Theory of Carrier-Mediated Magnonic Superlattices

We present a minimal one-dimensional model of collective spin excitations in itinerant ferromagnetic superlattices within the regime of parabolic spin-carrier dispersion. We discuss the cases of weakly and strongly modulated magnetic profiles finding evidence of antiferromagnetic correlations for long-wave magnons (especially significant in layered systems), with an insight into the ground state properties. In addition, the presence of local minima in the magnonic dispersion suggests the possibility of (thermal) excitation of spin waves with a relatively well controlled wavelength. Some of these features could be experimentally tested in diluted magnetic semiconductor superlattices based on thin doped magnetic layers, acting as natural interfaces between (spin)electronic and magnonic degrees of freedom.

Figure 1

Continuum of soft modes for fully [panels (a) and (b)] and partly [panel (c)] polarized carriers corresponding to weakly modulated local-spin density as sketched in the inset ($\alpha =0.1$). In all cases, the lower and upper curves limiting the continuum are defined by the extreme values ${\theta }_{\mp }=0$, $\pi$, respectively. Note the development of minima as $E_{\mathrm{F}}/|{\Delta }_0|$ increases, occurring even in the case of uniform magnetic profile (dashed curve). The mean-field limit corresponds to $\Omega /|{\Delta }_0|=x_{\mathrm{s}}=0.05$. In panels (b) and (c), the Stoner continuum (SC) lies between the curves $-{\Delta }_0+E_k\pm 2\sqrt{E_{\mathrm{F}}{E}_k}$ for $E_{\mathrm{F}}\le |{\Delta }_0|$ and also between $-{\Delta }_0-E_k\pm 2\sqrt{(E_{\mathrm{F}}+{\Delta }_0)E_k}$ for $E_{\mathrm{F}}>|{\Delta }_0|$.

Figure 2

Soft mode for fully [panels (a) and (b)] and partly [panel (c)] polarized carriers corresponding to strongly modulated local-spin density as sketched in the inset (${\Gamma }_0=0.5$). Note the negative excitation energy for small $k$ and the development of a minimum as $E_{\mathrm{F}}/|{\Delta }_0|$ increases. The mean-field limit corresponds to $\Omega /|{\Delta }_0|=x_{\mathrm{s}}=0.05$. The Stoner continuum (SC) in panels (b) and (c) coincides with that of Fig. 1.