Antiferromagnetic Dimers in the Parent Phase of a Correlated Kagome Superconductor

Abstract: Kagome metals are prone to charge-density wave (CDW), magnetic, and superconducting phases, with their flat electronic band conducive for correlated physics. In contrast to the weakly correlated $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) kagome metals with a $2\times2$ CDW, CsCr$_3$Sb$_5$ is a correlated metal with a flat band close to the Fermi level, and exhibits a $4\times1$ CDW intertwined with magnetic order. Under pressure, the intertwined orders are suppressed and give way to a dome of superconductivity that emerges from a non-Fermi liquid normal state. Here, we solve the crystal structure of the $4\times 1$ CDW state in CsCr$_3$Sb$_5$, and show it consists of Cr dimers separated by Cr chains. First-principles calculations show the dominant exchange interaction is antiferromagnetic within the dimers, while the intra-chain and dimer-chain couplings are much weaker. The CDW transition of CsCr$_3$Sb$_5$ is found to be more strongly first-order than those in $A$V$_3$Sb$_5$, without significant soft phonons or diffuse scattering above the CDW transition temperature. These findings suggest that fluctuating antiferromagnetic dimers may play a major role in the electron pairing of superconducting CsCr$_3$Sb$_5$.

• The paper identifies robust AFM Cr-Cr dimers as the key drivers of the 4×1 CDW phase, evidenced by a reduced bond length of roughly 2.56 Å.
• It employs single-crystal X-ray diffraction and IXS to reveal a non-sinusoidal CDW modulation with distinct primary and second-harmonic peaks and an absence of soft phonon modes.
• DFT calculations highlight an altermagnetic ground state with a 50 meV/dimer energy difference, pointing to a potential dimer-driven mechanism for unconventional superconductivity.

Antiferromagnetic Dimers and Charge-Magnetic Intertwining in CsCr$_3$Sb$_5$

Introduction

The manuscript rigorously investigates the structural and electronic order in the correlated kagome metal CsCr$_3$Sb$_5$, with a particular focus on the interplay between charge-density wave (CDW), magnetic order, and their implications for unconventional superconductivity in this system. The contrast between CsCr$_3$Sb$_5$ and its vanadium-based analogs ($A$V$_3$Sb$_5$) is systematically outlined, with attention paid to strong electronic correlations, quantum criticality under pressure, and the emergence of a superconducting dome from a non-Fermi liquid normal state.

Structural Solution of the $4 \times 1$ CDW State

Single-crystal X-ray diffraction comprehensively resolves the $_5$0 CDW phase in CsCr$_5$1Sb$_5$2, rejecting earlier suggestions of a significant monoclinic distortion. The CDW structure is orthorhombic ($_5$3), and is characterized by the formation of pronounced Cr-Cr dimers, which are spatially separated by chains of Cr atoms. Quantitatively, the Cr-Cr bond distance in the dimers is $_5$42.56 Å, significantly shorter than the average Cr—Cr separation ($_5$52.78 Å) elsewhere, evidencing strong local binding within dimers. The symmetry breaking associated with these dimers produces electronic nematicity, consistent with observed ultrafast optical signatures.

Importantly, the CDW modulation is non-sinusoidal, as evidenced by the appearance of both primary and second-harmonic superlattice peaks, and is fully three-dimensional—there is no rod-like diffuse scattering, indicating high stacking order along the $_5$6-axis. The first-order (rather than continuous) nature of the CDW transition is established crystallographically: superstructure Bragg intensity saturates within $_5$71 K of onset, and the critical exponent $_5$8 supports a strong first-order transition.

Absence of Soft Phonon Modes and Thermal Diffuse Scattering

IXS measurements report a notable absence of both soft phonon and thermal diffuse scattering above $_5$9 at the ordering vector; this is in sharp contrast with $_3$0V$_3$1Sb$_3$2 materials, where phonon softening and diffuse scattering are robust and persist to higher relative temperatures above the CDW transition. The lack of phonon softening in CsCr$_3$3Sb$_3$4 suggests that the lattice instability is not driven by electron-phonon coupling or Fermi surface nesting in a conventional sense, but is rather coupled to electronic/magnetic degrees of freedom. Additionally, nematic fluctuations (elastoresistance $_3$5 channel) in the normal state do not renormalize transverse acoustic phonons, implying weak lattice coupling—a distinction from the iron-based superconductors.

