Phase-transition-driven ferroic response in 2D CuMnP_2Se_6 under ultra-low electric fields

Domain: physics
Published: 2025-12-13
Editorial outcome: minor_revision

Abstract
Low-field electric control of magnetic phase transitions is critical for the development of energy-efficient spintronic and non-volatile memory technologies. Yet, the weak magnetoelectric coupling in most known two-dimensional multiferroics hinders their practical implementation. Here, using crystal structure prediction and high-throughput first-principles calculations, we identify four previously unexplored bimetallic thio(seleno) phosphate multiferroics, XMnP2(S/Se)6 (X=Cu, Au), all exhibiting robust in-plane spontaneous polarization—contrasting with the predominantly out-of-plane behavior in this material family—which effectively mitigates depolarization effects. In particular, CuMnP2Se6 hosts two stable C2-symmetric ferroelectric phases with opposite in-plane polarizations and distinct magnetic orders. Remarkably, an electric field as small as ~0.001 V/Å can simultaneously reverse the polarization and induce an antiferromagnetic-to-ferromagnetic transition. The associated barrier is exceptionally low (~49 meV/f.u.), yielding a sizable magnetoelectric coefficient of ~0.04 G⋅cm/V. These results highlight a viable strategy for realizing electric-field-driven magnetism in intrinsic two-dimensional multiferroics under experimentally feasible conditions.

Introduction
Electric-field control of magnetism offers a promising route to reduce energy consumption in spintronic and memory devices, paving the way for low-power, non-volatile information technologies that could transform future computing paradigms1–3. To date, two primary mechanisms have been extensively investigated: (i) electric-field-induced magnetization switching4–6, and (ii) electric-field-driven magnetic phase transitions7–10. The former enables binary logic operations through spin-orbit torque-driven reversal of magnetization, whereas the latter involves switching between distinct magnetic phases—such as ferromagnetic (FM) and antiferromagnetic (AFM)—offering dynamic tunability between writable and interference-robust memory states. Realizing such functionality requires material systems where electric polarization and magnetic order are strongly coupled and reversibly tunable under experimentally accessible conditions.

Multiferroics, which simultaneously host two or more ferroic orders—such as magnetism, ferroelectricity, or ferroelasticity—within a single phase11, offer a natural platform for realizing intrinsic magnetoelectric (ME) coupling. However, electric-field-induced magnetic phase transitions in existing multiferroics remain rare, primarily due to the generally weak coupling between electric and magnetic order parameters. As a result, polarization reversal alone is often insufficient to drive a magnetic transition12–22. An alternative strategy leverages van der Waals heterostructures composed of 2D magnets and ferroelectrics, where electric control of magnetism arises from interfacial ME effects6,23–27. However, such heterostructures often suffer from weak interfacial coupling and require precise lattice matching and stacking control, posing significant challenges for scalable fabrication and long-term device stability28. Thus, identifying single-phase 2D multiferroics with strong intrinsic ME coupling has become a central pursuit in the field29–31. Despite increasing interest, such materials remain scarce. Moreover, the substantial switching barriers (>several hundred meV/f.u.) observed in most reported materials demand high electric fields (>0.1 V/Å), creating a major bottleneck for their application in energy-efficient electronics.

In this study, we report four stable 2D bimetallic thio(seleno) phosphate (BMTP) multiferroics, XMnP2(S/Se)6 (X = Cu, Au), each exhibiting two inequivalent C2-symmetric phases with opposite in-plane spontaneous polarizations, which helps mitigate depolarization fields. Notably, CuMnP2Se6 features two such C2 phases with distinct magnetic ground states—FM and AFM. An ultralow electric field of ~0.001 V/Å can drive a structural transition between these phases, thereby reversing the polarization and switching the magnetic order simultaneously. The transition is characterized by a remarkably low switching barrier (~49 meV/f.u.) and a sizable ME coupling coefficient (~0.04 G⋅cm/V). These findings demonstrate strong ME coupling and ultralow switching barriers in 2D BMTPs, highlighting their potential as a promising platform for electric-field control of magnetic phase transitions under experimentally accessible conditions.

Results
In-plane polarization in CuMnP2Se6
The BMTPs with the general formula XYP2(S/Se)6 (X, Y = transition metals), crystallize in van der Waals layered structures and represent a versatile family of emerging piezoelectric, ferroelectric, and multiferroic materials32–35. Their compositional flexibility—achieved by varying X and Y elements such as Cu, Ag, In, Cr, and V—enables systematic tuning of electronic, ferroelectric, and magnetic properties36–39. Dimensional reduction to monolayers via mechanical exfoliation offers an effective pathway to tailor ferroic behaviors40–43, with improved control over polarization and magnetic states.

A prototypical 2D BMTP structure, exemplified by CuCrP2S6, consists of metal cations intercalated within a hexagonal framework composed of ethane-like [P2S6]4− units with C3 symmetry. The Cu1+ and Cr3+ cations alternately occupy interstitial sites, forming a secondary honeycomb sublattice. Each Cr3+ ion is centered within an octahedron of six S2− ligands, accounting for the magnetic behavior, while the out-of-plane displacement of Cu1+ ion gives rise to spontaneous polarization44. The out-of-plane (OOP) polarization switching proceeds through a nonpolar (NP) intermediate phase which possesses D3 symmetry. Notably, a broad range of 2D BMTPs can be derived by substituting different transition-metal species into this structural motif36–39,45.

To further explore the structural landscape of 2D BMTP family, we performed ab initio structure searches for CuMnP2Se6 using the CALYPSO method46–51. We selected Mn as the Y-site transition metal because Mn3+ possesses a high-spin d4 electron configuration. In an MnSe6 octahedral environment, the Mn3+ ion adopts a t2g3 eg1 configuration, which is well known to produce a strong Jahn-Teller instability (Supplementary Fig. 1). The singly occupied eg orbital (dz2 or dx2−y2) directly overlaps with the ligand p orbitals, leading to pronounced structural distortion of MnSe6 octahedra, involving tetragonal compression or tetragonal elongation (Supplementary Table 1). This situation stands in sharp contrast to other 2D BMTPs such as CuCrP2Se6 (Cr3+, t2g3), CuVP2Se6 (V3+, t2g2) and CuFeP2Se6 (Fe3+, t2g3 eg2), where the transition-metal ions are Jahn-Teller inactive. Consequently, the strong Jahn-Teller activity of Mn3+ may facilitate the emergence of new structural prototypes that are inaccessible to other transition metals.

As expected, two low-energy polar prototypes with C2 symmetry were identified, referred to as the D-type and C-type phases, characterized by the formation of Cu-Mn dimer-like units and -Cu-Mn-Cu-Mn-chain-like configurations, respectively. In contrast to conventional BMTP structures, where the X cation typically displaces vertically from the center of its octahedron, the X ion in both newly identified phases remains centered, accompanied by slight in-plane displacements. These displacements give rise to spontaneous in-plane polarization. Specifically, the D-type and C-type structures exhibit opposite in-plane polarization directions along [110] and [110], respectively. This behavior stands in sharp contrast to most previously reported 2D BMTP multiferroics, which typically display OOP polarization36,44.

The distinct polarization behavior in these systems arises from two key factors: Jahn-Teller activity and symmetry-forbidden s-d coupling44. The Jahn-Teller active Mn3+ ion (t2g3 eg1) lifts the eg orbital degeneracy, leading to tetragonal compression in the D-type phase and tetragonal elongation in the C-type phase (Supplementary Table 1). These distortions generate an in-plane anisotropic local potential, which drives lateral Cu displacement. In contrast, in BMTP compounds such as CuCrP2S6, where the Jahn-Teller effect is weak, the nearly symmetric crystal field fails to create such a gradient potential, thereby suppressing in-plane polarization.

Meanwhile, the local approximate Oh symmetry around the Cu+ ion in CuMnP2Se6 forbids s-d coupling because the s and d orbitals belong to different irreducible representations (Supplementary Table 2). This symmetry-forbidden s-d hybridization contrasts with the symmetry-allowed s-d coupling in CuInP2S6, which drives the OOP polarization44. This forbidden s-d coupling in CuMnP2Se6 is further supported by the projected density of states (PDOS) and band-decomposed charge density (Supplementary Fig. 2). Therefore, the combination of strong Jahn-Teller distortion and symmetry-forbidden s-d coupling collectively determines the emergence and stabilization of in-plane polarization in CuMnP2Se6. A more detailed discussion is provided in the Supplementary Information.

High-throughput screening and identification of in-plane ferroelectric phases and magnetic ground states
Having identified four structural prototypes, we employed high-throughput first-principles calculations to systematically investigate the possibility of D-type and C-type structures within this material family. As illustrated in Fig. 2a, we considered compounds with the formula XYP2(S/Se)6 (X=Cu, Ag, Au; Y=Mn, Tc), generated via targeted elemental substitution. The X-site elements (Cu, Ag, Au) were chosen as monovalent cation owing to their good displacive nature and can easily displace from the octahedral center, thus generating ferroelectric polarization. The Y-site transition metals were selected to ensure a high-spin t2g3 eg1 configuration (e.g., Mn3+ and Tc3+), which naturally leads to Jahn-Teller activity and strong coupling among orbital, lattice, and spin degrees of freedom.

A total of 48 candidate structures were initially generated based on the four structural prototypes. After full structural relaxation, 5 OOP-polarized phases were found to be unstable and spontaneously transformed into NP phases. The potential energy profile of Cu-ion displacement further confirms the energetic preference for the NP phase (Supplementary Fig. 3). Consequently, the final dataset comprises 43 stable configurations: 7 OOP, 12 NP, 12 D-type, and 12 C-type phases (Fig. 2a). Among these, all XYP2(S/Se)6 compounds in the D-type and C-type phases, except AgMnP2Se6, possess lower energies than their NP and OOP counterparts (Supplementary Table 3). Because the total energies of AgMnP2Se6 in different prototypes are nearly degenerate, indicating a structurally marginal system, it was excluded from subsequent phonon calculations.

Phonon spectrum calculations reveal that CuMnP2(S/Se)6 and AuMnP2(S/Se)6 are dynamically stable in both D-type and C-type configurations, whereas AgMnP2S6 is stable only in the C-type configuration (Supplementary Figs. 4, 5). We then determined the magnetic ground states of the dynamically stable compounds, excluding AgMnP2S6 since only its C-type phase is stable and no meaningful comparison between two polar phases can be made. For the remaining systems, we considered one FM and two possible AFM configurations (Supplementary Fig. 6). Interestingly, unlike other compounds where both polar phases prefer AFM ordering, CuMnP2Se6 displays two polar phases with different magnetic ground states—one FM and one AFM (Fig. 2b). This unique behavior allows an electric-field-induced polarization reversal to simultaneously trigger a magnetic phase transition between FM and AFM states. Consequently, we focus our subsequent discussion on CuMnP2Se6.

Distinct structural motifs, electronic properties and magnetic ground states in D-type and C-type CuMnP2Se6
Figure 3a and b show schematic structural diagrams of the D-type and C-type phases of CuMnP2Se6 in a 2×2×1 supercell, with the P and Se atoms omitted for clarity. In the D-type phase, Cu and Mn atoms form dimer-like units with a nearest-neighbor distance of 3.43 Å, and the distance between neighboring dimers is 3.82 Å. In the C-type phase, Cu and Mn atoms form chain-like units with a nearest-neighbor distance of 3.64 Å along the chain, and the distance between neighboring chains is 3.75 Å. The C-type phase is slightly lower in energy than the D-type phase by ~4 meV/f.u.

The cohesive energy of CuMnP2Se6 is calculated using the equation Ecoh = (Etot − ECu − EMn − 2EP − 6ESe)/10, where Etot is the total energy of 2D CuMnP2Se6, and ECu, EMn, EP, and ESe are the total energies of isolated Cu, Mn, P, and Se atoms, respectively. The cohesive energies for both D-type and C-type phases are similar, ~ -3.92 eV/atom, suggesting that both structures are thermodynamically stable and potentially synthesizable. Furthermore, Ab initio molecular dynamics simulations at 100 K confirm the thermal stability and in-plane long-range polarized order of CuMnP2Se6 (Supplementary Fig. 7).

The spin-polarized band structures show that both the D-type and C-type phases are semiconductors with indirect band gaps of 0.18 eV and 0.16 eV, respectively (Fig. 3c, d). Spin-orbit coupling has a negligible effect on the electronic structure and is therefore excluded from subsequent calculations (Supplementary Fig. 8). Spin density calculations show that the spin moments are mainly localized on Mn ions (Supplementary Fig. 9). The PDOS confirms that the spin polarization near the Fermi level mainly comes from Mn 3d orbitals. The formal spin moments for Mn and Cu are 4 μB and 0 μB, respectively, consistent with their expected valence states of Mn3+ and Cu1+. The overlap between the Mn 3d and Cu 3d orbitals is observed below the Fermi level in PDOS (Supplementary Fig. 10). In fact, the overlap originates from the strong hybridization of Mn 3d-Se 4p and Cu 3d-Se 4p states, making the Cu and Mn d states appear to overlap.

In the D-type phase, the valence band maximum is primarily derived from Mn dx2−y2 orbitals, while the conduction band minimum mainly originates from Mn dz2 orbitals (Fig. 3e). In contrast, the C-type phase shows the opposite orbital contributions to the valence and conduction bands (Fig. 3f). The calculated onsite energies of Mn d orbitals (Supplementary Table 4) confirm that the dx2−y2 orbital lies lower in energy than the dz2 orbital in the D-type phase, whereas the reverse holds for the C-type phase. This distinct orbital ordering enhances Mn dx2−y2 -Se pxy hybridization in the D-type phase and Mn dz2 -Se pz hybridization in the C-type phase (Fig. 3g, h; Supplementary Fig. 11). Structurally, the D-type phase exhibits tetragonal compression, which energetically favors the formation of Mn-Cu dimer-like units, whereas the C-type phase shows tetragonal elongation, stabilizing a chain-like -Mn-Cu-Mn-Cu- arrangement (Supplementary Table 1; Fig. 3a, b). This structural response reflects the system’s tendency to minimize total energy under different orbital hybridization conditions. In turn, these distinct structural configurations tend to modulate the Mn-Mn exchange pathways, which may lead to different magnetic ground states in the two phases.

The spin Hamiltonian is defined as H = − ∑i,j J1 Si Sj − ∑i,k J2 Si Sk, where J1 and J2 are the nearest-neighbor and next-nearest neighbor magnetic exchange parameters between Mn ions, respectively22,52–54. The summation i, j, and k run over all the Mn sites. S is the formal magnetic moment of Mn ion. The positive and negative J values represent the FM and AFM coupling, respectively. By energy mapping analysis on the considered magnetic configurations (Supplementary Fig. 6), the calculated J1 and J2 for the D-type are 4.70 meV and 1.30 meV, respectively, indicating the FM ground state. In contrast, the calculated J1 and J2 for the C-type are 4.67 meV and -4.72 meV, respectively, indicating the AFM ground state. Monte Carlo simulations show that the magnetic critical temperature for FM D-type and AFM C-type phases are ~31 K and ~18 K, respectively (Supplementary Fig. 12).

