Theory of Resolved and Unresolved Crystal Field Structure of ESR Spectra in Dilute Magnetic Alloys

Abstract

The influence of crystal fields on the dynamic transverse susceptibility of localized spin moments coupled to the conduction electrons in a metal is investigated. In Liouville-space, the projector onto the subspace is introduced which is spanned by the transverse component of the conduction electron magnetization and the transition operators of the crystal field energy levels. Within the framework of projector formalism, the susceptibility is expressed in terms of a transition matrix which is then calculated in lowest order perturbation theory. The found explicit expression of the susceptibility is valid for the isothermal case as well as for the bottleneck one. The theoretical predicted resolved and unresolved ESR spectra are discussed for high and low temperature. For the bottleneck and the isothermal case, a resolved spectrum is expected when crystal field splittings are greater than the Korringa relaxation rate.Es wird der EinfluB von Kristallfeldern auf die transversale dynamische Suszeptibilitat lokalisierter Spin-Momente untersucht, die an die Leitungselektronen in einem Metal1 angekoppelt sind. I m Liouville-Raum wird der Projektor auf den Unterraum eingefuhrt, der von der transversalen Komponente der Leitungselektronen-Magnetisierung und den tfbergangsoperatoren der Krist,allfeld-Energiezustande aufgespannt wird. Mit Hilfe des Projektorformalismus wird die Suszeptibilitat durch eine Ubergangsmatrix ausgedriickt, die dann in Storungstheorie niedrigster Ordnung bestimmt wird. Der gefundene explizite Ausdruck fur die Suszeptibilitat ist gultig sowohl fur den isothermen als auch den ,,bottleneck"-Fall. Die theoretisch vorhergesagten aufgelosten und unaufgelosten ESR Spektren werden fur hohe und tiefe Temperaturen diskutiert. Fur den ,,bottleneck" und den isothermen Fall wird ein aufgelostes Spektrum erwartet, falls die Kristallfeldaufspaltung groBer als die Korringa-R.elaxationsrate ist.

Exchange and crystal field effects in the ESR spectra ofEu2+inLaB6

“…It should be mentioned that Barnes 44 has developed a more complete and involved theory than Plefka. 45 To prove the validity of our analysis, using Plefka's approach, we compared the EPR spectra of Pt:Gd calculated with the Barnes theory, 48 with the one generated by Plefka, and the agreement between the spectra obtained by both theories is good. An eventual difference in the obtained parameters using both models does not compromise the main conclusion of our analysis.…”

“…39 This mechanism leads to the well known phenomenon of exchange narrowing of the fine structure and, as a function of and T, generates a variety of ESR spectra. 44,45 We have used this exchange narrowing theory to compute the expected ESR spectra at different angles and temperatures. 46,47 Such calculation takes into account the following spin Hamiltonian:…”

“…The transverse dynamic susceptibility of the local magnetic moments can be calculated following Ref. 45. The model includes the interaction between local magnetic moments, conduction electrons, and CF.…”

“…Our experiments are performed at concentrations where the conduction electron static susceptibility is much smaller than that of the local moments. In that limit the susceptibility for a system in the unbottleneck regime 39,45,47 is given by…”

Electron spin resonance and antiferromagnetic resonance of single crystals of yttrium doped with gadolinium

“…Plefka [10] and Barnes [11] were able to show that resolved fine structure spectra are to be expected if the splitting between adjacent resonance lines is larger than the Korringa relaxation rate of the localized magnetic moment to the conduction electrons. If this exchange rate exceeds the line separation a narrowing of the spectrum occurs.…”