The effect of the spin-orbit interaction strengths on the Faraday rotation in Pr-substituted yttrium iron garnet and in praseodymium trifluoride

Abstract

The effect of the spin-orbit interaction of both the ground and excited configurations on the Faraday rotation of the trivalent Pr ion in praseodymium-substituted yttrium iron garnet and praseodymium trifluoride is analysed. It is found that the influence of the spin-orbit coupling strength of the ground configuration on the Faraday rotation is large; however, the MO rotation does not scale linearly with the spin-orbit coupling. It is surprising that the influence of the spin-orbit coupling strength of the excited configuration on the Faraday rotation is small except when the light frequency is near an MO resonance frequency. It is demonstrated that the spin-orbit interactions of both the ground and excited configurations are not always needed to produce a net Faraday rotation. The underlying physical reasons for the differences between our theoretical results and those obtained by other authors and between the different results obtained for Pr:YIG and , respectively, are discussed.

Anisotropy of the magnetization and Faraday rotation in paramagnetic erbium gallium garnet under high magnetic field

“…To our knowledge, the light frequency is far from all the resonance frequencies at 633 and 550 nm wavelength [29]. In this case, the diamagnetic Faraday rotation is much smaller than the paramagnetic one [17].…”

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

“…In Bi-substituted YIG, using a qualitative molecular-orbital analysis, Dionne et al [32,33] attributed the huge MO enhancement to the large splitting of the excited configurations induced by the SO interaction. In the Pr:YIG garnet, our recent analysis of the Pr 3+ ions contribution to the Faraday rotation [34] led to three unexpected main conclusions: i) the spin-orbit coupling of the excited configuration is not an important factor; ii) on the contrary, the strength of the spin-orbit coupling of the ground configuration is a crucial parameter, iii) the relation between the Pr 3+ induced Faraday rotation and the SO coupling magnitude is nonlinear. Referring to these remarks, it is interesting to study the effect of the spin-orbit coupling of the ground configuration on both the MO and magnetic properties of Nd:YIG.…”

The role of the spin-orbit coupling strength in the MO effects of magnetic insulators

“…Since the introduction, in 1932, by Hulme [10] of the notion of spin-orbit (SO) interaction, some work has been devoted to the influence of the SO coupling on the MO effects (references in [11]). It was calculated that in different transition metals and their alloys, the Kerr rotation is scaling approximately linearly with the SO coupling strength [12], [13].…”