Interface Rescaling Approach Research Articles

The eigenvalues of quantized spin waves and theeffect of the uniaxial anisotropy

The eigenproblems of quantized spin waves in a (100) ferromagnetic bilayer system have been investigated theoretically by using the interface rescaling approach. The energy-band structure of the system has been obtained and the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands were explored thoroughly. It is found that there are bulk modes, perfect confined modes and interface modes in the biferromagnetic system, the existing condition of which is determined not only by the bulk exchange coupling constant, the interface exchange coupling constant, the spin of lattice, the number of atomic layers, but also by the uniaxial bulk anisotropy.

The energy bands of quantized spin waves and the uniaxial anisotropy in a biferromagnetic system

The eigenproblems of quantized spin waves in a (100) ferromagnetic bilayer system have been investigated theoretically using the interface rescaling approach. The energy-band structure of the system has been obtained and the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands are explored thoroughly. It is found that all kinds of eigenmodes of the spin waves in the biferromagnetic system are determined by the bulk exchange coupling constant, the interface exchange coupling constant, the spin of lattice, the number of atomic layers and the uniaxial bulk anisotropy. Especially, we explore the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands of first Brillouin zone and the existence condition of all kinds of the eigenmodes.

The phenomenon of even bulk mode variance in a ferromagnetic A–A bilayer system

The eigenproblems of spin waves in a symmetrical ferromagnetic bilayered system with periodic boundary conditions are solved using the interface-rescaling approach (IRA). The results show that interface coupling between two sublayers would not change the excitation energy of odd bulk modes, but change excitation energy of even bulk modes. We call this peculiar phenomenon the phenomenon of even bulk mode variance (PEBMV). There are two kinds of mechanisms which cause PEBMV: phase reversal and phase translation of the magnon at the interface, corresponding, respectively, to the antiferromagnetic and ferromagnetic interface coupling cases. PEBMV embodies the selective effect of the interface on different bulk magnons.

Spin waves modulated in a ferromagnetic bilayer system calculated using the interface rescaling approach

The eigenproblems of spin waves in a ferromagnetic bilayer system with periodic boundary conditions are solved using the interface-rescaling approach. The Brillouin zone mapping of the system is investigated. Besides three types of known eigenmodes, the bulk mode, the interface mode, and the perfect confined mode, we also find a type of eigenmode, the critical mode, on the boundary of those known eigenmodes, which is composed of the spin wave modulated. This spin wave possesses both the feature of the bulk spin wave and that of the interface spin wave.

Brillouin-zone mapping of the spin waves in a ferromagnetic bilayer system

The eigenproblems of spin waves in a heterogeneous ferromagnetic bilayer system with periodic boundary conditions are solved using the interface-rescaling approach. Brillouin zone mapping and the eigenmodes of the system are investigated. We find three types of spin waves may exist in the system: the bulk mode, the interface mode, and the perfect confined mode. The fine structure of the energy band in the heterogeneous bilayer system is first given for the whole two-dimensional Brillouin zone. Conditions for the existence of the interface mode are discussed. Finally, we analyze the resonant-confined spin waves in bulk modes and their oscillating behavior.

The energy bands and the dispersion relations of the spin waves in a ferromagnetic bilayer system

The eigenproblems of spin waves in a ferromagnetic bilayer system with periodic boundary conditions are solved by using the interface-rescaling approach. The energy bands and the dispersion relations of the system are investigated. In addition, the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands and the dispersion relations is also discussed. Furthermore, we conjecture that there may be the resonant-confined spin waves in the system.

Conditions for the existence of interface spin waves in a biferromagnetic interface

The eigenproblems of interface spin waves of a (100) biferromagnetic interface are solved exactly by use of the interface rescaling approach. Particularly, the necessary and sufficient conditions for the existence of interface spin waves are obtained analytically.

Properties of perfect confined modes and interface modes of spin-waves in a ferromagnetic bilayer system

The exact solutions of spin-wave modes in a ferromagnetic bilayer system with a periodic boundary condition are investigated by using the interface-rescaling approach. The dispersion relations of the modes in the sublayers are obtained. The perfect confined modes and the interface spin-wave modes are given and discussed.

Spin Waves in Magnetic Bilayer Films

AbstractThe relation of pinning parameters to the uniaxial anisotropy fields of bilayers is discussed in the interface rescaling approach. The effects of the interface, surface, and bulk anisotropy parameters on the spin wave energy and the amplitudes of the spin wave as well as its localization are studied in detail.

Interface-rescaling approach to the exact solutions of quantum low-energy eigenproblems for a ferromagnetic bilayer system.

Exact solutions of the low-energy quantum eigenstates and eigenvalues of spin waves in a ferromagnetic bilayer system with periodic boundary condition are investigated by use of the interface-rescaling approach and quantum theory. The relations between spin waves and interface coupling are discussed. It is shown that resonant confined modes of the spin waves occur when the interface coupling is comparatively strong and that the spin waves are nearly pinned at the interface.

Ferromagnetic-bilayer spin-wave resonance: Reassignment of interface-affected lines.

A microscopic theory of standing spin-wave resonance in exchange-coupled bilayer films is presented. The interface-inhomogeneity model (an effective interface exchange coupling and intrinsic uniaxial interface anisotropy parameters are introduced) and the Heisenberg model with spin (exchange and Zeeman) Hamiltonian are used to derive an energy dispersion relation and spin-wave-mode functions for exchange-coupled bilayer ferromagnetic films. The theory is valid for Bravais lattices with arbitrary film-surface or interface orientations in a configuration where the static external field is perpendicular to the film surface and the values of the ferromagnetic and antiferromagnetic interface exchange couplings are arbitrary. The analysis is based on the exact solution of the eigenvalue problem of a bilayer film achieved with the interface rescaling approach. It is shown that the pattern of the resonance spectrum is determined by the nature of the interface exchange-coupling integral ${\mathit{J}}^{\mathit{A}\mathit{B}}$, with the first two (high-field side) lines exhibiting pronounced intensities when the interface coupling is antiferromagnetic. We show moreover that the highest-field line arises by excitation of the mode that is localized on the bilayer interface. We also show that this mode represents a complex bilayer vibration formed by the in-phase combination of sublayer vibrations, and this result corrects the general belief of experimenters that the mode under consideration is due to an out-of-phase combination of sublayer vibrations.

Eigenvectors of bilayer film by interface-rescaling approach

The mathematical eigenproblem formalism specific to bilayer films is treated by the newly invented interface-rescaling approach. For the first time — to our knowledge — an exact solution of the eigenproblem, valid for quite arbitrary interface and surface conditions, is obtained and presented in simple closed form.