Realization of a triangular spin necklace in a verdazyl-based Ni complex

TL;DR

The study tackles designing and understanding geometrical frustration in a controllable 1D spin system by synthesizing a verdazyl-based Ni complex ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$]. Molecular-orbital calculations reveal a dominant AF exchange $J_0$ between inversion-related verdazyl radicals that forms singlets, leaving residual spins to create a frustrated triangular unit of $S_V=1/2$ and $S_{Ni}=1$. Magnetic susceptibility and specific heat measurements detect an AF-ordered state at $T_{ m N}=0.65$ K, whose signal is suppressed by an external field, consistent with field-induced decoupling of the spin-1 moments, further supported by ESR-determined easy-axis anisotropy with $D/k_B=-1.3$ K and $g$-values around $2.2$. The magnetization up to $51$ T indicates full polarization of the spin-1/2 and spin-1 components and supports a model where spin-1 decouples under field, thereby stabilizing long-range order through exchange couplings. This work demonstrates programmable molecular design as a platform for exploring frustration-driven quantum phases in low-dimensional materials.

Abstract

We successfully synthesized a verdazyl-based complex, ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$], in which Ni$^{2+}$ ions and verdazyl radicals form a one-dimensional, triangular spin necklace consisting of spin-1/2 and spin-1 units. Molecular orbital calculations reveal strong antiferromagnetic (AF) interactions between inversion-related radical pairs that form spin-1/2 singlet dimers. The remaining verdazyl and Ni$^{2+}$ spins form frustrated triangular units, creating a distinctive spin network. Magnetic susceptibility and specific heat measurements identify a phase transition to an AF order. The application of magnetic fields suppresses the phase transition signal, suggesting field-induced decoupling of the spin-1 moments. Electron spin resonance measurements are used to evaluate the easy-axis anisotropy of spin-1, which may promote the AF order. This work provides a rare example of a geometrically frustrated quantum spin chain realized via molecular design, thereby offering a platform for exploring frustration-driven quantum phases in low-dimensional materials.

Figures (4)

• Figure 1: (color online) (a) Molecular structure of ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$]. The hydrogen atoms have been omitted for clarity. (b) Molecular pair associated with the exchange interaction $J_0$. (c) Crystal structure forming a triangular spin necklace along the $c$ axis. The blue and green nodes represent the spin-1/2 on the radical and the spin-1 on the Ni ion, $S_{\rm{V}}$ and $S_{\rm{Ni}}$, respectively. The thick lines represent the exchange interactions. (d) Corresponding triangular spin necklace. (e) Crystal structure in the $ab$ plane. The broken line encloses the molecules comprising each triangular spin necklace along the $c$ axis.
• Figure 2: (color online) Temperature dependence of (a) the magnetic susceptibility ($\chi$ = $M/H$) and (b) $\chi$$T$ of ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$] at 0.1 T. The solid line represents the result calculated for a spin-1/2 AF dimer via $J_{\rm{0}}$. (b) Temperature dependence of the specific heat $C_{\rm{p}}$ of ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$]. The inset shows $C_{\rm{p}}$/$T$ at zero field with the expanded temperature regime.
• Figure 3: (color online) Magnetization curves of ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$] at 1.4 K under applied pulsed magnetic fields. The inset shows the low-field region measured in static magnetic fields at 1.8 K. The broken and solid lines represent the Brillouin function for spin-2 and spin-(1/2, 1), respectively.
• Figure 4: (color online) (a) Frequency dependence of ESR absorption spectra of ($m$-Py-V)$_3$[Ni(NO$_3$)$_2$] at 1.8 K. The arrows indicate the resonance fields. (b) Frequency-field plot of the resonance fields. Solid lines indicate the calculated resonance modes of the spin-1 monomer with on-site anisotropy. (c) Calculated energy branch of the the spin-1 monomer for $H$//$z$ and $H\perp z$. Arrows indicate spin-allowed transitions from the ground state, which correspond to the resonance modes.