Emergent dimensional reduction in a distorted kagome magnet $\mathrm{YCa_3(CrO)_3(BO_3)_4}$ driven by exchange hierarchy

Abstract

Frustrated kagome magnets provide a fertile platform for unconventional collective quantum phenomena, yet the role of lattice distortion in reorganizing magnetic degrees of freedom and controlling low-energy physics remains poorly understood. Here we report a rare realization of dimensional reduction in the distorted kagome material $\mathrm{YCa_3(CrO)_3(BO_3)_4}$, combining thermodynamic experiments with first-principles calculations and large-scale Monte Carlo simulations. Magnetic susceptibility and specific heat show no signatures of spin freezing or long-range magnetic order down to $65~\mathrm{mK}$ despite strong antiferromagnetic interactions. Instead, the susceptibility exhibits a broad maximum characteristic of quasi-one-dimensional spin correlations, while the magnetic specific heat follows a robust power law $C_{\mathrm{mag}}\sim T^2$ over more than a decade in temperature that remains unchanged in applied magnetic fields. This field-independent scaling rules out impurity or conventional magnon contributions and points to a collective low-energy excitation spectrum governed by frustration and local constraints. We show that a strongly hierarchical exchange network reorganizes the system into local antiferromagnetic dimers and weakly coupled spin chains, with frustrated inter-unit couplings suppressing three-dimensional order to ultralow temperatures. Our results demonstrate how a hierarchy of competing exchange interactions can reorganize a frustrated three-dimensional magnet into effectively lower-dimensional correlated units, stabilizing extended regimes of quantum-disordered behavior in realistic materials.

Figures (4)

