Abstract
The recently discovered infinitelayer nickelates show great promise in helping to disentangle the various cooperative mechanisms responsible for hightemperature superconductivity. However, lack of antiferromagnetic order in the pristine nickelates presents a challenge for connecting the physics of the cuprates and nickelates. Here, by using a quantum manybody Green’s functionbased approach to treat the electronic and magnetic structures, we unveil the presence of many two and threedimensional magnetic stripe instabilities that are shown to persist across the phase diagram of LaNiO_{2}. Our analysis indicates that the magnetic properties of the infinitelayer nickelates are closer to those of the doped cuprates, which host a stripe ground state, rather than the undoped cuprates. The computed longitudinalspin, transversespin, and charge spectra of LaNiO_{2} are found to contain an admixture of contributions from localized and itinerant carriers. Theoretically obtained dispersion of magnetic excitations (spinflip) is found to be in good accord with the results of recent resonant inelastic Xray scattering experiments. Our study gives insight into the origin of strong magnetic competition in the infinitelayer nickelates and their relationship with the cuprates.
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Introduction
The common thread linking the family of hightemperature superconductors is that competing interactions involving charge, spin, lattice, and orbital degrees of freedom conspire with electronic correlation effects to produce many complex properties in this materials family^{1}. The phase diagrams of transitionmetal oxides, for example, are astonishingly complex and exhibit unconventional superconducting pairing, pseudogap, and glassy phases, and colossal magnetoresistance in stark contrast to the standard metals^{2,3,4,5}. The highT_{c} cuprates have been of intense interest, where a wide variety of experiments have reported the presence of competing and intertwined inhomogeneous orders that could contribute to the pairing mechanism^{6,7,8,9}. However, deconstructing the mechanism of highTc superconductivity and possible contributions involved in the pairing process has remained a challenge. Understanding the electronic and magnetic properties of related materials can provide insight into the mechanism of superconductivity in the cuprates as well as other highTc superconductors.
Recently, superconductivity was discovered in doped infinitelayer nickelates^{10}. The RNiO_{2} (R = Nd,Pr,La) family of compounds is isostructural to the infinitelayer parent cuprate CaCuO_{2}^{11}, where the twodimensional (2D) NiO_{2} planes are separated by rare earth spacer layers^{12,13,14}. Due to the missing apical oxygens in RNiO_{2}, the nickel atoms take a 3d^{9} configuration that is equivalent to Cu^{2+} in the cuprates, thereby strengthening the hypothesis that these two materials’ families are electronically analogous^{15,16}.
A number of experimental techniques have been employed to elucidate possible connections between nickel and copperbased superconductivity and the role of competing orders in their phase diagrams. Transport measurements on the nickelates report key departures from the cuprate phenomenology. Specifically, no Mott or antiferromagnetic (AFM) parent phase is observed, with both the underdoped and overdoped nickelates only displaying a weakly insulating state^{13,14,17,18,19,20,21,22,23,24,25}. The Hall coefficient R_{H} is found to change sign at optimal doping (x ~ 0.17) in all nickelates that have been investigated, signaling the existence and importance of both hole and electron pockets at the Fermi level^{13,14,18,22,23,24,25,26,27}. Xray absorption spectroscopy (XAS) and resonant inelastic Xray scattering (RIXS) experiments find the doped holes to reside on the Ni\({d}_{{x}^{2}{y}^{2}}\) orbitals, with minor 5d electron doping due to Ni3d/La5d hybridization^{18,28,29,30}, suggesting the coexistence of multiple active orbitals at the Fermi level. Despite these differences, the nickelates exhibit signatures of stripe formation and singlets in the ground state, similar to the underdoped curpates^{14,30,31,32}.
The magnetic properties of the nickelates differ substantially from those of the cuprates in that the pristine undoped cuprates exhibit commensurate AFM order. In sharp contrast, no longrange AFM order is found in RNiO_{2}^{33,34,35,36}, despite the existence of robust twodimensional (2D) AFM spin wave dispersions observed in RIXS^{37,38}. Instead, strong nonlocal magnetic correlations and weak to intermediate glassy shortrange behavior appear to dominate the ground state^{35,39,40}. Moreover, a recent muon spin rotation/relaxation experiment finds the infinitelayer nickelates to be intrinsically magnetic and further provides direct evidence for the coexistence of superconductivity and magnetism, with phase separation only possible on the nano scale^{41}. This suggests that the magnetic properties of the infinitelayer nickelates are closer to those of the doped cuprates, where inhomogeneities comprise the ground state rather than the undoped cuprates, which present a pristine ordered phase.
Many density functional theory (DFT)^{11,42,43,44,45,46,47,48} and DFT + dynamical meanfield theory (DMFT)^{28,39,45,49,50,51} studies yield a magnetic ground state in the infinitelayer nickelates that are at odds with the experimental evidence. Dynamical vertex approximation (DΓA) and cellular dynamicalmean field theory (CDMFT) calculations^{39} capture the shortrange correlations but do not offer a transparent picture of the instabilities at play. In this connection, a variety of tightbinding models have been invoked^{52,53,54,55,56} to understand the lowenergy physics and magnetic instabilities in nickelates. These models, however, are fundamentally limited because the relevant orbitals involved remain unclear.
In this article, we propose that the absence of longrange order in the infinitelayer nickelates originates from a large number of competing symmetrybreaking magnetic instabilities in the pristine phase, which strongly couple at low temperatures as is common in glassy phases of matter. Upon hole doping, these instabilities, originating from the threedimensionality (3D) of the Fermi surface, pass through a 3D–2D crossover in the magnetic fluctuation spectrum near the onset of the superconducting dome. By using the Ctype AFM state as a model system, we simulate the charge and magnetic excitation spectra. By comparing our theoretical spectra to the results from RIXS experiments, we find that the observed dispersion can be reproduced with a renormalization factor of 0.63. Our analysis of the spinwave spectrum reveals a dominant Ni\(3{d}_{{x}^{2}{y}^{2}}\) contribution along with an admixture of contributions from Ni\(3{d}_{{z}^{2}}\) and La4f orbitals. Our stronglyconstrainedandappropriatelynormed (SCAN) metaGGAbased results are similar to those obtained using DMFT. A twoband model provides an adequate representation of both charge and magnetic instabilities and excitations.
Results and discussion
Electronic structure and competing fluctuations
Figure 1a shows the interpolated electronic band structure for LaNiO_{2} in the nonmagnetic (NM) phase [Fig. 1b]. In order to conduct an objective analysis of the relevant orbital degrees of freedom at the twoparticle level, our atomic orbital model of the NM phase explicitly considers the full set of Ni3d, La5d, and La4f atomic orbitals. We find the quality of the fit to be quite sensitive to the set of included orbitals. Specifically, due to mixing between the Ni and La states within a 2 eV window of the Fermi level, the removal of even a single 4f or 5d state results in a poor fit of the Ni\(3{d}_{{x}^{2}{y}^{2}}\) band at the M and A points in the Brillouin zone.
