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Abstract Spinel compounds are of great interest in both fundamental and application-oriented perspectives due to the geometric magnetic frustration inherent to their lattice and the resulting complex magnetic states. Here, we applied x-ray diffraction, magnetization, heat capacity and powder inelastic neutron scattering measurements, along with theoretical calculations, to study the exotic properties of chromite-spinel oxides CoCr₂O₄and MnCr₂O₄. The temperature dependence of the phonon spectra provides an insight into the correlation between oxygen motion and the magnetic order, as well as the magnetoelectric effect in the ground state of MnCr₂O₄. Moreover, spin-wave excitations in CoCr₂O₄and MnCr₂O₄are compared with Heisenberg model calculations. This approach enables the precise determination of exchange energies and offers a comprehensive understanding of the spin dynamics and relevant exchange interactions in complicated spiral spin ordering. 

Abstract Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides Equation missing<#comment/>(Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between Equation missing<#comment/>and Equation missing<#comment/>ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the Equation missing<#comment/>ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions. 

Abstract The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (J_eff) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho₂Ti₂O₇, and show that the magneto-chemical potential depends on the spin sublattice (αorβ), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates theJ_efffor theβ-sublattice. Additional simulations, including next-nearest neighbor interactions (J₂), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test forJ_effand the spin-spin interactions that contribute to it. 

Pyroxenes (AMX₂O₆) consisting of infinite one-dimensional edge-sharing MO₆chains and bridging XO₄tetrahedra are fertile ground for finding quantum materials. Thus, here, we have studied calcium cobalt germanate (CaCoGe₂O₆) and calcium cobalt silicate (CaCoSi₂O₆) crystals in depth. Heat capacity data show that the spins in both compounds are dominantly Ising-like, even after being manipulated by high magnetic fields. On cooling below the Néel temperatures, a sharp field–induced transition in magnetization is observed for CaCoGe₂O₆, while multiple magnetization plateaus beneath the full saturation moment are spotted for CaCoSi₂O₆. Our analysis shows that these contrasting behaviors potentially arise from the different electron configurations of germanium and silicon, in which the 3d orbitals are filled in the former but empty in the latter, enabling electron hopping. Thus, silicate tetrahedra can aid the interchain superexchange pathway between cobalt(II) ion centers, while germanate ones tend to block it during magnetization.