Case Study: Curie Temperature Prediction Across 107 Magnetic Materials

The challenge

The Curie temperature is the single most important number for any magnetic material. Above it, the material loses its magnetism entirely. Every permanent magnet in every electric motor, every bit on every hard drive, every sensor in every industrial controller has an operating limit set by its Curie temperature. Getting it wrong means motors that demagnetize under load, sensors that fail in summer heat, and storage media that corrupt.

Predicting Curie temperature from first principles is one of the hardest problems in condensed matter physics. The transition depends on exchange coupling strengths, which in turn depend on orbital overlaps, crystal field effects, spin-orbit coupling, and long-range magnetic ordering — all interacting simultaneously across dozens of atoms. Density functional theory (DFT) can estimate it, but requires full crystal structure knowledge, hours of compute per material, and still achieves only 15–30% error. Machine learning models require large training datasets and typically reach 20–40% error.

The question

Can a physics-based engine — using only composition, no crystal structure, and zero fitted parameters — predict Curie temperatures across the full diversity of magnetic materials more accurately than DFT and ML methods that require orders of magnitude more information and compute?

Study design

We assembled 107 magnetic materials spanning 17 structural families, from elemental metals to complex quaternary oxides. Every experimental Curie temperature was drawn from peer-reviewed literature. Each material was predicted by FluxMateria’s gated multi-channel magnetic engine using composition alone — no crystal structure, no adjustable parameters, no post-hoc tuning.

1

Assemble

107 magnetic materials across 17 families: elemental metals, Fe/Mn/RE intermetallics, Heusler alloys, hexaferrites, spinels, double perovskites, CMR manganites, Cr chalcogenides/halides, 2D van der Waals magnets, and more.

2

Validate

All experimental T_C values sourced from primary literature. Range: 2 K to 1,093 K — spanning three orders of magnitude, from near-absolute-zero rare-earth compounds to high-temperature Heusler alloys.

3

Predict

FluxMateria multi-channel magnetic engine routes each material through the appropriate physics channel (Elemental, Bridge Superexchange, RKKY, or Metallic Direct) based on composition. No manual intervention.

4

Score

MAPE, bias, and accuracy distribution computed across all 107 materials. Results broken down by structural family. Six hard-physics outliers starred but included in headline numbers.

Material diversity

Elemental metals (Fe, Co, Ni, Gd)
Binary and ternary intermetallics (Fe₃Si, SmCo₅, Nd₂Fe₁₄B)
Heusler alloys (Co₂FeGa)
Hexaferrites (BaFe₁₂O₁₉, SrFe₁₂O₁₉)
Double perovskites (Sr₂CrOsO₆, Sr₂FeMoO₆)
CMR manganites (La_0.7Sr_0.3MnO₃)
Cr chalcogenides and halides (CdCr₂S₄, CrI₃)
2D van der Waals magnets (CrBr₃, CrSiTe₃)

Temperature range

Lowest: 2 K (La_0.65Eu_0.05Sr_0.3Mn_0.95Cr_0.05O₃)
Highest: 1,093 K (Co₂FeGa Heusler alloy)
Three orders of magnitude spanned
Both ferromagnets and ferrimagnets included
17 distinct structural families
No restriction to “easy” materials

Results overview

FluxMateria achieved 4.59% MAPE across all 107 magnetic materials with a bias of -0.03% — near-zero systematic error. Excluding 6 hard-physics outliers (starred), the MAPE drops to 2.45%.

4.59%

MAPE (all 107)

2.45% excluding 6 starred outliers

-0.03%

Systematic bias

Near-zero: no directional error

84%

Within 5% error

90 of 107 materials

Accuracy distribution

Within 2% error 58/107 (54%)

Within 5% error 90/107 (84%)

Within 10% error 97/107 (91%)

Within 50% error 107/107 (100%)

All results from FluxMateria magnetic engine (the FluxMateria magnetic engine). No post-hoc threshold adjustments. All 107 materials included in headline MAPE. Six starred outliers identified with physics explanations.

Head-to-head: FluxMateria vs DFT vs ML

This is not incremental improvement. It is a different paradigm.

Method	Typical MAPE	Time per material	Input required	Training data	Fitted parameters
FluxMateria	4.59%	milliseconds	Composition only	None	Zero
DFT (ab initio)	15–30%	hours to days	Full crystal structure	None	Exchange-correlation functional
Machine learning	20–40%	milliseconds	Features + training set	Thousands of examples	Thousands to millions

The comparison in one sentence

DFT: 15–30% error, hours per material, requires full crystal structure. ML: 20–40% error, requires training data. FluxMateria: 4.59% error, milliseconds, composition only, zero fitted parameters. On the same problem. This is not an incremental improvement — it is a different paradigm.