In the lanthanumbased infinitelayer nickelates, three distinct bands cross the Fermi level: one is of nearly pure Ni\(3{d}_{{x}^{2}{y}^{2}}\) character, while the other two are derived from Ni3d_{xy/yz} and Ni\(3{d}_{{z}^{2}}\)/La5d orbitals. The latter bands give rise to spherical electron Fermi pockets at the Γ and A symmetry points in the Brillouin zone [Fig. 1c], and may be responsible for the experimentally observed metallic behavior of the resistivity at high temperature^{10,12,13,14,24,25,35,39}, along with a negative Hall coefficient^{10,13,14,24,25,35}. In contrast, the Ni\(3{d}_{{x}^{2}{y}^{2}}\) band generates a large, slightly warped quasi2D cylindrical Fermi surface similar to the cuprates. The relatively isolated Ni\(3{d}_{{x}^{2}{y}^{2}}\) state is the result of the oxygen deintercalation process used to convert RNiO_{3} to RNiO_{2}, thereby reorganizing the electronic states from that of an octahedral crystal field to a squareplanar geometry. The halffilled Ni\({d}_{{x}^{2}{y}^{2}}\) band closely resembles the corresponding band in the cuprates^{57}, except for an enhanced k_{z} dispersion due to the threedimensional (3D) nature of the crystal structure. This results in a shift in the position of the van Hove singularity (VHS) from below to infinitesimally above the Fermi level along the k_{z} direction in the Brillouin zone. Concomitantly, the Fermi surface transitions from being holelike (open) in the k_{z} = 0 plane to becoming electronlike (closed) in the k_{z} = π/c plane.
A key difference between the parent compounds of the cuprates and nickelates is the lack of longrange magnetic order in the nickelates. Instead, strong AFM correlations and glassy dynamics are observed to dominate throughout the phase diagram of RNiO_{2}. To gain insight into the landscape of charge and magnetic instabilities in the ground state, we examine the response (δρ) of the system to an infinitesimal perturbing source field (δπ). The associated response function is given by,
where the orbital indices have been suppressed, the spin indices (I, J, L, M) are given in the Pauli basis, v^{ML} is the generalized electron–electron interaction, and the polarizability is defined as:
Here, \(\bar{{{\Gamma }}}\) describes a multiple scattering process involving two quasiparticles with the vertex^{58}. Assuming the material exhibits sufficient screening, the vertex correction \(\bar{{{\Gamma }}}\) can be considered negligible and ignored. Then Eq. (1) can be solved outright, producing a generalized RPAtype matrix equation
Note that in order to solve for χ^{IJ}, we have introduced the matrix inverse of \(\left[1\bar{F}\right]\). Therefore, extra care must be taken when interpreting the response function. For a system exhibiting an ordered phase, e.g. AFM order, the poles \(1\bar{F}\) generated in the various spin and orbital channels predict bosonic quasiparticles, such as magnons. In a nonordered system, if χ^{IJ}(q, ω = 0) ≫ 1, then the ground state is unstable to a brokensymmetry phase. The specific charge and spin instabilities of the system can be made transparent by diagonalizing the kernel \(\bar{F}\),
where Λ_{F} is a diagonal matrix, and V is the eigenvector. Then
where α enumerates the instability ‘bands.’ Now, as the instability strength \({{{\Lambda }}}_{F}^{\alpha }({{{{{{{\bf{q}}}}}}}},\omega =0)\) approaches 1, χ^{IJ}(q, ω = 0) becomes singular, or physically, the ground state becomes unstable to an ordered phase. Additionally, the momentum satisfying \({{{\Lambda }}}_{F}^{{\alpha }_{{{{{\rm{max}}}}}}}({{{{{{{\bf{Q}}}}}}}},\omega =0)=1\), where α_{max} is the index of the maximum instability band, is the propagating vector Q of the emerging Stoner instability in the multiorbital spindependent system. The character of this instability may then be obtained by analyzing the associated eigenvectors, V.
Figure 2a presents the momentum dependence of the maximum instability \({{{\Lambda }}}_{F}^{0}({{{{{{{\bf{q}}}}}}}},\omega =0)\) for pristine LaNiO_{2} in the NM phase for various slices along q_{z} in the Brillouin zone. The overall peak structure in \({{{\Lambda }}}_{F}^{0}\) follows the folded Fermi surface of the Ni\(3{d}_{{x}^{2}{y}^{2}}\) band, with the main ridges displaying minimal q_{z} dispersion. The dominant peaks are concentrated around the M − A edge of the Brillouin zone, with weaker satellites along the path connecting the edge and the zone center. The momenta Q^{*} of the largest instability (blue and red ‘x’ marks) in each slice is found to evolve along the q_{z}axis, taking positions at (π − δ, π, 0), (π − δ, π, q_{z}), (π − δ, π − η, q_{z}), (π − ξ, π − ξ, q_{z}), and (π, π, π). These momentum points yield nearly degenerate instability strengths, where only 0.0178 separates the critical momenta in the q_{z} = 0 and q_{z} = π/c planes. A similar near degeneracy is found for various inplane momenta surrounding the M − A edge of the zone [Fig. 2b], with an instability strength difference of 0.0889 and 0.0023 between Q_{1} and Q_{2} in the Γ and Z planes, respectively. By analyzing the eigenvectors at the various marked Q^{*} points, we find magnetic fluctuations to dominate by order of magnitude over the charge sector. Moreover, the transverse and longitudinal magnetic fluctuations are predominantly composed of intraorbital Ni\(3{d}_{{x}^{2}{y}^{2}}\) weight, with additional weak interorbital contributions from Ni\({d}_{{x}^{2}{y}^{2}}\)/Nid_{xy/xz/yz} and Ni\({d}_{{x}^{2}{y}^{2}}\)/La4f (\(4{f}_{x({x}^{}3{y}^{2})}\) and \(4{f}_{y(3{x}^{2}{y}^{2})}\)) hybridization. In contrast, the charge channel is comprised of interorbital hybridization between Ni\(3{d}_{{x}^{2}{y}^{2}}\) and Ni3d_{xy} primarily, with smaller overlaps from Ni3d_{xz} and Ni3d_{yz} orbitals. An additional weak matrix element is found in the Ni\(3{d}_{{x}^{2}{y}^{2}}\)/La\(5{d}_{{x}^{2}{y}^{2}}\) channel. These results clearly show that the leading Gtype antiferromagnetic instability [Q^{*} = (π, π, π)] is virtually degenerate with a dense manifold of 2D and 3D incommensurate magnetic stripe orders. This is consistent with totalenergyDFT and DFT+DMFT results yielding a myriad of nearly degenerate magnetic configurations that lower the total energy with respect to the NM phase^{45,46,47,48,50,53}.
In Fig. 2a, b, the momentum dependence of the maximum instability is found to be quite flat throughout the Brillouin zone, producing a clear pileup of various magnetic configurations within an infinitesimally small instability strength. To make this statement more precise and accurately count the total number of competing magnetic configurations, we introduce the density of instabilities λ(Ω), where λ(Ω)δΩ is the number of instabilities in the system whose strengths lie in the range from Ω to Ω + δΩ. That is, λ(Ω) is defined as
where Ω is the instability strength and α enumerates the instability eigenvalues defined in Eq. (4). We further emphasize that λ(Ω) contains the instability information for all eigenvalues, not just for the maximum.