We further investigated the impact of the Hubbard U parameter on magnetic ordering and orbital-level splitting for both D-type and C-type phases, finding that the overall qualitative trends and key conclusions are robust over a broad range of U values (Supplementary Tables 5 and 6).

Electric-field-induced magnetic switching in CuMnP2Se6
Berry phase calculations yield an in-plane polarization of 0.9 × 10−10 C/m along the [110] direction for the D-type phase and 0.7 × 10−10 C/m along the [110] direction for the C-type phase (Supplementary Figs. 13, 14). Born effective charge analysis55,56 gives corresponding values of 0.4 × 10−10 C/m for the D-type phase and 0.2 × 10−10 C/m for the C-type phase, in good agreement with those obtained from the Berry-phase method. These values are larger than those reported for other DTMPs12,36,57,58, such as AgBiP2Se6 (1.2 × 10−12 C/m), CuCrP2S6 (0.79 × 10−12 C/m), AuZrP2S6 (9.74 × 10−12 C/m), and comparable to other 2D multiferroics13,16,59–61, such as (CrBr3)Li (0.92 × 10−10 C/m), and γ-AlOOH (0.85 × 10−10 C/m).

The polarization in both the D-type and C-type phases can only be switched by 120° through an in-plane rotation of 120° or 240° (Fig. 4a, b; Supplementary Fig. 15a, b). This process can also be understood as a lateral displacement of Cu ions. The corresponding energy barriers for ferroelectric switching are ~36 meV/f.u. for the D-type phase and ~32 meV/f.u. for the C-type phase. In contrast, a 180° polarization reversal within the same phase (either D-type or C-type) is prohibited, as the positions of Cu and Mn ions cannot be interchanged directly.

However, 180° polarization reversal remains feasible through an electric-field-induced phase transition between the D-type and C-type structures, accompanied by the migration or removal of Cu atoms (Fig. 4c; Supplementary Fig. 15c). Specifically, reversing the applied electric field—e.g., from [110] to [110]—can trigger a transition between the two phases, owing to their opposite polarization orientations. This electric-field-driven structural transformation simultaneously induces a magnetic phase transition, owing to the distinct magnetic ground states of the D-type and C-type structures. Figure 4c illustrates the energy barrier associated with this phase transition, which proceeds via an intermediate structure that closely resembles the D configuration and can be regarded as the NP phase (Supplementary Fig. 16). The calculated barriers for both D-to-C and C-to-D transitions are nearly identical, ~49 meV/f.u. This value is nearly an order of magnitude lower than those reported for other 2D multiferroics exhibiting electric-field-induced magnetic transitions29–31. Notably, the D-to-C transition can also be triggered by applying tensile strain (Supplementary Fig. 17).

The ME coupling coefficient can be estimated as α ≈ μ0 |ΔM|/Ec, where μ0 is the vacuum permeability, ΔM is the magnetization change per unit cell associated with polarization switching, and Ec is the coercive electric field62. As is well known, a direct evaluation of Ec from first-principles is very challenging, since in real ferroelectric materials, polarization reversal is typically dominated by domain-wall motion and defect-mediated processes rather than homogeneous switching, and Ec is also strongly temperature dependent63. Therefore, we adopted a more reasonable reference value based on experimentally accessible ferroelectric systems to estimate Ec. The values of energy barrier (4.9 meV/atom) and polarization (13 μC/cm2 for the D-type phase and 9 μC/cm2 for the C-type phase, assuming an effective thickness of 7 Å) in CuMnP2Se6 are comparable to those reported for ferroelectric Hf(Zr)1+xO2 thin films (7.3 meV/atom; 22.5 μC/cm2)64. Thus, we adopt the experimentally reported coercive field of Hf(Zr)1+xO2, 65 kV/cm, to estimate the ME coupling coefficient of CuMnP2Se6. This yields α ≈ 0.04 G⋅cm/V, which exceeds those of bulk multiferroic Fe/BaTiO3 (~0.01 G⋅cm/V)62, and 2D WReCl36 (~0.02 G⋅cm/V)29, indicating the strong ME coupling.

To evaluate the feasibility of in-plane electric-field-driven structural transitions between the D-type and C-type phases, we investigate the field-dependent total energies of both configurations (Fig. 4d). The two phases exhibit opposite responses: an electric field along the [110] direction stabilizes the C-type phase, while a field along [110] favors the D-type phase. Strikingly, an ultralow field of ~0.001 V/Å along [110] is sufficient to render the D-type phase more stable than its C-type counterpart, enabling an electric-field-induced C-to-D transition. The critical field lies well within experimentally accessible limits8,65, highlighting the potential of CuMnP2Se6 for practical multifunctional device applications.

In summary, we identify four stable 2D multiferroics of the form XMnP2(S/Se)6 (X = Cu, Au), each exhibiting two inequivalent C2-symmetric polar phases with opposite in-plane polarization directions, based on crystal structure prediction and high-throughput first-principles calculations. Jahn-Teller activity and symmetry-forbidden s-d coupling are identified as the two primary driving forces for the emergence of in-plane polarization in these systems. Notably, in CuMnP2Se6, the two polar phases differ not only in their polarization orientation but also in their magnetic ground states (FM and AFM), enabling electric-field-driven switching of both ferroic orders. The ultralow energy barrier (~49 meV/f.u.) and critical switching field (~0.001 V Å−1) render these coupled transitions experimentally accessible. These findings demonstrate a viable route for electric control of magnetism in single-phase 2D multiferroics and provide new insights into ferroic coupling in the BMTP family, with promising implications for low-power, non-volatile device applications. This work also opens a promising avenue for exploring ultralow-field electric control of magnetism enabled by Jahn-Teller-assisted phase-transition mechanisms.

Methods
First-principles calculations were performed based on density functional theory66 via the Vienna Ab initio Simulation Package (VASP)67,68 using the generalized gradient approximation with the projected augmented wave method69 with a 450 eV plane-wave energy cutoff. The Perdew-Burke-Ernzerhof function was adopted for the exchange-correlation functional70. A Γ-centered k-point grid of 11 × 11 × 1 was applied for sampling the Brillouin zone. The energy and force threshold for structural optimization are 10−7 eV and 0.001 eV/Å, respectively. An effective Hubbard U of 4 eV for Mn 3d, Cu 3d and Tc 4d orbitals71,72 was applied following the Dudarev formulation73. Phonon spectra were calculated using the finite displacement method implemented in the PHONOPY code74. The temperature-dependent effective potential method was used to determine the influence of thermal effects on phonon spectra75. Ab initio molecular dynamics simulations were performed utilizing the Nosé-Hoover chain thermostat for 5 ps with a time step of 1 fs with 3 × 3 × 1 supercell. Climbing image nudged elastic band calculations76 were performed to determine the energy barriers for ferroelectric switching. The polarization was estimated using the Berry phase approach77. An in-plane electric field was applied by imposing a finite homogeneous field using the perturbation expression after discretization approach78,79. The maximally localized Wannier functions are constructed by using the WANNIER90 code80.

