Calculations of Bulk and Surface Magnetic Polaritons in Modulated Antiferromagnetic / Non-Magnetic Superlattices
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Fred Lacy, Ernest L. Carter, Jr., and Steven L. Richardson Department of Electrical Engineering and Materials Science Research Center, School of Engineering, Howard University, 2300 Sixth Street NW, Washington, DC 20059
ABSTRACT
Recent advances in molecular beam epitaxy have renewed research on the physics of artificially structured magnetic superlattices.l In particular, there has been much theoretical research 2 3 on the propagation of magnetic spin waves or magnetic polaritons in magnetic superlattices. ' In this work, we have studied the effect of modulating both the period of an anfiferromagnetic/ non-magnetic semi-infinite superlattice and the relative thickness of its individual layers to see how the dispersion relationships co(k) for bulk and surface magnetic polaritons are effected. We have also calculated the effect of an external magnetic field on o~k) and our calculation goes beyond the magnetostatic approximation by taking retardation effects into account.
METHODOLOGY
The geometry of the magnetic unit cell or bilayer for our superlattice calculation is shown below in Figure 1, where dI is the width of the antiferromagnetic layer, d2 is the width of the non-magnetic layer, and r is the ratio of these two widths (i.e. r = dl/d2).
Vdl-q--
..
~.....
l,,gure 1. Ahe geometry tor the antiferromagnetic/non-magnetic superlat-
I
L'unit cell's
I
tice. The dark regions represent the magnetic layers of width d1, and the light regions represent the nonmagnetic layers of width d2 . The unit cell has a total width of d, = d1 + d,.
Our system is semi-infinite for z > 0 and extends to infinity in both the x and y directions. We assume that the magnetic superlattice is placed in the Voigt configuration, where the propagation of the magnetic polariton is parallel to the surface and perpendicular to the static magnetization MS, the exchange field, Hex, anisotropy field HA, and the external magnetic field H0 . For this calculation, MnF2 is the antiferromagnetic material, where MS = 0.6 kG, Hex = 550 kG, HA = 3.8 kG, and woo = 1168 Grad/s. We solve Maxwell's equations by using an anisotropic magnetic permeability tensor for the antiferromagnetic layers and employ Bloch's theorem and the transfer matrix technique 4 to compute dispersion relationships for the bulk and magnetic surface magnetic polaritons, both in the absence and presence of H0 , for various values of dt and r. Mat. Res. Soc. Symp. Proc. Vol. 313. 61993 Materials Research Society
66
RESULTS
Illustrated in the figures below are the results of our calculations of 0o(k) for bulk and surface magnetic polaritons as a function of geometry and applied magnetic field: 0/(0)0
Figure 2. The dispersion relationships for bulk (hatched region) and surface (dotted line) magnetic polaritons for an antiferromagnetic/non-magnetic super6 lattice where H0 = 0, dt = 2x10- m and r= 1.
SURFACE POLARITONS
BULK POLARITONS
-2
-1
1 0 k (x 104 rad/m)
(/0
2
(00
ý POLARITONS BULK
SURFACE POLARITONS
I
Figure 3. The dispersion relationships for bulk (hatched reg
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