We study spin excitation spectra of one-, two-, and three-dimensional magnets featuring nonmagnetic defects at a wide range of concentrations. Taking the Heisenberg model as the starting point, we tackle the problem by both direct numerical simulations in large supercells and using a semianalytic coherent-potential approximation. We consider the properties of the excitations in both direct and reciprocal spaces. In the limits of the concentration c of the magnetic atoms tending to 0 or 1 the properties of the spin excitations are similar in all three dimensions. In the case of a low concentration of magnetic atoms the spin excitation spectra are dominated by the modes confined in the real space to single atoms or small clusters and delocalized in the reciprocal space. In the limit of c tending to 1, we obtain the spin-wave excitations delocalized in the real space and localized in the reciprocal space. However, for the intermediate concentrations the properties of the spin excitations are strongly dimensionality dependent. We pay particular attention to the formation, with increase of c, of the Lorentzian-shaped peaks in the spectral densities of the spin excitations, which can be regarded as magnon states with a finite lifetime given by the width of the peaks. In general, low-dimensional magnets are more strongly affected by the presence of nonmagnetic impurities than their bulk counterparts. The details of the electronic structure, varying with the dimensionality and the concentration, substantially influence the spin excitation spectra of real materials, as we show in the example of the FeAl alloy.

We present an efficient methodology to study spin waves in disordered materials. The approach is based on a Heisenberg model and enables calculations of magnon properties in spin systems with disorder of an arbitrary kind and concentration of impurities. Disorder effects are taken into account within two complementary approaches. Magnons in systems with substitutional (uncorrelated) disorder can be efficiently calculated within a single-site coherent potential approximation for the Heisenberg model. From the computation point of view the method is inexpensive and directly applicable to systems like alloys and doped materials. It is shown that it performs exceedingly well across all concentrations and wave vectors. Another way is the direct numerical simulation of large supercells using a configurational average over possible samples. This approach is applicable to systems with an arbitrary kind of disorder. The effective interaction between magnetic moments entering the Heisenberg model can be obtained from first-principles using a self-consistent Green function method within the density functional theory. Thus, our method can be viewed as an ab initio approach and can be used for calculations of magnons in real materials.

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In this report we present a systematic study of the magnonic modes in the disordered Fe 0.5 Co 0.5 alloy based on the Heisenberg Hamiltonian using two complementary approaches. In order to account for substitutional disorder, on the one hand we directly average the transverse magnetic susceptibility in real space over different disorder configurations and on the other hand we use the coherent potential approximation (CPA). While the method of direct averaging is numerically exact, it is computationally expensive and limited by the maximal size of the supercell which can be simulated on a computer. On the contrary the CPA does not suffer from this drawback and yields a cheap numerical scheme. Therefore, we additionally compare the results of these two approaches and show that the CPA gives very good results for most of the magnetic properties considered in this report, including the magnon energies and the spatial shape of the eigenmodes. However, it turns out that while reproducing the general trend, the CPA systematically underestimates the disorder induced damping of the magnons. This provides evidence that the physics of impurity scattering in this system is governed by non-local effects missing in the CPA. Finally, we study the real space eigenmodes of the system, including their spatial shapes, and analyze their temperature dependence within the random phase approximation.

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