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.

Figures (15)

• Figure 1: Crystal structure of the quasi-1D CrSb$X_3$ ($X$=chalcogens) systems. (a) Top view in the $ac$ plane. The red-dashed line outlines the unit cell. The arrows indicate the spin directions for the AFM order with the easy axis $\hat{a}$ in CrSbS$_3$. (b) Cr$X_6$ double rutile chains, sharing four common edges, along the $\hat{b}$-axis. The blue, brown, and green spheres indicate Cr, Sb, and $X$ (S or Se) ions, respectively.
• Figure 2: Top: variations of energy difference $\Delta E_{\rm AFM-FM}$ between AFM and FM for both compounds, as changing the Cr-Cr bond length $d_{\rm Cr-Cr}$. The variations, indicated by the red (blue) lines for CrSbS$_3$ (CrSbSe$_3$), show approximately cubic variations, but evident discontinuities in the boundaries preceding the AFM–FM transition. In the mixed region of $3.48\lesssim d_{\rm Cr-Cr}\lesssim3.58$ (in units of Å), FM is energetically favored over AFM in CrSbS$_3$, while AFM is favored in CrSbSe$_3$. The experimental bond lengths for four AFM compounds ${\cal R}$CrS$_3$ (${\cal R}$= Sm, Nd, Ce, and La) and two FM compounds CrGdTe$_3$ and CrSiTe$_3$ are adapted from Ref. kikk and Ref. siber, respectively. Bottom: changes in Cr-$X2$-Cr bond angle, as varying $d_{\rm Cr-Cr}$, showing roughly linear variations. Here, $X_2$ denotes a chalcogen ion that mediates the intra-chain Cr–Cr superexchange interaction.
• Figure 3: NM total and atom-projected densities of states (DOSs) for $d_{\rm Cr-Cr}$=3.39, 3.48, 3.60, 3.66 Å (from top to bottom) in CrSbS$_3$ (a),(b), and CrSbSe$_3$ (c),(d). (a), (c) represent the experimental $d_{\rm Cr-Cr}$, while (b), (d) correspond to our optimized $d_{\rm Cr-Cr}$. These DOSs show a sharp peak at the Fermi energy $E_F$, characteristic in (quasi-)1D systems.
• Figure 4: FM band structure of CrSbSe$_3$, in the range of $-6$ eV to 4 eV containing Cr $d$ and $p$ bands of the other ions, at the experimental crystal structure with $d_{\rm Cr-Cr}=3.60$ Å. The top (bottom) panel corresponds to the majority (minority) channel, indicating an insulating state. Note that bands stick at the top of BZ along the $Z-U-R-T-Z$ line, as commonly appeared in the non-symmorphic crystals.
• Figure 5: FM total and atom-projected DOSs of CrSbSe$_3$, at the experimental structure with $d_{\rm Cr-Cr}=3.60$ Å, indicating an insulating state of $E_g\sim0.5$ eV and $t_{2g}^{3\uparrow}$.