Precise Determination of the Orientation of the Dzialoshinskii-Moriya Vector in $\kappa \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{C}\mathrm{u}[\mathrm{N}(\mathrm{C}\mathrm{N}{)}_2]\mathrm{C}\mathrm{l}$

A novel electron spin-reorientation transition is discovered by ${}^{13}\mathrm{C}$ NMR in the quasi-two-dimensional organic antiferromagnet $\kappa \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{C}\mathrm{u}[\mathrm{N}(\mathrm{C}\mathrm{N}{)}_2]\mathrm{C}\mathrm{l}$. The spin reorientation occurs as an external field is swept through the orientation of the characteristic vector of the Dzialoshinskii-Moriya (DM) interaction, thus providing a precise determination of the orientation of the DM vector. Such a spin reorientation could help to characterize the DM interaction in other antiferromagnetic systems.

Figure 1

Change of basis from sublattice moments ${\mathit{M}}_1$ and ${\mathit{M}}_2$ to staggered ${\mathit{M}}^{†}$ and ferromagnetic ${\mathit{M}}^F$ moments.

Figure 2

Two spin configurations with the same DM interaction energy are shown for the case of $\mathit{D}\parallel z$. The configuration on the left is the ground state for $\mathit{H}$ along $-x$, the configuration on the right the ground state for $\mathit{H}$ along $+x$.

Figure 3

Shift in ${}^{13}\mathrm{C}$ inner site resonance frequencies as a function of orientation of the applied field in the $a\mathrm{\text{−}}b$ plane. Lines are provided as a guide to the eye.

Figure 4

Shift in ${}^{13}\mathrm{C}$ resonance frequencies as a function of orientation of the applied field in the $a\mathrm{\text{−}}b$ plane ($\theta =90°$) and the $b\mathrm{\text{−}}c$ plane ($\varphi =90°$) for both layer $A$ (closed circles) and layer $B$ (open circles): (a) inner site; (b) outer site. Lines are from fits to the data using Eqs. (2, 3).