Number of atoms
Lattice constant
nm
Magnetic moment
μB
Curie constant
K*A/(T*m)

# Curie Constant Calculator

By Miłosz Panfil, PhD

This Curie constant calculator helps you calculate the Curie constant. The Curie constant characterizes a response of a paramagnetic material to the magnetic field. Keep on reading to learn more about the Curie constant equation and the Curie's law of magnetism.

## Curie's law of magnetism

The Curie law of magnetism states that the magnetization `M` of a paramagnetic substance is proportional to the Curie constant `C` and the magnetic field `B`. It is inversely proportional to the temperature `T`. In the form of the equation, we can write

`M = C/T * B`.

To learn more about the Curie's law check the Curie's law calculator. Here we focus on the Curie constant `C` and its dependence on the properties of the material considered.

## Curie constant equation

The Curie constant characterizes susceptibility of the paramagnetic material to the magnetic field. It depends on the strength of the magnetic moments in the atoms forming the substance and on the density of these moments. The equation is

`C = μ0/(3kB) * N / a³ * μ²`

• `μ0 = 4 * π * 10^(-7) T * m/A` is the permeability of free space,
• `kB = 1,381 * 10^(-7) J/K` is the Boltzmann constant,
• `N` is the number of atoms carrying the magnetic moment in a unit cell,
• `a [m]` is the lattice constant,
• `μ [J/T]` is the magnetic moment of a single atom.

The unit of the Curie constant is `[K * A/(T * m)]`. The magnetic moment `μ` is a characteristic number describing a magnetic property of a single atom (or a particle, molecule, etc.). You can learn more about the magnetic moment in quantum mechanics checking the Magnetic moment calculator.

## Curie constant calculator

You can quickly compute the Curie constant with our calculator. To simplify the computations we set the units of the lattice constant `a` to nanometers. Nanometers are an appropriate unit to describe the atomic world. For the same reason the magnetic moment `μ` is in the Bohr magneton `μB = 9.274 * 10^(−24) J/T` units.

For example, let us consider we take a crystal formed by atoms on a simple cubic lattice with a lattice constant `a = 0.2 nm`. In a simple cubic lattice there is one atom per unit cell. We assume that each atom carries magnetic moment `μ = 2 μB`. With the Curie constant calculator, we get that the Curie constant `C = 1.3047 K * A/(T * m)`.

Miłosz Panfil, PhD

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