The particle-swarm optimization method within the evolutionary algorithm, as implemented in the CALYPSO code46–51, was employed to search for the lowest-energy structures of the CuMnP2Se6 monolayer. Unit cells containing one and two formula units were considered. In the initial generation, random structures with specific symmetries were constructed by generating atomic coordinates through crystallographic symmetry operations. Local optimizations were carried out using the VASP code67,68 with the conjugate-gradient method and terminated when the Gibbs free-energy change was smaller than 1 × 10−4 eV per cell. After each generation, 40% of the low-energy structures were selected to construct the next generation through particle swarm optimization, while the remaining 60% were randomly generated. A structure fingerprinting technique based on the bond-characterization matrix was employed to avoid duplication and enhance population diversity, which is crucial for efficient global searching. In total, the search typically sampled 1200 structures (40 generations × 30 structures).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors J. Chen et al., in their manuscript “ Phase-Transition-Induced Ferroelectric and Magnetic Switching in Two-Dimensional CuMnP2Se6 under Ultra-Low Electric Fields”, have investigated four compounds XMnP2(S/Se)6 (X = Cu, Au) belonging to the family of bimetallic thio(seleno)phosphates using density functional theory based calculations. Their main observations are the presence of in-plane electric polarization in these four compounds as opposed to the out-of-plane polarization reported earlier for other members of the family. The authors also report that a tiny electric field can be used to switch the polarization direction in CuMnP2Se6 along with the magnetic order.\nI observe some serious issues with the conclusions drawn here by the authors which I outline below.\n1. The non-polar intermediate state D3, between the D-type and C-type phases, is metallic (see Fig. S11). Therefore, an electric field cannot be used to switch the direction of polarization. Another related question is when the non-polar D3 phase is metallic, how was the polarization quantum calculated? It is not possible to calculate it by following the standard procedure.\n2. The AIMD snapshots at 300K after 10 ps for both D and C-type (Fig. S4) show a significant change in the bond lengths which is the primary requirement for the structure to be called D-type or C-type (Fig. 3 (a) & (b)). Thus, at 300K, D and C-type phases of the structure don’t survive and there should be no net in-plane polarization given the loss of order in the bond lengths of the structures.\n3. Why a weak Jahn-Teller effect will give rise to out-of-plane polarization whereas a strong Jahn-Teller effect will give rise to in-plane polarization is not clear at all. The orbital resolved DOS presented in Fig. S7 shows Mn dz2 and dx2-y2 orbitals both present below the Fermi level. A strong Jahn-Teller effect would have split these two orbitals widely.\n4. How does distinct orbital ordering in C and D-type phases lead to the respective structural distortions? How do they give rise to different magnetic ground states for C and D-type phases? No explanation is provided. Moreover, the DOS in Fig. 3 (e) shows substantial contribution of both dz2 and dx2-y2 orbitals in the valence band whereas the band character plot shows dominant dx2-y2 contribution.\n5. The claim that there is no bonding like interaction between Cu and Mn is not very convincing. There seems to be a very strong overlap between Cu and Mn d states in the valence band (as seen in PDOS of Fig. 3(c), 3(d) and S7) which directly indicates a strong hybridization between Cu and Mn. The ELF plot also shows some bonding like behaviour particularly in the C-type structure. Also, the crystal field around Cu changes in a similar manner as that around Mn typical for a Cu-Mn bonding interaction (see Fig. 1(c), 1(d)). The non-polar phase PDOS (Fig. S11(b)) also shows a very strong Cu-Mn hybridization.\n6. If Cu-d orbitals do not hybridize with Mn-d orbitals as claimed, why doesn’t it exhibit s-d interaction and hence, an out-of-plane displacement as is the case with the materials without an eg electron (e.g., CuCrP2S6).\n7. How are the temperatures for phonon calculations in Fig. S2 decided? What about the dynamic stability at higher temperatures? The last phonon spectrum for AuMnP2S6 seems to have imaginary frequencies.\n8. There are a couple of typos. ( ‘insensitive’ instead of ‘sensitive’ and ‘eg’ instead of ‘t2g’ in the Supplementary mat.).\nFinally, I would like to mention that no new concept has been presented in this manuscript. The concept as well as the analysis is exactly similar to the work by Meiling Xu et al. , Phys. Rev. Lett. 124, 067602 (2020) (ref. [29] of the manuscript). Only the compound studied is different.\nIn view of the above serious issues, I can not recommend the manuscript for publication in the highly reputed journal Nature Communications.", "reviewer_2": "The work of Chen et al. uses a combination of first principles methods to identify a particular ferroelectric system, CuMnP2Se6, with two opposite polarizations, but with different magnetic ground states. Notably, a small electric field reverses the polarization and induces an AFM to FM transition. I find the work very interesting, clear, well-written, and of potential technological importance.\nThere are some small weaknesses that can be improved.\n1. Fig. 1, please add colored spheres in the figure to clarify the atoms types.\n2. Page 2, paragraph 5. Please justify the selection of X= Cu, Ag, Au, Y = Mn, Tc for the targeted elemental substitution. Why not consider other transition metals? What values of U were used for Mn and Tc?\n3. Page 2, paragraph 5. How was \"the number of candidate structures 48\" found? Using 3 for X, 2 for Y, 2 for S, Se, and 2 for C, D type I find 24.\n4. Page 2, paragraph 6. When computing the FM and AFM ground states. Did the author consider large supercells for AFM configurations? If so, how large? How was the supercell size cut-off chosen? Is there any experimental evidence to support any of these magnetic ground states in this or other BMTP systems?\n5. Page 2, paragraph 7. The sentence \"In the D-type phase... Cu-Mn dimer with a bong length ... shorter than the alternating Cu-Mn bond..\" was difficult to understand. What is the alternating bond? Please identify the alternating bond in Fig. 3.\n6. In Page 3, paragraph 3, the position of different Mn d orbital characters are discussed and shown in Fig. 3. What is the axis of quantization used to project the orbitals? Along the global z axis or along one of the octahedral axis? In the latter case, specify which one. Figs. 3g and 3h are not clear, are these in 2D or 3D? Are d_xy, d_yz, d_xz degenerate?\n7. Page 3, paragraph 5. How does the polarization computed for CuMnP2Se6 compare to the value computed for CuInP2S6 in this work?https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.L180101Please specify the polarization is in-plane.\n8. Page 4, paragraph 4. Since the values of U and P for CuMnP2Se6 are comparable to those of Hf(Zr)1+xO2, the authors adopt a coercive field of 65 kV/cm. However, how does this compare with a coercive field estimated as E_c ~ dE / (PV), where dE, P, V are the energy difference between nonpolar and polar structures, and P, V are the polarization and volume of the polar structure?\n9. In Page 5, paragraph 1. The two C2-symmetric opposite polarizations have different values, correct? If so, please report both values.\nI recommend acceptance after minor revisions.", "reviewer_3": "I don't find the work suitable for publication in Nature Communications. This work contains only the theoretical results, and it lacks the experimental evidence of the proposed structures. I still have some comments that may be helpful to improve the quality of the manuscript.\nIn Figure 1, it's difficult to differentiate the crystal structures (eg, top views in a and b, both views in c and d). I suggest highlighting the main difference among the structures in Figure 1 and explaining it clearly in the caption/main text.\nThe authors say, 'out-of-plane displacement of Cu1+ gives rise to spontaneous polarization.' Are they referring to the atom shown in yellow in Figure 1 (a)?\nJustify the sentence 'In an MnS(Se)6 octahedral environment, this t32ge1g configuration causes strong Jahn–Teller distortions, facilitating the emergence of new structural prototypes not accessible with other transition metals.' Why can't this happen for other TMs?\nThe authors mentioned D-type and C-type phases in the manuscript. The author should provide some context and relevant sources of other phases as well (such as A-type, B-type phases, if they exist), instead of directly using C or D-type phases. This will help the readability of the paper.\nWhat are the other unstable structures? Do they comprise Tc? Can you comment on why Tc - radioactive element - was considered in the calculations?In Figure 2(a), do they mean XYP2(S/Se)6 instead of XYP2S(Se)6?\nUSPEX has also been very popular in predicting novel crystal structures. The author should comment on their choice of CALYPSO over USPEX.\nFigure S1 (a, b) in Supporting Information: What are the displacement values? Do x-axes represent the number of images created?\nIn Figure S2 in Supporting Information, what do (2) and (4) represent? Also, are they simulated at different temperatures?\nThere is no consistency in atomic colors in the crystal structures throughout the manuscript, which should be fixed.\nThe authors should provide references for every equation/formula they have used in the manuscript. For example, the spin Hamiltonian on page 3, the ME coupling coefficient on page 4. I doubt the formula of the spin Hamiltonian used. Please see the following paper: https://pubs.rsc.org/en/content/articlehtml/2024/cp/d3cp05578g\nThe authors should explain in detail in the Supporting Information how they switched the polarization by 120 and 180 degrees. This will be a good reference for readers.\nIn the Methods section, it should be 450 eV instead of 450-eV.\nThe method section lacks information on the parameters used in CALYPSO.\nIn Supporting Information, Table SII, the sign of the deltaE (hence the magnetic state) of C-type AFMa is changed for the (Hubbard U) values of Mn = 4 and Cu = 5 eV. Please comment on this.", "reviewer_4": "The research focus on the electric field control of magnetic phase transitions, specially in cases where the necessary electric fields are small for practical reasons. The manuscript is very well written and all results look correct. The research lacks experimental results and focus only on first principle calculations and modeling with a spin Hamiltonian. However, the authors did a phonon analysis (with and without thermal effects), together with molecular dynamics to confirm thermal stability. Those are already the methods necessary within first principles to access the viability of the materials experimentally. Additionally, the authors used several methods to access the properties of the materials, such as: Berry phase method to calculate the in-plane polarizations; Wannier analysis for the orbital ordering; and NEB calculations to investigate different phase transitions. I conclude then that the manuscript is suitable for publication at Nature Materials after reviews:\n1 - In Figure 1, it is very difficult to understand the structural differences between the NP, C and D types (OOP is more obvious). The authors could improve the understanding by explicitly indicating which of the metal atoms are displaced to create the in-plane polarization. Also using different colors for top and bottom S/Se atoms can help.\n2 - The authors used DFT+U and tested some values of U, but they used a rather modest value of U throughout the manuscript and SI. Also they only compared the energy ordering for a small range of U (either 3 or 4eV).\na) What is the effect of energy ordering for U < 3eV? What happens for much larger values of U (perhaps up to 8 eV)? Specially Mn can be quite tricky to deal with.\nb) Is the orbital ordering also affected by the U values? I believe that higher values will increase the separation of the orbitals, but there is also a possibility of changing the ordering in case the occupation pattern shifts. What happens for U = 0 eV? Is it still S = 2 or does it go to S = 1?\n3 - By changing the U to lower values the authors could also investigate better the interactions between the Cu and Mn ions. It is reasonable to consider less strong localized orbitals, leading to more hybridization between Cu and Mn ions.\n4 - Can the authors comment further on the structures that present negative frequencies in the phonon spectra? What are the modes associated to them?"}, "author_response": "Response to Reviewers\nReviewer #1 (Remarks to the Author)\nCOMMENT:\nThe authors J. Chen et al., in their manuscript “Phase-Transition-Induced\nFerroelectric and Magnetic Switching in Two-Dimensional CuMnP Se under Ultra-\n2 6\nLow Electric Fields”, have investigated four compounds XMnP (S/Se) (X = Cu, Au)\n2 6\nbelonging to the family of bimetallic thio(seleno)phosphates using density functional\ntheory based calculations. Their main observations are the presence of in-plane electric\npolarization in these four compounds as opposed to the out-of-plane polarization\nreported earlier for other members of the family. The authors also report that a tiny\nelectric field can be used to switch the polarization direction in CuMnP Se along with\n2 6\nthe magnetic order.\nI observe some serious issues with the conclusions drawn here by the authors which I\noutline below.\nAuthors’ Reply: We very appreciate the Reviewer #1 for his/her thorough review and\nconstructive comments. We have made great efforts to address these issues and revised\nour manuscript accordingly. We hope that our revisions have adequately addressed the\nreviewer’s concerns and that our work can now be recommended for publication in\nNature Communications.\nCOMMENT 1:\nThe non-polar intermediate state D , between the D-type and C-type phases, is metallic\n3\n(see Fig. S11). Therefore, an electric field cannot be used to switch the direction of\npolarization. Another related question is when the non-polar D phase is metallic, how\n3\nwas the polarization quantum calculated? It is not possible to calculate it by following\nthe standard procedure.\nAuthors’ Reply: We thank the Reviewer for the insightful comments. We fell regret\nthat we failed to recognize that the polarization direction of a metallic phase cannot be\nswitched by applying an electric field. Actually, in our previous NEB calculations, a\nsimplified operation leads to a metallic intermediate state D . Specifically, the gamma\n3\nangles in the initial D-type phase and final C-type phase are 121.8° and 118.4°,\nrespectively. Nevertheless, for the sake of computational simplicity, we artificially set\nthe gamma angles at 120° due to the higher symmetry associated with this value. This\noperation inevitably leads to intermediate phases with a gamma angle of 120°. In this\nhighly symmetric structure, four d electrons occupy a triply degenerate t orbital and\n2g\ndoubly degenerate e orbital, leading to metallic nature. Moreover, we did not calculate\ng\nthe polarization quantum of this metallic D phase in our previous version, the\n3\npolarization quantum presented in the Page S17 in the Supplementary Information is\nthe result of D-type phase.\nIn the revised manuscript, we conducted accurate NEB calculations, taking into account\nthe actual initial and final structures. As expected, all intermediate phases have low\nsymmetry with gamma angle deviating from 120°, and we are pleased to report that all\nthese phases are insulators. Notably, the newly calculated energy barrier from the D-\ntype phase to C-type phase is ~49 meV, slightly lower than that (~51 meV) obtained in\nour previously calculation. The new results have been replotted in Figure 4c and\nSupplementary Fig. 13, and the corresponding discussions have been modified\naccordingly in the 1st paragraph of page 6 of main text.