperature, SrFeO3 exhibits a narrow peak at the onset of helical ordering that then broadens with decreasing temperature. Converting the FWHM to a correlation length, $\xi=2\pi/$FWHM, and plotting as a function of temperature in Fig. 3(e) demonstrates that the SrFeO3 correlation length is initially 4x greater than CaFeO3 and nearly 2x greater at lower temperatures. We note that the lower bound of the correlation length for an asymmetric Bragg peak of a thin film (e.g., the 111 reflection of a (001)-oriented film) is not limited to the film’s thickness.

The third major contrast between SrFeO3 and CaFeO3 is the significantly different peak shape evolution exhibited by SrFeO3. With decreasing temperature, the peak asymmetrically broadens, where the expansion occurs at higher values of $q$, as highlighted in Fig. 3(f), where a symmetric Gaussian function cannot replicate the peak at 21 K. Such broadening was not observed in previous RXMD measurements of a SrFeO3 film Chakraverty et al. (2013). This broadening ceases below 80 K (see Fig. 3(e)), which correlates with the previously determined Phase II$\rightarrow$I transition in SrFeO3 ($T_{N1}$ = 83 K) extracted from electrical resistivity and ZFC MR measurements. In contrast, the CaFeO3 scattering peak at 21 K is replicated by a symmetric Gaussian curve, as shown in Fig. 3(g).

.3 Film results discussion

The helical spin structures of our SrFeO3 film exhibit features equivalent to approximately 1% Co-doped SrFeO3 Long et al. (2012); Chakraverty et al. (2013), as demonstrated by the narrowing of the Phase II temperature window, a decrease in the magnetic field strength at which the MR slope changes sign, a decrease in the magnitude of the q vector as probed by RXMD, and a decreased Néel temperature. A decrease in the q vector implies that the real-space length of the helix increases or, analogously, the helical angle between neighboring (111) planes, $\phi$, decreases. A previous theoretical study of the helical state in these ferrates found that the helical ordering arises due to the double exchange effect coupled with a negative charge transfer energy, $\Delta$ Mostovoy (2005); Azhar and Mostovoy (2017), where a negative $\Delta$ arises from the high formal oxidation state of Fe4+ in these ferrates Mizokawa et al. (2000); Matsuno et al. (2002); Green et al. (2016); Rogge et al. (2018a). The helical angle tracks a single parameter $\delta=(\epsilon_{F}-\Delta+t_{pp})/(pd\sigma)$, where $\epsilon_{F}$ is the Fermi level position, $t_{pp}$ is the oxygen-oxygen hopping amplitude, and $pd\sigma$ is the $\sigma$ hybridization between $p$ and $d$ orbitals. Thus a decrease in $\phi$ corresponds to a decrease in $\delta$, which can occur for an increased $\Delta$, a decreased $t_{pp}$, and/or an increased $pd\sigma$. While tensile strain would be expected to decrease $pd\sigma$, it would also be expected to increase $\Delta$ and decrease $t_{pp}$, which can account for the reduction in $\delta$ and thus a reduction in q. In other words, we find that tensile strain acts to increase the ferromagnetic contribution to the SrFeO3 spin structure, likely due to an increase in $\Delta$ and/or a decrease in $t_{pp}$.

To demonstrate that a negative $\Delta$ plays an important role in the magnetic ordering in these ferrates, we measured the resonant magnetic scattering of the SrFeO3 film as a function of energy across the O $K$ edge on the Bragg condition ($q_{z}=0.3548$ Å-1) and slightly off the Bragg condition (detector offset by 2 degrees). As seen in Fig. 4, off the Bragg condition the measured intensity has features that resemble an x-ray absorption spectrum of these ferrates, as expected, where the strong prepeak feature between 527.0-529.5 eV arises from the oxygen ligand holes due to the negative charge transfer energy Abbate et al. (1992); Tsuyama et al. (2015); Rogge et al. (2018a). At the Bragg condition, there is a clear enhancement of the intensity within the prepeak region only. Taking the difference between the on and off Bragg conditions isolates the magnetic contribution to the scattered intensity and is shown in the lower panel of Fig. 4. The observation that the magnetic contribution to the scattered intensity occurs only in the prepeak region supports the conclusion that the charge transfer energy, $\Delta$, is indeed negative and that the interaction between the O $2p$ and Fe $3d$ states is very strong. For completeness, the resonant magnetic scattering across the Fe $L$ edge for the SrFeO3 and CaFeO3 films are shown in the Supplemental Material SI_ .

