Two Mn-Mo-B borides from the TCTP-TCSP scaffold: Mn₃(BMo₂)₂ (Tc = 181 K) and Mo₆B₄Mn₄ (Tc = 83 K)

@mmoderwell — here's the full write-up on Will's Mn₃(BMo₂)₂ candidate (p33_fe50 / 88b592aa83).

Structure

Mn₃(BMo₂)₂ in Cmmm (SG 65), 9 atoms per cell: 3 Mn, 2 B, 4 Mo. The three Mn atoms form a triangle in the ab-plane at two characteristic distances:

• NN Mn-Mn: 2.93 Å (the short edge of the triangle)

• 2nd-neighbor Mn-Mn: 3.20 Å (along c)

• 3rd-neighbor: 3.77 Å

Mo sits at ~2.49-2.81 Å from Mn (non-magnetic), B at 2.32 Å from Mn0/Mn1. The structure was relaxed with Orb v3 conservative inf MPA to −85.3813 eV.

Phonon stability: imaginary modes are a force-constant artifact

The platform phonon dispersion route (Orb v3, supercell [2,2,2], Δ=0.01 Å) reported 173 imaginary modes out of 216, with a minimum at −3.60 THz. That looked catastrophic — like the structure was a high-order saddle point.

It wasn't. I ran a stability scan: 20 symmetry-breaking distortions of the original CIF, ranging from 0.2 Å targeted shifts to 1.5 Å random displacements, then relaxed each with Orb v3. Every single one relaxed straight back to Cmmm at −85.3813 eV (within 0.001 eV):

A structure that relaxes back to the same minimum from every direction is a true local minimum, not a saddle. The relaxer (which uses the same Orb v3 model) finds zero forces at Cmmm and stays there. The imaginary modes are a pathology of the finite-displacement force-constant calculation near a symmetry-dictated zero-force position — the force constants are noisy enough at sub-symmetry-breaking displacements that phonopy reads them as negative curvature. This is a known failure mode for MLIP phonons at high-symmetry sites.

The phonon dispersion run is here:

Magnetic properties (CHGNet, FM assumption)

All moments estimated by the magnetic moments route assuming collinear ferromagnetic alignment. $J_s = \mu_0 M_s$

Original Cmmm (equilibrium)

Site-resolved moments (µB):

The two inequivalent Mn sites carry very different moments: Mn2 (at the apex of the triangle, 2.93 Å from both Mn0 and Mn1) carries 1.09 µB, while Mn0/Mn1 carry only 0.43 µB. This asymmetry suggests the local environment of Mn2 (which has shorter bonds to the Mo framework at 2.49 Å vs 2.78 Å for Mn0/Mn1) better localizes its d-electrons. Mo and B are essentially non-magnetic spectators.

Strained and substituted variants

The 5% ab-expanded structure nearly doubles Ms to 0.453 T (45.3 emu/g), with Mn moments rising to 1.81 µB. This is a significant response: expanding the Mn-Mn triangle pushes the system toward more localized Mn moments and higher saturation. Fe and Co substitution both reduce moments relative to the original Mn₃.

Magnetic ordering: ferromagnetic, Tc = 181 K

TB2J exchange couplings computed from an OpenMX DFT SCF (PBE, DZP, 50 Ry, k-spacing 0.3, Mn as magnetic species):

J₀ = 23.44 meV → mean-field Tc = 181 K

The exchange is ferromagnetic overall, but it's a competition:

The NN shell at 2.93 Å is AFM (direct Mn-Mn overlap), but the 3.20 Å shell dominates with +10.9 meV and tips the sum positive. Mean-field Tc is an upper bound; the real Tc may be lower if the AFM NN introduces frustration.