\nOur revision:\nIn response to this comment, we have updated several sentences in the 1st paragraph of\npage 6 of our main text, which read:\n“Figure 4c illustrates the energy barrier associated with this phase transition, which\nproceeds via an intermediate structure that closely resembles the D configuration and\n3\ncan be regarded as the NP phase (Supplementary Fig. 15)”\nSupplementary Fig. 13. Electronic structures of D-type, intermediate, and C-type phases\nalong the NEB pathway. a D-type phase. b-f intermediate phases. g C-type phase.\nCOMMENT 2:\nThe AIMD snapshots at 300 K after 10 ps for both D and C-type (Fig. S4) show a\nsignificant change in the bond lengths which is the primary requirement for the\nstructure to be called D-type or C-type (Fig. 3 (a) & (b)). Thus, at 300 K, D and C-type\nphases of the structure don’t survive and there should be no net in-plane polarization\ngiven the loss of order in the bond lengths of the structures.\nAuthors’ Reply: The AIMD simulations conducted at 300 K were solely carried out to\nassess the structural stability under ambient conditions. In actual applications, realizing\nFM-AFM switching necessitates operation below the magnetic transition temperature.\nTo investigate whether FM-AFM switching can be achieved in the considered\ncompound, we have incorporated AIMD calculations at 100 K, which is above the\nmagnetic transition temperatures. The results demonstrate that both the D-type and C-\ntype phases remain entirely stable throughout the entire simulation, with bond lengths\nand polarization patterns being well-maintained. These findings confirm the structural\nstability and polarization behavior. We have updated Supplementary Fig. 7 in the\nSupplementary Information and added the corresponding discussion in the second\nparagraph of page 4 of the revised manuscript.\nOur revision:\nIn response to this comment, we have updated one sentence in the 2nd paragraph of page\n4 of revised manuscript, which state:\n“Furthermore, ab initio molecular dynamics simulations at 100 K confirm the thermal\nstability and in-plane long-range polarized order of CuMnP Se (Supplementary Fig.\n2 6\n7).”\nSupplementary Fig. 7. Thermal stability of 2D CuMnP Se at 100 K. Evolution of the total\n2 6\nenergy during AIMD simulations for the D-type and C-type phases. The insets show representative\nstructural snapshots captured at the end of the 5 ps simulation period.\nCOMMENT 3:\nWhy a weak Jahn-Teller effect will give rise to out-of-plane polarization whereas a\nstrong Jahn-Teller effect will give rise to in-plane polarization is not clear at all. The\norbital resolved DOS presented in Fig. S7 shows Mn d and d orbitals both present\nz2 x2-y2\nbelow the Fermi level. A strong Jahn-Teller effect would have split these two orbitals\nwidely.\nAuthors’ Reply: We thank the Reviewer for raising this important point.\nThe Jahn-Teller effect occurs when degenerate d orbitals in a transition-metal\noctahedron are unevenly occupied (Supplementary Fig. 1). It is strongest for\nconfigurations with an odd number of electrons in the e orbitals (e.g., d9, low-spin d7,\ng\nor high-spin d4), because these orbitals point directly at the ligands and distortions can\nlower electrostatic repulsion. In contrast, when only the t orbitals are degenerate (e.g.,\n2g\nd1 or d2), the effect is much weaker since these orbitals interact less with the ligands.\nWe found that Jahn-Teller activity plays a key role in determining the polarization\ndirection in this system.\nIn CuMnP Se the Mn3+ ion has a high-spin t 3e 1 configuration and is therefore Jahn-\n2 6, 2g g\nTeller active. The degeneracy of the e orbitals is lifted, resulting in distortions of the\ng\nMn-Se octahedra (Supplementary Table 1). These distortions create a planar anisotropic\nlocal potential field around the Cu site, effectively introducing an in-plane potential\ngradient and the resulting in-plane Cu displacement. In some BMTP compounds such\nas CuCrP Se (Cr3⁺, t 3), CuVP Se (V3⁺, t 2) and CuFeP Se (Fe3⁺, t 3e 2), the e\n2 6 2g 2 6 2g 2 6 2g g g\norbital splitting is small and insufficient to dominate other lattice degrees of freedom.\nIn this case, the MSe (M=Cr, V, and Fe) octahedron maintains an almost symmetric\n6\ncrystal field, failing to provide a significant \"potential energy gradient\" within the plane\nand suppressing in-plane Cu displacement.\nAt the same time, we found that another key factor affecting the polarization direction\nin this family of materials is symmetry-controlled s-d coupling. Previous studies have\nshown that the symmetry-allowed s-d coupling plays a critical role in determining the\nCu out-of-plane displacements in CuInP S [Phys. Rev. B 108, L161406 (2023)]. In\n2 6\nfact, the s-d coupling strength is very sensitive to local site symmetry. When Cu1+ ion\noccupies a triangular site (e.g., CuInP S ), the local symmetry is C , with the Cu d\n2 6 3v\norbitals transforming the a and e representations. Meanwhile, the unoccupied s orbital\n1\ntransforms as a (Supplementary Table 2). Because the s and d orbitals share a common\n1\nrepresentation (a ), s-d coupling is allowed, lowering the system energy. This coupling\n1\nis the main driving force for the out-of-plane displacement of Cu and the resulting out-\nof-plane polarization.\nIn contrast, when the Cu1+ ion is at a distorted octahedral site (e.g., CuMnP Se ), the\n2 6\nlocal symmetry is approximately O . In this case, there is no common representation\nh\nbetween the d orbitals and the s orbitals, and the s-d coupling is forbidden\n(Supplementary Table 2). Thus, the out-of-plane displacement of Cu is greatly\nsuppressed.\nThis symmetry-forbidden s-d coupling in CuMnP Se is further illustrated by the\n2 6\nprojected density of states and band-decomposed charge density shown in\nSupplementary Fig. 2. For CuInP S , the conduction band contains delocalized s-like\n2 6\norbitals that are not localized on any atomic site. This delocalized character enhances\nthe s-d interaction and drives out-of-plane polarization [Phys. Rev. B 108, L161406\n(2023)]. In sharp contrast, no such delocalized s orbitals are observed in the conduction\nband of CuMnP Se , indicating the absence of s-d coupling.\n2 6\nTherefore, strong Jahn-Teller distortion and symmetry-forbidden s-d coupling provides\nthe underlying driving force that determines the emergence of in-plane polarization in\nCuMnP 2 Se 6.\nWe have added two paragraphs (5th and 6th paragraphs of page 2) in the revised\nmanuscript and updated Section I: In-plane polarization governed by Jahn-Teller active\nand symmetry-forbidden s-d coupling in the Supplementary Information.\nRegarding the Reviewer’s concern that the Mn d and d orbitals are not\nz2 x2-y2\nsignificantly split, we note that the apparent overlap of the two orbitals in the DOS\narises from strong Mn d - Se p hybridization. This hybridization broadens the d bands\nand causes partial overlap of their DOS peaks, which can mask the actual energy\nseparation of the two e orbitals in the DOS representation. We calculated the onsite\ng\norbital energies of Mn d states for both D-type and C-type phases (Supplementary Table\n4). Results show that the d and d orbitals are well separated in energy, indicating\nz2 x2-y2\na significant lifting of orbital degeneracy. This large splitting is fully consistent with the\npresence of a strong Jahn-Teller effect in the Mn3+ (t 3e 1) configuration.\n2g g\nThis strong Jahn-Teller splitting also correlates directly with the structural distortions\nobserved in our system (Supplementary Table 1). In the D-type phase, the occupied\nd orbital enhances in-plane Mn-Se p hybridization, resulting in tetragonal\nx2y2 xy\ncompression. In contrast, in the C-type phase, the occupied d orbital enhances Mn-Se\nz2\np hybridization, leading to tetragonal elongation. Therefore, while the DOS shows\nz\npartial overlap due to hybridization, the onsite orbital energies provide a more accurate\nand quantitative measure of the Jahn-Teller splitting.\nSupplementary Table 1. Summary Mn-Se bond lengths of MnSe octahedron in D- and C-type\n6\nphases.\nd (Å) d (Å) d (Å)\n1 2 3\nNonpolar 2.74114 2.74114 2.74114\nD-type 2.70390 2.80617 2.78310\nC-type 2.84205 2.72100 2.72361\nSupplementary Table 2. Summary of s-d coupling under different local symmetries. The s-d\nhybridization is symmetry-allowed only in C , where both orbitals share the same a representation,\n3v 1\nbut forbidden in O symmetry.\nh\nPoint group d s s-d coupling\nO e t a No\nh g 2g 1g\nC a 2e a Yes\n3v 1 1\nSupplementary Table 4. The onsite energy. Relative on-site energies for Mn-d orbitals of 2D\nCuMnP Se monolayer derived from the Maximumly Localized Wannier Functions (MLWFs)\n2 6\nconstructed by using the Wannier90 package.\nD-type C-type\nMn\n↑ ↑\nd -7.646668 -1.212646\nx2-y2\nd -1.394782 -7.736580\nz2\nd -7.639762 -7.744565\nxz\nd -7.498499 -7.529285\nyz\nd -7.543701 -7.404928\nxy\nSupplementary Fig. 1. The mechanism diagram of the Jahn-Teller effect. a, b Jahn-Teller effect\nobserved as tetragonal elongation and compression due to a net change in the energy of electrons. c\nNo Jahn-Teller effect occurred without a net change in energy. d Weak Jahn-Teller effect with only\nminor structural distortion.\nSupplementary Fig. 2. Symmetry-controlled s-d coupling. a, b Projected density of states (PDOS)\nof CuMnP Se in both D-type and C-type phases. c PDOS of CuInP S . d, e Partial charge density\n2 6 2 6\nof the conduction band for CuMnP Se in both D-type and C-type phases. f Partial charge density\n2 6\nof the conduction band for CuInP S The isosurface is 0.001e/Bohr3.\n2 6.\nOur revision:\nIn response to this comment, we have added two paragraphs (5th and 6th paragraphs of\npage 2) in the main text, which read:\n“The distinct polarization behavior in these systems arises from two key factors: Jahn-\nTeller activity and symmetry-controlled s-d coupling [44]. The strong Jahn-Teller effect\nof Mn3+ ion (t 3e 1) lifts the e orbital degeneracy, leading to tetragonal compression in\n2g g g\nthe D-type phase and tetragonal elongation in the C-type phase (Supplementary Table\n1). These distortions generate an in-plane anisotropic local potential, which drives\nlateral Cu displacement. In contrast, in BMTP compounds such as CuCrP S , where the\n2 6\nJahn-Teller effect is weak, the nearly symmetric crystal field fails to create such a\ngradient potential, thereby suppressing in-plane polarization.”\n“Meanwhile, the local approximate O symmetry around the Cu+ ion in CuMnP Se\nh 2 6\nforbids s-d coupling because the s and d orbitals belong to different irreducible\nrepresentations (Supplementary Table 2). This symmetry-forbidden s-d hybridization\ncontrasts with the symmetry-allowed s-d coupling in CuInP S , which drives the OOP\n2 6\npolarization [44]. This forbidden s-d coupling in CuMnP Se is further supported by\n2 6\nthe projected density of states (PDOS) and band-decomposed charge density\n(Supplementary Fig. 2). Therefore, the combination of strong Jahn-Teller distortion and\nsymmetry-forbidden s-d coupling collectively determines the emergence and\nstabilization of in-plane polarization in CuMnP Se . A more detailed discussion is\n2 6\nprovided in the Supplementary Information.”\nCOMMENT 4:\nHow does distinct orbital ordering in C and D-type phases lead to the respective\nstructural distortions? How do they give rise to different magnetic ground states for C\nand D-type phases? No explanation is provided. Moreover, the DOS in Fig. 3 (e) shows\nsubstantial contribution of both d and d orbitals in the valence band whereas the\nz2 x2-y2\nband character plot shows dominant d contribution.\nx2-y2\nAuthors’ Reply: We thank the Reviewer for this insightful question. Actually, the\ncoupling between charge, lattice, and spin degrees of freedom is highly complex, and a\nfully quantitative analysis is challenging. In our case, the distinct orbital ordering in the\nD-type and C-type phases primarily originates from the different occupations of Mn e\ng\norbitals. This orbital ordering drives characteristic lattice distortions, which in turn\nmodify the exchange interaction pathways and stabilize different magnetic ground\nstates.\nAs is well known, when d orbital is occupied, it strongly overlaps with the ligand\nx2-y2\np orbitals, enhancing in-plane hybridization and favoring tetragonal compression of\nxy\nthe metal octahedra (Supplementary Fig. 1). In contrast, when d orbital is occupied, it\nz2\nstrongly overlaps with the ligand p orbitals, promoting hybridization along the out-of-\nz\nplane direction and driving tetragonal elongation of the metal octahedra\n(Supplementary Fig. 1).\nIn the D-type phase, the valence band maximum is mainly derived from Mn d\nx2-y2\norbitals, resulting in strong in-plane Mn d x2-y2--Se p\nxy\nhybridization (Supplementary Fig.\n11). Structurally, the D-type phase exhibits tetragonal compression, which energetically\nfavors the formation of Mn-Cu dimer-like units (Supplementary Table 1 and Fig. 2a).\nIn contrast, in the C-type phase, the orbital energy sequence is reversed, with the d\nz2\norbital lying lower in energy than d . The occupied d orbital strongly overlaps with\nx2-y2 z2\nthe Se p orbitals (Supplementary Fig. 11). Structurally, the C-type phase exhibits\nz\ntetragonal elongation, which energetically favors the formation of chain-like -Mn-Cu-\nMn-Cu- arrangement (Supplementary Table 1 and Fig. 2b). This structural response\nreflects the system’s tendency to minimize total energy under different orbital\nhybridization conditions, which in turn modulate the Mn-Mn exchange pathways and\nstabilize different magnetic ground states in the D- and C-type phases.\nRegarding the Reviewer’s concern about the apparent inconsistency between the band\nstructure and DOS contributions of the Mn d and d orbitals, we clarify that this\nz2 x2-y2\nwas due to overlapping orbital projections in the original figure. We have now replotted\nthe projected band structures with the two orbitals displayed separately, which clearly\nreveals their respective contributions. This resolves the apparent discrepancy between\nFig. 3e and the DOS results.\nOur revision:\nIn response to this comment, we have updated the content in 4th paragraph of page 4 in\nour main text, which states:\n“This distinct orbital ordering enhances Mn d Se p hybridization in the D-type\nx2-y2- xy\nphase and Mn d -Se p hybridization in the C-type phase (Fig. 3g, h; Supplementary\nz2 z\nFig. 11). Structurally, the D-type phase exhibits tetragonal compression, which\nenergetically favors the formation of Mn-Cu dimer-like units, whereas the C-type phase\nshows tetragonal elongation, stabilizing a chain-like -Mn-Cu-Mn-Cu- arrangement\n(Supplementary Table 1; Fig. 3a, b). This structural response reflects the system’s\ntendency to minimize total energy under different orbital hybridization conditions. In\nturn, these distinct structural configurations tend to modulate the Mn-Mn exchange\npathways, which may lead to different magnetic ground states in the two phases.”\nSupplementary Fig. 11. PDOS of MnCuP\n6\nin the D-type and C-type phases.\nFig. 3 e Orbital-resolved spin-up band structures projected onto Mn d orbitals for the D-type phase.\nCOMMENT 5:\nThe claim that there is no bonding like interaction between Cu and Mn is not very\nconvincing. There seems to be a very strong overlap between Cu and Mn d states in the\nvalence band (as seen in PDOS of Fig. 3(c), 3(d) and S7) which directly indicates a\nstrong hybridization between Cu and Mn. The ELF plot also shows some bonding like\nbehaviour particularly in the C-type structure. Also, the crystal field around Cu changes\nin a similar manner as that around Mn typical for a Cu-Mn bonding interaction (see\nFig. 1(c), 1(d)). The non-polar phase PDOS (Fig. S11(b)) also shows a very strong Cu-\nMn hybridization.\nAuthors’ Reply: We thank the Reviewer for this valuable comment. In order to further\nverify the nature of the Cu-Mn interaction, we calculated the integrated crystal orbital\nHamilton population (ICOHP) values for Cu-Mn pairs, which are ~ -0.03 and ~ -0.01\neV per bond for the D-type and C-type phases, respectively. These values, being close\nto zero, clearly indicate the non-bonding like interaction between Cu and Mn atoms.\nRegarding the strong overlap between Cu and Mn d states in the valence band, this\noverlap actually originates from the strong hybridization of Mn 3d-Se p and Cu 3d-Se\np states, making the Cu and Mn states appear to overlap in the projected DOS.