Heisenberg Magnetization Calculator

Model quantum spin alignment using mean-field Heisenberg theory. Explore temperature, exchange, lattice, and field effects. Get magnetization, critical estimates, and clear unit conversions instantly.

Calculator

Large screens show 3 columns; smaller show 2; mobile shows 1.
Examples: 0.5, 1, 1.5, 2.
Often near 2 for many ions.
Tesla; can be negative.
Must be greater than 0 K.
Examples: 6, 8, 12.
Use positive J for ferromagnetic case.
If set, outputs M in A/m.
Helps convergence near Tc.
Higher values handle harder cases.
Stops when |m(n+1)-m(n)| is small.
Lower values stabilize oscillations.
Reset

Formula used

This mean-field model solves the self-consistent magnetization for an isotropic Heisenberg ferromagnet.

m = B_S( y )
y = ( g μB S B + z J S² m ) / ( kB T )
μ(per spin) = g μB S m

Tc is displayed as an estimate and depends on model conventions.

How to use

  1. Enter S, g, temperature, and magnetic field.
  2. Set z and exchange J for your lattice.
  3. Optionally add number density for A/m output.
  4. Press Submit to compute the self-consistent result.
  5. Use export buttons for CSV or PDF downloads.

Example data table

CaseSgB (T)T (K)zJ (meV)n (spins/m^3)
A0.52.01.030061.08.0e28
B1.02.10.25082.55.0e28
C2.52.0-0.5120120.8(blank)

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.