Curie's Law Calculator

Calculate magnetization of paramagnetic materials using Curie's law and temperature dependence

Calculate Magnetization Using Curie's Law

Material-specific constant characterizing magnetic response

External magnetic field strength

Absolute temperature affects thermal fluctuations of magnetic moments

Magnetization Results

0.000e+0
Magnetization (M)
A/m (SI units)
0.000e+0
Susceptibility (χ)
Dimensionless

Material Behavior Analysis

Example Calculation

Paramagnetic Material at Room Temperature

Given:

• Curie constant: C = 1.3 K⋅A/(T⋅m)

• Temperature: T = 20°C = 293.15 K

• Magnetic field: B = 1.0 T

Solution

Step 1: Calculate susceptibility

χ = C/T = 1.3 / 293.15 = 4.435 × 10⁻³

Step 2: Calculate magnetization

M = χ × B = 4.435 × 10⁻³ × 1.0

M = 4.435 × 10⁻³ A/m

Typical Curie Constants

Common Materials

Iron (Fe³⁺)4.4 K⋅A/(T⋅m)
Manganese (Mn²⁺)4.4 K⋅A/(T⋅m)
Chromium (Cr³⁺)1.9 K⋅A/(T⋅m)
Gadolinium (Gd³⁺)7.9 K⋅A/(T⋅m)

Temperature Ranges

Room temp: 293-298 K
Liquid nitrogen: 77 K
Liquid helium: 4.2 K

Key Principles

Curie's Law

M = (C/T) × B

Susceptibility

χ = C/T (inversely proportional)

Temperature Effect

Higher T → lower magnetization

Validity Range

Weak fields, moderate temperatures

Understanding Curie's Law

What is Curie's Law?

Curie's law describes the magnetization of paramagnetic materials as a function of applied magnetic field and temperature. It states that the magnetization is proportional to the magnetic field and inversely proportional to temperature.

Physical Origin

  • Paramagnetic atoms have unpaired electrons creating magnetic moments
  • External field tends to align these moments
  • Thermal energy opposes alignment through random motion
  • Balance determines net magnetization

Mathematical Formulation

Curie's Law:

M = (C/T) × B

Where M=magnetization, C=Curie constant, T=temperature, B=magnetic field

Magnetic Susceptibility:

χ = C/T

Dimensionless parameter characterizing material response

Alternative Form:

M = χB

Linear relationship between magnetization and field

Curie Constant and Material Properties

Factors Affecting Curie Constant

  • • Number density of magnetic atoms
  • • Magnetic moment of individual atoms
  • • Electronic configuration (unpaired electrons)
  • • Crystal field effects
  • • Spin-orbit coupling

Limitations of Curie's Law

  • • Valid only for weak magnetic fields
  • • Breaks down at very low temperatures
  • • Assumes no magnetic interactions
  • • Modified by crystal field effects
  • • Replaced by Curie-Weiss law for some materials