Antiferromagnetic Dimers and Altermagnetic Order

DFT-based high-throughput exploration of collinear magnetic arrangements constrained to the $_3$6 $_3$7 CDW lattice reveals a ground state with pronounced AFM order within Cr dimers and ferromagnetic (FM) order along Cr chains. The dominant exchange scale is the AFM dimer interaction, with an energy difference of $_3$850 meV/dimer between AFM and FM alignment. Dimer-chain and inter-dimer interactions are an order of magnitude weaker, leading to an effective decoupling of dimers from the rest of the lattice's magnetic ground state.

The resultant long-range magnetic ground state is altermagnetic: net-zero magnetization, but two spin sublattices are related by nontrivial glide mirror operations rather than conventional symmetry operations. This “altermagnetism” is directly evidenced by spin-polarized band structures and Fermi surfaces in DFT calculations, provided that interlayer coupling is ferromagnetic; if antiferromagnetic, the system realizes a “hidden” altermagnetic state.

First-Principles Energy Landscape and Competing Phases

DFT calculations indicate a small energy difference between the experimental $_3$9 and a $_5$0 CDW state (which is theoretically favored at perfect stoichiometry). Introduction of slight Sb $_5$1 Sn substitution renders the $_5$2 phase favorable, suggesting that small chemical disorder or subtle correlations not fully captured in standard DFT can tilt the energy balance—reflecting a highly frustrated, nearly degenerate landscape due to competing interactions.

Implications for Unconventional Superconductivity

The experimental phase diagram of CsCr$_5$3Sb$_5$4 features continuous suppression of intertwined CDW and magnetic order with pressure, culminating in a putative quantum critical point and a non-Fermi liquid regime out of which superconductivity emerges. The presence of robust, localized AFM dimers in the parent phase, combined with inelastic X-ray observations of two flat spin excitation branches, implies that magnetic-dimer fluctuations persist and may act as an effective pairing mechanism beyond the boundary of static CDW order.

The paper remarks on the formal analogy to resonating valence bond (RVB) physics: mobile spin singlets (dimers) could, if delocalized, furnish a mechanism for Cooper pair formation in the unconventional superconducting regime. Nevertheless, the experimental superconducting coherence length substantially exceeds the spatial scale of a single dimer, indicating that any such connection is nuanced.

Distinction from Related Kagome and Dimer Systems

CsCr$_5$5Sb$_5$6 is dissimilar in both structure and physics from $_5$7V$_5$8Sb$_5$9, where the $_3$0 “star of David” CDW does not involve magnetic order, and from ScV$_3$1Sn$_3$2/LuNb$_3$3Sn$_3$4, where CDW formation is dominated by $_3$5-axis trimerization with little in-plane character. In other correlated dimerized superconductors (e.g., IrTe$_3$6, CuIr$_3$7S$_3$8), the dimers are nonmagnetic and the quantum phase transitions are weakly first order, with superconductivity emerging from conventional metallic states.

Conclusion

This study unambiguously identifies AFM Cr-Cr dimers as the core building blocks of the $_3$9 CDW phase in CsCr$_5$0Sb$_5$1. The dominant AFM intra-dimer exchange, the absence of soft phonon signatures at the CDW wavevector, and the pronounced first-order character of the CDW transition collectively indicate that electronic correlation and spin-Jahn-Teller-driven lattice instability, rather than Fermi surface nesting or electron-phonon coupling, underlie the ordered phase. The proximity of long-lived dimer fluctuations and the emergence of unconventional superconductivity from a non-Fermi liquid normal state suggest a direct role for dimer-based spin excitations in Cooper pairing, motivating future studies of pressure-tuned fluctuation spectra and their coupling to emergent orders in correlated kagome superconductors.