Long-ranged dynamic magnetic interaction through low-dimensional systems

Magnetic units attached to low-dimensional metallic nanowires are known to interact via the conduction electrons of the wire leading to preferential alignment directions of the respective magnetic moments. In addition to this so-called static interaction, here we show that a very long-ranged interaction arises when these units are allowed to precess. This dynamic version of the magnetic interaction governs the spin dynamics of the magnetic moments. We are able to relate this interaction to the spin excitation spectrum of the system in which we establish a clear correspondence between the precession relaxation time and the features of the spin susceptibility. We show that the relaxation time is predominantly determined by the availability of noncoherent Stoner modes, a process analogous to Landau damping of plasmons in the electron gas. Contrary to expectations, our results indicate that the range of this interaction is robust against the introduction of disorder. Furthermore, we show that the interaction range is frequency dependent suggesting that it may be tunable by an adequate choice of excitation frequencies. We argue that this may pave the way to controlling the communication between distant parts of a spintronic device.

Figure 1

(Color online) Schematic representations of a section of the infinite metallic cylindrical nanowire with two lines containing magnetic atoms (shown as circles); (a) complete (ordered) magnetic lines and (b) disordered magnetic lines. Nonmagnetic atoms occupy the vertices of the underlying lattice.

Figure 2

(Color online) Typical excitation spectrum for two identical magnetic lines separated by $N=50$ atomic spacings. Dashed curve depicts the excitation spectrum projected on one of the magnetic lines; solid curve is the measure of dynamical coupling between lines A and B as a function of driving frequency $\Omega$.

Figure 3

(Color online) Dynamical coupling between two magnetic rings embedded in a nonmagnetic metallic nanowire as a function of the distance $N$ between them for different frequencies of the driving field: (a) $\Omega =0.008$, (b) $\Omega =0.009t$, (c) $\Omega =0.010t$, and (d) $\Omega =0.011t$.

Figure 4

Excitation spectrum of a tube with two magnetic rings where disorder has been introduced (see text). The distance between the magnetic rings is 20 atomic spacings.

Figure 5

(Color online) Dynamic coupling as a function of distance $N$ between disordered magnetic volumes $A$ and $B$ for selected mode energies: (a) $\Omega =0.01t$, (b) $\Omega =0.0056t$, (c) $\Omega =0.004t$, and (d) $\Omega =0.014t$.

Figure 6

(Color online) Half-width at half maximum of the FMR spectra for (a) two complete magnetic rings, (b) two magnetic rings with half of the magnetic atoms replaced randomly by nonmagnetic atoms, and (c) two magnetic atoms, all embedded in infinite wires, as functions of the distance between the rings. The red dashed line indicates the HWHM of the FMR spectrum of a single magnetic unity embedded in similar wires.