Frustration-driven C4 symmetric order in a naturally-heterostructured superconductor Sr2VO3FeAs

A subtle balance between competing interactions in iron-based superconductors (FeSCs) can be tipped by additional interfacial interactions in a heterostructure, often inducing exotic phases with unprecedented properties. Particularly when the proximity-coupled layer is magnetically active, rich phase diagrams are expected in FeSCs, but this has not been explored yet. Here, using high-accuracy 75As and 51V nuclear magnetic resonance measurements, we investigate an electronic phase that emerges in the FeAs layer below T0 ~ 155 K of Sr2VO3FeAs, a naturally assembled heterostructure of an FeSC and a Mott-insulating vanadium oxide. We find that frustration of the otherwise dominant Fe stripe and V Neel fluctuations via interfacial coupling induces a charge/orbital order in the FeAs layers, without either static magnetism or broken C4 symmetry, while suppressing the Neel antiferromagnetism in the SrVO3 layers. These findings demonstrate that the magnetic proximity coupling stabilizes a hidden order in FeSCs, which may also apply to other strongly correlated heterostructures. Iron-based superconductors exhibit complex couplings between different electronic degrees of freedom, leading to unusual correlated phases. Ok et al. show that Sr2VO3FeAs develops a hidden order state due to frustrated interactions between the magnetic fluctuations of its SrVO3 and SrFeAs layers.

I n strongly correlated electron materials, including cuprates, transition metal oxides (TMOs), and iron-based superconductors (FeSCs), competing interactions of spin, charge, and orbital degrees of freedom lead to complex and rich phase diagrams, extremely sensitive to external perturbations. Especially impressive is the modification of the phase diagram via introducing interfacial interactions, as intensively studied for the heterostructures of high-T c cuprates [1][2][3][4][5] or TMOs 6,7 , showing the enhanced T c or emergent phases that cannot be stabilized in their constituent layer alone. The similar effect has also been found in FeSCs, for example, in FeSe monolayers on top of nonmagnetic SrTiO 3 8- 10 showing drastically enhanced T c , arguably higher than 100 K. Although the underlying mechanism is yet to be confirmed, the interfacial coupling is considered to be critical and may further enhance T c in the superlattice 11 . Of particular interest is when the proximity-coupled layer is strongly correlated and magnetically active. As found in heterostructures of high-T c cuprates and magnetic TMOs [3][4][5] , additional interfacial spin interaction, e.g., in proximity of a Mott insulator, may also induce distinct ground states in FeSCs 12 , which however has not been explored so far. Sr 2 VO 3 FeAs is an unusual naturally assembled superlattice of [SrFeAs] +1 and [SrVO 3 ] −1 layers 13 . Initially Sr 2 VO 3 FeAs was thought to have, because of the V bands, an unusual Fermi surface topology, incompatible with s ± superconductivity scenario driven by spin fluctuation 14 . However, it was soon realized that the V 3d 2 electrons in the SrVO 3 layer are strongly correlated and form a Mott-insulating state [15][16][17] , while the partially filled Fe 3d 6 state in the FeAs layer has considerable itinerancy and superconducts at T c~3 5 K 13,14,18 . These contrasting ground states in Sr 2 VO 3 FeAs make this system prototypical for strongly correlated heterostructures based on FeSCs and TMOs. Sr 2 VO 3 FeAs has the Fermi surface structure similar to that in other FeSCs 15,17 , and thus is expected to show either the stripe antiferromagnetic (AFM) order with the wave vector Q = (π, 0), or the corresponding nematic phase, or enhanced spin fluctuations at low temperature with the same wave vector 19 . There is in fact a second-order transition observed at T 0~1 55 K with a sizable entropy loss of~0.2Rln2 (R is the gas constant) [20][21][22] . With no evidence of a static magnetic order or another apparent symmetry breaking, the hidden nature of this phase transition, similar to the famous hidden order in underdoped cuprates or a heavy fermion system URu 2 Si 2 , remains elusive and controversial [20][21][22][23][24][25][26] , posing a challenge to our understanding of the physics of FeSCs in proximity of a Mott insulator.