The resonant magnetic diffraction results for SrFeO3 correlate with the magnetic phase transitions identified by electrical transport while highlighting distinct differences compared to CaFeO3. The evolution of the SrFeO3 scattering peak is notably unconventional; while the CaFeO3 correlation length increases slightly upon cooling, as would be expected based on simple thermal considerations, the SrFeO3 correlation length decreases as a result of asymmetric peak expansion, which we attribute to the transition from Phase II to Phase I upon cooling. In contrast, the CaFeO3 scattering peak remains symmetric down to at least 21 K and thus suggests that CaFeO3 does not undergo additional magnetic phase transitions.

Recently, it has been proposed that SrFeO3 supports multi-q magnetic structures Ishiwata et al. (2018) such that the spin structure is a superposition of multiple q vectors along different crystallographic directions. Specifically, Phase II is proposed to be a single-domain quadruple-q structure consisting of proper screw helical ordering with propagation vectors along the four $\langle 111\rangle$ vectors of the cubic unit cell Ishiwata et al. (2018). The lack of hysteresis in the ZFC MR in Phase II is consistent with a single-domain structure. Additionally, the much larger domain size (correlation length) in Phase II SrFeO3 compared to CaFeO3 could arise from a single-domain structure, although we cannot rule out that the CaFeO3 film may be more defective than the SrFeO3 film and thus has a smaller domain size.

The source of the asymmetric change in peak shape and decreased correlation length exhibited by SrFeO3 at lower temperatures is harder to disentangle with these data alone. We discuss two possible scenarios. In the first scenario, a second, symmetric scattering peak forms at slightly higher q values, and grows in intensity with decreasing temperature. Such a scenario would be consistent with Ishiwata et al.’s Ishiwata et al. (2018) proposal of a multi-domain, double-q structure in Phase I, where each domain includes both a proper screw ($q_{1}$) and a vertical cycloid ($q_{2}$) ordering along one of the four $\langle 111\rangle$ directions, where $q_{1}$ and $q_{2}$ are along different $\langle 111\rangle$ directions, and the magnitude of $q_{1}$ is approximately equal to the magnitude of $q_{2}$. In this picture, the two scattering peaks measured along the same [111] direction arise from ordering in different domains: $q_{1}$ of proper screw along [111] of one domain orientation and $q_{2}$ of vertical cycloid along [111] of another domain orientation. An additional physical implication for this scenario is that the coherence length is dramatically underestimated because the two distinct peaks were treated as one broad peak. Ishiwata et al. also demonstrate that the scattering peak splits into 3 individual peaks upon transition to Phase I from Phase II, where the three peaks are given by ($q$, $q$, $q^{\prime}$), ($q$, $q^{\prime}$, $q$), ($q^{\prime}$, $q$, $q$) and $q^{\prime}>q$. In a second possible scenario, the asymmetric peak broadening could be due to this splitting, where the precise peak shape depends on the experimental measurement conditions, in particular how q-space is scanned and the positions of the three peaks.

The main takeaway of both scenarios, however, is that the peak shape evolution of SrFeO3 is not unexpected in context of the recent neutron diffraction measurements and is consistent with a transition from Phase II$\rightarrow$I. Thus our results, particularly the correlation length, highlight how x-ray scattering coupled with thin film effects provides another way to probe multi-q magnetic states beyond neutron diffraction measurements. Moreover, these results reveal that the Phase II$\rightarrow$I transition is not as abrupt as indicated in previous phase diagrams, because this transition has been determined based on electrical transport measurements. Here, electrical transport identifies Phase II within 110–83 K, but as seen by the change in the scattering peak shape (as proxied by the correlation length in Fig. 3(e)), the spin structure of SrFeO3 evolves almost constantly with temperature from 110 to 85 K in Phase II. Thus the single domain Phase II state may be stable only within a very narrow temperature range just below $T_{N2}$ (110 K). This may account for the lack of an observed decrease in total scattered intensity across the SrFeO3 Phase II/I transition (single domain to multi-domain structure) because the still rapidly changing total intensity near 110 K could obscure this effect (see Fig. 3(c)).

