Bond-Length-Driven Magnetic Transition in Quasi-One-Dimensional CrSb$X_3$ ($X$=S, Se)

Abstract: Using {\it ab initio} calculations, we investigate the magnetic ground states of quasi-one-dimensional insulating CrSb$X_3$ ($X$ = S, Se) with infinite double-rutile chains. Within conventional band theory, without explicit Coulomb correlations ($U$), we obtain band gaps in close agreement with experiment. Remarkably, we find that the magnetic order is highly sensitive to the Cr-Cr bond length $d_{\rm Cr-Cr}$: increasing the bond length induces a transition from antiferromagnetic to ferromagnetic order at a critical distance $d^c_{\rm Cr-Cr} \approx 3.53 (\pm 0.05)$ Å. Accordingly, CrSbS$_3$ lies near the transition boundary, whereas CrSbSe$_3$ is robustly ferromagnetic, in good agreement with experiment. Analysis of the exchange interactions reveals that the first-order phase transition is dominated by a sign reversal of the intrachain nearest-neighbor superexchange $J_1$ mediated by chalcogen ions, while the intrachain direct exchange $J_2$ remains ferromagnetic and changes only gradually. This behavior reflects an emergent Bethe-Slater-like behavior driven by competing exchange pathways in a quasi-1D transition-metal system, where the competition between $J_1$ and $J_2$ dictates the magnetic ground state. Besides, the electronic structures of the ground states of each compound are investigated.

• The paper demonstrates that a critical Cr–Cr bond length (≈3.53 Å) drives a first-order magnetic transition between antiferromagnetic and ferromagnetic states.
• DFT calculations with van der Waals corrections accurately capture the electronic structure, exchange interactions, and band-gap variations in quasi-1D CrSbX3.
• The study offers practical insights for tuning low-dimensional magnetism and pressure-induced superconductivity in Cr-based chalcogenides.

Bond-Length-Driven Magnetic Transition in Quasi-One-Dimensional CrSb$X_3$ ($X$=S, Se): Ab Initio Investigation

Introduction

This paper presents a comprehensive first-principles study of magnetic phase transitions in quasi-one-dimensional (1D) chromium antimony trichalcogenides CrSb$X_3$ ($X$=S, Se). These compounds, built from double-rutile Cr$X_6$ chains weakly connected by Sb$X_3$ pyramids, are of current interest due to their rich and tunable magnetic phase diagrams, proximity to Mott insulating behavior, and the coexistence of magnetic order and low-dimensional transport. The research focuses on elucidating the mechanisms underlying the distinct magnetic ground states observed in CrSbS$_3$ (antiferromagnetic, AFM) and CrSbSe$_3$ (ferromagnetic, FM), highlighting the sensitivity of these states to the Cr–Cr bond length $d_{\rm Cr-Cr}$.

The study utilizes density functional theory (DFT) with a focus on accurately capturing van der Waals effects and exchange interactions within these quasi-1D systems. The work systematically examines ground state energetics, magnetic interactions, electronic structure, and pressure-induced phase transitions, providing a rigorous basis for understanding experimentally observed phenomena and offering predictions for bond-length control of magnetism in related systems.

Crystal Structure and Computational Methodology

CrSb$X_3$ crystallizes in the orthorhombic $X$0 structure, incorporating infinite edge-sharing Cr$X$1 double rutile chains extending along the crystallographic $X$2-axis. These 1D chains manifest strong magnetic anisotropy and are weakly coupled across the $X$3 plane by van der Waals forces.

Figure 1: Crystal structure of CrSb$X$4 ($X$5=S, Se), showing double-rutile chains and AFM spin configuration within the unit cell.

Structural parameters were obtained by DFT-D3 optimization and benchmarked against experimental X-ray data. Notably, Cr–Cr bond lengths were carefully tuned and set as the key structural control parameter. All-electron full-potential codes ({\sc wien2k}, {\sc fplo}) were employed to avoid the underestimation of electronic band gaps ubiquitous in prior pseudopotential-based studies.

Magnetic Phase Transition and Energetics

The relative energies of AFM and FM states were mapped as a function of $X$6. The data reveal a sharp, first-order phase transition between AFM and FM ground states at a material-independent critical distance $X$7 Å, establishing bond length as a universal tuning parameter for this family.

In CrSbS$X$8, the experimental bond length places the compound at the critical threshold, correlating with sensitivity and reported variability in its magnetic ground state. CrSbSe$X$9, with a larger Cr–Cr distance, is robustly FM, consistent with all recent experimental reports.

Figure 2: Energy difference $X_3$0 as a function of $X_3$1, exhibiting a first-order phase transition and the corresponding evolution of superexchange bond angles.

These results directly contradict the Mott-insulator scenario previously advanced for these systems. Calculated band gaps within conventional GGA (using an all-electron approach) closely reproduce experiment, supporting a band-insulating—not correlation-driven—picture.

