Theoretical explanation of the antiferromagnetic anisotropy in organic superconductors: A probe for the spin-density-wave amplitude and nesting vector

The experimentally observed anisotropy, in the spin-density-wave (SDW) state of tetramethyl-tetraselenafulvalene and tetramethyltetrathiafulvalene salts ${\left(\mathrm{TMT}C\mathrm{F}\right)}_{2}X$ ($C=\mathrm{Se} or \mathrm{S}$ and $X=\mathrm{As}{\mathrm{F}}_6,\mathrm{Cl}{\mathrm{O}}_4,\dots$), is quantitatively explained by pure dipolar anistropy in sulfur compounds and a competition between dipolar and spin-orbit coupling in selenium salts. In sulfur compounds, dipolar anisotropy leads to a hard axis close to $\mathbf{a}$. In selenium compounds, the competing spin-orbit interactions favor the stacking axis $\mathbf{a}$ (perpendicular to the molecular plane) and permute the hard and intermediate axes, as experimentally observed. We prove that the variations of the nesting vector $\mathbf{Q}$, recently confirmed by proton NMR, are responsible for the large differences observed in the anisotropy axes for different compounds with the same TMTCF cation. We calculate the eigenstates of the anisotropy tensor in terms of $\mathbf{Q}$ and deduce from the experimental anisotropy axes and antiferromagnetic resonance (AFMR) frequencies the amplitude $\delta$ and $\mathbf{Q}$ vector of the SDW for all the salts that have been experimentally investigated. Although the electrical properties of Se and S compounds strongly differ, their SDW states are strikingly similar with $\delta$ of order 10% and $0.1b^{*}<Q_b<0.4\mathrm{}{b}^{*}$.