Figure 2c shows the density of instabilities for pristine LaNiO_{2} in the NM phase, along with an inset illustrating the region of origin of the various key features. The spectrum reveals two clear Van Hovelike singularities, one close to the maximum instability (\({\mathbb{I}}\)) and the other in the body just above 0.8 instability strength (\({\mathbb{II}}\)), along with a large step edge at the bottom of the spectrum (\({\mathbb{III}}\)). Furthermore, by decomposing the density of instabilities into the various band contributions, these peaks are found to originate from dense points in qspace (Van Hovelike) rather than a clustering of instability “bands”; see Supplementary Note 2 for details. As pointed out by Léon Van Hove^{59} in 1953, the appearance of singular features in the density of states of either electrons or phonons is intimately connected with the topology of the underlying band structure. Here, the presence of these singularities implies the existence of saddle points in the momentumdependent instability “bands” \({{{\Lambda }}}_{F}^{\alpha }\). For example, peak \({\mathbb{I}}\) originates from the very subtle change of \({{{\Lambda }}}_{F}^{0}\) from being a local minimum at (π, π, 0) to a global maximum at (π, π, π) [Fig. 2a], implying the existence of a critical \({q}_{z}^{* }\) where the concavity changes sign (saddle point). Peak \({\mathbb{II}}\) emerges from the flat plateau between the instability band edges, marked in the inset as the tips of the fourpointed star. The relative placement of the singularities, along with the stepedge \({\mathbb{III}}\), suggests that the fluctuations in LaNiO_{2} are 3D in nature. However, since peak \({\mathbb{I}}\) is in very close proximity to the maximum instability, the system is very close to a 3D–2D transition.
Much like the presence of a Van Hove singularity near the Fermi level can modify and enhance correlated physics of an interacting electron liquid^{60,61,62,63,64,65,66}, a similar “Van Hove scenario” arises when a saddle point in the density of instabilities nearly fulfills the Stoner criteria, Λ_{F} ~ 1. In the latter case, a large population of charge and magnetic instabilities with different propagating qvectors are able to interact and compete with one another, thus inducing strong correlation corrections to the lowtemperature behavior of the system^{67,68}. In line with this scenario, a complimentary study applying DMFT, DΓA, and CDMFT to a singleband Hubbard model for NdNiO_{2} finds the inclusion of vertex corrections to suppress longrange order, leaving strong shortrange correlations to dominate down to very low temperatures^{39}. This study gives credence to the important role that the density of instabilities can play in giving way to strong AFM fluctuations, local magnetism, and a pseudogaplike weakly insulating state.
Figure 3 shows the evolution of the momentum dependence of \({{{\Lambda }}}_{F}^{0}\) and the corresponding density of instabilities for LaNiO_{2} under various hole dopings. As hole carriers are added, the Ni\(3{d}_{{x}^{2}{y}^{2}}\) Fermi surface sheet expands in volume, gradually reducing and eliminating the electronlike Fermi surface in the k_{z} = π/c plane. Consequently, the areas of regions \({\mathbb{I}}\) and \({\mathbb{II}}\) in \({{{\Lambda }}}_{F}^{0}\) grow with increased hole concentration, as shown in Fig. 2c. Moreover, the concavity of \({{{\Lambda }}}_{F}^{0}\) at (π, π, π) goes from negative to positive around 10% hole doping, as illustrated by the critical momenta (red ‘x’ marks), which change location from (π, π, π) to (π − δ, π − η, π). This process is reflected in the density of instabilities where peak \({\mathbb{I}}\) transitions from a saddle point (x = 0.0) to a step edge (x = 0.30). The Van Hovelike singularity thus precipitates an effective dimensionality reduction of the fluctuations from 3D to 2D. Curiously, this transition appears just before the sign change in the Hall coefficient at the start of the superconducting dome^{24}. Finally, at x = 0.4, the leading edge of the densityofinstabilities softens, exhibiting the presence of a small number of instabilities and suggesting a severe reduction in the competition between the various magnetic configurations.
The persistence of the peak \({\mathbb{I}}\) at or near the maximum instability edge for both the underdoped and overdoped regimes suggests the preservation of strong competition between the magnetic states, despite the systematic reduction in the fluctuation strength with doping. The 3D to quasi2D transition in the nature of the fluctuations just before optimal doping makes LaNiO_{2} distinct from the cuprates, which display predominantly 2D fluctuations for all hole dopings. Furthermore, this suggests that 2D magnetic fluctuations, in particular, are important for Cooper pairing, with optimal T_{c} arising from the delicate balance between the dimensionality and strength of the fluctuations. In this connection, recent magnetotransport measurements find superconductivity to be quasitwodimensional in the infinitelayer nickelates^{69}.
Spin excitation spectra
So far, we have examined the manifold of possible magnetic states that may emerge from the nonmagnetic state of pristine and doped LaNiO_{2}. We now turn to examine the charge and spin excitations that occur within the magnetic state to gain insight into the measured magnetic excitation spectrum^{38,70}.
Figure 4a presents the band structure of LaNiO_{2} in the CAFM phase. Our model of the CAFM phase explicitly considers the full set of Ni3d, La\(5{d}_{{z}^{2}}\), La5d_{xy}, La\(4{f}_{{z}^{3}}\), and La\(4{f}_{x({x}^{2}3{y}^{2})}\) orbitals. Reducing the orbital projections further resulted in a poor fit. The AFM state stabilizes in the Ni\(3{d}_{{x}^{2}{y}^{2}}\) band with a gap of approximately 2 eV that opens up around the Fermi energy of the NM system. The partially filled Ni3d_{xy/yz} and Ni\(3{d}_{{z}^{2}}\) bands remain pinned to the Fermi level, with the Ni\(3{d}_{{z}^{2}}\) state becoming flat in the Z plane. Unlike the parent cuprate compounds, itinerant excitations are expected in addition to those of the local magnetic moments.
The charge \({{{{{{{\rm{Im}}}}}}}}{\chi }^{00}\), longitudinalspin \({{{{{{{\rm{Im}}}}}}}}{\chi }^{zz}\) and transversespin (spinflip) \({{{{{{{\rm{Im}}}}}}}}{\chi }^{+}\) excitation spectra are obtained from the corresponding components of the dynamical response χ^{IJ} [Eq. (3)] applied to the magnetic ground state. It is also useful to define the total spectrum \({\sum }_{\nu {\nu }^{{\prime} };\mu {\mu }^{{\prime} }}{\chi }_{\nu {\nu }^{{\prime} };\mu \mu {\prime} }^{IJ}\) where all four indices are integrated out and the maximum spectra tensor \({\max }_{{{{{{{{\bf{q}}}}}}}},\omega }\left\{\left\vert {\chi }_{\nu {\nu }^{{\prime} };\mu \mu {\prime} }^{IJ}({{{{{{{\bf{q}}}}}}}},\omega )\right\vert \right\}\) for the various charge (spin) components I, J. Finally, we introduce a scaled unit of energy \(\bar{\omega }={\varepsilon }_{r}\cdot \omega\) to evaluate the excitation energy under renormalization effects, which are common when itinerant carriers are present in an antiferromagnet^{71}. Moreover, ε_{r} is inversely proportional to the quasiparticle renormalization factor Z^{72}. Comparing our spectrum to the reported RIXS spectra^{38,70}, we find a renormalization ε_{r} value of 0.63 (Z = 1.58), which suggests LaNiO_{2} to be an intermediately coupled material. Interestingly, this renormalization also corresponds to ~26% holedoped La_{2}CuO_{4}^{73} and optimally doped BaFe_{2}As_{2}^{74}. We note that the dipole matrix elements of the RIXS measurement process may also be included to capture polarization effects^{75}.
