Spin Diffusion and Magnetic Eigenoscillations Confined to Single Molecular Layers in the Organic Conductors $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathbf{N}(\mathrm{CN}{)}_2]X$ ($X=\mathrm{Cl},\mathrm{Br}$)

The layered organic compounds, $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]X$ $X=\mathrm{Cl}$, Br) are metals at ambient temperatures. At low temperatures, the Cl compound is a weakly ferromagnetic Mott insulator while the isostructural Br compound is a superconductor. We find by conduction electron spin resonance and antiferromagnetic resonance (AFMR) an extreme anisotropy of spin transport and magnetic interactions in these materials. In the metallic state spin diffusion is confined to single molecular layers within the spin lifetime of ${10}^{-9}\mathrm{s}$. Electrons diffuse several hundreds of nm without interlayer hopping. In the magnetically ordered insulating phase of the Cl compound we observe and calculate the four AFMR modes of the weakly coupled single molecular layers. The interplane exchange field is comparable or less than the typically 1 mT dipolar field and almost ${10}^6$ times less than the intralayer exchange field.

Figure 1

Crystal structure of the $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_{2}X$, $X=\mathrm{Cl}$, Br layered compounds. ${\phi }_{ab}$ and ${\phi }_{ac}$ denote angles from $\mathit{a}$ in the ($\mathit{a}$, $\mathit{b}$) and ($\mathit{a}$, $\mathit{c}$) planes, respectively. Electronic overlap between ET molecules in adjacent $A$ and $B$ layers is small, typically $t_{\perp }=0.1\mathrm{meV}$. In the metallic state, the Larmor frequencies of the two chemically equivalent but magnetically inequivalent layers, $A$ and $B$, are different in general magnetic field orientations.

Figure 2

Conduction electron spin resonance in $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2\mathrm{Cl}$ at 222.4 GHz and 250 K. (a) Typical derivative CESR spectra. The resolved lines of $A$ and $B$ layers at fields in general directions (${\phi }_{ab}=45°$ and ${\phi }_{ab}=71°$) prove the two dimensionality of spin diffusion. When the $A$ and $B$ layers are magnetically equivalent (${\phi }_{ab}=90°$ and ${\phi }_{bc}=45°$) a single line appears. The $\mathrm{K}{\mathrm{C}}_{60}$ reference at $H_0=7.94\mathrm{T}$ has a $g$ factor of $g_0=2.0006$. (b) Angular dependence of the CESR shift $\Delta H=H_0(g_0-g)/g$ in the ($\mathit{a}$,$\mathit{b}$) plane. The principal axes of the $g$-factor tensors in the $A$ and $B$ layers are tilted from the orthorhombic $\mathit{a}$ and $\mathit{b}$ axes. It follows from the 4 mT line splitting at ${\phi }_{ab}=10°$ that interlayer spin diffusion is blocked for at least 1.4 ns. Spectra and $g$-factor anisotropies of Cl and Br compounds are similar.

Figure 3

Antiferromagnetic resonance in $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2\mathrm{Cl}$ at $T=4\mathrm{K}$ and $\mathit{H}\parallel \mathit{b}$. The 4 modes are the $\alpha$ (green, blue) and $\beta$ (red, black) eigenoscillations of weakly coupled canted antiferromagnetic $A$ and $B$ layers. (a) AFMR spectrum at 111.2 GHz. $5\times$ amplified spectra are shown for higher field lines. (b) Resonance-field-frequency mode diagram. Symbols denote measured AFMR, lines are model calculations.

Figure 4

Observed (symbols) and calculated (lines) AFMR magnetic fields at 111.4 GHz. (a) In the ($\mathit{a}$, $\mathit{b}$) plane the $\alpha$ modes of $A$ and $B$ layers diverge as $\mathit{H}$ is tilted towards the Dzyaloshinskii-Moriya vectors at ${\phi }_{ab}\approx 45°$ and 135°. They are little affected by the interlayer interaction except at mode crossings near $\mathit{a}$ and $\mathit{b}$. (b) The degenerate AFMR mode in the ($\mathit{b}$, $\mathit{c}$) symmetry plane is split by the interlayer interaction. The $\pm 5°$ uncertainty in sample orientations and approximations in the calculation described in the text explain differences between experiment and theory.