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Communications Physics

Momentum-resolved spin-conserving two-triplon bound state and continuum in a cuprate ladder

Yi Tseng, Eugenio Paris, Kai Phillip Schmidt, Wenliang Zhang, Teguh Citra Asmara, Rabindranath Bag, Vladimir N. Strocov, Surjeet Singh, Justine Schlappa, Henrik Moodysson Rønnow, Thorsten Schmitt

Published Jun 12, 2023• 4 citations
Publisher

Abstract

Abstract Studying multi-particle elementary excitations has provided unique access to understand collective many-body phenomena in correlated electronic materials, paving the way towards constructing microscopic models. In this work, we perform O K-edge resonant inelastic X-ray scattering (RIXS) on the quasi-one-dimensional cuprate $${{{{{{\rm{Sr}}}}}}}_{14}{{{{{{\rm{Cu}}}}}}}_{24}{{{{{{\rm{O}}}}}}}_{41}$$ Sr 14 Cu 24 O 41 with weakly-doped spin ladders. The RIXS signal is dominated by a dispersing sharp mode ~ 270 meV on top of a damped incoherent component ~ 400-500 meV. Comparing with model calculations using the perturbative continuous unitary transformations method, the two components resemble the spin-conserving ΔS = 0 two-triplon bound state and continuum excitations in the spin ladders. Such multi-spin response with long-lived ΔS = 0 excitons is central to several exotic magnetic properties featuring Majorana fermions, yet remains unexplored given the generally weak cross-section with other experimental techniques. By investigating a simple spin-ladder model system, our study provides valuable insight into low-dimensional quantum magnetism.

