Role of exchange interaction in effecting spin-lattice relaxation: Interpretations of data onCr3+inCu

Abstract

The particular role played by the exchange interaction modulated by lattice vibrations ͑phonons͒ in effecting spin-lattice relaxation in amorphous materials in conjunction with the spin-orbit coupling, along with the role played by the well-known mechanisms, such as coupling to tunneling level states ͑TLS͒ via dipolar and Fermi-contact hyperfine interactions, is investigated. From a review of experimental data, it is found that the relaxation rate as effected by the exchange interaction is two to three orders of magnitude faster than that due to coupling with TLS centers. In particular, it is deduced that both the exchange interaction and coupling to TLS centers via Fermi-contact hyperfine, or electron-nuclear dipolar interaction, lead, in general, to a quadratic temperature dependency of the relaxation rate at low temperatures changing into a linear temperature dependency at intermediate temperatures. However, when the exchange interaction is strong, the relaxation rate becomes independent of temperature at higher temperatures due to cross relaxation of a spin with an exchangecoupled pair of spins, coupled to it via the exchange interaction. This analysis is then applied to interpret the spin-lattice relaxation data on ͑i͒ Cr 3ϩ ions in the Cu 2ϩx Cr 2x Sn 2Ϫ2x spinel samples for xϭ0.1 and 0.2 in the semiconductor range (xр0.5), and ͑ii͒ dangling bonds, with spin 1 2 , in amorphous silicon.

Exchange-mediated spin–lattice relaxation of Fe3+ ions in borate glasses

“…They are based on the mechanisms discussed by Altshuler [7] (transition probability), Gill [8], Dalton et al [9] (averaging of exchange coupling over a broad distribution), and Stevens [10] (calculation of transition probability leading to SLR). An analysis along these lines was successfully applied to explain the published SLR data on Cr 3+ in Cu 2+x Cr 2x Sn 2À2x spinel and dangling bonds in amorphous silicon [3]. While the Cr 3+ ion has its orbital angular momentum (L) partially quenched, dangling bonds do not possess any angular momentum.…”

“…The role played by the exchange interaction, described here as JS 1 AE S 2 , between two spins S 1 and S 2 , in effecting spin-lattice relaxation (SLR) in amorphous materials was discussed in detail by Misra [3]. The spin-lattice relaxation mechanisms effective in amorphous materials have been reviewed in [6].…”

“…(1) the velocity of sound dependence has been explicitly retained in case the comparative results from the silicate and borate glasses shed some light on it's role. The form (2) was obtained by substituting the dependence of the exchange interaction on distances r ij between paramagnetic ions in the amorphous material as [3,9]: J = ÀJ 0 exp (-nr ij ), and integrating over all values of r ij . In particular, it was found in [3] that, depending on the absolute maximum value of the exchange interaction constant (J 0 ) between adjacent spins in an amorphous material, the SLR rate depended on the temperature (T) as T n with n depending on the value of J 0 as listed in Table [ 1].…”

“…As well, the data also afford the opportunity to extend SLR measurements on these samples to much lower temperatures than those reported previously by Zinsou et al [2] as measured by the amplitude-modulation technique in the range 10-250 K. The primary aim was to confirm the mechanism responsible for the spin-lattice relaxation process in these samples, which was not interpreted convincingly in [2] as these results were published well before the mechanism of relaxation due to the exchange interaction to describe T 1 times in these samples was pointed out in Ref. [3]. In [2], the observed linear temperature dependence of the SLR rate in the 25-100 K range was interpreted as being effected by TLS (tunneling level states) centers and/or electron-nuclear dipolar interaction via phonon modulation of the Fermi-contact interaction.…”

Application of microwave amplitude modulation technique to measure spin-lattice and spin-spin relaxation times accurately with a continuous-wave EPR spectrometer: Solution of Bloch’s equations by a matrix technique and least-squares fitting

“…Measurement of very short spin-lattice (also known as longitudinal) relaxation (SLR) times (T 1 -10-1~ -6 s) is of great importance to study relaxation processes, e.g., in glasses doped with paramagnetic ions [1], amorphous Si (dangling bonds) and copper-chromium-tin spinel (Cr 3+) [2], and polymer resins doped with rare-earth ions [3]. In particular, the SLR data on amorphous Si and copperchromium-tin spinel led to understand the role of exchange interaction in effecting spin-lattice retaxation, while the data on polymer resin doped with rareearth ions provided evidence of spin-fracton relaxation [4].…”