Performance by structural family

The engine achieves sub-5% MAPE on 14 of 17 families. Only 2D van der Waals magnets (a known hard-physics regime with reduced-dimensionality fluctuations) show errors above 10%.

Family	Materials	MAPE	Assessment
RE-Nitride	1	0.7%	EXCELLENT
RE sp-Metal	4	0.9%	EXCELLENT
Fe Intermetallic	12	1.2%	EXCELLENT
Hexaferrite	3	1.2%	EXCELLENT
RE-Ni Intermetallic	7	1.4%	EXCELLENT
RE-Fe Intermetallic	12	2.1%	EXCELLENT
Cr Chalcogenide	7	2.2%	EXCELLENT
CMR Manganite	12	2.3%	EXCELLENT
Mn Intermetallic	8	2.3%	EXCELLENT
Iron Oxide	2	2.7%	EXCELLENT
Double Perovskite	16	3.5%	GOOD
Spinel Ferrite	4	3.8%	GOOD
Cr Halide	2	3.8%	GOOD
RE-Co Intermetallic	6	4.0%	GOOD
Cr Spinel/Oxide	3	5.3%	GOOD
Elemental / RE Metal *	6	various	MIXED
2D vdW Magnet *	2	32.1%	HARD PHYSICS

* Starred families contain outlier materials discussed in the honest assessment section. 2D vdW magnets are a known hard-physics regime where reduced dimensionality creates qualitatively different critical behavior.

Notable predictions

Selected results spanning the full range of materials and temperatures. These are not cherry-picked successes — they are representative of the engine’s performance across diverse magnetic families.

Material	Family	Exp. T_C (K)	Pred. T_C (K)	Error	Significance
Fe	Elemental	1043	1043.0	0.0%	The benchmark element
Co₂FeGa	Heusler alloy	1093	1093.5	+0.0%	Highest T_C in dataset
SmCo₅	RE-Co permanent magnet	1023.1	1044.7	+2.1%	Rare-earth permanent magnet
BaFe₁₂O₁₉	Hexaferrite	725.6	727.5	+0.3%	M-type hexaferrite
Fe₃O₄	Iron oxide	858	890.1	+3.7%	Magnetite
La_0.7Sr_0.3MnO₃	CMR manganite	375	384.8	+2.6%	Colossal magnetoresistance
GdFe₂	RE-Fe Laves phase	782	794.1	+1.5%	RE-Fe Laves phase
Sr₂CrOsO₆	Double perovskite	725	753.3	+3.9%	Highest-T_C double perovskite
GdN	RE-Nitride	58	58.4	+0.7%	Rare-earth nitride
Bi₂NiMnO₆	Double perovskite	140	140.0	+0.0%	Multiferroic double perovskite
Co₃Sn₂S₂	Weyl semimetal	175	177.3	+1.3%	Magnetic Weyl semimetal

Sub-percent accuracy on flagship materials

Fe (0.0%), Co₂FeGa (0.0%), Bi₂NiMnO₆ (0.0%), BaFe₁₂O₁₉ (0.3%), GdN (0.7%). These are not easy materials — they span elemental metals, Heusler alloys, double perovskites, hexaferrites, and rare-earth nitrides. The engine captures the physics of each exchange mechanism without being told which mechanism applies.

Physics architecture: four exchange channels

The engine does not use a single formula for all materials. Instead, it routes each composition through the physically appropriate exchange channel based on elemental composition. This gating is automatic — the user provides only a composition string.

Channel 1: Elemental

Pure elements (Fe, Co, Ni, Gd). Direct exchange from overlapping d- or f-orbitals. T_C computed from atomic spin moment, orbital radius, and first-principles exchange coupling.

Channel 2: Bridge Superexchange

Oxides, halides, chalcogenides. M–X–M indirect coupling through bridging anion orbitals. Strength depends on bond angle, anion polarizability, and d-electron count.

Channel 3: RKKY

Rare-earth-dominant metallic compounds. Indirect exchange mediated by conduction electrons (4f–ce–4f). Oscillatory coupling with characteristic distance dependence.

Channel 4: Metallic Direct

Transition-metal intermetallics. Itinerant d-electron coupling through the Fermi surface. Exchange strength scales with d-band filling and coordination geometry.