Figure 4b shows the total transversespin excitation spectrum along the various highsymmetry lines in the NM Brillouin zone, with the experimental data overlaid^{38,70}. Highly dispersive magnetic excitations are found following the spin1/2 AFM magnons on a square lattice. Specifically, they disperse strongly with maxima at X and M/2, and linearly soften toward the AFM ordering wave vector at M in very good accord with the experimental spectra. Our theoretical excitations display a gap in the Γ plane compared to those in the plane through Z. This behavior is typical of infinitelayer perovskites, such as CaCuO_{2}^{76}, where a pronounced in and outofplane exchange coupling anisotropy can gap out magnetic excitations. By inspection of our electronic band’s structure, this gap can be attributed to the very small electron pockets at the Fermi level in the Γplane compared to those in the Zplane. Additional small anisotropies within the xyplane are also noticed.
Figure 4c, d presents the total longitudinalspin spectrum and the charge spectrum, respectively, along the various highsymmetry lines in the NM Brillouin zone. Both spectra are very similar, exhibiting a broad continuum of excitations. The excitation spectrum is amplified in the q_{z} = π plane as a consequence of the flat Ni\(3{d}_{{z}^{2}}\) band at the Fermi level. The incorporation of spinorbit coupling effects in the electronic structure gives rise to significant mixing between the transversespin and charge sectors, as indicated by the nonzero χ^{0−} and χ^{0+} susceptibility components, see Sec. S3 of Supplementary Note 3 for details, and yield a “shadow” of the spinflip excitations in the Γ plane and along Γ–Z in χ^{00}.
Figure 5a displays the maximum spectra tensor of the transversespin susceptibility as a heat map with the \(\nu ,\mu \,({\nu }^{{\prime} },{\mu }^{{\prime} })\) indices unrolled along the horizontal (vertical) axis. To help identify key atomicsite orbital components and asymmetries in the tensor, the left (right) distribution curve—given by the sum of each row (column)—is presented in the right (top) subpanel. The right and left distribution curves can be thought of as being similar to the spindensity \(({S}_{\mu \nu })\) amplitude, and their overlap \(\langle {S}_{\mu \nu }^{+}{S}_{{\mu }^{{\prime} }{\nu }^{{\prime} }}^{}\rangle\) is akin to the heat map.
Since the maximumspectratensor heat map is symmetric about the antidiagonal, the left and right distribution curves are equivalent. The distribution curves are quite sparse, exhibiting only a few prominent peaks in the (Ni\(3{d}_{{x}^{2}{y}^{2}}\),Ni\(3{d}_{{x}^{2}{y}^{2}}\)) channel, with smaller peaks present in the (Ni\(3{d}_{{z}^{2}}\),Ni\(3{d}_{{z}^{2}}\)) and (La\(4{f}_{x({x}^{2}3{y}^{2})}\),Ni\(3{d}_{{x}^{2}{y}^{2}}\)) components. In the heat map, these peaks appear as ‘hot’ horizontal and vertical lines, with maxima occurring at their intersection points (white arrows). These maxima identify the key atomicsite orbital components of the transversespin susceptibility. Specifically, our orbital analysis reveals that the magnetic excitations are dominated by Ni\(3{d}_{{x}^{2}{y}^{2}}\,\)\({\chi }_{\mu \mu ;\mu \mu }^{+}\) character, suggesting that the Ni\(3{d}_{{x}^{2}{y}^{2}}\) orbital plays an important role in the local magnetic moment. Ab initio calculations show a similar trend where the Ni\(3{d}_{{x}^{2}{y}^{2}}\) contributes 75% to the total Ni magnetic moment^{48}. The corresponding excitation spectrum of the Ni\(3{d}_{{x}^{2}{y}^{2}}\) component is given in Fig. 5b.
The subdominant spinexcitation components arise as offdiagonal components of the heat map that mix Ni\(3{d}_{{x}^{2}{y}^{2}}\) with other Ni3d and Ni4f states. The intrasite \({\chi }_{\mu \nu ;\mu \nu }^{+}\) term capturing \({}^{1}{{{{{{{\rm{Ni}}}}}}}}3{d}_{{x}^{2}{y}^{2}}{\to }^{1}{{{{{{{\rm{Ni}}}}}}}}3{d}_{{z}^{2}}\) transitions [Fig. 5c] contribute to the lowenergy part of the total spectrum near the center Γ(Z) and corner M(A) of the Brillouin zone. In contrast, longrange intersite \({\chi }_{\mu \nu ;\nu \mu }^{+}\) \({}^{1}{{{{{{{\rm{Ni}}}}}}}}3{d}_{{x}^{2}{y}^{2}}{\to }^{2}{{{{{{{\rm{Ni}}}}}}}}3{d}_{{x}^{2}{y}^{2}}\) excitations [Fig. 5e] have the greatest amplitude around 0.20 meV/ε_{r} centered around X(R) and M/2(A/2). The mixed term \({\chi }_{\mu \mu ;\nu \mu }^{+}\) captures the coupling of a local \({}^{1}{{{{{{{\rm{Ni}}}}}}}}3{d}_{{x}^{2}{y}^{2}}\) excitation to a nonlocal \({}^{1}{{{{{{{\rm{Ni}}}}}}}}3{d}_{{x}^{2}{y}^{2}}{\to }^{1}{{{{{{{\rm{Ni}}}}}}}}4{f}_{x({x}^{2}3{y}^{2})}\) transition [Fig. 5d]. This term indicates that nontrivial Ni–La hybridization can play a role (order of 2%) in influencing the magnon dispersion throughout the Brillouin zone and could contribute to the longrange behavior of the Heisenberg exchange parameters^{37}. This is in contrast to the cuprates, where spin excitations are highly localized on the copper atoms^{77}.
Comparison with other approaches
The discovery of a new class of superconductors not only brings forth new insights into the microscopic pairing mechanisms involved but it also provides a new data point for benchmarking and comparing various theoretical approaches toward superconductivity. Much of the existing theoretical analysis of the infinitelayer nickelates has been based on the standard DFT and DFT + DMFT frameworks. In this connection, it is useful to compare and contrast our results based on the more recently constructed SCAN metaGGA density functional, which has been shown to yield a systematic improvement in capturing the properties of wide classes of materials^{78,79}, with electronic structures of the infinitelayer nickelates available in the literature.