These results provide important context for analyzing the CaFeO3 scattering data. While previous studies have identified helical ordering in CaFeO3 Woodward et al. (2000); Kawasaki et al. (1998), it is unknown if CaFeO3 supports multi-q spin structures, which one may expect given its similarity to SrFeO3. However, the data here demonstrate distinct differences between SrFeO3 and CaFeO3. The CaFeO3 peak grows uniformly with decreasing temperature whereas the SrFeO3 peak asymmetrically grows and exhibits larger changes in q. Additionally, the CaFeO3 peak at low temperatures is symmetric, as seen in Fig. 3(g), suggesting that it does not replicate the presumed double-q ordering seen in SrFeO3 at low temperatures. Although we cannot definitively determine the precise details of the spin structure within CaFeO3, these results are consistent with a multi-domain, single-q helical structure, where different domains have helical ordering along one of the four $\langle 111\rangle$ directions. A multi-domain helical state in CaFeO3 is also consistent with the significantly reduced scattering intensity of CaFeO3 compared to SrFeO3–a 4x reduction would be expected given the 4 equivalent $\langle 111\rangle$ directions.

A possible reason for SrFeO3 hosting multi-q spin textures but not CaFeO3 is their different itinerancies. Previous theoretical studies predict that single-q ordering can be destabilized in itinerant systems and instead multi-q structures are preferred Martin and Batista (2008); Hayami and Motome (2014); Hayami et al. (2017, 2014). While a previous experimental study of the helimagnet Y3Co8Sn4 has attributed itinerancy to the source of its multi-q state, it also has a DM interaction and lattice frustration that can result in multi-q structures Takagi et al. (2018). Here, neither lattice frustration nor the DM interaction are present in cubic SrFeO3, thus leaving electron itinerancy as the likely source of multi-q states in SrFeO3. The fact that CaFeO3 is insulating below its Néel temperature further supports the conclusion that it has a simple single-q spin structure. Future magnetic field-dependent neutron diffraction measurements could confirm a single-q structure in CaFeO3. Interestingly, tuning the CaFeO3 metal-insulator transition temperature (e.g., through A-site substitution (Ca1-xSrxFeO3 Takeda et al. (2000)) or modification of the atomic structure (i.e., octahedral rotations Cammarata and Rondinelli (2013))) below its Néel temperature could enable further studies of the role of itinerancy in multi-q helimagnets.

.4 Superlattice results and discussion

In order to probe how these different helical structures interact, we synthesized superlattices of CaFeO3 and SrFeO3. Superlattices consisting of [(CaFeO3)20/(SrFeO3)n] x 3 for $n=$ 1, 4, and 6 unit cells were deposited on LaAlO3(001), as illustrated in Fig. 5(a). Non-resonant, hard X-ray reflectivity measurements, shown in Fig. 5(b), exhibit thickness oscillations and superlattice peaks consistent with the superstructures. The measured and simulated reflectivity for the $n=$ 1, 4, and 6 samples exhibits good agreement, and the corresponding scattering length density for the simulated data, shown in Fig. 5(c), confirms the superlattice structure. The top SrFeO3 layer is obscured in the scattering length density for the $n=1$ and 4 superlattices due to the surface roughness (10 Å and 14 Å, respectively). All three superlattices exhibit electrical transport similar to the monolithic CaFeO3 film SI_ .

