Engineering & Science
Curie-Weiss Paramagnetic Susceptibility & Effective Bohr Magneton (mu_eff)
Calculate molar magnetic susceptibility chi_m = C / (T - theta_CW) above magnetic ordering temperatures and extract unpaired d/f-electron effective moment mu_eff = SQRT(8 * C_cgs) in Bohr magnetons (mu_B).
Count unpaired transition-metal electrons and exchange sign from SQUID magnetometry!
Pierre Curie and Pierre Weiss showed that above a crystal’s magnetic ordering temperature (T > |theta_CW|), molar paramagnetic susceptibility follows chi_m = C / (T - theta_CW), where the Weiss temperature theta_CW (K) reveals inter-atomic exchange sign: theta_CW > 0 indicates ferromagnetic exchange alignment, theta_CW = 0 is an ideal non-interacting Curie paramagnet, and theta_CW < 0 indicates antiferromagnetic superexchange!
In coordination chemistry and solid-state SQUID magnetometry, the CGS molar Curie constant C_m (emu*K/mol) directly measures the effective magnetic moment per ion in Bohr magnetons via mu_eff = SQRT((3 * k_B * C_m) / (N_A * mu_B^2)) = SQRT(8.00 * C_m) ~ 2.828 * SQRT(C_m) (matching spin-only SQRT(n*(n + 2)) for n unpaired electrons)! For a S = 1 (n = 2 unpaired d-electrons, e.g., Ni2+ octahedral complex) material with C_m = 1.25 emu*K/mol and ferromagnetic theta_CW = +120 K at T = 300 K, chi_m = 0.00694 emu/mol and mu_eff = 3.162 mu_B—whereas an antiferromagnetic analog (theta_CW = -60 K) halves susceptibility to 0.00347 emu/mol!
| Magnetic Exchange Regime (Cm = 1.25 emu*K/mol, T = 300 K) | Weiss Temp thetaCW (K) | Molar Susceptibility chim (emu/mol) | Effective Moment mueff (muB) |
|---|---|---|---|
| Ferromagnetic Exchange Short-Range | +120 K (T > thetaCW) | 0.00694 emu/mol | 3.162 mu_B |
| Antiferromagnetic Superexchange | -60 K | 0.00347 emu/mol | 3.162 mu_B (Same Local Spin) |
| Below Ordering Temp (T <= thetaCW) | Spontaneous Ordering | "Below Paramagnetic Regime" | Curie-Weiss Divergence Guard |
Curie-Weiss Molar Paramagnetic Susceptibility chi_m = C_m / (T - theta_CW)
Guards against ferromagnetic divergence when T <= theta_CW or non-positive temperature T <= 0.
=IF(OR(B2 <= 0, B3 <= 0, B3 <= B4), "Below Paramagnetic Regime", ROUND(B2 / (B3 - B4), 5))Effective Magnetic Moment per Ion mu_eff (Bohr Magnetons) = SQRT(8 * C_m)
Extracts effective Bohr magneton number from CGS molar Curie constant C_m (emu*K/mol, cell B2).
=IF(B2 <= 0, "Below Paramagnetic Regime", ROUND(SQRT(8 * B2), 3))Try the example
Use the original values or change them to test your understanding.