Spin correlation and relaxational dynamics in molecular-based single-chain magnets

We report the combined measurements of the dc susceptibility ${\chi }_0$, the ac susceptibility ${\chi }^{\prime }$, and the NMR relaxation rate $T_1^{-1}$ for the molecular-based heterometallic single-chain magnet ${\left[\mathrm{Mn}\left(\text{saltmen}\right)\right]}_2\left[\mathrm{Ni}{\left(\mathrm{pao}\right)}_2{\left(\mathrm{py}\right)}_2\right]{\left(\mathrm{P}{\mathrm{F}}_6\right)}_2$. At low temperatures, this system is well described by a one-dimensional array of effective spin $S=3$ chains comprising the ${\mathrm{Mn}}^{\mathrm{III}}\text{−}{\mathrm{Ni}}^{\mathrm{II}}\text{−}{\mathrm{Mn}}^{\mathrm{III}}$ trimers and treated as the $S=3$ Ising chain with the single-ion term (Blume-Capel model). Using the exact solution of the model and based on the picture that the random motion of the local domain walls dominates the low-temperature spin dynamics, we succeeded in reproducing the experimental results of the dc susceptibility ${\chi }_0$, the ac susceptibility ${\chi }^{\prime }$, and the ${}^{19}\mathrm{F}\text{−}\mathrm{NMR}$ relaxation rate $T_1^{-1}$ in a consistent manner.

Figure 1

The chain structure of the compound comprising the $\left[{\mathrm{Mn}}^{\mathrm{III}}\text{−}{\mathrm{Ni}}^{\mathrm{II}}\text{−}{\mathrm{Mn}}^{\mathrm{III}}\right]$ trimers.

Figure 2

Profile of field-swept ${}^{19}\mathrm{F}$ NMR spectra for $120\mathrm{MHz}$ at different temperatures. The solid line indicates the free ${}^{19}\mathrm{F}$ resonance field for $120\mathrm{MHz}$.

Figure 3

A recovery of the intensity of a spin echo signal of ${}^{19}\mathrm{F}$ for $120\mathrm{MHz}$ at $T=5.0\mathrm{K}$. The solid line shows a two-exponential expression with $T_{1\mathrm{S}}=0.88\sec$ and $T_{1\mathrm{L}}=1.8\sec$.

Figure 4

Low-lying dispersion curves for one magnon, two magnons, three magnons, four magnons, and six magnons (cluster excitation), calculated by numerical exact diagonalization of finite-size clusters for the detailed Hamiltonian.

Figure 5

Lowest excitation energies plotted versus $S_{\mathrm{tot}}^z$ for $L=3$ and 4, shown as dashed and solid curves, respectively.

Figure 6

Excitation spectrum of the effective model (2) as a function of the total spin $S_{\mathrm{tot}}^z={\sum }_{i=1}^L{S}_i^z$ for the cases of (a) $L=3$ and (b) $L=4$ with the periodic boundary condition. We set $D∕J=-3.125$ (the same as those used to analyze the experimental data). The lower bounds of the spectrum are shown by the solid lines.

Figure 7

The experimental data for the dc susceptibility ${\chi }_0$, ac susceptibility ${\chi }^{\prime }$, and the NMR relaxation rate $T_{1\mathrm{S}}^{-1}$, respectively, for the applied dc magnetic field strength $H=1.5,2.0,3.0,4.0\mathrm{T}$. Fitting curves are given by Eqs. (3, 8, 7), respectively.

Figure 8

The same data of $T_{1\mathrm{S}}^{-1}$ as Fig. 4 are plotted against $1∕\sqrt{H}$. The curves are shifted parallel to the vertical axis to make the $1∕\sqrt{H}$ dependence easy to see.