In the NM state, SCAN and the local density approximation (LDA)^{16}—used to initialize the DMFT—yield very similar results in a ± 2eV energy window around the Fermi energy, with small differences appearing in band dispersions outside this energy window due to LaNi (Nit_{2g} and Ni\(3{d}_{{z}^{2}}\)) hybridization. LDA and SCAN are thus expected to yield the same instabilities. When the spin degrees of freedom are allowed to relax in SCAN, however, a CAFM ground state is obtained, whereas when spinpolarized DMFT corrections are applied, a GAFM ground state is found with a CAFM order only ~6 meV higher in energy^{80}. This small difference in total energies can be explained by the additional lattice relaxations involved in the SCAN calculations. The DMFT instabilities are similar to those found via our RPA instability analysis. Both SCAN and DFT + DMFT^{80} (spinpolarized) find the Ni\(3{d}_{{z}^{2}}\) states pushed to the Fermi level forming a flat band, as was also reported using DFT + U^{81}. The spinpolarized (CAFM) SCAN electronic dispersions are also similar to the PM DFT + DMFT and DFT + selfinteraction corrected DMFT (sicDMFT) results^{82}. Specifically, the atomicallyresolved band dispersions from SCAN are comparable to the Ni\(3{d}_{{t}_{2g}}\) states of DFT + DMFT and the Ni\(3{d}_{{x}^{2}{y}^{2}}\) and flat Ni\(3{d}_{{z}^{2}}\) states of DFT + sicDMFT, where Ni\(3{d}_{{x}^{2}{y}^{2}}\) bands are completely absent at the Fermi level. This suggests that SCAN is adequately capturing the spin correlations. Further studies involving larger crystallographic unit cells to reveal the emergence of shortrange spinsymmetry breaking would be interesting^{83}.
We turn next to compare the transversespin response within SCAN and DMFT. The PM DFT + sicDMFT spin response spectra^{84} appear to capture the linear softening of the magnon dispersion near Γ but fail to display the highenergy features at X and M/2, which are seen clearly in the experimental dispersion. The SCANbased results match the RIXS curves over the full Brillouin zone when a renormalization factor is applied, as is typical for doped antiferromagnets. This is consistent with the reports of shortrange magnetic dynamics over pure local moment fluctuations in LaNiO_{2}^{39}. Since both approaches use the same RPA framework to obtain the spin response, it will be interesting to evaluate corrections to the ground state using CDMFT or SCAN based on supercells involving large special quasirandom structures (SQS)^{85} to better capture the shortrange correlations.
Lowenergy models of the electronic structure are useful for disentangling the relationship between physical phenomena and the local chemistry, and indeed many such models have been invoked for the infinitelayer nickelates. Since we employ a multiorbital model spanning Ni3d, La5d, and La4f orbitals, we are in a position to help identify a minimal set of orbitals necessary to reproduce the fluctuation instabilities and excitations. Our analysis of the NM phase shows that a simple model composed of a single Ni\(3{d}_{{x}^{2}{y}^{2}}\) orbital can capture the magnetic fluctuations, consistent with the observations of Kitatani et al.^{54,86}. To reproduce both the charge and magnetic fluctuations, however, a minimum of two orbitals is required. The minimal Hamiltonian proposed by Hu et al.^{87} using Ni\(3{d}_{{x}^{2}{y}^{2}}\) and Ni3d_{xy} states is in good accord with our work, whereas the proposed Hamiltonians using Ni\(3{d}_{{z}^{2}}\)^{45,88,89,90}, Nis^{91}, or La5d^{29,92} states instead of Ni3d_{xy} are not wellsuited for modeling the NM state. However, if one wishes to selfconsistently include magnetic correlation effects into the model—a prerequisite for capturing the magnetic excitation spectrum—, twoband Hamiltonians using Ni\(3{d}_{{z}^{2}}\) states should be considered instead of those employing Ni3d_{xy} orbitals in order to reproduce the partially occupied flat band at the Fermi level. Finally, if capturing the subtle effects arising from nontrivial Nirare earth hybridization are important, three^{56,93,94,95} and fourband^{53,96} models provide a more faithful description.
Conclusions
Our study demonstrates that LaNiO_{2} supports myriad competing, incommensurate spin fluctuations and magnetic excitations that are spread over multiple atomic sites. The reduction in the dimensionality of the magnetic fluctuations (3D to 2D) is found to coincide with the emergence of superconductivity. With further hole doping, fluctuations weaken, and superconductivity disappears, suggesting a tradeoff between the dimensionality and the strength of magnetic fluctuations in controlling the value of T_{c}. This behavior is similar to that of the doped cuprates where 2D inhomogeneous magnetic stripes are manifest already in the ground state^{97}. Our study gives insight into the nature of strong correlations in nickelates and provides a pathway for investigating complex correlated materials more generally.
Methods
Firstprinciples calculations
Ab initio calculations were carried out by using the pseudopotential projectoraugmented wave method^{98} implemented in the Vienna ab initio simulation package (VASP) ^{99,100} with an energy cutoff of 520 eV for the planewave basis set. Exchangecorrelation effects were treated by using the stronglyconstrainedandappropriatelynormed (SCAN) metaGGA density functional^{101}. A 15 × 15 × 17 Γcentered kpoint mesh was used to sample the Brillouin zone. Spin–orbit coupling effects were included selfconsistently. We used the experimental lowtemperature P4/mmm crystal structure to initialize our computations^{34}. All atomic sites in the NM and CAFM unit cells, along with the cell dimensions, were relaxed using a conjugate gradient algorithm to minimize the energy with an atomic force tolerance of 0.01 eV/Å. A total energy tolerance of 10^{−5} eV was used to determine the selfconsistent charge density.
Tightbinding Hamiltonian details
The manybody theory calculations of the spin–orbital fluctuations and magnetic excitations were performed by employing a realspace tightbinding model Hamiltonian, which was obtained by using the VASP2WANNIER90^{102} interface. For LaNiO_{2}, the full manifold of Ni3d, La5d, and La4f states (a total of 17 orbitals) was included in generating the orbital projections, whereas in the CAFM phase the \({d}_{{z}^{2}}\), d_{xy}, \({f}_{{z}^{3}}\), and \({f}_{x({x}^{2}3{y}^{2})}\) were retained on the La sites (a total of 18 orbitals). We considered models employing a smaller number of basis functions for both the NM and CAFM phase, but the resulting fits were quite poor. The Fourier transform convention H_{ij}(k) = ∑_{R}e^{ik⋅R}H_{ij}(R), is used throughout this work.