Here we report that an emergent electronic phase is developed below T 0 = 155 K in Sr 2 VO 3 FeAs, which is highly distinct in nature from the transitions found in other FeSCs. Using highaccuracy 75 As and 51 V nuclear magnetic resonance (NMR) measurements on single crystals under various field orientations, we unambiguously show that the transition occurs in the FeAs layer, not the SrVO 3 layer, without breaking either time reversal symmetry or the underlying tetragonal lattice symmetry. This implies that the typical stripe AFM and C 2 nematic phases in the FeAs layers as well as the Neel antiferromagnetism in the SrVO 3 layer are significantly suppressed by the interfacial coupling between itinerant iron electrons and localized vanadium spins. We propose that the observed phase is a C 4 -symmetric charge/ orbital order, which to our knowledge has never been observed in iron or vanadium-based materials, triggered by frustration of the otherwise dominant Fe stripe and V Neel fluctuations. Such a strong modification of the ground state is not common in other strongly correlated TMO heterostructures [3][4][5] , which highlights that FeSCs, itinerant systems with complex interplay of spin/ charge/orbital degrees of freedom, have competing ground states related to the Fermi surface instabilities, and thus are extremely sensitive to additional interfacial interactions in heterostructures.

Results
Transport and magnetic properties. Our transport and magnetic measurements on single crystalline Sr 2 VO 3 FeAs shown in Fig. 1b, c confirm that the transition at T 0 is intrinsic. A weak, but discernible, anomaly is observed at T 0~1 55 K in the resistivity (ρ), even more pronounced in its temperature derivative dρ/dT. The magnetic susceptibility χ(T) also shows an anomaly at T 0 . Above T 0 , χ(T) is several times larger than in typical FeSCs and follows the Curie-Weiss law with a Curie-Weiss temperature T CW~− 100 K (see Supplementary Note 2). The effective magnetic moment is consistent with S = 1 expected for the V 3+ ions (Fig. 1a), suggesting that χ(T) is dominated by localized V spins. At T 0~1 55 K, χ(T) for both H || ab and H || c exhibits a small jump, which corresponds to a magnetization of~10 −3 μ B /f.u., three orders of magnitude smaller than typical values of V 3+ ions (~1.8 μ B ) in vanadium oxides 16 and Fe ions (~0.8 μ B ) in FeSCs 27 . Such weak anomalies in ρ(T) and χ(T), in contrast to a strong one in the specific heat [20][21][22] , question the previous conjectures of a long-range ordering of either V or Fe spins [20][21][22][23][24][25][26] , and suggest that this weak ferromagnetic response is only a side effect of the true transition. However, another anomaly at T N~4 5 K in both χ ab (T) and χ c (T) turns out to reflect a long-range ordering of Fe, but still not V spins, as discussed below. Notably, neither transition is consistent with the typical stripe AFM or nematic orders for FeSCs. 75 As and 51 V NMR spectroscopy. To gain further insight into the transition at T 0 on a microscopic level, we measured NMR on 75 As and 51 V nuclei as a function of temperature for field orientations parallel to a (100), c (001), and the (110) directions ( Fig. 2 and the Supplementary Fig. 4). The 51 V probes the V spin order directly and the 75 As is a proxy for the Fe sites, which allows us to probe the two magnetic ions separately. A dramatic change of the 75 As line occurs near T 0~1 55 K as shown in Fig. 2a, consistent with the anomalies in ρ(T) and χ(T). Near 180 K, the 75 As signal starts to lose its intensity rapidly and is not detectable between 150 and 170 K due to the shortening of the spin-spin relaxation time T 2 (ref. 26 ). Strikingly, the signal recovers below~150 K at substantially higher frequencies, in a similar fashion for both field orientations. We emphasize that these behaviors of 75 As NMR have never been observed so far in other FeSCs as clearly shown in Supplementary Fig. 5. This is better shown in terms of the Knight shift 75 K ≡ f À ν 0 ð Þ=ν 0 , where ν 0 ≡ γ n H with the nuclear gyromagnetic ratio γ n (see Fig. 2c). 75 K changes abruptly at T 0~1 55 K without any peak splitting or broadening of the full-width at half-maximum (FWHM) across T 0 . Conversely, the 51 V line barely shifts below T 0 and down to 20 K (Fig. 2b, d), while its FWHM gradually increases below T 0 . The nearly unchanged 51 V NMR line signals that the V spins remain disordered down to low temperatures. This contrasting behavior of the 75 As and 51 V spectra unambiguously proves that the transition at T 0 occurs in the FeAs layer and not in the SrVO 3 layer, contrary to previous claims [20][21][22][23][24][25] .
