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

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 $60\mathrm{K}$ from $300\mathrm{K}$, giving the effective spin value of each molecule at lower temperatures to be $S=1∕2$. Below $60\mathrm{K}$, the magnetic susceptibility increases ferromagnetically down to $1\mathrm{K}$, 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 $2z_f{J}_f∕k_B=6.0\mathrm{K}$ and $2z_{\mathrm{af}}{J}_{\mathrm{af}}∕k_B=-1.35\mathrm{K}$, which reasonably explains the observed value of the transition temperature $T_N\left(0\right)=0.74\mathrm{K}$ at the field $H=0\mathrm{T}$: 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 $T_N\left(H\right)=T_N\left(0\right){[1-{(H∕H_c)}^a]}^{\xi }$ with the values $T_N\left(0\right)=0.735\mathrm{K}$, $H_c=1.01\pm 0.01\mathrm{T}$, $a=2.05\pm 0.02$, and $\xi =0.48+0.01$, where $H_c=2H_{\mathrm{ex}}=2\times 2z_{\mathrm{af}}{J}_{\mathrm{af}}⟨S⟩∕g{\mu }_B$, 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 $\xi =0.5$ for nonfrustrated antiferromagnets with infinitesimally small anisotropy.

Figure 1

The prototype genuine organic mono-, bi-, and triradical molecules with ferromagnetic intermolecular interactions.

Figure 2

The schematization of intra- and intermolecular interactions in the case of biradical Dupeyredioxyl (a) and (b); $J_0$ is the intramolecular ferromagnetic interaction much stronger than the intermolecular interaction $J$ between $S=1∕2$-spins (a), and (b) is a schematized intermolecular interaction $J$ between $S=1$-spins (Ref. 5). The scheme (c) is a model of ferrimagnets composed of triradical molecules.

Figure 3

The magnetic susceptibility of Tris-NO measured in the field $0.5\mathrm{T}$, plotted $\chi T$ vs $T$ for $T>1.8\mathrm{K}$. The solid curve is the theoretical value for the triangular spin system for ${\Delta }_1=559\mathrm{K}$ and ${\Delta }_2=1015\mathrm{K}$ in Eq. (2). The inset is the low-temperature $\chi$ in the region $0.1–12\mathrm{K}$.

Figure 4

The low-temperature heat capacity of Tris-NO in the fields up to $8\mathrm{T}$. The solid line indicates the lattice contribution taken as $C_{\mathrm{l}}=0.02T^3(\mathrm{J}∕\mathrm{mol}∕\mathrm{K})$.

Figure 5

The temperature dependence of the magnetic entropy of Tris-NO at various external magnetic fields in the temperature region below $7\mathrm{K}$.

Figure 6

(a)The field dependence of low-temperature magnetic heat capacity of Tris-NO below $2\mathrm{K}$, for the field less than the critical field $H<H_c=1.01\mathrm{T}$. The absolute values are shifted for the eye. (b) The fully mapped $T\text{−}H$ phase diagram. The solid curve corresponds $T_N\left(H\right)=T_N\left(0\right){[1-{(H∕H_c)}^a]}^{\xi }$, with the values $T_c\left(0\right)=0.735\mathrm{K}$, $H_c=1.01\pm 0.01\mathrm{T}$, $a=2.05\pm 0.02$, and $\xi =0.48+0.01$.

Figure 7

The field dependence of the magnetic heat capacity of Tris-NO for the field $H<8\mathrm{T}$. The dotted curves correspond to the Schottky type heat capacities in the fields $H=3$, 5, and $8\mathrm{T}$.

Figure 8

The field dependence of the magnetization of Tris-NO at constant temperatures.

Figure 9

The magnetization of Tris-NO divided by the saturation value for $S=1∕2$ plotted against $g{\mu }_B{H}_0∕k_{B}T$. The solid curve is the Brillouin function for $S=1∕2$ with the value $\lambda =3.1(2zJ∕k_B=4.6\mathrm{K})$, and the dotted curve is for $S=3∕2$.

Figure 10

Molecular arrangement along the $c$ axis(a) and their projection on the $a\text{−}b$ plane(b) (Refs. 10, 18).