Directional selection of field-induced phases by weak anisotropy in triangular-lattice K$_2$Mn(SeO$_3$)$_2$

Abstract: Triangular-lattice systems host a variety of ground states, ranging from quantum spin liquids to magnetically ordered phases, the latter of which can exhibit a sequence of magnetic phase transitions under applied magnetic fields. Here, we report magnetic and thermodynamic measurements, combined with powder and single-crystal neutron diffraction, on a high-spin, nearly isotropic Mn$<sup>{2+}$ triangular-lattice system K$<em>2$Mn(SeO$_3$)$_2$. The compound undergoes long-range magnetic ordering below $T</em>\mathrm{N} \sim 4$~K in zero field. Contrary to expectations for an ideal Heisenberg system, the compound adopts an up-down-zero (UD0) magnetic structure down to the lowest temperature (0.05 K), rather than the commonly expected Y-type structure. This UD0 state is, however, highly sensitive to external magnetic fields. For fields applied along the $c$ axis, it is readily destabilized and replaced by the Y-type structure, followed by an up-up-down (UUD) phase corresponding to the 1/3 magnetization plateau. In contrast, when the field is applied within the triangular plane, the system evolves into a canted Y state at a higher critical field. These results reveal that weak anisotropy, though small in magnitude, exerts a strongly orientation-dependent influence, playing a key role in selecting the field-induced phases in this frustrated magnet.

• The paper demonstrates that weak anisotropy selects a novel up-down-zero (UD0) ground state instead of the expected Y-type order at zero field.
• Using magnetometry, calorimetry, and neutron diffraction, the study maps precise phase boundaries and quantized magnetization plateaus for different field directions.
• The findings underscore the key role of single-ion anisotropy and interlayer coupling in diverging from ideal Heisenberg behavior in triangular-lattice antiferromagnets.

Directional Selection of Field-Induced Phases by Weak Anisotropy in Triangular-Lattice K$_2$Mn(SeO$_3$)$_2$

Introduction

Triangular-lattice antiferromagnets provide a canonical platform for investigating geometric frustration, hosting a panoply of exotic ground states and field-induced phases, including spin liquids, spin supersolids, and various long-range ordered magnetic configurations. In the classical and near-Heisenberg limit, the prototypical expectation is a 120$^\circ$ non-collinear (Y-type) order at zero field, with field-tuned transitions to commensurate and incommensurate phases such as up-up-down (UUD) and V-type states. However, the extent to which weak anisotropy selects and modifies these phases, particularly in materials with high spin and negligible orbital angular momentum, remains largely unexplored. The study "Directional selection of field-induced phases by weak anisotropy in triangular-lattice K$_2$Mn(SeO$_3$)$_2$" (2604.12489) advances this direction by providing an in-depth experimental and symmetry analysis of K$_2$Mn(SeO$_3$)$_2$, a nearly isotropic $_3$0 triangular-lattice antiferromagnet.

Experimental Approach and Key Findings

Single crystals of K$_3$1Mn(SeO$_3$2)$_3$3 were synthesized via a high-temperature flux method. Extensive characterization involved dc/ac magnetometry, specific heat, and high-resolution neutron powder and single-crystal diffraction, yielding a comprehensive phase diagram as a function of temperature and external fields applied along distinct symmetry axes.

At zero field, long-range magnetic order develops below $_3$4 K. Contrary to the canonical Heisenberg scenario, the magnetic ground state is an up-down-zero (UD0) structure: one sublattice remains magnetically disordered (statistically zero moment), while the other two exhibit antiparallel alignment. This ground state persists down to 50 mK, as confirmed by both bulk thermodynamics and direct diffraction refinement. Notably, the expected coplanar Y-type state is not realized even at the lowest temperatures.

Application of modest external magnetic fields induces sharply different sequences of magnetic phases depending on orientation:

• For $_3$5 (easy axis): The zero-field UD0 phase is rapidly destabilized, giving way to the Y-type structure and subsequently to a classic UUD phase, evidenced by a quantized 1/3 magnetization plateau (magnetization $_3$6 1.64 μ$_3$7/Mn).
• For $_3$8 within the triangular plane ($_3$9 direction): The UD0 state evolves into a canted Y-type state via a distinct phase boundary at a higher critical field; the inverted-Y state scenario (Heisenberg expectation) is not realized.

Thermodynamic anomalies and neutron data are fully consistent with the proposed sequence, and the quantitative phase boundaries are mapped precisely. The refinement of propagation vectors and symmetry subgroups demonstrates that weak single-ion anisotropy ($_2$0) and interlayer coupling are non-negligible for spin orientation selection, despite nearly isotropic Curie-Weiss moments and negligible orbital contribution.