Response function calculations
In the NM state, a 51 × 51 × 51Γcentered kmesh was used to evaluate the response functions in the Brillouin zone. Only the 4 bands at the Fermi level were used in the summation over the bands in the Lindhard susceptibility. In the CAFM phase, a 23 × 23 × 23Γcentered kmesh was employed to sample the Brillouin zone, along with 101(2001)ωmesh(Xmesh) energy points spanning 0–1 eV (−10 eV to 10 eV). See Supplementary Note 1 for a detailed definition of the ω and X meshes used in the “binning” method^{103,104,105}. All the bands were used in the eigenvalue integration for the CAFM phase. A small broadening of 0.01 eV was used to simulate experimental conditions. Since our susceptibility code allows for finite temperatures, a very low value of the temperature of T = 0.001 K was used to mimic the DFT conditions and approximate a Heaviside step function. Coulomb interactions were included on the Nid orbitals and assumed to be rotationally symmetric, i.e. fulfilling the constraint \({U}^{{\prime} }=U2J\) and \(J={J}^{{\prime} }\)^{58}. The maximum instability \({{{\Lambda }}}_{F}^{0}({{{{{{{{\bf{Q}}}}}}}}}^{* })\) was found to equal 1 for U, \({U}^{{\prime} }\), and J values of 1.22 eV, 0.732 eV, and 0.244 eV, respectively. Our results are insensitive to changes in J and show the dominance of Ni\({d}_{{x}^{2}{y}^{2}}\) orbital at the Fermi level. We also find negligible effect of including U, \({U}^{{\prime} }\), and J Coulomb parameters on La5d states. The values of U, \({U}^{{\prime} }\), and J used were 3.675, 2.109, 0.782 eV, respectively, to simulate the magnon dispersion, where the ratio U/J = 5 was taken from SCAN ground state calculations^{48}.
Data availability
All data supporting the findings of this study are available from the corresponding author upon a reasonable request.
Code availability
The code used to calculate the spinorbital fluctuations and magnetic excitations is currently in the process of becoming open source. Requests about the code should be made to the corresponding author.
References
Dagotto, E. Complexity in strongly correlated electronic systems. Science 309, 257–262 (2005).
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to hightemperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Dagotto, E. Nanoscale Phase Separation and Colossal Magnetoresistance: The Physics Of Manganites And Related Compounds (Springer Science & Business Media, 2003).
Platzman, P. M. & Wolff, P. A. Waves and interactions in solid state plasmas, vol. 13 (Academic Press New York, 1973).
Sobota, J. A., He, Y. & Shen, Z.X. Angleresolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021).
Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457 (2015).
He, Y. et al. Rapid change of superconductivity and electronphonon coupling through critical doping in bi2212. Science 362, 62–65 (2018).
Li, H. et al. Coherent organization of electronic correlations as a mechanism to enhance and stabilize highT_{C} cuprate superconductivity. Nat. Commun. 9, 1–9 (2018).
Jiang, H.C. & Kivelson, S. A. Stripe order enhanced superconductivity in the hubbard model. Proc. Natl Acad. Sci. 119, e2109406119 (2022).
Li, D. et al. Superconductivity in an infinitelayer nickelate. Nature 572, 624–627 (2019).
Botana, A. S. & Norman, M. R. Similarities and differences between LaNiO_{2} and CaCuO_{2} and implications for superconductivity. Phys. Rev. X 10, 011024 (2020).
Osada, M. et al. A superconducting praseodymium nickelate with infinite layer structure. Nano Lett. 20, 5735–5740 (2020).
Osada, M. et al. Nickelate superconductivity without rareearth magnetism: (la,sr)nio_{2}. Adv. Mater. 33, 2104083 (2021).
Zeng, S. et al. Phase diagram and superconducting dome of infinitelayer Nd_{1−x}Sr_{x}NiO_{2} thin films. Phys. Rev. Lett. 125, 147003 (2020).
Anisimov, V., Bukhvalov, D. & Rice, T. Electronic structure of possible nickelate analogs to the cuprates. Phys. Rev. B 59, 7901 (1999).
Lee, K.W. & Pickett, W. Infinitelayer LaNiO_{2}: Ni^{1+} is not cu^{2+}. Phys. Rev. B 70, 165109 (2004).
Goodge, B. H. et al. Doping evolution of the Mott–Hubbard landscape in infinitelayer nickelates. Proc. Natl Acad. Sci. USA 118, e2007683118 (2021).
Gu, Q. & Wen, H. Superconductivity in nickel based 112 systems. The Innovation 3, 100202 (2022).
Hsu, Y.T. et al. Correlated insulating behavior in infinitelayer nickelates. Front. Phys. 10, 846639 (2022).
Chow, L. E. & Ariando, A. Infinitelayer nickelate superconductors: a current experimental perspective of the crystal and electronic structures. Front. Phys. 10, 20 (2022).
Nomura, Y. & Arita, R. Superconductivity in infinitelayer nickelates. Rep. Prog. Phys. 85, 052501 (2022).
Li, D. et al. Superconducting dome in Nd_{1−x}Sr_{x}Nio_{2} infinite layer films. Phys. Rev. Lett. 125, 027001 (2020).
Osada, M., Wang, B. Y., Lee, K., Li, D. & Hwang, H. Y. Phase diagram of infinite layer praseodymium nickelate Pr_{1−x}Sr_{x}NiO_{2} thin films. Phys. Rev. Mater. 4, 121801 (2020).
Zeng, S. et al. Superconductivity in infinitelayer nickelate La_{1−x}Ca_{x}NiO_{2} thin films. Sci. Adv. 8, eabl9927 (2022).
Lee, K. et al. Character of the normal state of the nickelate superconductors. Preprint at arXiv https://doi.org/10.48550/arXiv.2203.02580 (2022).
Mitchell, J. A nickelate renaissance. Front. Phys. 9, 813483 (2021).
Chen, Z. et al. Electronic structure of superconducting nickelates probed by resonant photoemission spectroscopy. Matter 5, 1806–1815 (2022).
Higashi, K., Winder, M., Kuneš, J. & Hariki, A. Corelevel Xray spectroscopy of infinitelayer nickelate: LDA+ DMFT study. Phys. Rev. X 11, 041009 (2021).
Hepting, M. et al. Electronic structure of the parent compound of superconducting infinitelayer nickelates. Nat. Mater. 19, 381–385 (2020).
Rossi, M. et al. Orbital and spin character of doped carriers in infinitelayer nickelates. Phys. Rev. B 104, L220505 (2021).
Rossi, M. et al. A broken translational symmetry state in an infinitelayer nickelate. Nat. Phys. 18, 869–873 (2022).
Tam, C. C. et al. Charge density waves in infinitelayer NdNiO_{2} nickelates. Nat. Mater. 21, 1116–1120 (2022).
Hayward, M., Green, M., Rosseinsky, M. & Sloan, J. Sodium hydride as a powerful reducing agent for topotactic oxide deintercalation: synthesis and characterization of the nickel (i) oxide LaNiO_{2}. J. Am. Chem. Soc. 121, 8843–8854 (1999).
Hayward, M. & Rosseinsky, M. Synthesis of the infinite layer Ni (i) phase NdNiO_{2+x} by low temperature reduction of NdNiO_{3} with sodium hydride. Solid State Sci. 5, 839–850 (2003).
Ikeda, A., Krockenberger, Y., Irie, H., Naito, M. & Yamamoto, H. Direct observation of infinite NiO_{2} planes in lanio_{2} films. Appl. Phys. Express 9, 061101 (2016).
