Magnetic ordering in a genuine organic crystal with triangular antiferromagnetic spin units

Abstract

A typical magnetic behavior has been studied in a genuine organic radical crystal of antiferromagnetic triangular spin units, N,N,N-Tris[p-(N-oxyl-tetra-butyamino)phenyl]amine. The magnetic susceptibility measurements indicate that a ground-state doublet is achieved within a molecule when the temperature is cooled down to about $60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ from $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, giving the effective spin value of each molecule at lower temperatures to be $S=1∕2$. Below $60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the magnetic susceptibility increases ferromagnetically down to $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, being followed by an antiferromagnetic decrease at lower temperatures. The analyses of the magnetic field dependence of heat capacity and magnetization reveals that the intermolecular ferromagnetic and antiferromagnetic interactions are working with the respective value $2{z}_{f}{J}_{f}∕{k}_{B}=6.0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $2{z}_{\mathrm{af}}{J}_{\mathrm{af}}∕{k}_{B}=\ensuremath{-}1.35\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which reasonably explains the observed value of the transition temperature ${T}_{N}(0)=0.74\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ at the field $H=0\phantom{\rule{0.3em}{0ex}}\mathrm{T}$: It is suggested that organic magnets order at the temperature predicted by Rushbrooke--Wood for isotropic Heisenberg spin systems, including not only the present tri-radical system, but also to the most typical genuine organic ferromagnets of mono-radical $(S=1∕2)$ and biradical $(S=1)$. A fully mapped temperature-magnetic field phase boundary is obtained to be described by a single formula ${T}_{N}(H)={T}_{N}(0){[1\ensuremath{-}{(H∕{H}_{c})}^{a}]}^{\ensuremath{\xi}}$ with the values ${T}_{N}(0)=0.735\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, ${H}_{c}=1.01\ifmmode\pm\else\textpm\fi{}0.01\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, $a=2.05\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\xi}=0.48+0.01$, where ${H}_{c}=2{H}_{\mathrm{ex}}=2\ifmmode\times\else\texttimes\fi{}2{z}_{\mathrm{af}}{J}_{\mathrm{af}}⟨S⟩∕g{\ensuremath{\mu}}_{B}$, without any trace of the existence of the bicritical point on it as seen in normal antiferromagnets with uniaxial anisotropy. It is discussed that the critical indices may be $a=2.0$ and $\ensuremath{\xi}=0.5$ for nonfrustrated antiferromagnets with infinitesimally small anisotropy.