Crystallography-driven molecularization of a two-dimensional spin-$3/2$ magnet

Abstract

Large-spin two-dimensional magnets are generally expected to develop conventional long-range order once the dominant exchange scale becomes appreciable. The layered spin-$3/2$ maple-leaf compound Na$_2$Mn$_3$O$_7$ defies this expectation: despite sizable antiferromagnetic interactions and no evident disorder, it exhibits no magnetic ordering and displays two well-separated thermodynamic crossover scales. We show that this behavior originates from a crystallography-driven molecularization of the magnetic degrees of freedom. The low-symmetry structure partitions the Mn sublattice into inequivalent exchange pathways, generating a pronounced hierarchy that nearly isolates antiferromagnetic hexagons. Magnetic correlations therefore develop in two stages: first within individual hexagons at a scale set by the dominant exchange, and only at much lower temperatures do frustrated inter-hexagon couplings attempt to establish coherence across the lattice. While isolated hexagons reproduce the two-step thermodynamic structure, the experimentally relevant temperature scales emerge only once the hexagons are embedded in the frustrated two-dimensional network. The resulting quantum ground state is magnetically disordered, characterized by strong intra-hexagon correlations and rapidly decaying inter-hexagon correlations. These results identify crystallographic inequivalence as a materials-level mechanism for stabilizing molecularized and quantum-disordered states even in large-spin two-dimensional magnets.

Figures (11)

• Figure 1: Hamiltonian of Na2Mn3O7 determined by DFT based energy mapping. (a) Nine exchange interactions of Na2Mn3O7 making up the maple leaf lattice as function of on-site interaction strength $U$, at fixed Hund's rule coupling $J_{\rm H}=0.76$ eV. The vertical line indicates the value $U=0.94$ eV at which the Heisenberg Hamiltonian parameters yield the Curie-Weiss temperature $T=-152$ K determined by Venkatesh et al.Venkatesh2020 from the experimental susceptibility. (b) Structure of the Na2Mn3O7 lattice with the nine "nearest neighbor" exchange paths constituting the distorted maple leaf lattice. Strong antiferromagnetic couplings $J_1$--$J_3$ stabilize local Néel order within hexagonal plaquettes. These hexagons are coupled by weaker, predominantly ferromagnetic interactions, which frustrate coherent inter-hexagon alignment and give rise to a stripe-like classical ordering tendency at an incommensurate wave vector which is classically determined to be $\mathbf{k}_0$ [see Eq. \ref{['eqn:k_classical']}]. The resulting classical state is only weakly stabilized and lies close to a regime where incipient order is melted by frustration rather than selected by order-by-disorder.
• Figure 2: Bulk thermodynamic properties obtained from cMC simulations of the full Heisenberg model given in Table \ref{['tab:couplings_transposed']}.(a) Magnetic specific heat $C(T)$ for several system sizes of $L\times L$ unit cells with periodic boundary conditions. The specific heat increases upon cooling and develops a broad plateau around $T\approx70$ K, followed by a weak low-temperature feature near $T\approx12$ K. (b) dc magnetic susceptibility $\chi(T)$ calculated under an applied magnetic field of $1.5$ T along the $z$ axis. A broad maximum appears near $T\approx116$ K. Dashed gray vertical markers indicate the temperatures of corresponding experimental features reported in Ref. Venkatesh2020.
• Figure 3: Equal-time spin correlations of the model given in Table \ref{['tab:couplings_transposed']}. (a) Momentum-resolved equal-time spin structure factor $S(\mathbf{q})$ obtained from cMC simulations at $T=1.8$ K, showing broad maxima at incommensurate wave vectors. Brillouin zone and extended Brillouin zone boundaries are shown by orange and green hexagons, respectively. (b) Form-factor-modulated powder-averaged structure factor $|F(q)|^2 S(q),\; (q = |\mathbf{q}|)$, computed from cMC and pf-FRG at $T=1.8$ K. Experimental neutron-scattering data and associated error profile (orange shaded region) are taken from Ref. Saha2023. The broad features and absence of sharp Bragg peaks reflect dominant short-range correlations and suppressed long-range magnetic order. (c) Static spin structure factor obtained from pf-FRG calculations. The structure factor displays broad maxima at wave vectors comparable to the classical results, yet remains smooth and finite, indicating that quantum fluctuations preserve the dominant short-range correlations while preventing their condensation into long-range order, consistent with a cluster-dominated quantum paramagnetic regime. The definitions of primitive lattice vectors and the basis vectors used to produce the above results are given in the Supplementary Note 3.
• Figure 4: Phase boundaries of the symmetrized nearest-neighbor maple-leaf model and the location of Na$_2$Mn$_3$O$_7$ in coupling space. The point marked as star is for the averaged nearest-neighbor couplings $J_h, J_t, J_d$ obtained from Table \ref{['tab:couplings_transposed']}, and the nine gray points are nine sets of nearest-neighbor $J_t-J_d$ combinations from the Table with the three nearest-neighbor $J_h$ averaged out. The region shaded in yellow is the best possible elliptical fit enclosing these ten coupling values. (a) Classical phase diagram (Luttinger--Tisza / energy minimization) in terms of the averaged couplings $(J_h,J_t,J_d)$, showing competing Néel, canted-$120^\circ$, and incommensurate (IC) phases. (b) Quantum phase boundaries from triplon mean-field theory (TMFT) [see Ref. Ghosh2024] and pf-FRG. While the two approaches give different quantitative estimates for the extent of the magnetically disordered regime, both bracket a finite parameter window where dipolar order is suppressed; the Na$_2$Mn$_3$O$_7$ coupling ratios fall inside this bracketed region.
• Figure 5: Real-space correlations from the pf-FRG analysis (symmetrized nearest-neighbor model, supplemented by leading further-neighbor couplings). Main panel: normalized equal-time correlations $|\langle S_0^z S_i^z\rangle|/|\langle S_0^z S_0^z\rangle|$ as a function of separation $|\mathbf{r}_i-\mathbf{r}_0|$, demonstrating strong antiferromagnetic correlations confined to individual hexagons and a rapid decay beyond the hexagonal unit. Inset: map of $|\langle S_0^z S_i^z\rangle|$ on the lattice; the reference site $0$ is highlighted explicitly. The finite but rapidly decaying inter-hexagon correlations distinguish this regime from a lattice of independent magnetic molecules.