\nIn the previous manuscript, the ELF scale bar was set to 0-0.3. However, in fact, only\nELF values above 0.5 indicate significant shared-electron interactions. Therefore, the\nlow ELF values observed between Cu and Mn atoms demonstrate the absence of\nsubstantial bonding between them.\nThe crystal field around Cu indeed changes like that around Mn, but this correlation\nreflects the cooperative lattice distortion mediated by shared Se ligands. The Mn-Se\noctahedral distortion modifies the local electrostatic potential transmitted through the\nSe framework, which indirectly alters the Cu coordination environment. In the nonpolar\nphase, the apparent Cu-Mn hybridization observed in the PDOS also primarily arises\nfrom the strong hybridization of Mn 3d-Se p and Cu 3d-Se p states.\nIn order to clearly explain the interactions between Cu and Mn atoms, we have added\nthe corresponding discussion in the 3rd paragraph of page 4 of revised manuscript and\na new Section XIII: The interaction between Cu and Mn ions, in the revised\nsupplementary Information.\nOur revision:\nIn response to this comment, we have added several sentences in the 3rd paragraph of\npage 4 of our revised manuscript, which read:\n“The overlap between the Mn 3d and Cu 3d orbitals is observed below the Fermi level\nin PDOS (Supplementary Fig. 10). In fact, the overlap originates from the strong\nhybridization of Mn 3d-Se 4p and Cu 3d-Se 4p states, making the Cu and Mn d states\nappear to overlap.”\nCOMMENT 6:\nIf Cu-d orbitals do not hybridize with Mn-d orbitals as claimed, why doesn’t it exhibit\ns-d interaction and hence, an out-of-plane displacement as is the case with the\nmaterials without an e electron (e.g., CuCrP S ).\ng 2 6\nAuthors’ Reply: We thank the Reviewer for this important comment. Indeed, Cu-d\norbitals do not hybridize with Mn-d orbitals. In addition, it does not exhibit s-d\ninteraction as the local symmetry around the Cu site approaches the O point group,\nh\nwhich forbids the s-d coupling (Supplementary Table 2).\nIn response to Comment 3, we have clarified the relationship between polarization\ndirection and Jahn-Teller active, as well as symmetry-controlled s-d coupling. In BMTP\ncompounds without an e electron on the transition-metal site (e.g., CuInP S ,\ng 2 6\nCuCrP S ), the MSe (M=In, Cu) octahedron remains nearly symmetric, generating a\n2 6 6\nplanar isotropic local potential field around the Cu site and thus failing to induce any\nlateral displacement of Cu ions. Meanwhile, the local C symmetry around Cu allows\n3v\nstrong s-d coupling, both belonging to the a representation (Supplementary Table 2).\ngiving rise to out-of-plane polarization [Phys. Rev. B 108, L161406 (2023)]. In contrast,\nin CuMnP Se , the lifting of the e orbital degeneracy induces strong Jahn–Teller\n2 6 g\ndistortions of the MnSe octahedra (tetragonal compression in the D-type phase and\n6\ntetragonal elongation in the C-type phase). This distortion generates a planar\nanisotropic local potential field around the Cu site, effectively introducing an in-plane\npotential energy gradient that favors lateral displacement of Cu ions. At the same time,\nthe local symmetry around the Cu site approaches the O point group, which forbids\nh\nthe s-d coupling. Therefore, the presence of in-plane displacement in CuMnP Se is\n2 6\ngoverned by the combined effects of Jahn-Teller distortion and symmetry-forbidden s-\nd coupling.\nCOMMENT 7:\nHow are the temperatures for phonon calculations in Fig. S2 decided? What about the\ndynamic stability at higher temperatures? The last phonon spectrum for AuMnP S\n2 6\nseems to have imaginary frequencies.\nAuthors’ Reply: Thank you for your insightful question.\nOur work mainly focuses on CuMnP Se , whose D-type and C-type phases exhibit the\n2 6\nmagnetic critical temperature of ~31 K and ~18 K, respectively. To realize the FM–\nAFM phase transition, the system must operate below these critical temperatures.\nTherefore, we chose 15 K for the D-type phase and 10 K for the C-type phase in the\nphonon spectra calculations. For the other materials exhibit minor imaginary\nfrequencies, we uniformly set the calculation temperature to 50 K. For consistency, we\nalso recalculated the phonon spectra of both D-type and C-type phases at 50 K, and\nthey are dynamically stable.\nThe small imaginary frequencies observed near the Γ point in the phonon spectra of\nAuMnP S are likely numerical artifacts, commonly encountered in 2D materials [npj\n2 6\nComputational Materials, 8, 236 (2022)]. We used a larger supercell to recalculated its\nphonon spectra and found that the imaginary frequencies were significantly eliminated.\nCOMMENT 8:\nThere are a couple of typos. (‘insensitive’ instead of ‘sensitive’ and ‘eg’ instead of ‘t2g’\nin the Supplementary mat.).\nAuthors’ Reply: Thank you for your careful reading. We have corrected.\nCOMMENT 9:\nFinally, I would like to mention that no new concept has been presented in this\nmanuscript. The concept as well as the analysis is exactly similar to the work by Meiling\nXu et al., Phys. Rev. Lett. 124, 067602 (2020) (ref. [29] of the manuscript). Only the\ncompound studied is different.\nAuthors’ Reply: We sincerely thank the Reviewer for the careful evaluation and for\nhighlighting the comparison with Phys. Rev. Lett. 124, 067602 (2020). We would like\nto emphasize that this PRL paper was led by one of the corresponding authors of the\npresent work. In that paper, our contribution was to propose, for the first time, the\nmechanism of electric-field control of magnetic phase transitions in type-I multiferroics,\nand to provide a candidate material capable of realizing this mechanism. To advance\nthe potential applications of electric-field control of magnetism, however, it remains\nessential to reduce the required external electric field. The present study is exactly\ncentered on this issue and, at the same time, reveals new underlying physics.\n(i) We show that an electric field as small as 0.001 V Å−1 can induce the FM–AFM\nphase transition in CuMnP Se , which is nearly two orders of magnitude lower than the\n2 6\n∼\ncritical field reported in the PRL work. This extremely low threshold makes the\nswitching mechanism much more experimentally accessible, significantly reducing the\ntechnical barriers for device implementation and enhancing its practical relevance for\nlow-power spintronic and memory applications.\n(ii) We report, for the first time, the emergence of robust in-plane ferroelectric\npolarization in members of the BMTP family, in clear contrast to the predominantly\nout-of-plane polarization commonly observed in this material family. This in-plane\nconfiguration is particularly advantageous because it mitigates depolarization effects,\nenhances ferroelectric retention, and facilitates integration into planar device\narchitectures.\n(iii) We uncover Jahn-Teller activity and symmetry-controlled s-d coupling as the\nfundamental microscopic factors governing the polarization direction and\nmagnetoelectric coupling in this system. This provides a clear and generalizable\nphysical picture and may guide the search for other low-field multiferroics with coupled\nferroic orders.\nTaken together, these advances represent a substantial conceptual and physical\nextension of the previous PRL work, moving toward experimentally realizable low-\nfield electric control of magnetism in 2D multiferroics. We believe these findings\nconstitute a genuine advance that aligns well with the scope and standards of Nature\nCommunications.\nCOMMENT 10:\nIn view of the above serious issues, I can not recommend the manuscript for publication\nin the highly reputed journal Nature Communications.\nAuthors’ Reply: We respectfully thank the Reviewer’s comment and suggestions. We\nhave carefully revised the manuscript to address all concerns and to clarify the\nconceptual advances. We believe that, after these substantial revisions, the novelty,\nphysical insights, and significance of our results are now clearly demonstrated, and we\nsincerely hope the manuscript can be reconsidered for publication.\nReviewer #2 (Remarks to the Author)\nCOMMENT:\nThe work of Chen et al. uses a combination of first principles methods to identify a\nparticular ferroelectric system, CuMnP Se , with two opposite polarizations, but with\n2 6\ndifferent magnetic ground states. Notably, a small electric field reverses the\npolarization and induces an AFM to FM transition. I find the work very interesting,\nclear, well-written, and of potential technological importance. I recommend acceptance\nafter minor revisions.\nAuthors’ Reply: We thank Reviewer #2 for his/her thoughtful comment, valuable\nsuggestion, and positive recommendation.\nCOMMENT 1:\nThere are some small weaknesses that can be improved.\nFig. 1, please add colored spheres in the figure to clarify the atom’s types.\nAuthors’ Reply: We thank the Reviewer for this helpful suggestion. Colored spheres\nhave been added in Fig. 1 to clearly distinguish the different atomic species.\nCOMMENT 2:\nPage 2, paragraph 5. Please justify the selection of X= Cu, Ag, Au, Y = Mn, Tc for the\ntargeted elemental substitution. Why not consider other transition metals? What values\nof U were used for Mn and Tc?\nAuthors’ Reply: We thank the Reviewer for this valuable question. The choice of X =\nCu, Ag, Au, and Y = Mn, Tc was guided by both valence configurations and chemical\nconsiderations. The X-site elements (Cu, Ag, Au) were chosen as monovalent cations\nwith closed d-shells and can easily displace from the octahedral center and thus generate\nferroelectric polarization. The Y-site transition metals were selected to ensure a high-\nspin t 3e 1 configuration (e.g., Mn3+ and Tc3+), which naturally leads to Jahn-Teller\n2g g\nactivity and strong coupling among orbital, lattice, and spin degrees of freedom--\nessential for realizing switchable ferroelectric and magnetic orders. The combination of\na Jahn-Teller-active Y site and a highly mobile, displacive X site thus provides an\neffective coupling pathway between structure and magnetism.\nIn all calculations, the on-site Coulomb interactions were treated using the GGA+U\napproach, with U =4.0 eV for Mn and Tc, consistent with previous studies [Phys. Rev.\neff\nMater. 5, 054409 (2021), Phys. Rev. B 105, 195153 (2022)]. We have added the\ncorresponding description in the Methods section.\nOur revision:\nIn response to this comment, we have added several sentences in the 1st paragraph of\npage 3 and 5th paragraph of page 6 in our main text, which read:\n“The X-site elements (Cu, Ag, Au) were chosen as monovalent cations owing to their\ngood displacive nature and can easily displace from the octahedral center, thus\ngenerating ferroelectric polarization. The Y-site transition metals were selected to\nensure a high-spin t 3e 1 configuration (e.g., Mn3+ and Tc3+), which naturally leads to\n2g g\nJahn-Teller activity and strong coupling among orbital, lattice, and spin degrees of\nfreedom.”\n“An effective Hubbard U of 4 eV for Mn 3d, Cu 3d, and Tc 4d orbitals [71, 72] was\napplied following the Dudarev formulation [73].”\nCOMMENT 3:\nPage 2, paragraph 5. How was \"the number of candidate structures 48\" found? Using\n3 for X, 2 for Y, 2 for S, Se, and 2 for C, D type I find 24.\nAuthors’ Reply: We thank the Reviewer for the careful observation. In fact, the\ncandidate structures were constructed based on the four structural prototypes, i.e., out-\nof-plane (OOP) polarization, nonpolar (NP), D-type, and C-type phases, combined with\nthree choices for X (Cu, Ag, Au), two for Y (Mn, Tc), and two for chalcogen atoms (S,\nSe), giving 4 × 3 × 2 × 2 = 48 possible configurations.\nFor better readability, we updated Fig. 2 and rewrote the corresponding description in\nthe 2nd paragraph of page 3 of our main text, as indicated below:\n“A total of 48 candidate structures were initially generated based on the four structural\nprototypes shown in Fig. 1.”\nCOMMENT 4:\nPage 2, paragraph 6. When computing the FM and AFM ground states. Did the author\nconsider large supercells for AFM configurations? If so, how large? How was the\nsupercell size cut-off chosen? Is there any experimental evidence to support any of these\nmagnetic ground states in this or other BMTP systems?\nAuthors’ Reply: Thanks for the question. To determine the magnetic ground states, we\nconstructed 2 × 2 × 1 supercells for all antiferromagnetic (AFM) configurations, which\nallowed us to capture both nearest-neighbor and next-nearest-neighbor exchange\ninteractions within the layer. To verify convergence with respect to supercell size, we\nalso tested larger 4 × 4 × 1 supercells for representative AFM configurations. The\nresulting total energy differences were found to change by less than 1 meV per unit cell,\nconfirming that the 2 × 2 × 1 supercell is sufficiently large to accurately describe the\nmagnetic ordering in this system.\nIn addition, this supercell size has been widely adopted in previous theoretical studies\non bimetallic thio(seleno)phosphates (BMTP) [Sci. Bull. 66, 233 (2021), J. Phys.:\nCondens. Matter 35, 395501 (2023)], where similar exchange pathways govern the\nmagnetic behavior. Experimental studies on related monometallic\nthio(seleno)phosphates (e.g., MnPSe [Phys. Rev. B 103, 024414 (2021), Nat.\n2 6\n14, 840 (2023), Nat. Commun. 15, 3029 (2024)]) have confirmed the presence of long-\nrange magnetic order, lending further confidence to the theoretical framework\nemployed in this study.\nCOMMENT 5:\nPage 2, paragraph 7. The sentence \"In the D-type phase... Cu-Mn dimer with a bong\nlength ... shorter than the alternating Cu-Mn bond..\" was difficult to understand. What\nis the alternating bond? Please identify the alternating bond in Fig. 3.\nAuthors’ Reply: We thank the Reviewer for the helpful comment. In the original\nmanuscript, the “alternating bond” refers to the longer Cu-Mn connections between\nadjacent dimers. Just as the Reviewer pointed out, the term “alternating bond” may\nconfuse. Therefore, we have revised the text in the 1st paragraph of page 4 of our main\ntext as “In the D-type phase, Cu and Mn atoms form dimer-like units with a nearest-\nneighbor distance of 3.43 Å, and the distance between neighboring dimers is 3.82 Å”\nCOMMENT 6:\nIn Page 3, paragraph 3, the position of different Mn d orbital characters are discussed\nand shown in Fig. 3. What is the axis of quantization used to project the orbitals? Along\nthe global z axis or along one of the octahedral axis? In the latter case, specify which\none. Figs. 3g and 3h are not clear, are these in 2D or 3D? Are d , d , d degenerate?\nxy yz xz\nAuthors’ Reply: We thank the Reviewer for these detailed questions. The orbital\nprojections shown in Fig. 3 were performed with the quantization axis aligned along\none of the local octahedral axes, specifically, the Mn-Se bond direction corresponding\nto either the longest or the shortest Mn-Se bond length was defined as the z-axis in the\nMnSe octahedron, as illustrated in Figs. 3g and 3h. This choice ensures that the orbital\n6\ncomponents (d , d , d , d , and d ) are referenced consistently with respect to the\nz2 x2-y2 xy xz yz\ndistorted MnSe octahedron. To improve clarity, Figs. 3g and 3h have been replotted in\n6\na 3D view. Because the MnSe octahedron is distorted, the t orbitals (d , d , and d )\n6 2g xy xz yz\nare not degenerate, consistent with Jahn-Teller-induced symmetry breaking. The\nrelative on-site energies of Mn-d orbitals in CuMnP Se further support this conclusion\n2 6\n(Supplementary Table 4). We have replotted Figs. 3g and 3h to clearly present the\norbital orientations and orbital ordering.\nFig. 3 e, f Orbital-resolved spin-up band structure projected onto Mn d orbitals for the D-type and\nC-type phases. g, h Mn d4 orbital energy levels with electron occupation for the D-type and C-type\nphases.\nSupplementary Table 4. The onsite energy. Relative on-site energies for Mn-d orbitals of 2D\nCuMnP Se monolayer derived from the Maximumly Localized Wannier Functions (MLWFs)\n2 6\nconstructed by using the Wannier90 package.\nD-type C-type\nMn\n↑ ↑\nd 2 2 -7.646668 -1.212646\nx -y\nd 2 -1.394782 -7.736580\nz\nd -7.639762 -7.744565\nxz\nd -7.498499 -7.529285\nyz\nd -7.543701 -7.404928\nxy\nCOMMENT 7:\nPage 3, paragraph 5. How does the polarization computed for CuMnP Se compare to\n2 6\nthe value computed for CuInP S in this work?\n2 6\nhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.L180101. Please specify\nthe polarization is in-plane.