• Figure 1: Structure and magnetization for YCa$_3$(CrO)$_3$(BO$_3$)$_4$. a Rietveld refinement of the powder x-ray diffraction pattern of polycrystalline YCa$_3$(CrO)$_3$(BO$_3$)$_4$ collected at room temperature, confirming phase purity and crystallization in the hexagonal space group $P6_3$. b Schematic representation of the crystal structure, highlighting the distorted kagome network of Cr$^{3+}$ ions within the $ab$ plane and the stacking of kagome layers along the crystallographic $c$ direction. c Temperature dependence of the magnetic susceptibility $\chi(T)$ measured down to 2 K under different applied magnetic fields. The broad maximum around $\sim 30$ K indicates dominant short-range spin correlations. The inset shows the magnetization isotherm at 2 K, demonstrating the absence of a hysteresis. d Temperature dependence of inverse magnetic susceptibility $1/\chi(T)$ with a Curie--Weiss fit at high temperatures (solid red line), yielding a large negative Curie--Weiss temperature. The inset shows the temperature dependence of zero-field-cooled (ZFC) and field-cooled (FC) susceptibilities, confirming the absence of spin- freezing.
• Figure 2: Specific heat for YCa$_3$(CrO)$_3$(BO$_3$)$_4$. a Temperature dependence of the total specific heat $C_p(T)$ measured in zero magnetic field. The solid red line represents the lattice contribution obtained from Debye--Einstein fit. The inset shows the magnetic specific heat $C_{\mathrm{mag}}(T)$ (left axis) and the corresponding magnetic entropy $\Delta S(T)$ (right axis), revealing substantial entropy release well above the lowest temperatures. b Magnetic specific heat $C_{\mathrm{mag}}(T)$ plotted on logarithmic scales under applied magnetic fields up to 9 T. The solid red lines indicate fits to a quadratic power law $C_{\mathrm{mag}}\sim T^2$. The persistence of this scaling and its insensitivity to magnetic field rule out impurity, Schottky, or conventional magnon contributions and point to a collective, constraint-dominated low-energy excitation spectrum governed by robust linearly dispersing modes.
• Figure 3: Hamiltonian and classical Monte Carlo calculations for $\mathrm{YCa_3(CrO)_3(BO_3)_4}$a Network of Cr$^{3+}$ ions in YCa$_3$(CrO)$_3$(BO$_3$)$_4$, illustrating the dominant and subdominant exchange paths obtained from first-principles energy mapping. The strongest antiferromagnetic coupling $J_1$ binds Cr$^{3+}$ moments into local dimers, while the second strongest coupling $J_2$ forms quasi-one-dimensional chains along the crystallographic $c$ direction. Weaker inter-dimer and inter-chain couplings form a dense but frustrated residual network, which suppresses coherent three-dimensional magnetic order. b Exchange couplings $J_i$ of YCa$_3$(CrO)$_3$(BO$_3$)$_4$ obtained from density-functional theory based energy mapping as a function of the on-site interaction strength $U$. Two exchange scales clearly dominate: the strong antiferromagnetic dimer coupling $J_1$ and the weaker but still substantial chain coupling $J_2$, while all remaining interactions are at least an order of magnitude smaller. The value of $U$ reproducing the experimental Curie--Weiss temperature ($\theta_{\mathrm{CW}}=-140$ K) is indicated, highlighting the strong separation of exchange energy scales in the material. c- d Classical Monte Carlo results for the realistic Heisenberg model of YCa$_3$(CrO)$_3$(BO$_3$)$_4$. c Uniform magnetic susceptibility $\chi(T)$ computed for increasing system sizes, exhibiting a broad maximum characteristic of low-dimensional antiferromagnetic correlations. d Magnetic specific heat $C_{\mathrm{mag}}(T)$ showing a low-temperature anomaly associated with the ordering tendency of the classical model. The smooth susceptibility maximum and the strong suppression of the classical ordering scale reflect the strong separation of energy scales imposed by the exchange hierarchy.
• Figure 4: The uniform susceptibility $\chi(T)$ of YCa$_3$(CrO)$_3$(BO$_3$)$_4$ combining classical Monte Carlo (cMC) simulations and experiment.a Fit of the cMC susceptibility (computed on a $4\times4\times10$ supercell with 2880 spins, shown per spin in simulation units) in the intermediate-temperature regime $10\le T\le120~\mathrm{K}$ to $\chi(T)=A\,\chi_{\mathrm{chain}}(T;J_{\mathrm{eff}})+b_0+b_1T$, where $\chi_{\mathrm{chain}}$ is a Bonner--Fisher--type Heisenberg-chain lineshape used as a shape function and the background is allowed to vary linearly. Weighted $\chi^2$ minimization yields $J_{\mathrm{eff}}=26.64\pm0.79~\mathrm{K}$ ($1\sigma$). b Same data fitted to $\chi(T)=A\,\chi_{\mathrm{chain}}(T;J_{\mathrm{eff}})+b_0$ with a constant background. This yields $J_{\mathrm{eff}}=23.71\pm0.24~\mathrm{K}$ ($1\sigma$). The systematic upward shift of $J_{\mathrm{eff}}$ in panel a quantifies the presence of additional smooth non-chain contributions to $\chi(T)$ arising primarily from strong dimer correlations. c Direct comparison with a pure Heisenberg-chain susceptibility at fixed exchange $J=J_2=33.4~\mathrm{K}$ (rescaled by a single prefactor to match the hump height). The dashed vertical line marks the maximum of the raw cMC data. Including the exact multiplet susceptibility of an antiferromagnetic $S=3/2$ dimer with $J_1\simeq116~\mathrm{K}$ improves the high-temperature curvature while leaving the position of the maximum essentially unchanged. This demonstrates that the temperature scale of the broad maximum is controlled by the quasi-one-dimensional chain coupling $J_2$, whereas strong dimer correlations primarily renormalize the Curie weight and smooth background of $\chi(T)$. d Experimental susceptibility (1000 Oe) compared to the cMC result converted to physical units using a single overall normalization factor $A$. After rescaling, the simulated curve reproduces the position and width of the experimental hump in the range $20$--$120~\mathrm{K}$ without additional adjustable energy scales. This agreement establishes that the microscopic exchange hierarchy derived from first principles quantitatively captures the dominant correlation scale governing the uniform susceptibility.