The resonant magnetic scattering data obtained from the three superlattices are shown in Fig. 6(a) and reveal three trends. First, as seen in Fig. 6(b), the onset temperature is near 115 K for all three superlattices. This is 15 K higher than that measured for the monolithic CaFeO3 film and is closer to that measured for the SrFeO3 film ($T_{N3}=117$ K). The intensity of the $n=1$ superlattice trends differently with temperature compared to the other two superlattices, decreasing below 75 K and increasing again below 60 K. Second, the q vector of all three superlattices is approximately equal to that of the monolithic CaFeO3 film and the trend of the temperature dependent $q$ vector resembles that of the CaFeO3 film as well.

Third, the correlation length decreases with increasing SrFeO3 thickness, indicating that the SrFeO3 layers disrupt the helical ordering. At the lowest temperatures, we find that the coherence length is 37 nm for the $n=1$ superlattice and decreases to 16 nm for $n=6$. For the $n=1$ superlattice, the film thickness along [111] is 41 nm, and in the simple case in which the magnetic domains are isotropic, this would indicate that the helical ordering is coherent through the entire superlattice such that the magnetic moments in the SrFeO3 layers are ordered coherently with those in the neighboring CaFeO3 layers. For $n=6$, the 16 nm correlation length is comparable to the thickness of the individual CaFeO3 layers (${\sim}13$ nm), indicating that the helical ordering within the CaFeO3 layers does not propagate through the now thicker SrFeO3 layers. Although measuring down to $q=0.35$ Å-1, below the SrFeO3 wavevector, did not show scattered intensity (not shown), the SrFeO3 layers may be too thin to detect magnetic ordering, and thus we cannot ascertain definitively if the SrFeO3 layers of the $n=6$ superlattice are magnetically ordered or not. However, propagation through $n=1$ but not $n=6$ offers further evidence that the helical spin structures of SrFeO3 and CaFeO3 are different. Given that both compounds exhibit helical ordering with comparable wavevectors, it is surprising that only 6 SrFeO3 unit cells disrupts the helical ordering if the spin texture is that of a single q helix. The coherence of the spin structure in the $n=1$ superlattice implies that the multi-q spin texture of SrFeO3 has been converted to a single-q texture due to proximity to CaFeO3 and/or confinement effects.

In summary we have explored the role of electron itinerancy in the formation of non-collinear spin textures by studying the magnetic structures of metallic SrFeO3 and insulating CaFeO3. We confirm that our SrFeO3 film exhibits magnetotransport signatures consistent with its previously determined multi-q magnetic structure, and further demonstrate that its resonant soft x-ray magnetic diffraction behavior with temperature is consistent with a multi-q spin structure. CaFeO3, on the other hand, is found to exhibit significantly different magnetic diffraction characteristics compared to SrFeO3, which we attribute to a single-q spin helix in CaFeO3. Additionally, by synthesizing CaFeO3/SrFeO3 superlattices, we demonstrated that relatively thin layers (6 unit cells) of SrFeO3 is sufficient to disrupt spin coherency through the superlattice, further supporting the conclusion that SrFeO3 and CaFeO3 have different helical magnetic structures. The lack of a Dzyaloshinskii-Moriya interaction and lattice frustration in cubic SrFeO3, and the presence of only a single-q helical ordering in insulating CaFeO3, supports the conclusion that electron itinerancy plays a critical role in the formation of the multi-q spin structures in SrFeO3. Thus, tuning electron itinerancy in other non-collinear spin structures can potentially be a path towards controlling multi-q spin structures and their topologically non-trivial spin structures.

Acknowledgements.

We thank J. A. Borchers and M. R. Fitzsimmons for useful discussions. PCR and SJM were supported by the Army Research Office, grant number W911NF-15-1-0133, and film synthesis at Drexel utilized deposition instrumentation acquired through an Army Research Office DURIP grant (W911NF-14-1-0493). RJG was supported by the Natural Sciences and Engineering Research Council of Canada. Research described in this paper was performed at the Canadian Light Source, which is supported by the Canada Foundation for Innovation, Natural Sciences and Engineering Research Council of Canada, the University of Saskatchewan, the Government of Saskatchewan, Western Economic Diversification Canada, the National Research Council Canada, and the Canadian Institutes of Health Research.