\nAuthors’ Reply: We thank the Reviewer for drawing our attention to this important\nreference [Phys. Rev. B 108, L180101 (2023)], which has now been cited as Ref. 58 in\nthe revised manuscript. In that work, the polarization strength P of bulk CuInP S is not\n2 6\ndirectly provided. We have estimated its value using the relation p =V b P/2π, where\n3 cell 3\nV is the unit-cell volume, b is the third reciprocal lattice vector, and P is the Berry-\ncell 3\nphase polarization. From this, we obtained P=0.035 C/m2 for bulk CuInP S .\n2 6\nTo ensure a meaningful comparison, we converted our calculated polarization values\nfor 2D CuMnP Se to the same units by considering the effective thickness of ~7 Å.\n2 6\nThe resulting in-plane polarizations are 0.13 C/m2 for the D-type phase and 0.09 C/m2\nfor the C-type phase, which are slightly larger than the bulk CuInP S value.\n2 6\nWe have added a new table (Supplementary Table 7) summarizing the polarization\nmagnitude and direction for common 2D ferroelectric materials.\nSupplementary Table 7. Summary of the polarization magnitude and direction of common 2D\nferroelectric materials.\nCompounds Polarization (C/m) Polarization direction Refs.\nCuMnP Se D-type 0.9 × 10−10 In plane This work\n2 6\nCuMnP Se C-type 0.7 × 10−10 In plane This work\n2 6\nAgBiP Se 1.2 × 10−12 Out of plane [5]\n2 6\nCuCrP S 0.79 × 10−12 Out of plane [6]\n2 6\nAuZrP S 9.74 × 10−12 Out of plane [7]\n2 6\n(CrBr ) Li 0.92 × 10−10 In plane [8]\n3 2\nγ-AlOOH 0.85 × 10−10 In plane [9]\nCOMMENT 8:\nPage 4, paragraph 4. Since the values of U and P for CuMnP Se are comparable to\n2 6\nthose of Hf(Zr) O , the authors adopt a coercive field of 65 kV/cm. However, how\n1+x 2\ndoes this compare with a coercive field estimated as E ~ dE / (PV), where dE, P, V are\nc\nthe energy difference between nonpolar and polar structures, and P, V are the\npolarization and volume of the polar structure?\nAuthors’ Reply: We thank the Reviewer for this insightful suggestion. Following the\nReviewer’s advice, we estimated the coercive field using the relation\nE ≈ΔE/(P×V),\nc\nwhere ΔE is the energy difference between the polar and nonpolar states, and P and V\nare the polarization and volume of the polar structure, respectively. The calculated\ncoercive fields are ~1763 kV/cm for the D-type phase and ~2209 kV/cm for the C-type\nphase. These values are clearly unphysically large, as this simple estimation does not\naccount for realistic switching mechanisms [Phys. Rev. B 95, 104104 (2017)]. In real\nferroelectric materials, polarization reversal is typically dominated by domain-wall\nmotion and defect-mediated processes rather than homogeneous switching, and E is\nc\nalso strongly temperature dependent. Therefore, the direct estimation of E remains\nc\nhighly nontrivial. For this reason, we emphasized the difficulty of accurately estimating\nE and adopted a more reasonable reference value based on experimentally accessible\nc\nferroelectric systems, such as Hf(Zr) O thin films, in our main text.\n1+x 2\nOur revision:\nIn response to this comment, we have added several sentences in the 2nd paragraph of\npage 6 of our main text, which read:\n“As is well known, a direct evaluation of E from first-principles is very challenging,\nc\nsince in real ferroelectric materials, polarization reversal is typically dominated by\ndomain-wall motion and defect-mediated processes rather than homogeneous switching,\nand E is also strongly temperature dependent [63]. Therefore, we adopted a more\nc\nreasonable reference value based on experimentally accessible ferroelectric systems to\nestimate E .”\nc\nCOMMENT 9:\nPage 5, paragraph 1. The two C -symmetric opposite polarizations have different\n2\nvalues, correct? If so, please report both values.\nAuthors’ Reply: We thank the Reviewer for the question. The two C -symmetric\n2\nopposite polarizations indeed have slightly different magnitudes, with 0.9 × 10⁻10 C/m\nalong the [1 0] direction for the D-type phase and 0.7 × 10⁻10 C/m along the [ 10]\ndirection for the C-type phase. These values have now been clearly stated in the 3rd\n1̅ 1̅\nparagraph of page 5 in the revised manuscript.\nReviewer #3 (Remarks to the Author)\nCOMMENT:\nI don't find the work suitable for publication in Nature Communications. This work\ncontains only the theoretical results, and it lacks the experimental evidence of the\nproposed structures. I still have some comments that may be helpful to improve the\nquality of the manuscript.\nAuthors’ Reply: We fully agree that the combination of theory and experiment\nprovides the most powerful route for advancing materials discovery. Indeed, if our\npredicted material could be experimentally synthesized and its ferroelectric and FM–\nAFM switching under ultralow electric fields verified, it would represent a significant\nstep forward toward next-generation information storage and spintronic devices.\nHowever, performing such synthesis and characterization is currently beyond the\nexperimental capabilities of our group, as all co-authors focus on the development of\ncomputational methods and theoretical modeling of materials.\nNevertheless, we are confident that the predicted phase can be experimentally realized,\nsince many materials predicted using our self-developed CALYPSO code, such as H O-\n3 3\nLett. 128, 106001 (2022)], LaH [Phys. Rev. Lett. 122, 027001 (2019)], and CaH\n10 6\n[Phys. Rev. Lett. 128, 167001 (2022)], have already been successfully synthesized,\nseveral of which were originally proposed by the authors of this work.\nFurthermore, our current work offers several key findings beyond the specific material\nprediction:\n(i) First identification of in-plane ferroelectricity in the BMTP family: Previous\nexperimental works on bimetal thio(seleno)phosphate BMTP compounds, such as\nCuInP S [Nat. Commun. 7, 12357 (2016)] and CuCrP S [Nat. Commun. 14, 7304\n2 6 2 6\n(2023)], have revealed out-of-plane ferroelectric polarization. To the best of our\nknowledge, our work is the first to predict robust in-plane ferroelectric polarization in\nthis family, which effectively mitigates the depolarization fields that often suppress out-\nof-plane ferroelectricity in ultrathin layers. Moreover, in-plane ferroelectricity is\nparticularly attractive for nonvolatile memory and low-power electronic switches, as it\nenables device geometries that are compact, scalable, and nondestructive in operation,\nas recently demonstrated in in-plane ferroelectric systems such as SnTe and In Se\n2 3\n[Science 353, 274-278 (2016); Sci. Adv. 4, eaar7720 (2018)]. These features make the\nproposed structure a realistic and experimentally meaningful target for synthesis and\ndevice applications.\n(ii) Proposal of the microscopic mechanism of in-plane ferroelectricity: We uncover\nJahn-Teller activity and symmetry-controlled s-d coupling as the fundamental\nmicroscopic factors governing the polarization direction and magnetoelectric coupling\nin this system. This provides a clear and generalizable physical picture that goes beyond\nthe material-specific case and may guide the search for other low-field multiferroics\nwith coupled ferroic orders.\n(iii) Experimental accessibility of the predicted electric-field-driven magnetic\nswitching: Ultralow-field control of magnetism through an electric-field-driven phase\ntransition makes the system highly appealing for experiments, as the required switching\nfield (~0.001 V/Å) can be easily achieved under typical laboratory conditions. For\ninstance, electric fields up to ~0.1 V/Å have already been achieved experimentally in\nsystems such as CrI [Nat. Mater., 17, 406-410 (2018)] and WTe -based ferroelectric\n3 2\nheterostructures [Nat. Nanotech. 18, 861-866 (2023)].\nThese findings establish a comprehensive and predictive theoretical framework that we\nbelieve fully justifies publication of our work in Nature Communications.\nCOMMENT 1:\nIn Figure 1, it's difficult to differentiate the crystal structures (eg, top views in a and b,\nboth views in c and d). I suggest highlighting the main difference among the structures\nin Figure 1 and explaining it clearly in the caption/main text.\nAuthors’ Reply: We thank the Reviewer for this helpful suggestion. To improve clarity,\nwe have added colored spheres in Fig. 1 to distinguish different atomic species.\nAdditionally, we included four insets to highlight the distinct coordination\nenvironments and local symmetries of the Cu ions. We have also revised the figure\ncaption to clearly describe these structural differences.\nFig. 1 Crystal structures of four structural prototypes of 2D XYP (S/Se) viewed from the top\n2 6\nand side. a Out-of-plane (OOP) ferroelectric phase with C symmetry. b Nonpolar (NP) phase with\n3 2\n(D-type). d In-plane ferroelectric phase with C symmetry, polarized along the [ 10] direction (C-\n2 1̅\ntype). Blue and purple spheres represent X and Y metal atoms, respectively; green and yellow\n1̅\nspheres correspond to S/Se atoms on the top and bottom layers, respectively; pink spheres denote P\natoms. Red arrows indicate the polarization directions. Four insets highlight the distinct\ncoordination environments, local symmetries, and off-center displacement of the Cu ions.\nCOMMENT 2:\nThe authors say, 'out-of-plane displacement of Cu1+ gives rise to spontaneous\npolarization.' Are they referring to the atom shown in yellow in Figure 1 (a)?\nAuthors’ Reply: Yes, the Cu1+ ion exhibiting out-of-plane displacement indeed\ncorresponds to the yellow atom in Fig. 1a of the original version. In response to the\nReviewer #2’s comment, we have changed its color to blue in the revised figure (Fig.\n1) for clearer visual distinction.\nCOMMENT 3:\nJustify the sentence 'In an MnS(Se) octahedral environment, this t 3e 1 configuration\n6 2g g\ncauses strong Jahn–Teller distortions, facilitating the emergence of new structural\nprototypes not accessible with other transition metals.' Why can't this happen for other\nTMs?\nAuthors’ Reply: We thank the Reviewer for this insightful question. We found that the\nstrong Jahn-Teller activity of Mn3+ may facilitate the emergence of new structural\nprototypes that are inaccessible to other transition metals.\nIn an Mn(S/Se) octahedral environment, the Mn3+ ion adopts a high-spin t 3e 1\n6 2g g\nconfiguration, which is well known to produce a strong Jahn-Teller instability because\nthe singly occupied e orbital (d or d ) directly overlaps with ligand p orbitals\ng z2 x2-y2\n(Supplementary Fig. 1). This orbital-ligand repulsion drives a large tetragonal distortion\nof the Mn(S/Se) octahedron (tetragonal elongation in C-type and tetragonal\n6\ncompression in D-type shown in Supplementary Table 1). In contrast, other transition-\nmetal ions do not exhibit this behavior. Ions with filled e orbitals (Fe3+), filled t\ng 2g\norbitals (Cr3+) are Jahn-Teller inactive, as there is no orbital degeneracy to lift. The\npartially filled t orbitals (e.g., Ti3+, V3+) may show weak Jahn-Teller effects, but these\n2g\ndistortions are much smaller and typically do not induce symmetry breaking.\nTherefore, the strong Jahn-Teller distortion unique to high-spin Mn3+ and Tc3+\nfacilitates the emergence of new polar structural prototypes that are not accessible in\ncompounds containing electronically inactive or low-spin transition metals. We also\nnote that other possible candidates, such as low-spin Ni3+ (d7, t 3↑e 1↑t 3↓e 0),\n2g g 2g g\nor other\nbimetallic combinations satisfying similar Jahn-Teller instability criteria, may exhibit\nrelated behavior and warrant future investigation.\nWe have updated the corresponding description in 3rd paragraph of page 2 of our main\ntext.\nSupplementary Fig. 1. The mechanism diagram of the Jahn-Teller effect. a, b Jahn-Teller effect\nobserved as tetragonal elongation and compression due to a net change in the energy of electrons. c\nNo Jahn-Teller effect occurred without a net change in energy. d Weak Jahn-Teller effect with only\nminor structural distortion.\nSupplementary Table 1. Summary Mn-Se bond lengths of MnSe octahedron in D- and C-type\n6\nphases.\nd (Å) d (Å) d (Å)\n1 2 3\nNonpolar 2.74114 2.74114 2.74114\nD-type 2.70390 2.80617 2.78310\nC-type 2.84205 2.72100 2.72361\nOur revision:\nIn response to this comment, we have added the following sentences in 3rd paragraph\nof page 2 of our main text, which read:\n“We selected Mn as the Y-site transition metal because Mn3+ possesses a high-spin d4\nelectron configuration. In an MnSe octahedral environment, the Mn3+ ion adopts a\n6\nt 3e 1 configuration, which is well known to produce a strong Jahn-Teller instability\n2g g\n(Supplementary Fig. 1). The singly occupied e orbital (d or d ) directly overlaps\ng z2 x2-y2\nwith the ligand p orbitals, leading to pronounced structural distortion of MnSe\n6\noctahedra, involving tetragonal compression or tetragonal elongation (Supplementary\nTable 1). This situation stands in sharp contrast to other 2D BMTPs such as CuCrP Se\n2 6\n(Cr3+, t 3), CuVP Se (V3+, t 2) and CuFeP Se (Fe3+, t 3e 2), where the transition-\n2g 2 6 2g 2 6 2g g\nmetal ions are Jahn-Teller inactive. Consequently, the strong Jahn-Teller activity of\nMn3+ may facilitate the emergence of new structural prototypes that are inaccessible to\nother transition metals.”\nCOMMENT 4:\nThe authors mentioned D-type and C-type phases in the manuscript. The author should\nprovide some context and relevant sources of other phases as well (such as A-type, B-\ntype phases, if they exist), instead of directly using C or D-type phases. This will help\nthe readability of the paper\nAuthors’ Reply: We thank the Reviewer for this suggestion. In fact, there are two well-\nknown structural prototypes in this system, namely the out-of-plane polarized phase\nand the nonpolar phase. In the present manuscript, we identify two additional low-\nenergy structures, which exhibit Cu-Mn dimer-like units and a chain-like -Cu-Mn-Cu-\nMn- arrangement, respectively. Therefore, we named them as the D-type and C-type\nphases throughout the paper.\nOur revision:\nIn response to this comment, we have added the corresponding description in the 4th\nparagraph of page 2 of our main text, which read:\n“As expected, two low-energy polar prototypes with C symmetry were identified (Fig.\n2\n1c, d), referred to as the D-type and C-type phases, characterized by the formation of\nCu-Mn dimer-like units and -Cu-Mn-Cu-Mn- chain-like configurations, respectively.”\nCOMMENT 5:\nWhat are the other unstable structures? Do they comprise Tc? Can you comment on\nwhy Tc - radioactive element - was considered in the calculations? In Figure 2(a), do\nthey mean XYP (S/Se) instead of XYP S(Se) ?\n2 6 2 6\nAuthors’ Reply: Thank you for the comment. In the XYP (S/Se) systems (X = Cu, Ag,\n2 6\nAu; Y = Mn, Tc), the (Cu/Au)TcP (S/Se) compounds in both D-type and C-type\n2 6\nconfigurations and AgMnP S in the D-type phase were found to be dynamically\n2 6\nunstable (Supplementary Fig. 5). Indeed, all these unstable structures contain Tc.\nTc was included in our study because it belongs to the same group as Mn and shares\nsimilar electronic configurations. Although Tc is radioactive, it is commonly used in\ntheoretical studies [Phys. Rev. B 85, 012201 (2012), Phys. Chem. Chem. Phys. 18,\n28791 (2016), RSC Adv. 6, 16197 (2016)].\nIn Fig. 2a, the correct formula should indeed read XYP (S/Se) rather than XYP S(Se) ,\n2 6 2 6\nand this has been corrected in the revised manuscript.\nOur revision:\nIn response to this comment, we have added the following clarification in the 3rd\nparagraph of page 3 of the main text, which state:\n“Phonon spectrum calculations reveal that CuMnP (S/Se) and AuMnP (S/Se) are\n2 6 2 6\ndynamically stable in both D-type and C-type configurations, whereas AgMnP S is\n2 6\nstable only in the C-type configuration (Supplementary Figs. 4, 5).”\nCOMMENT 6:\nUSPEX has also been very popular in predicting novel crystal structures. The author\nshould comment on their choice of CALYPSO over USPEX.\nAuthors’ Reply: There are already several well-established crystal structure prediction\nsoftware, such as CALYPSO, USPEX, AIRSS, and MAGUS, whose effectiveness has\nbeen extensively demonstrated. In this work, we chose to use CALYPSO because one\nof the co-authors is a core developer of the code, which allows us to apply the method\nwith the higher efficiency in predicting and analyzing structural prototypes.