Crespin, M., Levitz, P. & Gatineau, L. Reduced forms of LaNiO_{3} perovskite. Part 1. Evidence for new phases: La_{2}Ni_{2}O_{5} and LaNiO_{2}. J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 79, 1181–1194 (1983).
Lu, H. et al. Magnetic excitations in infinitelayer nickelates. Science 373, 213–216 (2021).
Krieger, G. et al. Charge and spin order dichotomy in ndnio_{2} driven by the capping layer. Phys. Rev. Lett. 129, 027002 (2022).
Ortiz, R. et al. Magnetic correlations in infinitelayer nickelates: an experimental and theoretical multimethod study. Phys. Rev. Res. 4, 023093 (2022).
Lin, H. et al. Universal spinglass behaviour in bulk LaNiO_{2}, PrNiO_{2} and NdNiO_{2}. N. J. Phys. 24, 013022 (2022).
Fowlie, J. et al. Intrinsic magnetism in superconducting infinitelayer nickelates. Nat. Phys. 18, 1043–1047 (2022).
Botana, A. S., Lee, K.W., Norman, M. R., Pardo, V. & Pickett, W. E. Low valence nickelates: launching the nickel age of superconductivity. Front. Phys. 9, 813532 (2022).
Kapeghian, J. & Botana, A. S. Electronic structure and magnetism in infinitelayer nickelates RNiO_{2} (R = LaLu). Phys. Rev. B 102, 205130 (2020).
LaBollita, H. & Botana, A. S. Electronic structure and magnetic properties of higherorder layered nickelates: La_{n+1}Ni_{n}O_{2n+2} (n= 4–6). Phys. Rev. B 104, 035148 (2021).
Wan, X., Ivanov, V., Resta, G., Leonov, I. & Savrasov, S. Y. Exchange interactions and sensitivity of the ni twohole spin state to Hund’s coupling in doped ndnio_{2}. Phys. Rev. B 103, 075123 (2021).
Liu, Z., Ren, Z., Zhu, W., Wang, Z. & Yang, J. Electronic and magnetic structure of infinitelayer NdNiO_{2}: trace of antiferromagnetic metal. npj Quantum Mater. 5, 1–8 (2020).
Jung, M.C., LaBollita, H., Pardo, V. & Botana, A. S. Antiferromagnetic insulating state in layered nickelates at half filling. Sci. Rep. 12, 17864 (2022).
Zhang, R. et al. Magnetic and felectron effects in lanio_{2} and ndnio_{2} nickelates with cupratelike \(3{d}_{{x}^{2}{y}^{2}}\) band. Commun. Phys. 4, 1–12 (2021).
Wang, Y., Kang, C.J., Miao, H. & Kotliar, G. Hund’s metal physics: from SrNiO_{2} to LaNiO_{2}. Phys. Rev. B 102, 161118 (2020).
Lechermann, F. Dopingdependent character and possible magnetic ordering of NdNiO_{2}. Phys. Rev. Mater. 5, 044803 (2021).
Gu, Y., Zhu, S., Wang, X., Hu, J. & Chen, H. A substantial hybridization between correlated Nid orbital and itinerant electrons in infinitelayer nickelates. Commun. Phys. 3, 1–9 (2020).
Sakakibara, H. et al. Model construction and a possibility of cupratelike pairing in a new d^{9} nickelate superconductor (Nd,Sr)NiO_{2}. Phys. Rev. Lett. 125, 077003 (2020).
Gu, Y., Zhu, S., Wang, X., Hu, J. & Chen, H. A substantial hybridization between correlated Nid orbital and itinerant electrons in infinitelayer nickelates. Commun. Phys. 3, 84 (2020).
Kitatani, M. et al. Nickelate superconductors—a renaissance of the oneband Hubbard model. npj Quantum Mater. 5, 59 (2020).
Zhou, T., Gao, Y. & Wang, Z. Spin excitations in nickelate superconductors. Sci. China Phys. Mech. Astron. 63, 1–9 (2020).
Lechermann, F. Multiorbital processes rule the Nd_{1−x}Sr_{x}NiO_{2} normal state. Phys. Rev. X 10, 041002 (2020).
Lane, C. et al. Antiferromagnetic ground state of La_{2}CuO_{4}: a parameterfree ab initio description. Phys. Rev. B 98, 125140 (2018).
Lane, C. & Zhu, J.X. Identifying topological superconductivity in twodimensional transitionmetal dichalcogenides. Phys. Rev. Mater. 6, 094001 (2022).
Van Hove, L. The occurrence of singularities in the elastic frequency distribution of a crystal. Phys. Rev. 89, 1189 (1953).
Irkhin, V. Y., Katanin, A. & Katsnelson, M. Effects of van Hove singularities on magnetism and superconductivity in the \(t{t}^{{\prime} }\) Hubbard model: a parquet approach. Phys. Rev. B 64, 165107 (2001).
Schulz, H. Superconductivity and antiferromagnetism in the twodimensional Hubbard model: scaling theory. Europhys. Lett. 4, 609 (1987).
Markiewicz, R. A survey of the van Hove scenario for hightc superconductivity with special emphasis on pseudogaps and striped phases. J. Phys. Chem. Solids 58, 1179–1310 (1997).
Bok, J. & Bouvier, J. Superconductivity and the Van Hove scenario. J. Superconduct. Nov. Magn. 25, 657–667 (2012).
Newns, D., Krishnamurthy, H., Pattnaik, P., Tsuei, C. & Kane, C. Saddlepoint pairing: an electronic mechanism for superconductivity. Phys. Rev. Lett. 69, 1264 (1992).
Zheleznyak, A. T., Yakovenko, V. M. & Dzyaloshinskii, I. E. Parquet solution for a flat fermi surface. Phys. Rev. B 55, 3200 (1997).
Zanchi, D. & Schulz, H. Weakly correlated electrons on a square lattice: a renormalization group theory. Europhys. Lett. 44, 235 (1998).
Moriya, T. Spin Fluctuations in Itinerant Electron Magnetism, vol. 56 (Springer Science & Business Media, 2012).
Tremblay, A.M. S. Twoparticleselfconsistent approach for the Hubbard model. in Strongly Correlated Systems, 409–453 (Springer, 2012).
Sun, W. et al. Evidence for quasitwodimensional superconductivity in infinitelayer nickelates. Preprint at arXiv https://doi.org/10.48550/arXiv.2204.13264 (2022).
Lu, H. et al. Magnetic excitations in infinitelayer nickelates. Science 373, 213–216 (2021).
Igarashi, J.i & Fulde, P. Spin waves in a doped antiferromagnet. Phys. Rev. B 45, 12357 (1992).
Das, T., Markiewicz, R. & Bansil, A. Intermediate coupling model of the cuprates. Adv. Phys. 63, 151–266 (2014).
Meyers, D. et al. Doping dependence of the magnetic excitations in La_{2−x}Sr_{x}CuO_{4}. Phys. Rev. B 95, 075139 (2017).
