Ferrite Gyromagnetic Resonance
A biased ferrite has electron spins that precess about the DC field at the Larmor frequency f₀ = γH₀ (about 2.8 MHz per oersted). Near this frequency the material's permeability becomes a tensor — the Polder tensor with diagonal element μ and off-diagonal element κ — which is what makes non-reciprocal devices (isolators, circulators, phase shifters) work. Sample shape shifts the resonance through demagnetisation (the Kittel equation). This tool computes f₀, the saturation frequency fm, the shape-dependent resonance, and μ, κ at your operating frequency.
Equations & Parameters ▸
\(\gamma/2\pi = 2.80\,(g/2)\) MHz/Oe, \(f_0=\gamma H_0\), \(f_m=\gamma(4\pi M_s)\)
sphere \(f_{res}=f_0\); in-plane film \(f_{res}=\sqrt{f_0(f_0+f_m)}\); ⟂ film \(f_{res}=f_0-f_m\)
Polder tensor: \(\mu=1+\dfrac{f_0 f_m}{f_0^2-f^2},\quad \kappa=\dfrac{f\,f_m}{f_0^2-f^2}\)
sphere \(f_{res}=f_0\); in-plane film \(f_{res}=\sqrt{f_0(f_0+f_m)}\); ⟂ film \(f_{res}=f_0-f_m\)
Polder tensor: \(\mu=1+\dfrac{f_0 f_m}{f_0^2-f^2},\quad \kappa=\dfrac{f\,f_m}{f_0^2-f^2}\)
| H0 | Internal DC bias field (Oe). |
| 4πMs | Saturation magnetisation (Gauss); e.g. 1780 for YIG. |
| f | Operating frequency (GHz) for the tensor. |
| g | Landé g-factor (≈2 for most ferrites). |
| Shape | Sphere, in-plane thin film, or perpendicular film. |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., §9.2.
Inputs
Oe
DC fieldG
Sat. mag.GHz
For μ, κ≈ 2
Demag
Results
Precession frequencies
γ/2π—
Larmor f₀—
fm (4πMs)—
Kittel resonance—
Polder tensor at f
μ—
κ—
μ± = μ ± κ—
Effective μeff—
Spin precession