Substituent effects on exchange anisotropy in single- and multiorbital organic radical magnets

The contribution of heavy-atom substituents to the overall spin-orbit interaction in two classes of organic radical molecular magnets is discussed. In “single-orbital” radicals, spin-orbit coupling (SOC) effects are well described with reference to pairwise anisotropic exchange interactions between singly occupied spin-bearing orbitals on neighboring molecules; anisotropy requires the presence of spin density on heavy-atom sites with principal quantum number $n>3$. In “multiorbital” radicals, SOC involving virtual orbitals also contributes to anisotropic exchange and, as a result, the presence of heavy ($n>3$) atoms in formally non-spin-bearing sites can enhance pseudodipolar ferromagnetic interaction terms. To demonstrate these effects, ferromagnetic and antiferromagnetic resonance spectroscopies have been used to probe the exchange anisotropy in two organic magnets, one a “single-orbital” ferromagnet, the other a “multiorbital” spin-canted antiferromagnet, both of which contain a heavy-atom iodine ($n=5$) substituent. While the symmetry of the singly occupied molecular orbital in both radicals precludes spin-orbit contributions from iodine to the overall exchange anisotropy, the symmetry and energetically low-lying nature of the lowest unoccupied molecular orbital in the latter allows for appreciable spin density at the site of iodine substitution and, hence, a large exchange anisotropy.

Figure 1

Valence bond (VB) representations of (a) “single-orbital” and (b) “multiorbital” bisdithiazolyl radicals 1 and 2 and their selenium-containing variants. Kohn-Sham singly occupied molecular orbital (SOMO) for (c) prototypal model 1A ($R_1/R_2=\mathrm{H}$) and (d) SOMO/LUMO pair for 2A ($R_2=\mathrm{H}$). (e) Two-site, two-orbital interaction diagram for two adjacent radicals, 1, expressing site-to-site exchange coupling, $J_{ij}$, in terms of the on-site Coulomb potential, $U$, and electron hopping, $t_{ij}^{00}$. (f) Two-site, four-orbital interaction diagram for two radicals, 2, with a small SOMO-LUMO gap, Δε. The SOMO-SOMO ($t_{ij}^{00}$) and SOMO-LUMO ($t_{ij}^{10}$ and $t_{ij}^{01}$) hopping integrals, and the SOMO-LUMO electron exchange integral, $K_{ii}^{01}$, are indicated [15].

Figure 2

(a) Herringbone packed arrays of slipped π stacks of 1D ($R_1/R_2=\mathrm{Et}$/Cl), space group $P\overline{4}{2}_{1}m$, viewed parallel to the $b$ axis [16]. (b) Head-over-tail packed layers of radicals in 2A•EtCN ($R_2=\mathrm{I}$), space group Pnma, viewed parallel to the $c$ axis [30]. (c) Magnetization $M$ versus $T$ at $H=100$ Oe for 1D ($R_1/R_2=\mathrm{Et}$/Cl) [16] and (d) for 2A•EtCN ($R_2=\mathrm{I}$) [30]. Hysteresis in $M$ versus $H$ at $T=2$ K for (e) 1D ($R_1/R_2=\mathrm{Et}$/Cl) [16] and (f) 2A•EtCN ($R_2=\mathrm{I}$) [30].

Figure 3

Calculated weighting function, ${\mathcal{P}}_{\mathrm{tot}}\left(0,\mathcal{E}\right)$, for 1A–1D ($R_1/R_2=\mathrm{Et}$/Cl) as a function of the width of the energy window $\mathcal{E}$ [15]. The limiting values of ${\mathcal{P}}_{\mathrm{tot}}\left(0,\mathcal{E}\right)$ appear in the same ratio as the average SOC constants for the heavy (S, Se) atoms in the molecule.

Figure 4

Calculated weighting functions (a) ${\mathcal{P}}_{\mathrm{tot}}\left(0,\mathcal{E}\right)$ for the SOMO and (b) ${\mathcal{P}}_{\mathrm{tot}}\left(1,\mathcal{E}\right)$ for the LUMO of 2A with $R_2=\mathrm{F}$, Cl, Br, I, as a function of the width of the energy window $\mathcal{E}$ [15].

Figure 5

(a) Normalized FMR spectra of 1D ($R_1/R_2=\mathrm{Et}$/I) and (b) AFMR spectra of 2A•EtCN ($R_2=\mathrm{I}$), shown both as a function of frequency (at 5 K) and temperature (see lower-right insets, with horizontal scale expanded); the frequencies and temperatures are indicated in the plots. The two observable turning points in (a) correspond to the easy-axis $\left({\mathbf{H}}_{\mathrm{app}}//z\mathrm{or}c\right)$ and hard-plane $\left({\mathbf{H}}_{\mathrm{app}}//xy\mathrm{or}ab\right)$ components of the spectra, as expected for a uniaxial system. The three features labeled $x, y$, and $z$ in (b) correspond to the spectral components of an orthorhombic spin-canted antiferromagnet, two of which vanish below 60 GHz (see main text and Fig. 6). A noticeable $g=2$.00 impurity signal (∗) can also be observed, most likely arising from solvent loss upon grinding the polycrystalline material. Although this signal appears quite strong in derivative mode, the double-integrated area accounts for less than 1% of the total spectral density and can thus be neglected in the analysis.

Figure 6

Resonance frequency versus field plot for the different spectral components (open circles) deduced from Fig. 5 for (a) 1D ($R_1/R_2=\mathrm{Et}$/I) and (b) 2A•EtCN ($R_2=\mathrm{I}$). The solid curves are fits to the data according to (a) Eq. (16) and (b) Eq. (17), from which the anisotropy fields, $H_{\mathrm{A}}$, are determined. The cyan dashed line and solid square data points in (b) correspond to the $g=2$.00 impurity signal (∗). The intercept on the abscissa at 20.6 kOe in (b) gives the spin-flop field $H_{\mathrm{SF}}$, while the inset shows a comparison between 2A ($R_2=\mathrm{F}$) [45] and 2A•EtCN ($R_2=\mathrm{I}$) at 112 GHz. This demonstrates a clear augmentation of the anisotropy upon introducing a heavier substituent at the $R_2$ position.