Interacting triplons in frustrated spin ladders: Binding and decay in ${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$

Letter

Interacting triplons in frustrated spin ladders: Binding and decay in ${BiCu}_{2} {PO}_{6}$

Leanna B. Müller and Götz S. Uhrig

Phys. Rev. B 107, L081102 – Published 3 February 2023

Abstract

Establishing a comprehensive model of the rich spin dynamics in ${BiCu}_{2} {PO}_{6}$ has been a challenge over the last decade. Inelastic neutron scattering experiments revealed that its elementary triplons are nondegenerate, showing the existence of significant anisotropic spin couplings. Evidence for triplon decay into two triplons has been found, but two prominent downturns in the dispersions eluded an explanation. Level repulsion due to hybridization of single triplons with the continuum of two-triplon scattering states has been proposed as an explanation. We show that this concept may explain the weak downturn at higher energies, but fails for the most pronounced downturn at lower energy. In turn, we provide evidence that this downturn is the signature of a two-triplon bound state of essentially singlet character pointing to a triplon-triplon interaction as the second crucial ingredient of the spin dynamics in this exemplary system.

Received 31 October 2022
Revised 16 January 2023
Accepted 23 January 2023

DOI:https://doi.org/10.1103/PhysRevB.107.L081102

Physics Subject Headings (PhySH)

Magnetic interactions Spin dynamics Triplon

Approximation methods for many-body systems Spin lattice models

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Leanna B. Müller and Götz S. Uhrig ^*

Condensed Matter Theory, TU Dortmund University, Otto-Hahn-Straße 4, 44227 Dortmund, Germany

^*goetz.uhrig@tu-dortmund.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 107, Iss. 8 — 15 February 2023

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Left: Sketch of the spin model for ${BiCu}_{2} {PO}_{6}$ ; blue spheres denote the ${Cu}^{2 +}$ ions hosting the spins $S = 1 / 2$ . The isotropic couplings $J_{0}, J_{1}$ , and $J_{2}$ define a single frustrated ladder while the isotropic interladder coupling $J^{'}$ weakly links adjacent ladders forming planes. Right: Sign of nonvanishing DM terms along the legs, parity with respect to reflection. The parity given for $D_{0}^{y}$ refers to its term in the Hamiltonian, not to $D_{0}^{y}$ itself.
Reuse & Permissions
Figure 2
Energies in the bilinear model for ${BiCu}_{2} {PO}_{6}$ for the parameters $J_{0} = 9.4 meV, J_{1} = 1.2 J_{0}, J_{2} = 0.9 J_{1}, J^{'} = 1.5 meV, D_{0}^{y} = 0, D_{1}^{x} = 0.48 J_{1}, D_{1}^{y} = 0.61 J_{1}, D_{2}^{x} = 0$ , and $D_{2}^{z} = - 0.02 J_{2}$ . Unlinked symbols are the experimental data from Refs. [5, 62].
Reuse & Permissions
Figure 3
Dispersion in the trilinear model. Energetically low-lying dispersion including the hybridization between the one- and the two-triplon states. A weak down-bending occurs before the single triplon dispersion enters the two-triplon continua at about $k = 0.75$ r.l.u. The parameters used are $J_{0} = 8.0 meV, J_{1} = 1.2 J_{0}, J_{2} = 0.9 J_{1}, J^{'} = 0.16 J_{0}, D_{0}^{y} = 0.1 J_{0}, D_{1}^{x} = 0.25 J_{1}, D_{1}^{y} = 0.38 J_{1}, D_{2}^{x} = 0.0$ , and $D_{2}^{z} = - 0.09 J_{2}$ . The dashed lines represent the lower edges of the two-triplon continua. The yellow curve is computed from the highest yellow dispersion, and the green one from the green dispersion. All other four continua edges lie between the two depicted continuum edges. Unlinked open circles are the experimental data from Refs. [5, 62]. The unlinked open triangles indicate resonances within the two-triplon continuum and the vertical bars show their half width at half maximum (HWHM) being proportional to the decay rate.
Reuse & Permissions
Figure 4
Isolated spin ladder for $J_{1} = 1.2 J_{0}, J_{2} = 0.9 J_{1}$ : The one-triplon dispersion in black, and two-triplon continuum is colored; the $S_{tot} = 0$ bound state is shown by the dotted red line, and the $S_{tot} = 1$ bound state by the dotted gray line. The wave number is given in units of $π$ with a lattice constant of unity. This corresponds to the reciprocal lattice units of ${BiCu}_{2} {PO}_{6}$ where the lattice constant is the distance between next-nearest-neighbor rungs [2, 6].
Reuse & Permissions
Figure 5
Energies in the quadrilinear model for ${BiCu}_{2} {PO}_{6}$ for $J_{0} = 8.0 meV, J_{1} = 1.2 J_{0}, J_{2} = 0.9 J_{1}, J^{'} = 0.16 J_{0}, D_{0}^{y} = 0.1 J_{0}, D_{1}^{x} = 0.25 J_{1}, D_{1}^{y} = 0.38 J_{1}, D_{2}^{x} = 0.0$ , and $D_{2}^{z} = - 0.06 J_{2}$ . The green (blue) dashed line shows the lower continuum edge derived from the dispersion displayed as a green (blue) solid line. Unlinked open circles are the experimental data from Refs. [5, 62]. The unlinked open triangles indicate resonances within the two-triplon continuum and the vertical bars show their HWHM being proportional to the decay rate.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Interacting triplons in frustrated spin ladders: Binding and decay in ${BiCu}_{2} {PO}_{6}$

Leanna B. Müller and Götz S. Uhrig

Phys. Rev. B 107, L081102 – Published 3 February 2023

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Interacting triplons in frustrated spin ladders: Binding and decay in BiCu2PO6

Leanna B. Müller and Götz S. Uhrig

Phys. Rev. B 107, L081102 – Published 3 February 2023

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Interacting triplons in frustrated spin ladders: Binding and decay in ${BiCu}_{2} {PO}_{6}$