Having established that the phase transition at T 0 occurs in the FeAs layer, we examined the low-energy Fe spin dynamics, as probed by the 75 As spin-lattice relaxation rate T À1 1 , which reflects local spin fluctuations. As shown in Fig. 3, at T ≳ 240 K, (T 1 T) −1 exhibits a typical Curie-Weiss-like behavior with an anisotropy T À1 1;a =T À1 1;c ≈ 1.5. This is expected for a directionally disordered state with local stripe AFM correlations with Q = (π, 0) and has been observed in many FeSCs 28,29 (see Supplementary Note 6). With lowering temperature, a critical slowdown of the (π, 0) spin fluctuations usually condenses into the C 2 stripe AFM phase. For Sr 2 VO 3 FeAs, however, this critical growth is arrested at T~200 K, showing a broad peak of (T 1 T) −1 with an unusually large   While the 51 V spectrum is nearly temperature independent down to 20 K, the 75 As spectra in both field directions show a sudden shift at T 0~1 55 K. c, d Temperature dependences of the 75 As and 51 V spectra in terms of the Knight shift (K) and the full-width at half-maximum (FWHM), respectively. Below T 0 , a nearly isotropic large jump of the 75 As Knight shift takes place without any magnetic line broadening, contrasting with the 51 V spectra that remain unchanged T À1 1;a =T À1 1;c ≈ 6, and then the fluctuations harden all the way down to T 0 . Across T 0 , (T 1 T) −1 barely changes and then quickly reaches a constant below T 0 , behaving as a paramagnetic metal. This completely unexpected behavior in both 75 K and (T 1 T) −1 confirms that the transition at T 0 in Sr 2 VO 3 FeAs is unlike any transitions observed in FeSCs so far.
Let us now discuss possible orders established below T 0 . First of all, we can eliminate the usual suspects: stripe, double-Q 30-33 , and bicollinear 34 AFM orders, observed in other FeSCs. In the first case Q = (π, 0) and the Fe spins aligned along the a axis (s || a) generate a hyperfine field H hf~1 .5 T along the c axis. This would be visible in the 75 As NMR spectra as a peak splitting of~10 MHz for H || c, which is far larger than the FWHM of our spectra (~0.05 MHz) and easily detectable. Similarly, for s || c, an 75 As peak splitting is expected for H || a. Even for s || b, in which case no transferred H hf and thus no peak splitting are expected, considerable line broadening due to the directional fluctuations of Fe spins should be seen in experiments. Neither splitting nor broadening is observed in our experiments (Fig. 2a). For the double-Q AFM state [30][31][32][33] , a combination of two spin density waves with Q = (π, 0) and (0, π), the magnetization vanishes at one of the two Fe sublattices and is staggered in the other. Thus, the 75 As peak splitting is expected for either H || c (s || a) or H || a (s || c), as discussed in the Supplementary Note 5, which can be ruled out by experiments. The bicollinear AFM order 34 can also be excluded with even more confidence. In this case, the As environment is spin-imbalanced (three neighboring Fe spins are aligned in one direction, and the fourth one in the opposite), and already a plain exchange coupling would generate two inequivalent As sites and thus a measurable splitting for any direction of external fields. Similarly, other AFM orders with more complicated spin structures, such as a plaquette AFM order, are excluded as discussed in the Supplementary Note 5. This conclusion is further supported by the absence of the diverging behavior in (T 1 T) −1 across T 0 (Fig. 3).
