Magnetic excitations in quasi-one-dimensional helimagnets: Magnon decays and influence of interchain interactions

Abstract

We present a comprehensive study of the magnetic properties of the long-range ordered quasi-one dimensional J1-J2 systems with a newly developed torque equilibrium spin-wave expansion approach, which can describe the spin Casimir and magnon decay effects in a unified framework. While the framework does not lose the generality, our discussion will be restricted to two representative systems, each of which has only one type of inter-chain coupling (J3 or J4) and is referred to the J3-or J4-system respectively. In spite of the long-range spiral order, the dynamical properties of these systems turn out to be highly nontrivial due to the incommensurate noncollinear spin configuration and the strong quantum fluctuation effects enhanced by the frustration and lowdimensionality. Both the systems show prominent spin Casimir effects induced by the vacuum fluctuation of the spin waves and related modification of the ordering vector, Lifshitz point's position and sublattice magnetization. In addition to these static properties, the dynamical behaviors of these systems are also remarkable. Significant and spontaneous magnon decay effects are manifested in the quantum corrections to the excitation spectrum, including the broadening of the spectrum linewidth and downward renormalization of the excitation energy. Furthermore, the excitation spectrum appears to be very sensitive to the types of the inter-chain coupling and manifests three distinct features: (i) the magnon decay patterns between J3-and J4-system are very different, (ii) the renormalized spectrum and the overall decay rate of the J3-and J4-systems show very different sensitivity to the magnetic anisotropy, and (iii) there is a nearly flat mode in the renormalized magnon spectrum of the J4-system along the X-M direction. By adjusting the strength of magnetic anisotropy and varying the approximation scheme, it is revealed that these striking distinct features are quite robust and have deep connection with both the spin Casimir and the magnon decay effects. Thus these special consequences of the inter-chain coupling on the spin wave dynamics may be served as a set of probes for different types of inter-chain couplings in experiments. At last, to guide experimental measurements such as inelastic neutron scattering in realistic materials and complement our theoretical framework, we develop the analytical theory of the dynamical structure factor within the torque equilibrium formulism and provide the explicit results of the quasi-one dimensional J1-J2 systems. arXiv:1610.06365v2 [cond-mat.str-el]a 4 c FIG. 1: Crystallographic structure of coupled edge-shared chain magnetic oxides with main intra-and inter-chain couplings J1, J2, J3 and J4 marked by red solid line, green solid arc, orange dotted line, and purple dash dotted line, respectively.

Torque equilibrium spin wave theory study of anisotropy and Dzyaloshinskii-Moriya interaction effects on the indirect K -edge RIXS spectrum of a triangular lattice antiferromagnet

“…Inclusion of DM interaction rounds the singularity with an angle that is greater than 2π. The root cause of this divergence originates from spin Casimir torque [28,29]. In a frustrated spiral system, the strong quantum fluctuation effect leads to failure in the first-order correction.…”

“…al. [28,29] it was clearly established that in certain situations a standard spin wave theory is no longer applicable due to the spin Casimir quantum effect, even when the system is long-range ordered. A important consequence of these quantum fluctuations is on the spiral state which can become unstable, which is different from the case of long-range-order melting.…”

“…We diagonalize H 2 ( α, η, Q) and treat H c 2 as a counterterm. Since we are considering a 1/S theory, we neglect the counterterm contributions from H c 3 and H c 4 [28,29]. Thus, we can write the Hamiltonian as…”

“…An appropriate theoretical treatment of interactions in a TLAF must consider spin wave quantum fluctuation effects [27]. Zero-point quantum fluctuations of a noncollinear ordered quantum magnet gives rise to spin Casimir effect [28,29]. As a spin analog of the Casimir effect in vacuum, the spin Casimir effect describes the various macroscopic Casimir forces and torques that can potentially emerge from the quantum spin system.…”

“…al. [28,29], proposed the torque equilibrium spin-wave theory (TESWT). The regularization scheme of TESWT formalism removes the naturally occuring divergences within the interacting 1/S-SWT formalism of the anisotropic quantum lattice model.…”