Electronic Structure Analysis

The nonmagnetic (NM) and magnetically ordered electronic structures were systematically studied:

• The NM density of states (DOS) features a quasi-1D $X_3$2 manifold and a prominent $X_3$3 singularity at $X_3$4, indicative of 1D electronic confinement.
• In the FM state (CrSbSe$X_3$5), the majority spin channel displays a well-separated $X_3$6 manifold, a direct band gap $X_3$7 eV, and a robust Cr$X_3$8 configuration.

  Figure 3: FM band structure of CrSbSe$X_3$9 at experimental geometry. The system is an insulator with strong quasi-1D dispersion.

  

  Figure 4: FM total and atom-projected DOSs, showing a 0.5 eV gap and high spin-polarization in CrSbSe$X$0.

• In the AFM state (CrSbS$X$1), the $X$2 band is narrower (reflecting decreased $X$3), with the gap increased to 0.8 eV, matching experiment.
• The band structures in both FM and AFM cases show pronounced 1D features and non-symmorphic band sticking.

Microscopic Mechanism: Exchange Pathways and Bethe–Slater Analogy

The intra-chain exchange constants $X$4 and $X$5 were determined by mapping ab initio results onto a classical Heisenberg model. $X$6 corresponds to the chalcogen-mediated superexchange and can change sign (AFM/F) as a function of bond length, while $X$7 is the direct FM Cr–Cr exchange, remaining FM but varying in strength.

• The first-order transition is due to a discontinuous sign change in $X$8, a hallmark of Bethe–Slater-like physics, where the relative strength of antiferromagnetic and ferromagnetic exchange is set by interatomic separation.
• $X$9 varies smoothly but does not sign-reverse.

  Figure 5: Calculated exchange parameters in CrSbS$X_6$0 at the AFM ground state ($X_6$1=3.39 Å), showing dominant intra-chain interactions.

  

  Figure 6: Evolution of dominant exchange parameters $X_6$2, $X_6$3, $X_6$4, and $X_6$5 with $X_6$6. Discontinuity in $X_6$7 underpins the first-order phase boundary.

The energetic competition between $X_6$8 and $X_6$9 thus governs the experimentally observed and pressure/strain-inducible FM–AFM transition in the CrSb$X_3$0 series. This mechanism is theoretically robust and likely extends to the wider class of low-dimensional Cr-based magnets.

Pressure Effects and Superconductivity

Under high pressure ($X_3$1–40 GPa), CrSbSe$X_3$2 transitions from FM insulator to an itinerant AFM phase, with a further transition to a superconducting state above 33 GPa. High-pressure calculations confirm a collapsed volume, vanishing magnetic order, and emergent 1D Fermi surfaces prone to nesting—features correlated with superconductivity in quasi-1D systems.

Figure 7: Electronic structure and Fermi surfaces of nonmagnetic CrSbSe$X_3$3 at 40 GPa, with DOS at $X_3$4 dominated by Cr 3$X_3$5, and strongly 1D Fermi sheets suggestive of instability towards superconductivity.

AFM fluctuations likely play the dominant role in pairing, given the suppression of FM order at the insulator–metal boundary.

Experimental Implications and Open Questions

• The proximity of CrSbS$X_3$6 to the critical point explains the variance in literature regarding its magnetic ground state and invites careful structural characterization.
• The experimental observation of a charge-transfer transition in CrSbS$X_3$7 (Cr$X_3$8 Cr$X_3$9 near 94 K) is not reproduced by conventional DFT; this signals the need for advanced many-body methods and high-resolution structural probes.
• Bond length—potentially tunable by chemical substitution, strain, or pressure—offers a practical parameter for engineering and switching between 1D AFM and FM states.

Conclusion

This comprehensive first-principles analysis elucidates the bond-length-driven first-order transition between AFM and FM ground states in quasi-1D CrSb$_3$0 ($_3$1=S, Se). The decisive tuning parameter is the Cr–Cr separation, which controls the competition between chalcogen-mediated superexchange ($_3$2) and direct exchange ($_3$3), yielding a discontinuous Bethe–Slater-like transition. The theoretical framework is validated by strong correspondence with experimental magnetic and electronic properties, and it predicts that bond-length engineering offers a route to switchable 1D magnetism in this material family. The pressure-induced superconductivity, accompanied by a drastic change in magnetic and electronic structure, is strongly indicative of unconventional pairing mechanisms. The work also identifies outstanding questions regarding the nature of thermally induced charge transfer and the precise role of many-body effects at the AFM–FM instability.

---

Reference: "Bond-Length-Driven Magnetic Transition in Quasi-One-Dimensional CrSb$_3$4 ($_3$5=S, Se)" (2604.01810)