Having excluded static magnetic order, we consider now nematic or, as it is occasionally called, vestigial partners of various AFM orders. The only nematic order observed so far in FeSCs is the stripe-nematic order that creates an imbalance in the orbital population between Fe d xz and d yz states (Fig. 4b). This, in turn, induces an imbalance between As p x and p y orbitals and dipolar in-plane anisotropy of the As Knight shift in the twinned crystals, as observed in e.g., LaFeAsO for H || a below the nematic transition temperature 29 . A similar behavior is expected for the nematic partner of the bicollinear order (Fig. 4c), which breaks the C 4 symmetry such that the (110) and (110) directions are not equivalent 35,36 . If the generated imbalance between the corresponding orbital Fe-d xz ± d yz is of the same order as in the stripenematic case, a peak splitting for H || (110) should be detected. And, for the nematic partner of the plaquette magnetic order, two inequivalent sites and thus a sizable splitting are expected for every field direction. Yet, none of these signatures appear in our 75 As spectra for H || a (100), c (001), and (110) directions (Fig. 2a, b and the Supplementary Fig. 4). Furthermore, our single-crystal X-ray diffraction (XRD) (see Supplementary Note 1) as well as the recent ARPES study 17 do not reveal any signature of a C 4 symmetry breaking.
Since the transition at T 0 retains the C 4 symmetry, and in the absence of a long-range magnetic order, this transition must generate a change in the relative occupations of the C 4 orbitals, namely d xy , d z 2 , d x 2 Ày 2 , and d xz ± id yz . Given that at high temperature we see clear indications of strong spin fluctuations, we looked for a spin-driven scenario conserving the C 4 symmetry; a good candidate is the vestigial (nematic) partner of the double-Q AFM order 37 . It can be visualized (Fig. 4d) as a superposition of two charge/orbital density waves with Q = (π, 0) and (0, π), which preserves the C 4 symmetry without unit-cell doubling. This phase has a broken translational symmetry in the Fe-only square lattice, but not in the unit cell doubled to include the As atoms 37 . Formation of the intra-unit-cell charge/orbital density wave affects the Fe-As hybridization and modifies the hyperfine coupling via isotropic Fermi-contact and core-polarization interactions, accounting for the nearly isotropic 75 K Knight shift (Fig. 2). One may note that due to dipole or orbital hyperfine interactions, the Knight shift can split for a field parallel to (110), because half of the As sites have paramagmetic neighbors along (110), and half along (110). However, the difference in the d orbital occupations between nonmagnetic and paramagnetic Fe are expected to be small, likely a few percent (see Supplementary Note 5), in which case the splitting will be below detection, consistent with our experiments.
If we assume a nonmagnetic origin, another plausible candidate could be an orbital-selective Mott transition. In this case, the most correlated Fe orbital state, likely d xy , experiences a Mott-Hubbard transition, becoming essentially gapped, while the other orbitals remain itinerant. The resulting occupation change in the d xy state of all Fe sites (Fig. 4e) uniformly changes the hyperfine field at the As sites, retaining the C 4 symmetry and explaining the nearly isotropic change of 75 K (Fig. 2). Indeed a possibility of such transition has been discussed, but, admittedly, not in undoped pnictides, but in more strongly correlated chalcogenides 38 and (strongly underdoped) KFe 2 As 2 39,40 . We note that as compared to the orbital-selective Mott phase, the former vestigial double-Q phase breaks the additional translational