Zhou, K.J. et al. Persistent highenergy spin excitations in ironpnictide superconductors. Nat. Commun. 4, 1470 (2013).
Kaneshita, E., Tsutsui, K. & Tohyama, T. Spin and orbital characters of excitations in iron arsenide superconductors revealed by simulated resonant inelastic Xray scattering. Phys. Rev. B 84, 020511 (2011).
Peng, Y. et al. Influence of apical oxygen on the extent of inplane exchange interaction in cuprate superconductors. Nat. Phys. 13, 1201–1206 (2017).
Kastner, M., Birgeneau, R., Shirane, G. & Endoh, Y. Magnetic, transport, and optical properties of monolayer copper oxides. Rev. Mod. Phys. 70, 897 (1998).
Sun, J. et al. Accurate firstprinciples structures and energies of diversely bonded systems from an efficient density functional. Nat. Chem. 8, 831–836 (2016).
Pokharel, K. et al. Sensitivity of the electronic and magnetic structures of cuprate superconductors to density functional approximations. npj Comput. Mater. 8, 31 (2022).
Leonov, I. Effect of lattice strain on the electronic structure and magnetic correlations in infinitelayer (Nd,Sr)NiO_{2}. J. Alloy. Compd. 883, 160888 (2021).
Choi, M.Y., Pickett, W. E. & Lee, K.W. Fluctuationfrustrated flat band instabilities in ndnio_{2}. Phys. Rev. Res. 2, 033445 (2020).
Chen, H., Hampel, A., Karp, J., Lechermann, F. & Millis, A. J. Dynamical mean field studies of infinite layer nickelates: physics results and methodological implications. Front. Phys. 10, 16 (2022).
Wang, Z., Zhao, X.G., Koch, R., Billinge, S. J. & Zunger, A. Understanding electronic peculiarities in tetragonal FeSe as local structural symmetry breaking. Phys. Rev. B 102, 235121 (2020).
Kreisel, A., Andersen, B. M., Rømer, A. T., Eremin, I. M. & Lechermann, F. Superconducting instabilities in strongly correlated infinitelayer nickelates. Phys. Rev. Lett. 129, 077002 (2022).
Zunger, A., Wei, S.H., Ferreira, L. & Bernard, J. E. Special quasirandom structures. Phys. Rev. Lett. 65, 353 (1990).
Kitatani, M. et al. Optimizing superconductivity: from cuprates via nickelates to palladates. Phys. Rev. Lett. 130, 166002 (2023).
Hu, L.H. & Wu, C. Twoband model for magnetism and superconductivity in nickelates. Phys. Rev. Res. 1, 032046 (2019).
Kang, C.J. & Kotliar, G. Optical properties of the infinitelayer La_{1−x}Sr_{x}NiO_{2} and hidden Hund’s physics. Phys. Rev. Lett. 126, 127401 (2021).
Zhang, Y.H. & Vishwanath, A. TypeII tJ model in superconducting nickelate Nd_{1−x}Sr_{x}Nio_{2}. Phys. Rev. Res. 2, 023112 (2020).
Werner, P. & Hoshino, S. Nickelate superconductors: multiorbital nature and spin freezing. Phys. Rev. B 101, 041104 (2020).
Plienbumrung, T., Daghofer, M., Schmid, M. & Oleś, A. M. Screening in a twoband model for superconducting infinitelayer nickelate. Phys. Rev. B 106, 134504 (2022).
Been, E. et al. Electronic structure trends across the rareearth series in superconducting infinitelayer nickelates. Phys. Rev. X 11, 011050 (2021).
Hirayama, M., Nomura, Y. & Arita, R. Ab initio downfolding based on the gw approximation for infinitelayer nickelates. Front. Phys. 10, 824144 (2022).
Wu, X. et al. Robust \({d}_{{x}^{2}{y}^{2}}\)wave superconductivity of infinitelayer nickelates. Phys. Rev. B 101, 060504 (2020).
Nomura, Y. et al. Formation of a twodimensional singlecomponent correlated electron system and band engineering in the nickelate superconductor ndnio_{2}. Phys. Rev. B 100, 205138 (2019).
Gao, J., Peng, S., Wang, Z., Fang, C. & Weng, H. Electronic structures and topological properties in nickelates Ln_{n+1}Ni_{n}O_{2n+2}. Natl Sci. Rev. 8, nwaa218 (2021).
Zhang, Y. et al. Competing stripe and magnetic phases in the cuprates from first principles. Proc. Natl Acad. Sci. USA 117, 68–72 (2020).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 59, 1758–1775 (1999).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Kresse, G. & Hafner, J. Ab initio molecular dynamics for openshell transition metals. Phys. Rev. B 48, 13115–13118 (1993).
Sun, J., Ruzsinszky, A. & Perdew, J. Strongly constrained and appropriately normed semilocal density functional. Phys. Rev. Lett. 115, 036402 (2015).
Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter 32, 165902 (2020).
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419 (2012).
Miyake, T. & Aryasetiawan, F. Efficient algorithm for calculating noninteracting frequencydependent linear response functions. Phys. Rev. B 61, 7172 (2000).
Shishkin, M. & Kresse, G. Implementation and performance of the frequencydependent g w method within the paw framework. Phys. Rev. B 74, 035101 (2006).
Acknowledgements
The authors would like to thank Dr. Peter Mistark for many fruitful discussions. The work at Los Alamos National Laboratory was carried out under the auspices of the US Department of Energy (DOE) National Nuclear Security Administration under Contract No. 89233218CNA000001. It was supported by the LANL LDRD Program, the Quantum Science Center, a U.S. DOE Office of Science National Quantum Information Science Research Center, and in part by the Center for Integrated Nanotechnologies, a DOE BES user facility, in partnership with the LANL Institutional Computing Program for computational resources. Additional computations were performed at the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DEAC0205CH11231 using NERSC award ERCAP0020494. The work at Tulane University was supported by the U.S. Office of Naval Research (ONR) Grant No. N000142212673. The work at Tulane University was also supported by startup funding from Tulane University, the Cypress Computational Cluster at Tulane, the Extreme Science and Engineering Discovery Environment (XSEDE), and the National Energy Research Scientific Computing Center. The work at Northeastern University was supported by the US Department of Energy, Office of Science, Basic Energy Sciences Grant No. DESC0022216 and benefited from Northeastern University’s Advanced Scientific Computation Center and the Discovery Cluster, and the National Energy Research Scientific Computing Center through DOE Grant No. DEAC0205CH11231. B.B. acknowledges support from the COST Action CA16218.
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C.L. and R.Z. performed computations, and C.L., R.Z., B.B., R.S.M., and J.Z. analyzed the data. C.L., A.B., J.S., and J.Z. led the investigations, designed the computational approaches, provided computational infrastructure, and analyzed the results. All authors contributed to the writing of the paper.
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Lane, C., Zhang, R., Barbiellini, B. et al. Competing incommensurate spin fluctuations and magnetic excitations in infinitelayer nickelate superconductors. Commun Phys 6, 90 (2023). https://doi.org/10.1038/s42005023012130
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DOI: https://doi.org/10.1038/s42005023012130
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