\nAdditionally, CALYPSO has been extensively benchmarked and has successfully\npredicted numerous experimentally confirmed compounds, such as H O-OH\n2\nmonolayer [J. Am. Chem. Soc. 2025, 147, 21162 (2025)], H O-OH multilayer [Nat.\n10 6\n[Phys. Rev. Lett. 128, 167001 (2022)]. These successes highlight CALYPSO’s\npredictive power and reliability for exploring complex energy landscapes and\ndiscovering stable structural prototypes.\nCOMMENT 7:\nFigure S1 (a, b) in Supporting Information: What are the displacement values? Do x-\naxes represent the number of images created?\nAuthors’ Reply: Thanks for the comment. In the previous version, the x-axes in Fig.\nS1 (now Supplementary Fig. 3) represented the displacement of the Cu ion along the\npathway connecting the out-of-plane polarized and nonpolar phases. Upon further\nconsideration, we realized that using displacement as the x-axis is not appropriate,\nespecially for Supplementary Fig. 3b, because we relaxed the intermediate structures,\nwhich caused the Cu atomic positions to change. Therefore, the x-axis now corresponds\nto the relaxed intermediate structures rather than fixed displacements. We have updated\nthe Supplementary Fig. 3 in the revised version.\nSupplementary Fig. 3. Energy evolution from the out-of-plane polarized (OOP) phase to the\nnonpolar (NP) phase of 2D CuMnP Se calculated using two methods. a full self-consistent\n2 6\ncalculation, and b fixed Cu z-coordinate with relaxation of all other degrees of freedom.\nCOMMENT 8:\nIn Figure S2 in Supporting Information, what do (2) and (4) represent? Also, are they\nsimulated at different temperatures?\nAuthors’ Reply: In the previous Supplementary information, labels (2) and (4) in Fig.\nS2 represent the D-type and C-type phases, respectively. In the revised version, the\noriginal Fig. S2 was reordered to Supplementary Fig. 4, and labels (2) and (4) have\nbeen replaced with D-type and C-type.\nCOMMENT 9:\nThere is no consistency in atomic colors in the crystal structures throughout the\nmanuscript, which should be fixed.\nAuthors’ Reply: We thank the Reviewer for pointing this out. We have now\nstandardized the atomic color scheme across all crystal structure figures throughout the\nmanuscript and Supporting Information.\nCOMMENT 10:\nThe authors should provide references for every equation/formula they have used in the\nmanuscript. For example, the spin Hamiltonian on page 3, the ME coupling coefficient\non page 4. I doubt the formula of the spin Hamiltonian used. Please see the following\npaper: https://pubs.rsc.org/en/content/articlehtml/2024/cp/d3cp05578g\nAuthors’ Reply: We thank the Reviewer for kind reminder. We have cited the\ncorresponding literature for the formula in the revised version. In fact, the spin\nHamiltonian used in our work is a simplified version of the one presented in the paper\nmentioned by the Reviewer [Phys. Chem. Chem. Phys. 26, 10111 (2024)]. It is derived\nby omitting the last two terms corresponding to single-ion anisotropy and anisotropic\nexchange interactions, as their contributions are relatively small in this system.\nSpecifically, in PCCP, the spin Hamiltonian employed is written as\n𝑧 2 𝑧 𝑧\nH = −J∑S𝑖 ∙S𝑗 −A∑(S𝑖 ) −B∑S𝑖 ∙S𝑗\n𝑖,𝑗 𝑖 𝑖,𝑗\nwhere J represents the isotropic Heisenberg exchange interaction, A is the single-ion\nanisotropy, and B corresponds to the anisotropic exchange term.\nIn our work, the Hamiltonian is simplified by retaining only the Heisenberg exchange\nterm, which is sufficient to capture the essential magnetic ordering in CuMnP Se .\n2 6\nThis is justified by our calculations showing that the magnetocrystalline anisotropy energies\nof the D-type and C-type phases are 36.5 μeV/atom and 35.7 μeV/atom, respectively,\nan order of magnitude smaller than the magnetic exchange parameters. Additionally,\nthe exchange anisotropy B is reported to be very small compared to the single-ion\nanisotropy A [Phys. Chem. Chem. Phys. 26, 10111 (2024)]. Therefore, our model\nprovides a reliable estimation of the magnetic transition temperature.\nFinally, we note that our Hamiltonian is consistent with previous theoretical studies on\nBMTP and related layered magnetic materials [J. Am. Chem. Soc. 145, 2485 (2023);\nNano Lett. 17, 2771 (2017); Phys. Rev. B 91, 235425 (2015)]. We have cited these\nreferences as Refs. 22 and 52-54 in the revised manuscript to make the theoretical\nframework clearer.\nCOMMENT 11:\nThe authors should explain in detail in the Supporting Information how they switched\nthe polarization by 120 and 180 degrees. This will be a good reference for readers.\nAuthors’ Reply: We thank the Reviewer for the helpful reminder. As illustrated in\nSupplementary Fig. 15, we have now provided a detailed description of the polarization\nswitching pathways by 120° and 180°.\nThe 120° switching process can be realized through an in-plane rotation of 120°\n(Supplementary Fig. 15a, b), corresponding to the application of an external electric\nfield along different in-plane directions, which leads to equivalent final states. This\nprocess can also be understood as a lateral displacement of Cu ions. In contrast, a 180°\npolarization reversal within the same phase (either D-type or C-type) is prohibited, as\nthe positions of Cu and Mn ions cannot be interchanged directly, nor can the entire\nstructure be rotated by 180° (Supplementary Fig. 15c). However, 180° ferroelectric\nswitching can still be achieved through an electric-field-induced phase transition\nbetween the D-type and C-type structures, accompanied by the migration or removal of\nCu atoms.\nWe have updated Fig. 4 to clearly present 120° and 180° switching processes and added\na new Supplementary Fig. 15 to serve as a clearer reference for readers.\nSupplementary Fig. 15. Schematic illustration of the 120° and 180° polarization switching\nprocesses. a, b 120° switching in the D-type and C-type phases achieved through in-plane rotation\nby 120°. c 180° switching pathway from the D-type to C-type phase.\nFig. 4. Energy barriers for ferroelectric (FE) switching pathways and electric-field-induced\nmagnetic transitions. a Energy barrier (E in meV/f.u.) for the 120° ferroelectric switching of\nbarrier\nthe D-type CuMnP Se . b Energy barrier (in meV/f.u.) for the 120° ferroelectric switching of the C-\n2 6\ntype CuMnP Se . c Energy barrier (in meV/f.u.) for the D-to-C phase transition, corresponding to a\n2 6\n180° reversal of polarization. The insets show the spin density distributions of the two phases (with\nP and Se atoms omitted), revealing ferromagnetic (FM) and antiferromagnetic (AFM) ground states,\nrespectively. d Energy difference between the C-type and D-type phases, defined as ΔE = E(D-type)\n-E(C-type), as a function of the applied in-plane electric field. Gradient orange hollow arrows\nindicate the direction of in-plane polarization. Positive and negative electric fields correspond to the\n[1 0] and [ 10] crystallographic directions, respectively.\nCO1̅ MME1̅NT 12:\nIn the Methods section, it should be 450 eV instead of 450-eV.\nAuthors’ Reply: Thanks. We have corrected it.\nCOMMENT 13:\nThe method section lacks information on the parameters used in CALYPSO.\nAuthors’ Reply: Thanks. We have provided detailed computational parameters for the\nCALYPSO structure prediction in the Methods section, as described below:\nThe particle-swarm optimization method within the evolutionary algorithm, as\nimplemented in the CALYPSO code [46-51], was employed to search for the lowest-\nenergy structures of the CuMnP Se monolayer. Unit cells containing one and two\n2 6\nformula units were considered. In the initial generation, random structures with specific\nsymmetries were constructed by generating atomic coordinates through\ncrystallographic symmetry operations. Local optimizations were carried out using the\nVASP code [67, 68] with the conjugate-gradient method and terminated when the Gibbs\nfree-energy change was smaller than 1×10-4 eV per cell. After each generation, 40% of\nthe low-energy structures were selected to construct the next generation through PSO,\nwhile the remaining 60% were randomly generated. A structure fingerprinting\ntechnique based on the bond-characterization matrix was employed to avoid duplication\nand enhance population diversity, which is crucial for efficient global searching. In total,\nthe search typically sampled 1200 structures (40 generations × 30 structures).\nCOMMENT 14:\nIn Supporting Information, Table SII, the sign of the deltaE (hence the magnetic state)\nof C-type AFMa is changed for the (Hubbard U) values of Mn = 4 and Cu = 5 eV.\nPlease comment on this.\nAuthors’ Reply: Thanks for this comment. Indeed, as shown in Supplementary Table\n5, the energy difference (ΔE) (hence the magnetic ground state) of the C-type AFMa\nconfiguration is changed when the Hubbard parameters are set to U = 4 and U = 5\nMn Cu\neV. This occurs because the energy competition between the AFM and FM\nconfigurations in the C-type phase is very small, on the order of only a few meV per\nformula unit, so slight variations in U can shift their relative stability.\nTo further assess this sensitivity, we examined a wider range of U values, as Mn-\nMn\ncontaining systems are known to be sensitive to on-site correlation corrections. In the\nlow-U regime (U = 1-3 eV), the FM configuration is the ground state; however, for\nMn\nU = 4-6 eV (a physically reasonable regime), the AFMa ordering becomes more\nMn\nfavorable and even remains stable up to U = 8 eV (Supplementary Table 5).\nMn\nImportantly, the D-type phase consistently maintains a robust FM ground state across\nall tested U values.\nThese results demonstrate that while the magnetic ordering of the C-type phase is\nslightly sensitive to the Hubbard U parameter, the overall magnetic behavior of the\nMn\nCuMnP Se system remains robust. Within the physically realistic range (U = 4-6 eV),\n2 6 Mn\nthe D-type and C-type phases exhibit distinct FM and AFM ground states, respectively,\nthereby preserving the mechanism of electric-field-induced FM-AFM switching.\nThe effect of the Hubbard U term on magnetic ordering is summarized in\nSupplementary Table 5. To maintain the smooth flow of the main text, a detailed\ndiscussion of this effect has been included in Section IX: The effect of Hubbard U terms\non magnetic ordering of the revised Supplementary Information.\nOur revision:\nIn response to this comment, we have added several sentences in 2nd paragraph of page\n5 of our main text and a new Section IX to the Supplementary Information, which read:\n“We further investigated the impact of the Hubbard U parameter on magnetic ordering\nand orbital-level splitting for both D-type and C-type phases, finding that the overall\nqualitative trends and key conclusions are robust over a broad range of U values\n(Supplementary Table 5 and Table 6).”\n“Section IX: The effect of Hubbard U terms on magnetic ordering: we note that the\nmagnetic ground state of the C-type phase is changed when the Hubbard parameters\nare set to (U = 4, U = 5 eV) and (U =1-3 eV, U =0 eV). This occurs because the\nMn Cu Mn Cu\nenergy competition between the AFM and FM configurations in the C-type phase is\nvery small, on the order of only a few meV per formula unit, so slight variations in U\ncan shift their relative stability. In fact, U = 4-6 eV and U 1-4eV are the physically\nMn Cu=\nreasonable regimes. Importantly, the D-type phase consistently maintains a robust FM\nground state across all tested U values. These results demonstrate that while the\nmagnetic ordering of the C-type phase is sensitive to the Hubbard U parameter, the\nMn\noverall magnetic behavior of the CuMnP Se system remains robust. Within the\n2 6\nphysically realistic range (U = 4-6 eV), the D-type and C-type phases exhibit distinct\nMn\nFM and AFM ground states, respectively, thereby preserving the mechanism of electric-\nfield-induced FM ↔ AFM switching.”\nSupplementary Table 5. Relative energies of different magnetic orders with respect to the\nferromagnetic state, calculated for both D-type and C-type phases using various Hubbard U values.\nD-type C-type\nHubbard U\nvalues\nFM AFMa AFMab FM AFMa AFMab\nU = 4, U = 3 0 11.9 5.2 0 -0.01 13.7\nMn Cu\nU = 4, U = 4 0 12.0 5.2 0 -0.2 18.7\nMn Cu\nU = 4, U = 5 0 13.2 7.1 0 0.5 14.3\nMn Cu\nU = 3, U = 3 0 19.1 9.6 0 -0.1 14.5\nMn Cu\nU = 0, U = 0 0 48.4 21.5 0 -3.2 15.0\nMn Cu\nU = 1, U = 0 0 52.2 33.4 0 6.2 21.0\nMn Cu\nU = 2, U = 0 0 33.4 25.9 0 2.5 19.4\nMn Cu\nU = 3, U = 0 0 21.9 15.2 0 0.4 16.9\nMn Cu\nU = 4, U = 0 0 18.0 11.1 0 -0.4 15.3\nMn Cu\nU = 5, U = 0 0 15.6 8.7 0 -0.9 14.2\nMn Cu\nU = 6, U = 0 0 13.7 6.7 0 -1.3 13.2\nMn Cu\nU = 7, U = 0 0 12.4 5.4 0 -1.6 12.4\nMn Cu\nU = 8, U = 0 0 11.3 4.4 0 -1.9 11.7\nMn Cu\nReviewer #4 (Remarks to the Author)\nCOMMENT:\nThe research focus on the electric field control of magnetic phase transitions, specially\nin cases where the necessary electric fields are small for practical reasons. The\nmanuscript is very well written and all results look correct. The research lacks\nexperimental results and focus only on first principle calculations and modeling with a\nspin Hamiltonian. However, the authors did a phonon analysis (with and without\nthermal effects), together with molecular dynamics to confirm thermal stability. Those\nare already the methods necessary within first principles to access the viability of the\nmaterials experimentally. Additionally, the authors used several methods to access the\nproperties of the materials, such as: Berry phase method to calculate the in-plane\npolarizations; Wannier analysis for the orbital ordering; and NEB calculations to\ninvestigate different phase transitions. I conclude then that the manuscript is suitable\nfor publication at Nature Communications after reviews:\nAuthors’ Reply: We sincerely thank the Reviewer for the positive and encouraging\nfeedback. We also appreciate the Reviewer’s recommendation for publication.\nCOMMENT 1:\nIn Figure 1, it is very difficult to understand the structural differences between the NP,\nC and D types (OOP is more obvious). The authors could improve the understanding\nby explicitly indicating which of the metal atoms are displaced to create the in-plane\npolarization. Also using different colors for top and bottom S/Se atoms can help.\nAuthors’ Reply: We thank the Reviewer for this suggestion. To improve the readability\nof Fig. 1, we have explicitly indicated the metal atoms displaced to generate the in-\nplane polarization in the C- and D-type phases. In addition, we have used different\ncolors for the top and bottom S/Se atoms for visualization. These modifications make\nthe structural differences among the NP, C, and D types more intuitive and have been\nreflected in both the revised figure and caption.\nFig. 1 Crystal structures of four structural prototypes of 2D XYP (S/Se) viewed from the top\n2 6\nand side. a Out-of-plane (OOP) ferroelectric phase with C symmetry. b Nonpolar (NP) phase with\n3 2\n(D-type). d In-plane ferroelectric phase with C symmetry, polarized along the [-110] direction (C-\n2\ntype). Blue and purple spheres represent X and Y metal atoms, respectively; green and yellow\nspheres correspond to S/Se atoms on the top and bottom layers, respectively; light pink spheres\ndenote P atoms. Red arrows indicate the polarization directions. Four insets highlight the distinct\ncoordination environments, local symmetries, and off-center displacement of the Cu ions.\nCOMMENT 2:\nThe authors used DFT+U and tested some values of U, but they used a rather modest\nvalue of U throughout the manuscript and SI. Also they only compared the energy\nordering for a small range of U (either 3 or 4 eV).\na) What is the effect of energy ordering for U < 3eV? What happens for much larger\nvalues of U (perhaps up to 8 eV)? Specially Mn can be quite tricky to deal with.\nAuthors’ Reply: We thank the Reviewer for this thoughtful comment. Indeed, the\nchoice of Hubbard U is particularly important for Mn-based systems. In response to the\nReviewer's suggestion, we systematically tested U values ranging from 0 to 8 eV.