Geometrical frustration in the spin liquid beta'-Me3EtSb[Pd(dmit)2]2 and the valence bond solid Me3EtP[Pd(dmit)2]2

Abstract: We show that the electronic structures of the title compounds predicted by density functional theory (DFT) are well described by tight binding models. We determine the frustration ratio, J'/J, of the Heisenberg model on the anisotropic triangular lattice, which describes the spin degrees of freedom in the Mott insulating phase for a range of Pd(dmit)2 salts. All of the antiferromagnetic materials studied have J'/J < 0.5 or J'/J > 0.9, consistent with predictions for the Heisenberg model. All salts with 0.5 < J'/J < 0.9, where many-body theories find a number of competing ground states, are known, experimentally, to be charge ordered, valence bond solids or spin liquids.

• The paper analyzes the electronic structure and frustration ratios ($J'/J$) of Me3EtSb[Pd(dmit)2]2 and Me3EtP[Pd(dmit)2]2 using density functional theory.
• Calculated $J'/J$ values fall within an intermediate range ($0.5<J'/J<0.9$) predicted to exhibit spin liquid and valence bond solid states rather than typical antiferromagnetic order.
• The findings support the Heisenberg model's predictions for geometrically frustrated magnets and suggest pathways for designing new materials or tuning quantum states through pressure.

Geometrical Frustration in Organic Mott Insulators: Insights from Pd(dmit)$_2$ Salts

The study of geometrical frustration in the organic charge transfer salts Me$_{4-n}$Et$_nPn$[Pd(dmit)$_2$]$_2$ provides significant insights into the complex interplay of electronic correlations and lattice geometry, revealing intriguing phenomena like spin liquids and valence bond solids (VBS). This paper examines the electronic structures of Me$_3$EtSb[Pd(dmit)$_2$]$_2$ (Sb-1) and Me$_3$EtP[Pd(dmit)$_2$]$_2$ (P-1) through density functional theory (DFT) and situates these findings within the context of the Heisenberg model on an anisotropic triangular lattice.

Key Findings

1. Electronic Structure Analysis:
   • The band structures derived from DFT for both Sb-1 and P-1 suggest that these compounds can be effectively described using tight binding models. This analysis facilitates a deeper understanding of the complicated charge dynamics inherent in these systems. The Pd(dmit)$_2$ dimers play a crucial role in the electronic structure, with antibonding combinations of highest occupied molecular orbitals forming the primary conduction bands.
2. Frustration Ratio and Material Classification:
   • Calculations yield distinct frustration ratios, $J'/J$, for these materials. The values for Sb-1 ($J'/J \approx 0.62$) and P-1 ($J'/J \approx 0.75$) reside within a controversial intermediate region ($0.5AFM) order. Materials with $J'/J$ below 0.5 or above 0.9 generally exhibit AFM order, underscoring these theoretical predictions.
3. Role of Heisenberg Model:
   • The Heisenberg model with such geometric parameters predicts the absence of long-range magnetic order within the controversial range, aligning with experimental findings of spin liquid states in organic superconductors such as $\kappa$-(BEDT-TTF)$_2$Cu(CN)$_3$.
4. Implications of Ring Exchange:
   • The study postulates the role of ring exchange and higher-order terms in influencing ground state configurations where $J'/J$ lies within the critical interval. However, variations across salts are not attributed primarily to these factors, but rather, to competition among multiple near-degenerate states.

Implications and Future Directions

The implications of this research are multifaceted, both enhancing theoretical frameworks and guiding experimental explorations:

• Theoretical Enhancement:
  • This work enriches understanding of frustrated magnetism in organic Mott insulators, specifying computational parameters that correlate robustly with complex quantum states. The results encourage refining many-body theories to include competing interactions potentially overlooked in simpler models.
• Experimental Strategy:
  • Experimentally, these findings motivate targeted studies involving pressure application to modulate $J'/J$ ratios, possibly tuning superconductivity or other quantum phases by leveraging geometrical frustration.
• Material Design:
  • Insights into how alterations in chemical structure impact electronic properties pave the way for custom-designing new materials with desired quantum properties, bridging fundamental research with practical applications in future quantum technologies.

The presented research affords a coherent pathway for further theoretical and experimental studies, particularly in elucidating the intricate quantum behaviors near critical points in geometrically frustrated Mott insulators.