Long wavelength spin dynamics in diluted magnetic systems: Scaling of magnon lifetime Akash Chakraborty a , Georges Bouzerar b,n a Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany b Institut Lumière Matière, Université Lyon 1-CNRS, F-69622 Villeurbanne Cedex, France article info Article history: Received 20 November 2014 Received in revised form 22 December 2014 Accepted 22 December 2014 Available online 24 December 2014 abstract Spin wave excitations in disordered magnetic systems have been one of the most widely studied fields in condensed matter physics for several decades. However, a careful and extensive search reveals a long- standing controversy on one important aspect, which is the wave-vector dependence of the spin wave intrinsic linewidth. We theoretically investigate the low-temperature spin wave excitations in disordered (diluted) ferromagnetic systems with a particular focus on the linewidth behavior in the long wavelength limit (q 0 → ). The linewidth is extracted from a proper finite size analysis of the dynamical spectral functions, taking into account the effects of disorder and spin fluctuations treated within self-consistent local RPA. We obtain an unambiguous q 5 scaling of the intrinsic linewidth, which is attributed to the disorder induced damping of the spin waves. This is in agreement with some previous theoretical studies on the Heisenberg ferromagnets, although the exchange interactions were mostly restricted to nearest neighbors unlike in our case. We also demonstrate the difficulties in extracting the correct scaling of the linewidth as it is sensitive to the q values considered, and one can obtain an incorrect q-dependence if the q's are not sufficiently small. Finally, our findings are discussed in the light of prospective spintronics applications. & 2014 Elsevier B.V. All rights reserved. The long wavelength elementary excitations in magnetic sys- tems, better known as spin waves or magnons, have been of fun- damental interest in order to understand the underlying spin dy- namics in a wide class of systems such as alloys [1,2], manganites [3,4], multiferroics [5,6], and pnictides [7,8]. In ferromagnetic manganites, for instance, the unusual magnon softening and damping near the Brillouin zone (BZ) boundary was believed to be an indication of collective excitations involving spin, lattice and orbital degrees of freedom [4]. With the advancement of inelastic neutron scattering techniques, the study of spin wave excitations has received a huge boost over the past decades. Inelastic neutron scattering is one of the most powerful experimental tools in this context as the magnon dispersion and damping can be measured directly and accurately. However, despite the existence of a con- siderable amount of experimental and theoretical work, one im- portant aspect which still requires further clarification is the wave- vector dependence of the spin wave intrinsic linewidth in dis- ordered ferromagnetic systems. The linewidth measures the broadening of the magnetic excitations due to disorder, which maybe magnetic or structural disorder, or due to the magnon– magnon interactions. Over the years, many different studies have predicted this wave-vector dependence to be as varied as q 2 to q 7 , but no general agreement has prevailed till now. In one of the earlier works, spin waves in the Heisenberg fer- romagnets were studied by Murray in the low-energy limit [9]. Along with the spin-wave energies and the scattering cross section the author also calculated the lifetimes (which is inversely pro- portional to the linewidth) within the Born approximation, and a q 5 dependence was reported. However, in this study, the exchange interactions were restricted to nearest neighbors only. Later on using an effective medium approximation in the amorphous Hei- senberg ferromagnets [10], a similar q 5 dependence of the spin- wave linewidth, in the low temperature and long wavelength limit, was found. Note that in this case, spatially dependent ex- tended exchange interactions were assumed between the mag- netic sites. Green's functions based calculations on amorphous ferromagnets by Mano [11] also led to an identical behavior of the linewidth in the long wavelength regime. The randomness in the magnitude of the spins led to a finite linewidth of the spin wave excitations, which increased rapidly with decreasing wavelength. Also the discrepancy between the observed magnetization beha- vior and that predicted by elementary spin-wave theory in these systems was attributed to this finite linewidth of the spin waves. On the other hand, Kaneyoshi [12] studying spin waves in similar Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials http://dx.doi.org/10.1016/j.jmmm.2014.12.064 0304-8853/& 2014 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: georges.bouzerar@univ-lyon1.fr (G. Bouzerar). Journal of Magnetism and Magnetic Materials 381 (2015) 50–55