\nMn\nAs shown in Supplementary Table 5, when U is set to 1-3 eV (a low and physically\nMn\nless meaningful regime), the C-type phase exhibits FM ordering. In the physically\nreasonable range of U = 4-6 eV, the C-type phase stabilizes in the AFMa\nMn\nconfiguration. This energetic trend is further preserved up to U = 8 eV. The D-type\nMn\nphase consistently maintains a robust FM ground state across all tested U values. These\nresults demonstrate that while the magnetic ordering of the C-type phase is sensitive to\nthe Hubbard U parameter, the overall magnetic behavior of the CuMnP Se system\nMn 2 6\nremains robust. Within the physically realistic range (U = 4-6 eV), the D-type and C-\nMn\ntype phases exhibit distinct FM and AFM ground states, respectively, thereby\npreserving the mechanism of electric-field-induced FM ↔ AFM switching.\nThe effect of the Hubbard U term on magnetic ordering is summarized in\nSupplementary Table 5. To maintain the smooth flow of the main text, a detailed\ndiscussion of this effect has been included in Section IX: The effect of Hubbard U terms\non magnetic ordering of the revised Supplementary Information.\nOur revision:\nIn response to this comment, we have added several sentences in 2nd paragraph of page\n5 of our main text and a new Section IX in the revised Supplementary Information,\nwhich read:\n“We further investigated the impact of the Hubbard U parameter on magnetic ordering\nand orbital-level splitting for both D-type and C-type phases, finding that the overall\nqualitative trends and key conclusions are robust over a broad range of U values\n(Supplementary Table 5 and Table 6).”\n“Section IX: The effect of Hubbard U terms on magnetic ordering: we note that the\nmagnetic ground state of the C-type phase is changed when the Hubbard parameters\nare set to (U = 4, U = 5 eV) and (U =1-3 eV, U =0 eV). This occurs because the\nMn Cu Mn Cu\nenergy competition between the AFM and FM configurations in the C-type phase is\nvery small, on the order of only a few meV per formula unit, so slight variations in U\ncan shift their relative stability. In fact, U = 4-6 eV and U 1-4eV are the physically\nMn Cu=\nreasonable regimes. Importantly, the D-type phase consistently maintains a robust FM\nground state across all tested U values. These results demonstrate that while the\nmagnetic ordering of the C-type phase is sensitive to the Hubbard U parameter, the\nMn\noverall magnetic behavior of the CuMnP Se system remains robust. Within the\n2 6\nphysically realistic range (U = 4-6 eV), the D-type and C-type phases exhibit distinct\nMn\nFM and AFM ground states, respectively, thereby preserving the mechanism of electric-\nfield-induced FM ↔ AFM switching.”\nSupplementary Table 5. Relative energies of different magnetic orders with respect to the\nferromagnetic state, calculated for both D-type and C-type phases using various Hubbard U\nvalues for Mn atom.\nD-type C-type\nHubbard U\nvalues\nFM AFMa AFMab FM AFMa AFMab\nU = 4, U = 3 0 11.9 5.2 0 -0.01 13.7\nMn Cu\nU = 4, U = 4 0 12.0 5.2 0 -0.2 18.7\nMn Cu\nU = 4, U = 5 0 13.2 7.1 0 0.5 14.3\nMn Cu\nU = 3, U = 3 0 19.1 9.6 0 -0.1 14.5\nMn Cu\nU = 0, U = 0 0 48.4 21.5 0 -3.2 15.0\nMn Cu\nU = 1, U = 0 0 52.2 33.4 0 6.2 21.0\nMn Cu\nU = 2, U = 0 0 33.4 25.9 0 2.5 19.4\nMn Cu\nU = 3, U = 0 0 21.9 15.2 0 0.4 16.9\nMn Cu\nU = 4, U = 0 0 18.0 11.1 0 -0.4 15.3\nMn Cu\nU = 5, U = 0 0 15.6 8.7 0 -0.9 14.2\nMn Cu\nU = 6, U = 0 0 13.7 6.7 0 -1.3 13.2\nMn Cu\nU = 7, U = 0 0 12.4 5.4 0 -1.6 12.4\nMn Cu\nU = 8, U = 0 0 11.3 4.4 0 -1.9 11.7\nMn Cu\nb) Is the orbital ordering also affected by the U values? I believe that higher values will\nincrease the separation of the orbitals, but there is also a possibility of changing the\nordering in case the occupation pattern shifts. What happens for U = 0 eV? Is it still S\n= 2 or does it go to S = 1?\nAuthors’ Reply: Indeed, the Hubbard U parameter can influence both the degree of\norbital splitting and, in some cases, the orbital occupation pattern. To evaluate this effect,\nwe calculated the relative on-site energies of Mn-d orbitals and magnetic moments\nacross a range of U values (0-8 eV), taking the D-type phase as an example. As shown\nMn\nin Supplementary Table 6, and consistent with the Reviewer’s expectation, higher U\nvalues lead to an increased separation of the d orbitals, particularly within the e\ng\nmanifold.\nWhen U = 1-2 eV, the d and d orbitals are nearly indistinguishable because\nMn z2 x2-y2\nCuMnP Se exhibits metallic behavior (Supplementary Fig. 18), reflecting the weak d\n2 6\norbital localization at low U. As U increases, CuMnP Se becomes semiconducting,\nMn 2 6\nand the energy separation between the d and d orbitals gradually increases from\nz2 x2-y2\n3.23 eV to 7.02 eV as U rises from 3 to 7 eV. Importantly, the d and d orbital\nMn z2 x2-y2\nordering remains unchanged across the entire range of U values considered.\nAt U = 0 eV, the Mn ion still retains a high-spin configuration (S=2), consistent with\nMn\nthe nominal t 3e 1 occupation of Mn3+, yielding a magnetic moment of 4  .\n2g g B\nOur revision:\nIn response to this comment, we have added a new Section X in the Supplementary\nInformation, which read:\n“Section X: The effect of Hubbard U terms on orbital ordering: Hubbard U parameter\ncan influence both the degree of orbital splitting and, in some cases, the orbital\noccupation pattern. To evaluate this effect, we analyzed the relative on-site energies of\nMn-d orbitals and magnetic moments across a range of U values (0-8 eV), taking the\nMn\nD-type phase as an example. As shown in Supplementary Table 6, higher U values lead\nto an increased separation of the d orbitals, particularly within the e manifold. When\ng\nU =1-2 eV, the d and d orbitals are nearly indistinguishable because CuMnP Se\nMn z2 x2-y2 2 6\nexhibits metallic behavior (Supplementary Fig. 18). As U increases, CuMnP Se\nMn 2 6\nbecomes semiconducting, and the energy separation between the d and d orbitals\nz2 x2-y2\ngradually increases from 3.23 eV to 7.02 eV as U rises from 3 to 7 eV. Importantly,\nMn\nthe d and d orbital ordering remains unchanged across the entire range of U values\nz2 x2-y2\nconsidered.\nAt U = 0 eV, the Mn ion still retains a high-spin configuration (S = 2), consistent with\nMn\nthe nominal t 3e 1 occupation of Mn3+, yielding a magnetic moment of 4  .”\n2g g B\nSupplementary Table 6. Relative on-site energies for Mn-d orbitals of D-type CuMnP Se\n2 6\nmonolayer derived from the Maximumly Localized Wannier Functions (MLWFs) constructed by\nusing the Wannier90 package and formal magnetic moments across a range of U values (0-8 eV).\nMagnetic\nd 2 2 (eV) d 2 (eV) d (eV) d (eV) d (eV)\nx -y z xz yz xy\nmoment ( )\nB\nU = 0\nMn\n-5.8785 -5.7135 -5.8641 -5.2233 -5.3200 4\nU = 0\nCu\nU = 1\nMn\n-6.3233 -6.1050 -6.3102 -5.6955 -5.8758 4\nU = 0\nCu\nU = 2\nMn\n-6.7812 -6.7259 -6.7872 -1.0158 -6.4236 4\nU = 0\nCu\nU = 3\nMn\n-5.0922 -1.8653 -3.5157 -6.8615 -6.9107 4\nU = 0\nCu\nU = 4\nMn\n-7.6101 -1.0942 -7.6040 -7.3134 -7.4375 4\nU = 0\nCu\nU = 5\nMn\n-8.1184 -1.1188 -8.1084 -7.8012 -7.9738 4\nU = 0\nCu\nU = 6\nMn\n-8.5268 -1.8761 -8.5138 -8.1724 -8.5105 4\nU = 0\nCu\nU = 7\nMn\n-9.0625 -2.0404 -8.9884 -8.5356 -9.0011 4\nU = 0\nCu\nU = 8\nMn\n-9.4147 -7.4777 -9.2345 -1.0642 -0.6121 4\nU = 0\nCu\nCOMMENT 3:\nBy changing the U to lower values the authors could also investigate better the\ninteractions between the Cu and Mn ions. It is reasonable to consider less strong\nlocalized orbitals, leading to more hybridization between Cu and Mn ions.\nAuthors’ Reply: We thank the Reviewer for this valuable suggestion. Indeed, lowering\nthe Hubbard U parameter reduces the localization of Mn and Cu d electrons and can\nenhance the degree of overlap between Mn d and Cu d states. To examine this effect,\nwe calculated the projected density of states (PDOS) of CuMnP Se in both D-type and\n2 6\nC-type phases using smaller U values (1 and 2 eV for Mn and 0 eV for Cu), as shown\nin Supplementary Fig. 18. As expected, the Mn and Cu d orbital bandwidths broaden,\nleading to increased overlap between Cu 3d and Mn 3d states.\nIn order to investigate the interactions between the Cu and Mn ions, we calculated the\nintegrated crystal orbital Hamilton population (ICOHP) values for Cu-Mn pairs\nconsidering U =1 and 2 eV for Mn. Results show the ICOHP values are being close to\nzero (0.12 for D-type and 0.02 for C-type at U=1 eV; 0.08 for D-type and 0.01 for C-\ntype at U=2 eV), clearly indicating the non-bonding like interaction between Cu and\nMn atoms. Therefore, the strong overlap between Cu and Mn d states in the valence\nband actually originates from the strong hybridization of Mn 3d-Se p and Cu 3d-Se p\nstates, making the Cu and Mn states appear to overlap in the projected DOS\n(Supplementary Fig. 18).\nOur revision:\nWe have added a new Section XIII to elucidate the overlap between Cu and Mn d states\nin the revised Supplementary Information, which read:\n“As shown in Fig. 3c, d and Supplementary Figs. 10, 11, the overlap between the Cu\nand Mn 3d states in the PDOS arises primarily from the strong hybridization of Mn 3d-\nSe p and Cu 3d-Se p states. The integrated crystal orbital Hamilton population (ICOHP)\nvalues for Cu-Mn pairs, which are approximately -0.03 and -0.01 eV per bond for the\nD-type and C-type phases, respectively. These values, being close to zero, clearly\nindicate the non-bonding like interaction between Cu and Mn atoms.\nLowering the Hubbard U parameter reduces the localization of Mn and Cu d electrons\nand can enhance the degree of overlap between Mn d and Cu d states. To examine this\neffect, we recalculated the projected density of states (PDOS) of CuMnP Se in both\n2 6\nD-type and C-type phases using smaller U values (1 and 2 eV for Mn and 0 eV for Cu),\nas shown in Supplementary Fig. 18. As expected, the Mn and Cu d orbital bandwidths\nbroaden, leading to increased overlap between Cu 3d and Mn 3d states. However, at\nthis case, the ICOHP values are still being close to zero (0.12 for D-type and 0.02 for\nC-type at U=1 eV; 0.08 for D-type and 0.01 for C-type at U=2 eV), clearly indicating\nthe non-bonding like interaction between Cu and Mn atoms.”\nSupplementary Fig. 18. Projected density of states (PDOS) of CuMnP Se in both D-type and\n2 6\nC-type phases onto the Mn/Cu d orbitals using different Hubbard U values. a U =1, U =0.\nMn Cu\nb U =2, U =0. c U =4, U =4.\nMn Cu Mn Cu\nCOMMENT 4:\nCan the authors comment further on the structures that present negative frequencies in\nthe phonon spectra? What are the modes associated to them?\nAuthors’ Reply: Thanks for the comment. As illustrated in Supplementary Fig. 5,\nCu(Ag/Au)TcP (S/Se) compounds in both D-type and C-type configurations, as well\n2 6\nas AgMnP S in the D-type phase were found to be dynamically unstable, exhibiting\n2 6\nimaginary phonon modes, particularly along the first acoustic branch across the entire\nBrillouin zone.\nBecause these imaginary frequencies appear throughout the Brillouin zone, it is difficult\nto display and analyze all vibration modes in detail. Therefore, we selected the  point\nas a representative example to illustrate the vibration modes corresponding to the\nimaginary frequencies. As shown in Supplementary Fig. 5, these vibration modes are\nrather complex and are mainly associated with the vibrations of the S/Se atoms.\nA new figure (Supplementary Fig. 5) presenting these phonon spectra and the\ncorresponding vibration analysis has been incorporated into the revised Supplementary\nInformation.\nSupplementary Fig. 5. Phonon spectra and the vibration modes of the first acoustic branch\nnear the  point. a, b CuTcP Se . c, d CuTcP S . e, f AgTcP Se . g, h AgTcP S i, j AuTcP Se . k,\n2 6 2 6 2 6 2 6. 2 6\nl AuTcP S . m AgMnP S\n2 6 2 6.\nResponse to Reviewers\nReviewer #1 (Remarks to the Author):\nCOMMENT: The authors have mostly addressed the concerns raised by me earlier.\nTherefore, I recommend the publication of the manuscript.\nAuthors’ Reply: Thank you very much for your positive evaluation and\nrecommendation. We are pleased that the revisions have addressed your earlier\nconcerns. We sincerely appreciate Reviewer’s constructive comments, which\nsignificantly improved its clarity and quality.\nReviewer #2 (Remarks to the Author):\nCOMMENT: I thank the authors for their diligent efforts in addressing my comments\nand those of the other referees. The revisions have significantly enhanced the clarity,\nquality, and overall impact of the manuscript. I believe the authors have thoroughly and\nsatisfactorily responded to all questions and concerns raised during the review process.\nTherefore, I recommend that the article be accepted for publication in its current form.\nAuthors’ Reply: We sincerely thank the Reviewer for the careful assessment and for\nthe positive recommendation. We greatly appreciate the Reviewer’s time and\nconstructive input, which have helped strengthen the work.\nReviewer #3 (Remarks to the Author):\nCOMMENT: The authors have adequately addressed all of my questions, and I believe\nthat my comments have significantly contributed to improving the quality of the\nmanuscript. Therefore, I recommend publishing the manuscript in Nature\nCommunications.\nAuthors’ Reply: We sincerely thank the Reviewer for the positive assessment and\nrecommendation. We are pleased that all questions have been adequately addressed in\nthe revised manuscript.\nReviewer #4 (Remarks to the Author):\nCOMMENT: I have reviewed the responses to the comments and the revised\nmanuscript entitled \"Phase-Transition-Driven Ferroic Response in 2D CuMnP Se\n2 6\nunder Ultra-Low Electric Fields\". I confirm that all concerns from myself and the other\nreferees have been satisfactorily addressed through the revisions.\nWhile it is noted, as other referees highlighted, that the work would be strengthened by\nexperimental validation, the simulation data presented is comprehensive, robust, and\nprovides significant theoretical insight. I believe this manuscript will be helpful for\nguiding future experimental work and for advancing the fundamental understanding of\nphase transitions in 2D ferroic materials.\nGiven the conceptual advance of the paper and the thoroughness of the revision, I\nbelieve it now meets the high standard for publication in Nature Communications and\nI support its acceptance as is.\nAuthors’ Reply: We thank the Reviewer for the careful re-evaluation and for\nsupporting acceptance. We are pleased that all concerns from the Reviewer and the\nother referees have been satisfactorily addressed. We appreciate the comment regarding\nexperimental validation, and we are glad that the comprehensive simulation results are\nconsidered robust and valuable for guiding future experiments and understanding phase\ntransitions in 2D ferroic materials."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have mostly addressed the concerns raised by me earlier. Therefore, I recommend the publication of the manuscript.", "reviewer_2": "I thank the authors for their diligent efforts in addressing my comments and those of the other referees. The revisions have significantly enhanced the clarity, quality, and overall impact of the manuscript. I believe the authors have thoroughly and satisfactorily responded to all questions and concerns raised during the review process. Therefore, I recommend that the article be accepted for publication in its current form.", "reviewer_3": "The authors have adequately addressed all of my questions, and I believe that my comments have significantly contributed to improving the quality of the manuscript. Therefore, I recommend publishing the manuscript in Nature Communications.", "reviewer_4": "I have reviewed the responses to the comments and the revised manuscript entitled \"Phase-Transition-Driven Ferroic Response in 2D CuMnP2S6 under Ultra-Low Electric Fields\". I confirm that all concerns from myself and the other referees have been satisfactorily addressed through the revisions.\nWhile it is noted, as other referees highlighted, that the work would be strengthened by experimental validation, the simulation data presented is comprehensive, robust, and provides significant theoretical insight. I believe this manuscript will be helpful for guiding future experimental work and for advancing the fundamental understanding of phase transitions in 2D ferroic materials.\nGiven the conceptual advance of the paper and the thoroughness of the revision, I believe it now meets the high standard for publication in Nature Communications and I support its acceptance as is."}, "author_response": ""}]

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