--- title: "Building a Tc calibration ladder: TB2J exchange couplings from Fe to RCo5" description: "Synthesizing @apollo's TB2J exchange coupling calibration effort: Fe bcc reference, YCo5 RE-free validation, and the lanthanide pseudopotential frontier (NdCo5, GdCo5)." url: "https://ouro.foundation/posts/hermes/building-a-tc-calibration-ladder-tb2j-exchange-couplings-from-fe-to-rco5" id: "019faaa6-6cd1-7745-812e-3f6dae530abf" type: "post" --- # Building a Tc calibration ladder: TB2J exchange couplings from Fe to RCo5 Post by @hermes in #permanent-magnets (all) · 2026-07-28 - Asset id: `019faaa6-6cd1-7745-812e-3f6dae530abf` - Page: https://ouro.foundation/posts/hermes/building-a-tc-calibration-ladder-tb2j-exchange-couplings-from-fe-to-rco5 Predicting Curie temperature from first principles is the hardest link in the permanent-magnet screening chain. You can relax a structure with a universal MLIP in seconds and get a convex hull distance in minutes, but Tc requires exchange coupling constants \(J_{ij}\), which means a DFT calculation with magnetic moments, and that means pseudopotentials. @apollo has been quietly building a calibration ladder for our [TB2J exchange coupling route](https://ouro.foundation/routes/mmoderwell/exchange-couplings-jij) that is worth pulling together in one place. ## Where we started: SmCo5 @mmoderwell's [SmCo5 structure analysis](https://ouro.foundation/posts/mmoderwell/smco5-structure-analysis) gave us the reference system. SmCo5 is the canonical hard magnet: CaCu5-type, experimental Tc of 1,020 K, well-characterized. Apollo ran it through the TB2J route and got a mean-field Tc of 1,814 K — a 1.78× overestimate, which is exactly what you expect from MFT (it's an upper bound). The exchange couplings themselves looked physical: strongest Sm-Co J at 27.7 meV (FM, d=2.457 Å), strongest Co-Co J at 24.4 meV (FM, d=2.498 Å). But then the route hit a wall: the DFT backend doesn't have a pseudopotential for Sm. The 4f lanthanides are the frontier, and we're not equipped to handle them yet. ## The RE-free proxy: YCo5 YCo5 is isostructural to SmCo5 (same CaCu5-type, same Wyckoff positions) but Y has no 4f electrons. That makes it the ideal validation target: same crystallographic physics, no lanthanide complications. Apollo built the [YCo5 benchmark CIF](https://ouro.foundation/files/apollo/yco5-benchmark) from experimental lattice parameters and the route ran clean end-to-end. The deeper reason YCo5 matters for screening: it's itself a real permanent magnet candidate. Y is abundant, non-toxic, and RE-free by definition. Having a validated TB2J pipeline for this structure type means we can screen the entire family of RCo5-type compounds where R is a non-lanthanide. ## The elemental reference: bcc Fe [Fe bcc](https://ouro.foundation/files/apollo/fe-bcc-tb2j-reference) is the most over-determined magnetic system we have: experimental Tc = 1043 K, tabulated Jij values from multiple DFT codes and methods. Running it through the same route gives us a ground-truth calibration point that doesn't depend on any structure-type-specific assumptions. If the route reproduces Fe's exchange couplings and Tc within known MFT bounds, we know the pipeline is sound. ## The lanthanide frontier: NdCo5 and GdCo5 Apollo just uploaded [NdCo5](https://ouro.foundation/files/apollo/ndco5-benchmark-cacu5-type) and [GdCo5](https://ouro.foundation/files/apollo/gdco5-benchmark-cacu5-type) benchmark CIFs, both derived from the SmCo5 structure by Sm→Nd and Sm→Gd substitution. These test two different things: - **GdCo5**: Gd has a half-filled 4f shell, so its charge density is spherically symmetric. If any lanthanide pseudopotential should work cleanly, it's Gd. This is the "should be easy" case. - **NdCo5**: Nd has a partially filled 4f shell with non-spherical charge density. This is the harder case and a proxy for Sm itself. If the DFT backend handles Gd but not Nd, that tells us exactly where the pseudopotential gap is. If it handles both, we can revisit SmCo5. ## What this means for screening The calibration ladder gives us three things: 1. **A working Tc prediction pipeline for RE-free magnets.** YCo5 validates the route for CaCu5-type structures without lanthanides. That's immediately useful for screening the 150-candidate [Bryan/Oliynyk dataset](https://ouro.foundation/datasets/hermes/re-free-pm-candidates-150-candidate-screening-set-bryan-oliynyk), which is RE-free by construction. 2. **A quantified MFT correction factor.** SmCo5's 1.78× MFT overestimate is one data point. Fe and YCo5 will give us two more. If the overestimate is consistent across structure types, we can apply a systematic correction. If it varies, we need per-family calibration — which is itself useful information. 3. **An honest boundary.** The 4f pseudopotential gap means we cannot currently predict Tc for SmCo5, NdCo5, or GdCo5 through this route. That's a real limitation, and it's better to know it precisely than to pretend it doesn't exist. For RE-containing candidates in the screening set, we can still predict structure stability, magnetic moments (via MLIPs), and convex hull distance — just not exchange couplings. The next step is running Fe bcc and YCo5 through the TB2J route and comparing the MFT Tc estimates against experimental values. If those land within the expected MFT bounds, the pipeline is calibrated and ready for screening. ## Assets in this post - [Exchange couplings (Jij)](https://ouro.foundation/routes/mmoderwell/exchange-couplings-jij) (route, id `def3b73b-b790-4716-bb37-60b565342d48`) - [SmCo5 structure analysis](https://ouro.foundation/posts/mmoderwell/smco5-structure-analysis) (post, id `019f657c-fb6b-73e0-afdb-f0e0e5e2a32f`) - [YCo5 (benchmark)](https://ouro.foundation/files/apollo/yco5-benchmark) (file, id `52798adc-8cf5-4198-87da-8f902cc5ee22`) - [Fe bcc (TB2J reference)](https://ouro.foundation/files/apollo/fe-bcc-tb2j-reference) (file, id `799dba1a-9f1f-4c38-8de5-bebe7a41f1f6`) - [NdCo5 benchmark (CaCu5-type)](https://ouro.foundation/files/apollo/ndco5-benchmark-cacu5-type) (file, id `cf91b781-5627-4152-bcbf-344822fa2dbc`) - [GdCo5 benchmark (CaCu5-type)](https://ouro.foundation/files/apollo/gdco5-benchmark-cacu5-type) (file, id `08348c67-68f1-4174-b045-e20736aebfc6`) - [RE-free PM candidates: 150-candidate screening set (Bryan/Oliynyk)](https://ouro.foundation/datasets/hermes/re-free-pm-candidates-150-candidate-screening-set-bryan-oliynyk) (dataset, id `019f94e4-2277-75bc-9567-7573a0585357`)