How this instrument works
Magnetic susceptibility, χ, measures how readily a material's internal moments line up with an applied field: large positive χ means that material magnetizes easily, while a value near zero means it barely responds at all. In a paramagnet, each atom carries its own small, independent magnetic moment, like a compass needle free to spin. Left alone, thermal motion points these needles every which way, so their fields cancel; switch on an external field and slightly more needles tip toward it than away, and that tiny excess is what χ measures.
Curie's law, χ = C ⁄ T, ties that response to temperature through a single material constant, C. Pierre Curie found this pattern experimentally in 1895, years before Boltzmann statistics explained why: an applied field's aligning pull competes against heat's scrambling effect, and for weak fields that competition works out to an exact inverse. Raise temperature and each needle jostles harder, so a given field wins over fewer of them — χ falls in direct proportion to 1 ⁄ T. Constant C folds in everything specific to a sample: how many moments sit in a given volume, and how strong each one is.
This law is not universal. It describes moments acting independently, so it holds for dilute paramagnets but breaks down once neighboring moments start interacting — in iron below its ordering point, or in an antiferromagnet, exchange forces compete with temperature and χ stops tracing a straight line through the origin when plotted against 1 ⁄ T. A practical fix, the Curie–Weiss law χ = C ⁄ (T − θ), adds constant θ, which shifts that singularity away from absolute zero and marks where ordering sets in.
- Enter a sample's value in the Curie constant, K field — a property of that material, not of current temperature.
- Enter the sample's absolute temperature in the Temperature, K field. Kelvin only; add 273.15 first if you measured in Celsius.
- Read the result in the Magnetic susceptibility field — a small positive number for an ordinary paramagnet.
- Change the temperature and watch susceptibility move the other way: doubling T exactly halves the result, at fixed C.
Worked example — a paramagnetic salt at 300 K
Take a paramagnetic salt whose measured Curie constant is 0.5 K, sitting on a lab bench at room temperature, 300 K. Curie's law gives χ = 0.5 ⁄ 300 = 0.00166666666667, or about 1.667 × 10⁻³ — small and positive, typical of a paramagnet, where diamagnets instead sit near −10⁻⁵ and ferromagnets can run thousands of times larger.
Move that same sample into an oven at 600 K; C stays fixed, only T changes: χ = 0.5 ⁄ 600 = 0.000833333333333, exactly half the room-temperature figure. That clean halving on a doubled temperature is a signature materials labs look for before trusting a sample as genuinely Curie-law paramagnetic, rather than something with hidden exchange effects already at play.
Questions
What does the Curie constant actually measure?
It packages everything specific to the sample into one number: how many independent magnetic moments sit in a given volume, and how large each moment is. A salt with more unpaired electron spins per unit volume, or spins of greater magnitude, carries higher C — and therefore higher χ at any given temperature.
Why does susceptibility fall as temperature rises?
Because thermal motion competes with an applied field for control of each moment's direction. At low temperature, that field wins over more moments and χ is large; heat a sample and its moments jostle harder, so fewer stay aligned, and χ drops in direct proportion to 1 ⁄ T — precisely the shape χ = C ⁄ T describes.
Does Curie's law apply to every magnetic material?
No — only to paramagnets whose moments act independently. Ferromagnets and antiferromagnets have neighboring moments that interact strongly, so below their ordering temperature the simple χ = C ⁄ T fails; the Curie–Weiss law, χ = C ⁄ (T − θ), replaces it, with θ marking where ordering begins. Diamagnets follow neither law — their weak, negative χ barely shifts with temperature.
What size of susceptibility counts as typical?
Paramagnets usually land between about 10⁻⁵ and 10⁻³ on a dimensionless volume scale this calculator uses — 0.00167 in this worked example sits comfortably in that band. Diamagnets run smaller and negative, near −10⁻⁵, while ferromagnets can reach into hundreds or thousands under an applied field.
Can the Curie constant be negative?
Physically, no. C derives from the square of each moment's magnitude, so it stays zero or positive for a true paramagnet; zero just means no unpaired moments remain to align. A negative reading in real data usually means diamagnetism from the holder or surrounding material is swamping a weaker paramagnetic response underneath.
Who discovered Curie's law, and when?
Pierre Curie, in his 1895 doctoral thesis on magnetism in different states of matter — years before his later, better-known work on radioactivity with Marie Curie. He established the 1 ⁄ T dependence from measurement alone; the microscopic explanation, resting on Boltzmann statistics of jostled moments, came afterward.