symmetry, which may allow experimental distinction by neutron scattering when bigger crystals become available. T. The error bars reflect the uncertainty in the fitting procedure. At high temperatures, (T 1 T) −1 is well described by a Curie-Weiss (CW) law (solid line). Below~240 K, it deviates from the diverging behavior and drops at lower temperatures, forming a large peak centered at~190 K. At low temperatures below 120 K, (T 1 T) −1 reaches a constant value comparable to that observed at the high temperature limit, implying that the spin fluctuations are completely gapped out. (T 1 T) −1 sharply turns up at~50 K, indicating critical slowing down of spin fluctuations toward a magnetic order. In the inset, T N~4 5 K (green arrow) was identified from the sharp peak observed for H || c. (T 1 T) −1 drops at T c , determined by the resistivity measurements under H || ab (red arrow) and H || c (blue arrow), microscopically probing bulk superconductivity in the magnetically ordered state As mentioned, Sr 2 VO 3 FeAs experiences another transition at T N ≈ 45 K, which can be identified as a spin density wave highly distinct from the typical stripe AFM. Indeed, (T 1 T) −1 climbs sharply below 60 K (( T 0 ) for both H || a and H || c, indicating a critical slow-down of spin fluctuations toward a magnetic ordering at T N~4 5 K. However, T À1 1;a =T À1 1;c remains isotropic, suggesting that the coupling between Fe spins and As is due to hybridization, which can only generate a magnetic moment on As if As environment is spin-imbalanced. This excludes such AFM orders as stripe, Neel, or double-Q, but would be consistent with a longer period AFM order. Also the progressive broadening of 75 As spectrum at low temperatures, as shown in Fig. 2a, c, suggests a long wavelength, and possibly incommensurate, spin density wave. Neutron diffraction 23,24 , which observed magnetic Bragg peaks at Q = (1/8, 1/8, 0) below T N~4 5 K, is consistent with this conclusion, although it was incorrectly attributed to an ordering of V spins in the previous studies 16,[20][21][22][23][24][25] . Upon further temperature lowering, (T 1 T) −1 abruptly drops at T c . This proves that the superconducting gap opens up on the magnetic Fe sites, and emerges on the background of the remaining, but still strong, spin fluctuations with a C 4 symmetry below T N . How spin density wave competes or cooperates with superconductivity remains an important question.

Discussion
We shall now address an essential question: what suppresses the expected stripe order in the FeAs layer and the Neel order in the SrVO 3 layer? The former can be suppressed via the mechanism in which Neel-type spin fluctuations of the localized magnetic moments are coupled to the itinerant electrons' stripe spin fluctuation 12 . The stripe order, with Q = (π, 0) or (0, π), is relatively fragile and can give way to bicollinear, double-Q, and, possibly, plaquette orders, due to AFM fluctuation with additional Q's 12,37,41 . Such magnetic frustration is due to the long-range magnetic interactions, reflecting the itinerancy of Fe electrons. Fluctuation at Q = (π, π), normally weak in FeSCs, can be enhanced through coupling to the Q = (π, π) fluctuations of V spins 12 (Fig. 4a). This destabilizes the C 2 stripe AFM or nematic orders, but encourages the C 4 symmetric vestigial charge/orbital density wave phases 12,37 . Note that in Sr 2 (Mg,Ti) O 3 FeAs and Ca 2 AlO 3 FeAs, isostructural compounds with nonmagnetic oxide layers, the standard stripe ordering is not suppressed 42,43 . Clearly additional Neel V spin fluctuations, frustrated with stripe Fe spin fluctuations via magnetic proximity coupling, are essential to stabilize an unusual hidden phase in Sr 2 VO 3 FeAs.