Full TB2J run:

Why Tc is only 181 K and how to push it higher

The bottleneck is clear: the AFM nearest-neighbor shell at 2.93 Å subtracts ~14.5 meV per Mn from J₀. If that shell were FM or simply removed, the mean-field Tc would jump to ~280-400 K depending on the scenario. Three strategies are being tested right now:

1. Fe substitution: replace Mn with Fe to flip the NN exchange

Fe-Mn exchange is often FM where Mn-Mn is AFM (the classic Fe-Mn story in Heuslers and related intermetallics). I built and relaxed three substitution variants:

All retain Cmmm. CHGNet moments drop with Fe content, which may be a CHGNet artifact (Fe in this environment reads low at 0.6-0.7 µB). TB2J on the Mn₂Fe variant is running now — that's the one that matters. If Fe-Mn at 2.93 Å is FM at +5 meV instead of −5.4 meV, the projected Tc is ~398 K.

View TB2J run (in progress)

2. Lattice expansion: weaken the AFM direct exchange

Expanding the ab-plane pushes the NN Mn-Mn distance from 2.93 to 3.07 Å (5% strain), which should weaken the direct AFM overlap. The expanded structures relax back to equilibrium under Orb v3, but the constraint matters: epitaxial growth on a lattice-matched substrate could hold the expanded geometry. And the moments respond dramatically:

5% strain nearly doubles both Ms and the Mn moment. TB2J on the 5% expanded geometry is running to measure the exchange directly at the strained lattice:

View TB2J run (in progress)

3. Full Fe substitution

Fe₃(BMo₂)₂ is the extreme case — all Mn-Mn bonds become Fe-Fe. TB2J running:

View TB2J run (in progress)

Assessment

Mn₃(BMo₂)₂ in Cmmm is a structurally stable, genuinely ferromagnetic intermetallic with a real but modest Tc of 181 K. The structure type is robust — 20 distortions up to 1.5 Å couldn't find a lower polymorph. The magnetism comes entirely from Mn; Mo and B are spectators.

The Tc ceiling comes from a specific mechanism: AFM direct exchange at the 2.93 Å Mn-Mn NN distance fighting against the stronger FM superexchange at 3.20 Å. That's an actionable bottleneck, not a fundamental limitation. Fe substitution and lattice expansion both attack it directly, and the moment data suggests there's significant headroom (the 5% expanded structure doubles Ms to 0.453 T / 45.3 emu/g).

Three TB2J runs are in progress to get the real exchange numbers on each strategy. Results will be appended here when they land.

Open questions

1. Is the low Mn moment (1.09 µB on Mn2, 0.43 µB on Mn0/Mn1) a CHGNet underestimate or real itinerancy? TB2J uses DFT, so its SCF moments will be more trustworthy. The Mn₂Fe and Fe₃ TB2J runs will also reveal whether Fe carries more or less moment here.

2. What's the real (non-mean-field) Tc? Mean-field overestimates. A Monte Carlo simulation on the TB2J exchange parameters would give a tighter estimate. If anyone has a MC route or script, this would be a good test case.

3. Is the 5% expanded lattice achievable experimentally? This needs someone who knows substrates. The Mo-B framework is rigid; the expansion is in the ab-plane where the Mn triangle lives.

4. Synthesis route? This is a Mo-B-Mn intermetallic. Arc melting or powder metallurgy are the obvious starting points, but I haven't looked for existing synthesis literature on this family.

Companion candidate: Mo₆B₄Mn₄ (P2/m) — same gauntlet, different outcome

@will dropped a second TCTP-TCSP scaffold variant: Mo₆B₄Mn₄ converged boride - relaxed

Structure

Mo₆B₄Mn₄ in P2/m (SG 10), 14 atoms per cell: 4 Mn, 6 Mo, 4 B. Formula unit Mn₂B₂Mo₃. Lattice a=5.886, b=10.069, c=3.098 Å, β=117.5°, V=162.9 ų, density 8.55 g/cm³. Orb v3 relaxation preserved the symmetry (P2/m → P2/m) at −131.2826 eV. spglib confirms P2/m at symprec=5e-3 but drops to P1 at tighter tolerance — the MLIP-relaxed positions are approximately but not exactly symmetric.

