Kondo-Assisted Néel Order Achieves Magnetic Phase Transition in Spin-(1/2,1) Model

Researchers have long sought to understand how the Kondo effect and magnetic order compete within materials. Hironori Yamaguchi (Osaka Metropolitan University), Shunsuke C. Furuya (Saitama Medical University and the University of Tokyo), Yu Tominaga, et al, demonstrate a surprising result in this field with their investigation of the Kondo necklace model. They realised this model in a nickel-based complex, creating a simplified system that isolates spin interactions and reveals a novel mechanism where Kondo coupling actually stabilises Néel magnetic order. This finding challenges the conventional understanding of Kondo physics, establishing a crucial boundary: Kondo interactions promote singlet formation with spin-1/2 moments, but surprisingly favour magnetic order when coupled to spin-1 and higher.

They realised this model in a nickel-based complex, creating a simplified system that isolates spin interactions and reveals a novel mechanism where Kondo coupling actually stabilises Néel magnetic order.

Kondo Interactions Stabilising Magnetism in Ni-complexes are increasingly

Perturbative analysis corroborates these findings, establishing a clear picture of how the spin interactions are governed by the Kondo effect in this unique system. The Ni-based complex, [Ni(p-Py-V-p-F)(H2O)5]·2NO3, features a molecular structure where Ni atoms are surrounded by pyridine and water ligands, creating a six-coordinate environment conducive to the desired spin interactions. The observed magnetic susceptibility exhibits a temperature dependence consistent with the Kondo necklace model, and magnetization curves demonstrate a clear response to external magnetic fields. Quantitative Monte Carlo (QMC) calculations, utilising J1/kB = 20.3 K and J2/kB = 9.9 K, align closely with experimental data, validating the theoretical framework and confirming the crucial role of the J2/J1 ratio in determining the magnetic behaviour. This research opens avenues for exploring exotic gapless symmetry-protected topological phases and provides a versatile platform for investigating entangled quantum states, potentially impacting future developments in spintronics and quantum materials.

Kondo Necklace Model and Magnetic Phase Transitions

Experiments employed a combination of Quantum Monte Carlo (QMC) methods and specific heat measurements to characterise the system’s behaviour. The team calculated the J2/J1 dependence of the magnetization curve using the QMC method, analysing data presented in figures detailing Cp (J/mol K) values at varying temperatures. Specific heat measurements were performed on [Ni(p-Py-V-p-F)(H2O)5]·2NO3, with temperature dependence of Cp recorded at magnetic fields ranging from 0 to 9.0 T, all for H//b, perpendicular to the chain direction. Low-temperature data was shifted for clarity, revealing a Schottky-type specific heat behaviour for the spin-1 monomer, obtained using an on-site anisotropy of D/kB=−1.2 K and gy=2.25.

To further investigate the field-induced decoupling state of the Ni spin, researchers performed Electron Spin Resonance (ESR) measurements on powder samples at 1.8 K. The team plotted resonance fields in a frequency-field diagram, assuming the spin-1 monomer corresponded to the decoupled S, and considered the on-site anisotropy as H = D(Sz)2 −μBH gS. Energy levels were calculated using evaluated parameters, D/kB=−1.2 K, gx=2.20, gy=2.25, and gz=2.34, demonstrating the field-induced decoupling of S and aligning with experimental results. The study also investigated the ground state using the spin Hamiltonian H = J1X j sj · sj+1 + J2X j sj · Sj + D X j (Sz j )2, revealing a Tomonaga, Luttinger liquid (TLL) state in the limit J2 ≪J1.

Kondo Necklace Model Exhibits Phase Transitions at Finite

The team measured the temperature dependence of magnetic susceptibility, finding that the product of susceptibility and temperature (χT) reached a maximum value, indicating the onset of magnetic ordering. Specifically, susceptibility measurements at 0.1 Tesla showed a peak, and the corresponding χT values were plotted, providing crucial data for understanding the magnetic behaviour. Data shows that the Ni-based complex exhibits a magnetization curve at 1.4 Kelvin, revealing a clear saturation of the magnetic moment. The observed magnetization curve was compared with Quantum Monte Carlo (QMC) calculations, with excellent agreement achieved using parameters J1/kB = 20.3 K and J2/kB = 9.9 K, validating the model’s accuracy. Measurements confirm that the ratio J2/J1 significantly influences the magnetization behaviour, with a clear 1/3 plateau emerging for J2/J1 ≥ 1.0, indicating full polarization of the effective spin-1/2 dimer. Conversely, for J2/J1 ≪ 1.0, the magnetization exhibits a steep rise towards 2/3, consistent with the model predictions.

Néel Order and Kondo Decoupling in Nickel Complex

Scientists have synthesized a nickel-based complex, [Ni(p-Py-V-p-F)(H2O)5]·2NO3, which embodies a spin-(1, 1/2) Kondo necklace model. This Néel order then induces symmetry breaking in the spin-1/2 chain, resulting in long-range magnetic order throughout the system, challenging the conventional Doniach scenario of magnetic suppression by Kondo interactions. The research establishes a clear boundary in Kondo physics: Kondo coupling drives spin-1/2 moments into singlets, but for spin ≥1, it universally stabilises long-range order. The authors acknowledge that the precise nature of the high-field phase requires further investigation. Future research directions include inelastic neutron scattering to directly track gap closing and excitations, and nuclear magnetic resonance to probe local fields and spin relaxation, providing deeper insight into the quantum correlations of the high-field phase. This work not only expands fundamental understanding of Kondo lattice physics but also suggests a mechanism for quantum-state control through the application of magnetic fields.