The coupling between the itinerant Fe electrons and the localized V spins also suppress the Neel order in the SrVO 3 layer. In the SrVO 3 layers, the nearest neighbor superexchange interaction would dominate and generate a stable Neel order. In fact, compared to other V 3+ perovskite oxides, such as LaVO 3 , SrVO 3 FeAs should have stronger exchange coupling, because of the straighter V-O-V bonds. However, the measured Curie-Weiss temperature of T CW~− 100 K in Sr 2 VO 3 FeAs is considerably lower than T CW~− 700 K in LaVO 3 44 . The unexpectedly low T CW comes from an additional ferromagnetic coupling between the V spins via indirect double-exchange-like interaction mediated by the Fe electrons 45 . This frustrates and weakens the V AFM superexchange interaction suppressing the long-range V spin order at low temperatures. Indeed, in our detailed LDA + U calculations, we found that the calculated magnetic interaction is extremely sensitive to the on-site Coulomb energy U and the Hund's coupling J (note that these corrections were only applied to V, and not to Fe orbitals). At U − J = 5 eV, the superexchange interaction, which is inversely proportional to U, is significantly suppressed, while the Fe-mediated one is enhanced, so that the net magnetic interaction becomes weakly ferromagnetic in the planes. For U − J = 4, it changes sign and becomes antiferromagnetic, consistent with a previous report 16 . This demonstrates that the  36 , and the vestigial double-Q phase (only the translational symmetry broken) 37 . e d xy orbital order driven by a possible orbital-selective Mott transition. As opposed to b-d, there is no symmetry breaking at all in this phase compared to the hightemperature phase. In b and c, the symmetry breaks because some bonds are predominantly ferromagnetic (red) and some predominantly antiferromagnetic (blue). In d, green circles indicate completely nonmagnetic Fe sites, while open circles correspond to fluctuation paramagnetic sites. The As sites above (up-triangle) and below (down-triangle) the Fe plane are also shown. Note that only d and e are consistent with the observed C 4 symmetry, as discussed in the main text, and are our favorite candidates for the hidden order below T 0 SrVO 3 lies on the borderline of competing phases due to a delicate balance between the superexchange and the additional indirect interactions. At the same time, coupling between the stripe fluctuations in the Fe plane at Q = (π, 0) and Neel fluctuations in the V plane Q = (π, π) suppresses both orders even further 12 and prevents V spins form ordering. The interfacial Fe-V interaction is again crucial for the Mott-insulating SrVO 3 layers to remain in a nearly paramagnetic ground state. Our findings therefore manifest that the physics of FeSCs can become even richer in the proximity of other correlated systems and also offer an avenue for exploring unusual ground state in the correlated heterostructures.  2 mg) were stacked together. All single crystals were carefully aligned along the c-axis or the ab-plane.

Methods
These measurements further confirm the quality of our single crystals. In heterostructured compounds, antisite mixing, here between Fe and V atoms, is known to be detrimental to maintain their intrinsic properties. The As NMR line width and the superconducting transition width are particularly sensitive to the antisite mixing. In our crystals, we found that the As NMR line width is~30 kHz at 280 K, comparable with typical values of~5-40 kHz found in other single crystalline FeSCs. Also that the V NMR line width of our single crystal is~50 kHz at 280 K, much smaller than~160 kHz, observed in polycrystalline sample 26 . Furthermore we also found that the superconducting transition in our Sr 2 VO 3 FeAs single crystal has a sharper resistive transition with a temperature width of ΔT c~3 K, than found in polycrystalline Sr 2 VO 3 FeAs whose ΔT c is typically larger than 5 K 13 . These observations consistently suggest that the antisite mixing, if any, cannot be sufficient to induce the observed unusual behavior in our Sr 2 VO 3 FeAs single crystal.
Nuclear magnetic resonance. 51 V (nuclear spin I = 7/2) NMR and 75 As (I = 3/2) NMR measurements were carried out at external magnetic fields of 14.983 and 11.982 T, respectively. The sample was rotated using a goniometer for the exact alignment along the external field. The NMR spectra were acquired by a standard spin-echo technique with a typical π/2 pulse length 2-3 μs and the spin-lattice relaxation rate was obtained by a saturation method.
Band structure calculations. Band structure calculations were performed using two standard codes: an all-electron linearized augmented plane wave method implemented in the WIEN2k package 46 , and a pseudopotential VASP code 47 . In both cases the gradient-corrected functional of Perdew, Burke, and Ernzerhof was used, and special care was taken to ensure proper occupancy of V orbitals in the LDA + U calculations. LDA + U calculations are known to occasionally converge to metastable minima with incorrect orbital occupancy. Some calculations in the literature suffer from this problem. We ensured, by a proper selection of the starting configuration, that our calculations converge to the correct occupancy, and verified that by analyzing the calculated density of states for each independent run.