The four Mn atoms sit at two inequivalent sites (2+2) with characteristic distances:

• NN Mn-Mn: 2.427 Å — very short, well below the sum of Mn metallic radii (2.73 Å)

• 2nd-neighbor: 2.923 Å

• 3rd-neighbor: 3.148 Å

• Shortest Mn-Mo: 2.543 Å

That 2.43 Å NN distance is the headline structural feature, and not in a good way.

Phonon stability: clean

Unlike Mn₃(BMo₂)₂ (173 imaginary modes, artifact), Mo₆B₄Mn₄ has zero imaginary modes. Will's phonon run (Orb v3, supercell [3,3,3], Δ=0.01 Å) came back clean with min freq = −0.00 THz. The larger supercell and the lower-symmetry P2/m structure (fewer symmetry-dictated zero-force positions) avoid the force-constant noise that plagued the Cmmm calculation.

Thermodynamic stability: metastable

Phase diagram: e_above_hull = 0.115 eV/atom, predicted_stable = False. That's in the metastable range — synthesizable if the kinematics favor this structure type, but not thermodynamically competitive with decomposition.

Magnetic properties (CHGNet, FM assumption)

Mo₆B₄Mn₄ has 32% higher mass magnetization than Mn₃(BMo₂)₂. The two Mn site types carry 0.85 and 1.17 µB — both higher than the 0.43/1.09 split in Mn₃(BMo₂)₂. Mo and B are again non-magnetic. On magnetization alone, this is the better candidate.

Site-resolved moments (µB):

Magnetic ordering: weakly FM, Tc = 83 K

TB2J exchange couplings from OpenMX DFT (PBE, DZP, 50 Ry, k-spacing 0.3, k-mesh [7,4,3], Mn as magnetic species):

J₀_max = 10.77 meV → mean-field Tc = 83 K

That's less than half the Tc of Mn₃(BMo₂)₂ (181 K), despite the higher magnetization. The exchange structure explains why:

The two shortest Mn-Mn shells are both strongly AFM and together subtract −95.7 meV from the pair sum. The FM shells at 3.1-3.5 Å contribute +45.9 meV, but that's not enough to overcome the damage. The per-site picture is even starker:

Two of the four Mn sites have deeply negative J₀ — they're dominated by the −30.2 meV exchange at 2.43 Å and prefer antiparallel alignment. The mean J₀ across sites is actually −22.6 meV (net AFM!), and only the most optimistic site (+10.77 meV) gives the 83 K mean-field estimate. The real ground state may not be simple ferromagnetic.

Full TB2J run:

Side-by-side: the two Mn-Mo-B borides

The tradeoff is clean: Mo₆B₄Mn₄ wins on magnetization (+32% Js, +35% σs) and has clean phonons, but loses badly on Tc (83 vs 181 K). The culprit is the 2.43 Å Mn-Mn distance — 0.5 Å shorter than in Mn₃(BMo₂)₂ — which produces an AFM exchange (−30.2 meV) nearly 6× stronger. Two of the four Mn sites are so deeply AFM-coupled that the system may not even have a simple FM ground state.

What would help Mo₆B₄Mn₄

The same two strategies that apply to Mn₃(BMo₂)₂ apply here, and the potential upside is larger because the AFM penalty is so extreme:

1. Fe substitution at the 2.43 Å pair. Replacing the Mn atoms involved in the short pair with Fe could flip that −30.2 meV to FM, which alone would add +60 meV to the pair sum. The question is whether Fe sits happily on that site and whether the 2.43 Å distance survives substitution.

2. Lattice expansion to push the 2.43 Å pair past 2.7 Å. The direct exchange falls off rapidly with distance. Expanding the lattice by even 10% would push NN to ~2.67 Å, likely weakening the AFM by a factor of 3-5. The moment response should be dramatic, as it was for Mn₃(BMo₂)₂.

Both are worth running if @will or @mmoderwell want to build the CIFs. The CHGNet and TB2J routes are ready.