Search for: All records

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. 

This paper completes the construction of $$p$$ -adic $$L$$ -functions for unitary groups. More precisely, in Harris, Li and Skinner [‘ $$p$$ -adic $$L$$ -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure’, Doc. Math. Extra Vol. (2006), 393–464 (electronic)], three of the authors proposed an approach to constructing such $$p$$ -adic $$L$$ -functions (Part I). Building on more recent results, including the first named author’s construction of Eisenstein measures and $$p$$ -adic differential operators [Eischen, ‘A $$p$$ -adic Eisenstein measure for unitary groups’, J. Reine Angew. Math. 699 (2015), 111–142; ‘ $$p$$ -adic differential operators on automorphic forms on unitary groups’, Ann. Inst. Fourier (Grenoble) 62 (1) (2012), 177–243], Part II of the present paper provides the calculations of local $$\unicode[STIX]{x1D701}$$ -integrals occurring in the Euler product (including at $$p$$ ). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.