JMLB - jmb22@nyu.edu

Condition of resonance and angular dependence of H_res

In polar coordinate, H. Suhl [H. Suhl, Phys. Rev. 97, 555 (1954)]derived the following expression for the condition of resonance:

$\omega_{\mathrm{res}}=\frac{\gamma}{M \mathrm{sin}\theta} \ \left(\frac{\partial^2 E}{\partial \theta^2} \times \frac{\partial^2 E}{\partial \phi^2} \ - \ \left(\frac{\partial^2E}{\partial \theta \partial \phi} \right)^2\right)^{1/2}$

The total magnetic energy is composed of:

The Zeeman energy $E_z=-\vec{M} \bullet \vec{H}$

The uniaxial anisotropy energy inclusing term of the first and second order.

The shape anisotropy $E_s=-\vec{M} \bullet \vec{N}$

We can simplify the expression of the energy for a polycrystalline, where all directions of the applied magnetic field in the film plane are equivalente. With $\theta_H = \frac{\pi}{2}$ , the total magnetic energy density is:

$E\ = \ -M H \mathrm{sin}\theta \mathrm{cos}(\phi_H-\phi)+\frac{1}{2}$ $(4 \pi M_s^2)\mathrm{sin}^2 \theta \mathrm{sin}^2 \phi - K_1 \mathrm{sin}^2 \theta \mathrm{sin}^2 \phi$

AngularDep_Bres_hres1 (save as)*
This Mathematica script calculates the direction of equilibrium of the magnetization and the condition of resonance for different out-of-plane directions of the magnetic field. it also calculates the angular dependence of the different contributions to the field linewidth.

The file is password protected. Please send me an email to get the password.