DOI
10.1038/s42005-023-01250-9

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Abstract Studying multi-particle elementary excitations has provided unique access to understand collective many-body phenomena in correlated electronic materials, paving the way towards constructing microscopic models. In this work, we perform O K-edge resonant inelastic X-ray scattering (RIXS) on the quasi-one-dimensional cuprate Sr14Cu24O41{{{{{{\rm{Sr}}}}}}}_{14}{{{{{{\rm{Cu}}}}}}}_{24}{{{{{{\rm{O}}}}}}}_{41}Sr14​Cu24​O41​ Sr 14 Cu 24 O 41 with weakly-doped spin ladders. The RIXS signal is dominated by a dispersing sharp mode ~ 270 meV on top of a damped incoherent component ~ 400-500 meV. Comparing with model calculations using the perturbative continuous unitary transformations method, the two components resemble the spin-conserving ΔS = 0 two-triplon bound state and continuum excitations in the spin ladders. Such multi-spin response with long-lived ΔS = 0 excitons is central to several exotic magnetic properties featuring Majorana fermions, yet remains unexplored given the generally weak cross-section with other experimental techniques. By investigating a simple spin-ladder model system, our study provides valuable insight into low-dimensional quantum magnetism.
Resonant inelastic x-ray scattering (RIXS) has become an important tool for studying elementary excitations in correlated materials. Here, we present a systematic theoretical investigation of the Cu LLL-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC) and spin-conserving (SC) channels. The spectra are rich and host many exotic excitations. In the NSC channel of the undoped case, we identify one-triplon and bound triplet two-triplon excitations in the strong rung coupling limit, as well as confined spinons in the weak rung coupling limit. In the doped case, we observe a quasiparticle excitation formed from a bound charge and spin-1/21/21/2 in the strong rung coupling limit. In the SC channel, we also identify several new features, including bound singlet two-triplon excitations and confined spinons in the undoped ladders in the strong and weak rung coupling limits, respectively. Conversely, in the doped case, the SC channel primarily probes both gapless and gapped charge excitations. Finally, we revisit the available data for the ladder compound Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ in the context of our results.
We investigate magnetic excitations in the spin-ladder compound Sr_{14}Cu_{24}O_{41} using high-resolution Cu L_{3} edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as 100 +/- 30 meV. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.
Resonant inelastic x-ray scattering (RIXS) has proven a powerful tool to investigate dynamic magnetic correlations, yielding complementary insights compared to neutron scattering. A key issue is the interpretation of spectroscopic measurements in terms of quasi-particle excitations. In this paper we study the spin-conserving channel of RIXS spectra for two-leg quantum spin ladders using continuous unitary transformations. We find that multi-triplon continua and bound states are the leading contribution, opening new venues for observing and characterizing multi-triplons in quantum spin systems.
Resonant inelastic x-ray scattering (RIXS) at the oxygen K -edge has recently accessed multi-spinon excitations in the one-dimensional antiferromagnet (1D-AFM) Sr 2 CuO 3 , where four-spinon excitations are resolved separately from the two-spinon continuum. This technique, therefore, provides new opportunities to study fractionalized quasiparticle excitations in doped 1D-AFMs. To this end, we carried out exact diagonalization studies of the doped t – J model and provided predictions for oxygen K -edge RIXS experiments on doped 1D-AFMs. We show that the RIXS spectra are rich, containing distinct two- and four-spinon excitations, dispersive antiholon excitations, and combinations thereof. Our results highlight how RIXS complements inelastic neutron scattering experiments by accessing additional charge and spin components of fractionalized quasiparticles.
Abstract One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and emergent phenomena. The spin-1/2 Heisenberg chain with antiferromagnetic nearest neighbour interactions is an important reference system; its elementary magnetic excitations are spin-1/2 quasiparticles called spinons that are created in even numbers. However, while the excitation continuum associated with two-spinon states is routinely observed, the study of four-spinon and higher multi-spinon states is an open area of research. Here we show that four-spinon excitations can be accessed directly in Sr2CuO3 using resonant inelastic x-ray scattering (RIXS) in a region of phase space clearly separated from the two-spinon continuum. Our finding is made possible by the fundamental differences in the correlation function probed by RIXS in comparison to other probes. This advance holds promise as a tool in the search for novel quantum states and quantum spin liquids.
We compute the KKK- and L3{L}_{3}L3​-edge resonant inelastic x-ray-scattering (RIXS) spectrum of the columnar and the staggered quantum dimer states accessible to the square lattice Heisenberg magnet. Utilizing a bond-operator representation mean-field theory we investigate the RIXS features of the one- and two-triplon excitation spectrum supported by the quantum dimer model in the background of condensed singlet excitation. We find that the two-triplon excitation boundary lies within an energy range of 2.7J2(1.7J2)2.7{J}_{2}\phantom{\rule{0.28em}{0ex}}(1.7{J}_{2})2.7J2​(1.7J2​) to 9J2(7.5J2)9{J}_{2}\phantom{\rule{0.28em}{0ex}}(7.5{J}_{2})9J2​(7.5J2​) for the columnar (staggered) phase, where J2{J}_{2}J2​ is the interbond coupling strength. We estimated the two-triplon gap to be 2.7J22.7{J}_{2}2.7J2​ (1.7J2)(1.7{J}_{2})(1.7J2​) for the columnar (staggered) dimer phase. The highest intensity of the KKK-edge RIXS spectrum is localized approximately around the $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ point for both the columnar and the staggered phases. At the L3{L}_{3}L3​ edge we study the one- and two-triplon signal considering experimental scattering geometry, polarization restriction, and experimental resolution effects. Our calculations find a contribution to the two-triplon RIXS signal that originates from the local hard-core dimer constraint. This leads to a finite nonzero signal at the (0,0) momentum transfer which can offer an explanation for the existing ladder RIXS experiments and also predicts a nonzero signal for the two-dimensional quantum dimer system. We find that the L3{L}_{3}L3​-edge RIXS response of the one- and two-triplon signal could exist in antiphase rung modulation for zero and $\ensuremath{\pi}$ as found in inelastic neutron scattering. Since the disordered phase has the potential to harbor a variety of quantum paramagnetic states, our RIXS calculations provide useful signatures to identify the true nature of the ordering pattern.