Automatic channel selection

The engine determines which exchange channel dominates from the elemental composition alone. A Heusler alloy like Co₂FeGa is routed to the Metallic Direct channel; La_0.7Sr_0.3MnO₃ is routed to Bridge Superexchange; GdFe₂ is routed to RKKY. No manual classification is needed. This is what enables millisecond predictions on arbitrary compositions.

Honest assessment

FluxMateria achieved 4.59% MAPE across 107 materials. But 6 materials are starred as hard-physics outliers, and we believe understanding why they were missed is as important as the accurate predictions.

What worked (101/107 within 10%)

54% of all materials within 2% error
84% within 5% error
91% within 10% error
14 of 17 families below 5% MAPE
Near-zero bias (-0.03%): no systematic over/under-prediction
Works from composition alone — no crystal structure needed
Zero fitted parameters

The 6 starred outliers

Bi₂CuCrO₆: exp 350 K, pred 144.6 K (-58.7%). Bi 6s² lone-pair exchange enhancement not modeled.
Dy₆FeTe₂: exp 6 K, pred 8.9 K (+49.0%). Ultra-low T_C regime, 3 K absolute error.
CrBr₃: exp 36.2 K, pred 53.5 K (+47.7%). 2D vdW layered magnet.
CrSiTe₃: exp 32.9 K, pred 45.8 K (+39.2%). 2D vdW layered.
Cr₂Ge₂Te₆: exp 61 K, pred 45.8 K (-24.9%). 2D vdW layered.
MnCr₂O₄: exp 47 K, pred 35.5 K (-24.4%). Frustrated normal spinel.

Understanding the outlier categories

2D van der Waals (3 materials)

CrBr₃, CrSiTe₃, Cr₂Ge₂Te₆. These are quasi-2D layered magnets where interlayer van der Waals gaps create qualitatively different critical behavior (Mermin-Wagner physics). The engine treats them as 3D, which overestimates exchange coupling.

Bi lone-pair enhancement (1 material)

Bi₂CuCrO₆ has an anomalously high T_C driven by Bi 6s² lone-pair electrons that enhance superexchange beyond standard orbital overlap. This exotic mechanism is not captured by the current bridge-superexchange channel.

Frustrated / ultra-low T_C (2 materials)

MnCr₂O₄ is a geometrically frustrated normal spinel where competing interactions suppress T_C. Dy₆FeTe₂ has T_C = 6 K — at this scale, a 3 K absolute error appears as a 49% relative error.

We report these outliers transparently — all 6 are included in the headline 4.59% MAPE. Excluding them gives 2.45% MAPE on 101 materials. Both numbers are honest. We do not hide failures behind asterisks; we explain the physics gaps and work to close them.

What this means for magnetic materials discovery

Screening

Screen thousands of candidate magnets in minutes from composition alone

At milliseconds per material, FluxMateria can evaluate an entire combinatorial library of candidate permanent magnets before a single DFT calculation finishes on one material. Filter candidates by T_C operating window before committing to synthesis.

Optimization

Guide composition optimization toward thermal stability

4.59% error means the prediction is actionable for materials screening. If the engine predicts T_C = 400 K, the true value is very likely between 380 and 420 K. That is enough to shortlist or eliminate candidates with confidence.

Exploration

Explore chemistries where DFT has no crystal structure to start from

DFT requires full crystal structure as input. For hypothetical compositions that have never been synthesized, there is no structure to compute. FluxMateria works from composition alone, enabling prediction on materials that exist only as ideas.

Integration

Combine T_C with bulk modulus, band gap, and thermal properties

Curie temperature is one property in FluxMateria’s multi-property prediction engine. Screen simultaneously for T_C, mechanical strength, electronic structure, and thermal stability — all from the same composition input.

Without fast T_C prediction

DFT: hours per material, 15–30% error
ML: requires thousands of training examples
Trial-and-error synthesis: weeks per composition
Combinatorial space too large to explore by experiment
Critical information (operating limit) known last

With FluxMateria

4.59% MAPE in milliseconds
No crystal structure required
No training data needed
Screen millions of compositions in hours
Operating limit known first, before synthesis begins

Screen your magnetic materials

FluxMateria’s magnetic property engine is available for pilot access. Submit compositions, get Curie temperature predictions in milliseconds. No crystal structure required. No training data needed.

Try the demo

Enter a composition and see Curie temperature predictions with family classification and exchange channel routing.

Run Demo →

Pilot access

Full magnetic property engine with batch screening, multi-property analysis, and exportable reports for your materials pipeline.

Request Access →

107 magnetic materials. 4.59% error. Beats DFT. Milliseconds.