Numerical and Symmetry Analysis

Curie-Weiss temperatures, effective moments, and high-field magnetization evidence suggest that K$_2$1Mn(SeO$_2$2)$_2$3 is close to the Heisenberg limit. However, the weak but finite easy-axis anisotropy (with the c axis favored) impacts both ground state selection and the field-dependence of magnetic transitions.

Critical exponents extracted from the field-temperature phase boundaries reveal 3D Bose-Einstein condensation (BEC) signatures for the UUD state, with $_2$4 when fitted for $_2$5, close to the universal value for three-dimensional order ($_2$6). In zero field, the entropy measured via calorimetry evidences strong short-range order above $_2$7 and a first-order order-disorder transition, consistent with partial moment freezing expected for partially disordered (UD0) states.

Magnetic structure solutions utilize symmetry analysis (irreducible representations, magnetic space groups), allowing unambiguous distinction between competing models (e.g., UD0 vs. Y-type). The UD0 structure is decisively selected by moment-size analysis, refined neutron intensities, and temperature/field evolution.

Strong or Contradictory Claims

• Deviation from the archetypal Y-state at zero field: The realization of a robust UD0 ground state in a nearly Heisenberg, high-spin triangular magnet is not anticipated by standard models, especially given the small measured anisotropy. This challenges the common assumption that Heisenberg (or near-Heisenberg) systems would always favor Y-type order in zero field.
• Dominance of weak anisotropy in field-induced phase selection: Even extremely weak single-ion anisotropy ($_2$8 on the order of 0.001 meV) is sufficient to select markedly different field-induced phases depending on the direction of field application, in contradiction to naïve expectations for an isotropic system.
• Role of interlayer coupling: The data demonstrates that interlayer exchange, although weak, is essential to stabilize the 3D long-range order and the partial moment disorder.

Implications and Theoretical Significance

These findings highlight that real triangular-lattice antiferromagnets, even with large $_2$9 and minimal orbital effects, are generically susceptible to weak anisotropies and small additional interactions. In such systems, the phase space accessible under external field can deviate qualitatively from classic Heisenberg or XXZ model predictions.

On the theoretical side, the stabilization of a UD0 ground state in K$^\circ$0Mn(SeO$^\circ$1)$^\circ$2 calls for a re-examination of the role of anisotropies, especially in light of recent studies on the emergence of disordered, partially ordered, and supersolid phases in easy-axis quantum magnets. The clear experimental demonstration that such partial disorder can be the true ground state (not just a finite-$^\circ$3 effect, as in some earlier models) sets a benchmark for future theoretical work.

Moreover, the realization of 3D BEC universality class transitions in the phase diagram, and the dominance of field orientation in selecting field-induced order, provide a stringent testbed for effective spin Hamiltonians.

Outlook and Prospective Developments

Practically, these results underscore the necessity for precise characterization of anisotropic terms and interlayer couplings when modeling any transition-metal-based triangular lattice magnets, even in the limit of high spin and apparent quasi-isotropy.

Theoretically, future studies should address several directions:

• The possible existence of analogous partial-disorder ground states in other families (e.g., Na$^\circ$4BaCo(PO$^\circ$5)$^\circ$6, K$^\circ$7Co(SeO$^\circ$8)$^\circ$9) and clarify the parameter regimes where quantum or classical fluctuations select the UD0 state.
• The impact of the disordered sublattice on the low-energy excitation spectrum, specifically whether it induces spectral continua as observed in related compounds.
• Potential connections to nontrivial transport (e.g., anomalous Hall effect) or topological phenomena in frustrated magnets with partial disorder.

Experimentally, further inelastic neutron and resonance techniques are warranted to resolve the dynamical signatures of the UD0 and canted Y states.

Conclusion

The investigation of K$_2$0Mn(SeO$_2$1)$_2$2 reveals that even minimal single-ion anisotropy and weak interlayer interactions are capable of directing the selection of ground and field-induced phases in triangular-lattice antiferromagnets. The realization of a robust partially disordered UD0 ground state and field-orientation-dependent phase selection contradicts expectations from ideal isotropic models and compels a reconsideration of phase diagrams for "nearly Heisenberg" magnets. This work supplies an essential empirical reference for the future theoretical modeling of frustrated spin systems, with implications for quantum magnetism, magnetic order selection, and the emergent physics of field-tuned quantum phases.