A multi-frequency EPR spectroscopy approach in the detection of boson peak excitations Marina Kveder a,⇑ , Dalibor Merunka a , Amon Ilakovac b , Boris Rakvin a a Ru - der Boškovic ´ Institute, Bijenic ˇka 54, 10000 Zagreb, Croatia b Faculty of Science, Bijenic ˇka 32, 10000 Zagreb, Croatia article info Article history: Received 21 June 2011 Revised 4 August 2011 Available online 31 August 2011 Keywords: Boson peak Multi-frequency EPR Electron spin–lattice relaxation abstract The influence of boson peak (BP) excitations on low-temperature spin–lattice relaxation rate of a para- magnetic center embedded in a glassy matrix is investigated in the context of multi-frequency electron paramagnetic resonance (EPR) detection. In the theoretical analysis, the transition rate of spin one-half in the presence of a phonon field is calculated within the approximation of Fermi’s golden rule. Several pho- non densities of states are compared, among which one originating from a model of quasi-localized vibra- tions has been introduced into electron spin relaxation formalism for the first time. The respective frequency dependencies of spin–lattice relaxation rates are predicted which should lead to observable effects of BP modes if a multi-frequency study at very low temperatures is performed. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction One of the ubiquitous properties of almost all glasses is an excess in the vibrational density of states q(x) over the prediction of the Debye theory [1]. This phenomenon shows up as a maximum in q(x)/x 2 and is termed the boson peak (BP) [2]. For different materi- als, the maximum densities of states at the peak appear in the range of frequencies between 0.4 and 2 THz [3]. The very nature of the BP is still extensively debated in the theory of condensed matter physics proposing specific theoretical models [4–7], while different experi- mental techniques have addressed the issue [8–11]. In this context, conventional X-band electron paramagnetic resonance (EPR) spectroscopy has presented very few results in which the impact of the BP has been discussed [3,12,13], the reason being that the EPR frequency only partially overlaps the BP frequency range. However, with advances in high frequency EPR spectrometers, the method is challenged to contribute toward the understanding of BP-related phenomena providing experimental data within the specific range of frequencies [14,15]. BP excitations are expected to play a role in electron spin –lattice relaxation, T 1 , at low temperatures where phonon mecha- nisms dominate the energy exchange between the spin system and the lattice [16]. In this context, one-phonon processes are as- sumed to be the most important ones governing spin relaxation and exhibiting the linear temperature dependence of the respective 1/T 1 data at the X-band EPR frequency [13,17]. These processes include several mechanisms, BP excitations being only one of them. Therefore, it is not possible to resolve the BP contribution by con- sidering the temperature dependence of spin relaxation measure- ments performed at only one EPR frequency. For that reason, the aim of this study was to show how EPR spectroscopy performed at multiple frequencies and at low temperatures can contribute to- ward the detection of the BP contribution via frequency depen- dence of spin–lattice relaxation time measurements. Primary attention was focused on high-field EPR measurements, in which the resonant frequency approaches the BP maximum. It should be mentioned that lattice phonons can modulate different interac- tions, causing an energy exchange between the electron spin sys- tem and the lattice, which becomes frequency/magnetic-field dependent. For instance, in the direct or resonant process, the elec- tron spin state is changed due to the absorption or emission of a res- onant phonon, giving rise to 1=T direct 1 / x 2 T in the context of Debye theory [18]. When phonon modulation of g tensor anisotropy, Dg, is important, the frequency dependent electron spin–lattice relaxa- tion rate should be additionally considered [19]. Phonon modula- tion of the electron spin–orbit coupling was extensively elaborated, showing that in the context of Debye model of phonon density of states, electron spin–lattice relaxation rates exhibit strong frequency dependence, 1=T Kramers 1 / x 4 T and 1=T non-Kramers 1 / x 2 T for Kramers and non-Kramers systems, respectively [16,20]. The analysis presented here is focused on the frequency/mag- netic-field dependence of the electron spin–lattice relaxation rate, 1/T 1 , due to the BP excitations emerging from one-phonon mecha- nisms, such as the phonon modulation of electron-nuclear spin dipole–dipole coupling. Regarding multi-phonon processes, such 1090-7807/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jmr.2011.08.029 ⇑ Corresponding author. E-mail address: kveder@irb.hr (M. Kveder). Journal of Magnetic Resonance 213 (2011) 26–31 Contents lists available at SciVerse ScienceDirect Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr