Self-organised magnon condensation in quasi-1D edge-shared cuprates without external fields

TL;DR

The paper addresses the challenge of stabilizing multimagnon bound states (MBS) in low-dimensional quantum magnets and proposes a self-organised mechanism in quasi-one-dimensional edge-shared cuprates where small antiferromagnetic interchain couplings act as an effective internal field, enabling magnon condensation at zero external field ($h=0$) via collinear antiferromagnetic ordering; this approach is supported by theory, numerical simulations, and experimental data across Li$_2$CuO$_2$, Ca$_2$Y$_2$Cu$_5$O$_{10}$, LiCuSbO$_4$, and PbCuSO$_4$(OH)$_2$. The authors introduce the magnon binding energy framework $E_b(M,p)$ to quantify bound states in 1D chains under external fields and show how the bound-state number $p$ evolves with $J_2/|J_1|$, predicting nematic ($p=2$) and triatic ($p=3$) ground states near saturation. Using mean-field and DMRG/DDMRG techniques, they demonstrate that interchain couplings generate an effective staggered field $h_{ m stag}$, driving CAFO and enabling zero-field MBS, with magnetisation $m=rac{1}{l_x l_y}ig| extstyle extstyleig|ig|ig|ig|ig|ig|ig|ig|$ and MES spectra $G_p(
omega)$ revealing ground states dominated by $p=2$ or $p=3$. The work identifies experimental pathways to realize zero-field MBS, notably via pressure- or chemical-tuning to strengthen interchain couplings in materials like Li$_2$CuO$_2$, LiCuSbO$_4$, Ca$_2$Y$_2$Cu$_5$O$_{10}$, and PbCuSO$_4$(OH)$_2$, with potential applications in magnon-based quantum computing and low-power spintronics.

Abstract

Multimagnon bound states were predicted nearly a century ago and have since been a key topic in condensed matter physics due to their intriguing quantum properties. However, their realization in natural materials remains elusive, especially in low-dimensional quantum magnets, where stabilizing them is particularly challenging due to the traditionally required extreme external magnetic fields. Therefore, we introduce a novel mechanism that enables the stabilization of multimagnon bound states in quasi-one-dimensional edge-shared cuprates. Our theoretical framework, supported by numerical simulations and experimental data, demonstrates that small antiferromagnetic interchain couplings act as effective internal magnetic fields, promoting a collinear antiferromagnetic order and enabling magnon condensation even at zero external field. This intrinsic stabilisation mechanism eliminates the need for high external fields, offering a platform that is more accessible for experimental realization. We validate this concept by applying it to representative materials such as Li$_2$CuO$_2$, Ca$_2$Y$_2$Cu$5$O$_{10}$, LiCuSbO$_4$, and PbCuSO$_4$(OH)$_2$. Beyond its experimental feasibility, this mechanism could drive advancements in magnon-based quantum computing, low-power spintronic devices, and high-speed magnonic circuits. Moreover, our findings reveal that small interchain and/or interlayer couplings can generally unlock previously overlooked magnetic phenomena, redefining the nature of magnetically ordered states and expanding the frontiers of quantum magnetism.

Figures (5)

• Figure 1: (a) Schematic illustration of the MBS driven by interchain coupling, corresponding to a triatic state with three magnons bound together. The yellow lines represent transverse spin fluctuations. Crystal structures of (b) Li$_2$CuO$_2$, showing two CuO$_2$ chains per unit cell along the b axis, and (c) Ca$_2$Y$_2$Cu$5$O$_{10}$, showing two CuO$_2$ chains per unit cell along the a axis. Red and blue arrows in (b) and (c) indicate an example of symmetry-broken magnetisation directions in the CAFO state. Structure of interchain couplings for compounds such as (d) Li$_2$CuO$_2$ and Ca$_2$Y$_2$Cu$5$O$_{10}$, and (e) LiCuSbO$_4$ and PbCuSO$_4$(OH)$_2$. (f) Schematic of the chain positions used in the numerical 2-chain, 4-chain, and 8-chain calculations, where the dashed lines denote the interchain coupling (see also Ref. J_Phys_Conf_Ser_400_032069).
• Figure 2: (a) Schematic illustrations of (top) the fully polarised state, (middle) the state with two flipped spins far apart -- individual magnons --, and (bottom) the state with two adjacent flipped spins -- bounded magnons --. (b) Propagation number $\theta$ (black circles) of the $J_1$-$J_2$ chain at zero magnetic field as a function of $J_2/\lvert J_1\rvert$, and the relationship between the number of bound magnons $p$ in the MES at the saturation field. The propagation number is fitted by $\theta/\pi=0.69(J_2/\lvert J_1\rvert)^{0.29}$ near $J_2/\lvert J_1\rvert=1/4$. (c) Magnon binding energy $E_b(M_{\rm s}, p)$ corresponding to $p$ in the MES at the saturation field. The dashed line denotes $E_b(M_{\rm s}, p) \propto (J_2/\lvert J_1\rvert)^{\pi/2}$. (d) Ground state phase diagram for MBS as a function of $J_1/J_2$ (and $J_2/\lvert J_1\rvert$) and $M/M_{\rm s}$, with the magnon binding energy $E_b(M, p)$ depicted in a colour density plot corresponding to each phase.
• Figure 3: Magnetisation per site in the thermodynamic limit ($l_x \to \infty$) for various strengths of the XXZ anisotropy, evaluated at representative ratios $J_2/\lvert J_1\rvert=1/3$ and $1/2$. The magnetisation is presented as a function of the interchain couplings $J_{\rm a}$ and $J_{\rm b}$. Panels (a) and (b) illustrate the effects of introducing XXZ anisotropy on inchain and interchain couplings, respectively. The parameters used in the calculations of MES are marked with circles (see Fig. \ref{['fig:mes']}).
• Figure 4: (a) Schematic illustration distinguishing a MBS from a non-MBS within the MES framework. (b,c) DDMRG results for the MES $G_p(\omega)$ at various values of $p=1$, $2$, $3$, and $4$, for representative ratios $J_2/\lvert J_1\rvert=1/3$ and $1/2$, with the XXZ anisotropy applied to (b) intrachain and (c) interchain couplings. (d) Angle-resolved MES $G_1(k,\omega)$ and $G_2(k,\omega)$ for $J_2/\lvert J_1\rvert=1/2$, $J_{\rm a}/\lvert J_1\rvert=1.0$, and $\Delta_{\rm a}=0.1$.
• Figure 5: (a) DDMRG results for $G_p(\omega)$ ($p=1$ to $4$) using Li$_2$CuO$_2$ parameter set with $12 \times 8$-chain cluster. (b) Intensity map of the INS data extracted from Ref. Lorenz2009. (c,d) DDMRG results for $G_p(\omega)$ ($p=1$ to $4$) using the intrachain couplings for LiCuSbO$_4$ and PbCuSO$_4$(OH)$_2$ with $24 \times 4$-chain cluster. The interchain AFM couplings are set to be tunable parameter.