Reprogrammability of magnonic band structure in layered Permalloy/Cu/Permalloy nanowires is demonstrated to depend on the relative orientation of the two layers magnetization. By using Brillouin light spectroscopy, we show that when the layers are aligned parallel two dispersive modes, with positive and negative group velocity, are observed while when the magnetic layers are aligned anti-parallel, only one dispersive mode, with positive group velocity, is detected. Our findings are successfully compared and interpreted in terms of a microscopic (Hamiltonian-based) method.An explanation for the observed behavior can be attributed to mode-mixing (or hybridization) effect when the two magnetic layers are aligned anti-parallel. This work opens the path to magnetic fieldcontrolled reconfigurable magnonic crystals with multi-modal frequency transmission characteristics.

Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.

A theoretical analysis is described for the spin waves in single- and double-layered nanorings using a microscopic, or Hamiltonian-based, formalism. The calculations, which yield the frequencies and spatially-dependent intensities of the quantized spin waves, are applied to the vortex and onion (bi-domain) states in a single nanoring, as well as to the field-induced switching. In the case of asymmetric double-layered nanorings (with a nonmagnetic spacer) there are coupled spin waves controlled by varying the spacer thickness to change the strength of the inter-ring dipolar interactions. The different possible magnetic states, depending on the applied magnetic field, may involve vortex states (with the same or opposite chirality) in both layers, a vortex state in one layer and onion state in the other, or onion states in both layers. Numerical applications are made to permalloy nanorings with realistic dimensions and magnetic parameter values.

A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole-dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein-Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states.

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