Ising Supercriticality and Universal Magnetocalorics in Spiral Antiferromagnet Nd$_3$BWO$_9$

The celebrated analogy between the pressure-temperature phase diagram of a liquid-gas system and the field-temperature phase diagram of ferromagnet has long been a cornerstone for understanding universality of phase transitions and critical phenomena. Here we extend this analogy to a highly frustrated antiferromagnet, the kagome-layered spiral Ising compound Nd$3$BWO$9$. In its field-temperature phase diagram, we identify a metamagnetic transition line with a critical endpoint (CEP) and corresponding Ising supercritical regime (ISR). The CEP is located at $μ_0H{\mathrm{c}} \simeq 1.04$ T and $T{\mathrm{c}} \simeq 0.3$ K. Above this point, the ISR emerges with supercritical crossover lines that adhere to a universal scaling law, as evidenced by the specific heat and magnetic susceptibility measurements. Remarkably, we observe a highly sensitive field dependence in the magnetic cooling near the emergent CEP, characterized by a divergent magnetic Grüneisen ratio following $Γ_H \propto 1/t^{β+γ-1}$, with $β+ γ\simeq 1.563$ the critical exponents of 3D Ising universality class and $t \equiv (T-T_{\rm c})/T_{\rm c}$ the reduced temperature. Our adiabatic demagnetization measurements on Nd$_3$BWO$_9$ reveal a lowest temperature of 195 mK, achieved from the initial condition of 2 K and 4 T. The findings here pave the way for studying supercritical phenomena and magnetic cooling in rare-earth RE$_3$BWO$_9$ family and, more broadly, in Ising-anisotropic magnets like spin ices.

💡 Research Summary

This paper investigates the low‑temperature thermodynamic and magnetocaloric properties of the kagome‑layered spiral Ising antiferromagnet Nd₃BWO₉, revealing a magnetic‑field‑temperature phase diagram that mirrors the classic liquid‑gas analogy. The authors identify a first‑order metamagnetic transition line separating a 1/3‑magnetization plateau (“liquid‑like”) from a partially polarized phase (“gas‑like”). This line terminates at a critical endpoint (CEP) located at μ₀H_c ≈ 1.04 T and T_c ≈ 0.30 K. Above the CEP, an Ising supercritical regime (ISR) emerges, characterized by universal scaling laws of the three‑dimensional Ising universality class.

Specific‑heat measurements under c‑axis magnetic fields down to 100 mK show a sharp peak at the Néel temperature T_N ≈ 0.29 K, which shifts and broadens with field. A broad hump at T* ≈ 1 K, associated with short‑range correlations, evolves into two ridges (T*_L and T*_R) that delineate the ISR. These ridge positions obey the scaling relation h ∝ t^{β+γ}, where h = (H‑H_c)/H_c, t = (T‑T_c)/T_c, and β + γ ≈ 1.563, the sum of the 3D Ising critical exponents (β ≈ 0.326, γ ≈ 1.237). The authors further demonstrate that the singular part of the free energy yields a universal specific‑heat form C(H,T)=t^{‑α} Φ_C(x) with x = h t^{‑(β+γ)}, and the experimental data collapse onto the theoretical scaling function Φ_C.

Magnetization measurements provide the magnetic susceptibility χ = dM/dH. In the ISR, χ follows χ(H,T)=t^{‑γ} Φ_χ(x) with the same scaling variable x. By rescaling χ·t^{γ} versus x, the data from various temperatures collapse onto a single curve that matches the analytically calculated 3D Ising scaling function Φ_χ, confirming the universality of the supercritical regime.

Adiabatic demagnetization refrigeration (ADR) experiments map isentropic trajectories for different initial conditions (e.g., (H_i,T_i) = (4 T, 4 K) and (4 T, 2 K)). Within the ISR, the isentropes display pronounced dips, reflecting strong spin fluctuations. The magnetic Grüneisen ratio Γ_H ≡ (1/T)(∂T/∂H)_S exhibits a peak‑dip structure that sharpens as T → T_c, and the peak amplitude follows Γ_H ∝ t^{‑(β+γ‑1)} (≈ t^{‑0.563}) for T > T_c. Below T_c, the extrema diminish rapidly, indicating reduced cooling efficiency in the ordered phase.

The ADR measurements reveal a remarkable cooling performance: starting from 2 K at 4 T, the system cools to a minimum temperature of 195 mK when the field is reduced to the spin‑flip field μ₀H_SF ≈ 0.65 T. This “self‑cascading” cooling combines two mechanisms: (i) the supercritical magnetocaloric effect near H_c, driven by divergent fluctuations, and (ii) a release of proximate zero‑point entropy (ZPE) at H_SF, associated with topological domain‑wall proliferation in the spiral Ising tubes. Model calculations based on the spiral Ising tube Hamiltonian reproduce a macroscopic ground‑state degeneracy with an entropy S₀ ≈ 0.481 R per unit cell, accounting for the observed ZPE contribution.

Quantitatively, a modest 1 T field change ending at H_c yields a volumetric entropy change ΔS_m ≈ 83 mJ K⁻¹ cm⁻³ in the sub‑kelvin range, surpassing that of conventional paramagnetic salts such as CMN or NBCP. The high spin density (N ≈ 16.9 nm⁻³) of Nd₃BWO₉ underlies this large ΔS_m, while the low T_c ensures that the critical fluctuations remain accessible at millikelvin temperatures. Comparisons with other high‑density refrigerants (e.g., LiHoF₄, Dy₂Ti₂O₇) highlight that Nd₃BWO₉ uniquely combines a suppressed CEP due to frustration with a high spin concentration, making it an especially efficient sub‑kelvin magnetic refrigerant.

The authors discuss the broader significance of their findings. The liquid‑gas analogy, long established for ferromagnets via the Curie point, now extends to a frustrated antiferromagnet, confirming that the supercritical fluid concept is not limited to liquids or ferromagnets. The universal scaling observed suggests that any magnetic system belonging to the 3D Ising class and possessing a finite‑temperature CEP should exhibit similar supercritical magnetocaloric behavior. Potential candidates include spin‑ice materials (e.g., Dy₂Ti₂O₇) and pressure‑tuned quantum magnets such as SrCu₂(BO₃)₂, where a CEP has been reported in the pressure‑temperature plane.

In conclusion, the paper provides the first experimental demonstration of Ising supercriticality in a frustrated antiferromagnet, validates the associated universal scaling laws through specific heat, susceptibility, and Grüneisen ratio analyses, and leverages the supercritical regime to achieve record‑low temperatures via magnetic refrigeration. These results open a new avenue for exploring critical phenomena in frustrated magnets and for developing high‑performance, low‑temperature magnetic coolants based on Ising‑anisotropic materials.