Possible Bose-Einstein condensation of magnons in a S = 5/2 honeycomb lattice

TL;DR

This work demonstrates field-induced quantum criticality consistent with magnon Bose–Einstein condensation in a quasi-two-dimensional $S=5/2$ honeycomb antiferromagnet, K$_4$MnMo$_4$O$_{15}$. Through combined thermodynamic measurements and density functional theory, the authors identify a dominant intraplanar exchange $J_1$ with weak interlayer coupling, observe a saturation field at $igl(mu_0 H_sigr)=6.4$ T, and extract critical exponents $T_N \,\propto \, (H_s - H)^{2/d}$ with $d=3$ and $C_{ m mag} \propto T^{1.45}$, signaling a 3D XY BEC quantum critical point. The results extend magnon BEC physics to high-spin, quasi-2D honeycomb systems and emphasize the influence of interplanar interactions and anisotropy on quantum critical behavior. These findings broaden the landscape of BEC-related quantum criticality and may guide future experimental probes of magnon bound states near $H_s$.

Abstract

Quantum magnets offer a unique platform for exploring exotic quantum phases and quantum phase transitions through external magnetic fields. A prominent example is the field-induced Bose--Einstein condensation (BEC) of magnons near the saturation field. While this behavior has been observed in low-spin systems, its realization in high-spin, quasi-two-dimensional magnets -- where multiple on-site excitations are possible -- remains exceptionally rare. Here, we report thermodynamic and density functional theory results on single crystals of the honeycomb-lattice antiferromagnet K$_{4}$MnMo$_{4}$O$_{15}$ with $S = 5/2$. The system undergoes a field-induced transition to a fully polarized state at the critical field $μ_{0}H_{\rm s} = 6.4$~T. Our results reveal possible thermodynamic signatures of magnon BEC, $T_{\mathrm{N}} \sim (H_{\rm s} - H)^{2/d}$ ($d = 3$), expanding the purview of BEC-driven quantum criticality to a high-spin, quasi-two-dimensional antiferromagnets with negligibly small anisotropy.

Figures (5)

• Figure 1: (a) Schematic of unit cells of K$_{4}$MnMo$_{4}$O$_{15}$, where Mn$^{2+}$ ions form a honeycomb lattice stacked along the $c$-axis. The interplanar interaction is indicated by the red dotted line labeled as $J{2}$. (b) Perpendicular view of the honeycomb plane formed by octahedrally coordinated Mn$^{2+}$ ions, where each Mn$^{2+}$ ion is connected to its nearest neighbor via the MoO$_4$ tetrahedra. The intraplanar nearest- and next-nearest-neighbor interactions are labeled as $J_1$ and $J_3$, respectively. (c) Powder X-ray diffraction pattern of a single crystal which has a preferred orientation of indexed (h00) peaks. Inset shows the optical images of single crystals of K$_4$MnMo$_4$O$_{15}$.
• Figure 2: (a) Temperature dependence of magnetic susceptibility measured in a field of $\mu_0H = 0.01$ T applied parallel and perpendicular to the ab-plane, with the $x$-axis plotted on a logarithmic scale. The solid green line represents the Curie–Weiss fit, while the dashed vertical lines indicate the broad maximum at $T_{\rm max} = 4.2$ K and the Néel temperature at $T_{\rm N} = 2.21$ K. The top inset displays the derivative of magnetic susceptibility as a function of temperature for the field applied perpendicular to the ab-plane. (b) Isothermal magnetization as a function of magnetic field parallel and perpendicular to the ab-plane at 1.8 K. (c) Temperature dependence of specific heat in zero field, where the solid orange line represents the Debye–Einstein model of the lattice contribution. The bottom inset zooms into the low-temperature region, revealing an anomaly at $T_{\rm N}$. (d) Magnetic specific heat as a function of temperature showing an anomaly at $T_{\rm N}$. The top inset shows the temperature dependence of the calculated entropy change in zero field.
• Figure 3: Variation of the three exchange interactions with respect to the on-site Coulomb interaction strength $U$. The vertical dashed pink line indicates the specific value for which the calculated exchange couplings reproduce the experimental Curie--Weiss temperature
• Figure 4: (a) Isothermal magnetization as a function of magnetic field and (b) its derivative. The dashed vertical lines indicate the position of the quantum critical point at the saturation field $\mu_0H_{\rm s} = 6.4$ T. (c) Temperature dependence of magnetic susceptibility at low temperatures under several magnetic fields. Dashed vertical lines indicate $T_{\rm N}$ and $T_{\rm max}$ at $\mu_0H = 0.01$ T, with their field-dependent shifts highlighted by orange arrows (for $T_{\rm max}$) and pink star arrows (for $T_{\rm N}$). (d) Temperature dependence of magnetic susceptibility in fields $\mu_{0}H\geq 6.4$ T at low temperatures. (e) Temperature dependence of specific heat at low-temperatures in several fields. The inset shows a magnified view of the anomaly up to 1.6 T. The orange and sky-blue arrows indicate the progressive shifts of $T_{\rm N}$ toward higher and lower temperatures, respectively. (f) Temperature dependence of specific heat divided by temperature for fields $\mu_{0}{H}> 6.4$ T. The solid lines represent a combination of fits to the nuclear Schottky contribution and the gapped behavior, as described in the text. Inset shows the field-dependent specific heat at $T$ = 300 mK. In all panels, the magnetic field was applied perpendicular to the ab-plane.
• Figure 5: (a) Temperature–magnetic field phase diagram with phase boundaries determined from the thermodynamic measurements, as indicated in the legend. The background shows a contour map of the magnetic specific heat divided by temperature. The dashed red line shows a linear field dependence of gap. (b) Scaling behaviour of $T_{\rm N}$ as a function of $\mu_{0}(H_{\rm s}-H)$ on a logarithmic scale. (c) Temperature dependence of magnetic specific heat at the critical field $\mu_{0}H_{\rm s}$ = 6.4 T on a logarithmic scale. The solid line indicates a $\sim T^{1.45}$ power-law behaviour.