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Journal of Physics Condensed Matter

2DNL dynamical response of the magnetoelectrically driven dimerized XXZ-chain

Wolfram Brenig

Published Oct 20, 2026• 0 citations
Publisher

Abstract

A study of the dynamical two-dimensional (2D) nonlinear response of the dimerized spin-1/2 chain to external electric fields is presented. The coupling of the spin system to light is set to arise from the inverse Dzyaloshinskii-Moriya interaction. In the XY-limit, we provide analytical expressions for the second-order nonlinear dynamical response function. Apart from multi spinon continua, this response displays a strong antidiagonal, i.e. galvanoelectric, feature in the 2D frequency plane. This allows to read off scattering rates of the fractional spinon excitations. For the XXZ-case, we focus on the interaction-driven renormalization of the light-matter coupling by considering vertex corrections which are induced by the zz-exchange. We show this renormalization to modify the spinon joint density of states significantly, potentially allowing for the formation of in-gap bound states. As a result, the vertex corrected light-matter coupling can induce a dramatic spectral weight transfer to lower energies for the dynamical response function within the 2D frequency plane.

DOI
10.1088/1361-648x/aeb697

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A study of the dynamical two-dimensional (2D) nonlinear response of the dimerized spin-1/2 chain to external electric fields is presented. The coupling of the spin system to light is set to arise from the inverse Dzyaloshinskii-Moriya interaction. In the XY-limit, we provide analytical expressions for the second-order nonlinear dynamical response function. Apart from multi spinon continua, this response displays a strong antidiagonal, i.e. galvanoelectric, feature in the 2D frequency plane. This allows to read off scattering rates of the fractional spinon excitations. For the XXZ-case, we focus on the interaction-driven renormalization of the light-matter coupling by considering vertex corrections which are induced by the zz-exchange. We show this renormalization to modify the spinon joint density of states significantly, potentially allowing for the formation of in-gap bound states. As a result, the vertex corrected light-matter coupling can induce a dramatic spectral weight transfer to lower energies for the dynamical response function within the 2D frequency plane.
Two-dimensional nonlinear dynamical response of the magnetoelectrically driven dimerized spin-1/21{/}21/2 chain
A study of the dynamical two-dimensional (2D) nonlinear response of the dimerized spin-1/21{/}21/2 chain to external electric fields is presented. The coupling of the spin system to those fields is set to arise from the inverse Dzyaloshinskii-Moriya interaction. In the XY-limit, we provide analytical expressions for the second-order nonlinear dynamical response function. Apart from multi spinon continua, this response displays a strong antidiagonal, i.e. galvanoelectric, feature in the 2D frequency plane. This allows to read off scattering rates of the fractional spinon excitations. For the XXZ-case, we focus on the interaction-driven renormalization of the light-matter coupling by considering vertex corrections which are induced by the zz-exchange. We show this renormalization to modify the spinon joint density of states significantly, potentially allowing for the formation of in-gap bound states. As a result, the vertex corrected light-matter coupling can induce a dramatic spectral weight transfer to lower energies for the dynamical response function within the 2D frequency plane.
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We consider a simple integrable model of a spin chain exhibiting the magnetoelectric effect (MEE). Starting from the periodic S=1/2S=1/2S=1/2 XXZ chain with Dzyaloshinskii-Moriya terms, which we consider as a local electric polarization in the spirit of the Katsura-Nagaosa-Baladsky (KNB) mechanism, we perform the mapping onto the conventional XXZ chain with twisted boundary conditions. Using the techniques of quantum transfer matrix and nonlinear integral equations we obtain the magnetization, electric polarization, and magnetoelectric tensor as functions of magnetic and electric field for arbitrary temperatures. We investigate these dependencies as well as the thermal behavior of the above-mentioned physical quantities, especially in the low-temperature regime. We found several regimes of polarization. Adjusting the magnetic field one can switch the system from one regime to another. The features of the critical properties connected with the MEE are also illustrated.
A spin-1/2 XYXYXY chain model of magnetoelectrics on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. Using nonuniform spin rotations, the model is reduced to a dimerized XYXYXY chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model and the zero- and finite-temperature magnetoelectric effects and obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.
The research presented here focuses on the theoretical investigation of spinons in quasi one-dimensional quantum spin chains from the perspective of neutron scattering, with emphasis placed on the calculation of dynamic spin structure factors for both unpolarised and polarised incident neutrons. Two anisotropic versions of the Heisenberg spin chain are considered for such an examination: the spin-1/21/21/2 antiferromagnetic XXZXXZXXZ model and the spin-1/21/21/2 ferromagnetic XYZXYZXYZ model.The XYZXYZXYZ model supports spinon scattering (modelled at finite temperature) and is related to the so-called Villain mode. The introduction of a perturbation in the form of an external transverse magnetic field or Dzyaloshinskii-Moriya interaction (DMI) leads to the emergence of incommensurability in the system; such a result is a signature of fractional excitations. The presence of these interactions also give rise to a chiral response associated with the spinons in the polarised term of the scattering cross section. The inelastic scattering cross section is computed for both unpolarised and polarised neutrons.In relation to the antiferromagnetic XXZXXZXXZ model, emphasis is on spinon pair creation (modelled at T=0rmKT = 0 {rm K}T=0rmK). Motivated by the presence of a chiral response in the case of the XYZXYZXYZ model mentioned above, a new technique is developed in order to incorporate DMI and the transverse magnetic field so that one can determine if there is a chiral property associated with the two-spinon system. This technique is numerical in nature and is based on Green function methods. Using the results produced by the Green function approach, the inelastic cross section in the presence of an external transverse magnetic field is computed for the first time. The result is compared with experimental neutron scattering data; good agreement is demonstrated between theory and experiments on rmCsCoBr3{rm CsCoBr}_3rmCsCoBr3​.Finally, the Green function approach is generalised to account for the interactions between spin chains in magnetic compounds described by a staggered field. Various dynamic structure factors are computed for this scenario with results compared to experiment; good agreement between the theory and experiments on rmRbCoCl3{rm RbCoCl}_3rmRbCoCl3​ is shown.