Spin-density distribution in the partially magnetized organic quantum magnet ${\mathrm{F}}_2\mathrm{PNNNO}$

Polarized neutron diffraction experiments on an organic magnetic material reveal a highly skewed distribution of spin density within the magnetic molecular unit. The very large magnitude of the observed effect is due to quantum spin fluctuations. The data are in quantitative agreement with direct diagonalization results for a model spin Hamiltonian, and provide insight on the actual microscopic origin of the relevant exchange interactions.

Figure 1

(Color online) (a) Molecular structure of ${\mathrm{F}}_2\mathrm{PNNNO}$. Hydrogen atoms are not shown. The shaded rectangles represent $S=1∕2$ carrying unpaired electrons distributed over the nitronyl nitroxide and tert-butyl nitroxide groups. (b) A schematic representation of the 4-spin Heisenberg Hamiltonian for a two-molecule ${\mathrm{F}}_2\mathrm{PNNNO}$ unit. $J_F$ and $J_{\mathrm{AF}}$ are ferromagnetic and antiferromagnetic exchange interactions, respectively. Vertical arrows represent individual spins in the classical ground state $\mid \uparrow \uparrow \downarrow \downarrow ⟩$. The actual quantum ground state has zero spin density throughout the tetramer.

Figure 2

(a) Calculated field dependence of the energy levels of an ${\mathrm{F}}_2\mathrm{PNNNO}$ spin tetramer. Heavy solid lines are the lowest energy $S=0$ and $S=1$ states. Dashed lines are $S=2$ states. More excited states are present above $35\mathrm{meV}$. The plot is laid over a filled-contour plot of the thermal population function $\exp (-\hslash \omega ∕T)$ for $T=10\mathrm{K}$ (0.1 contour step). (b) Calculated temperature dependence of the sum (dashed line) and difference (solid line) of the spin populations of the nitronyl nitroxide and tert-butyl nitroxide groups. The arrow indicates the experimental temperature.

Figure 3

(Color online) Experimental spin-density distribution in a ${\mathrm{F}}_2\mathrm{PNNNO}$ spin-tetramer at $T=10\mathrm{K}$, as reconstructed using the maximum entropy method. (a) and (b) are projections onto the $(a,b)$ and $(b,c)$ crystallographic planes, respectively. Overlaid are skeletal representations of ${\mathrm{F}}_2\mathrm{PNNNO}$ molecules as they are positioned within the crystallographic unit cell. Areas outlined with thick dashed lines were used to estimate the spin populations on the nitronyl nitroxide and tert-butyl nitroxide groups (see text).

Figure 4

(Color online) Experimental spin-density distribution in a ${\mathrm{F}}_2\mathrm{PNNNO}$ spin-tetramer at $H=7\mathrm{T}$ and $T=10\mathrm{K}$, as reconstructed using orbital model refinement (see text). The isosurfaces are drawn at $1\times {10}^{-3}{\mathrm{\mu }}_B∕{\mathrm{\AA }}^3$ (orange) and $-1\times {10}^{-3}{\mathrm{\mu }}_B∕{\mathrm{\AA }}^3$ (blue) levels. The axes show Cartesian coordinates in angstroms.