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Physical review. B, Solid state

Dispersion of the Magnon and Optical-Exciton States of Gd Cl3 and Gd (OH)3 and Their Effect upon the Single-Ion-Induced Absorption Line Shapes

Richard S. Meltzer, Henry W. Moos

Published Jul 1, 1972• 40 citations
Publisher

Abstract

The high-resolution optical-absorption spectra of the magnetic insulators Gd${\mathrm{Cl}}_{3}$ and Gd${(\mathrm{OH})}_{3}$ in a 35-kG magnetic field are used to demonstrate, for the first time, the influence of the magnon dispersion on the line shapes of single-ion-induced optical transitions. The absorption line shapes for transitions from the first thermally populated spin state to several single-ion states of the $^{6}P_{\frac{7}{2}}$ and $^{6}P_{\frac{5}{2}}$ manifolds of the ${\mathrm{Gd}}^{+3}$ ion are calculated. The initial and final states are properly treated as a magnon and exciton, respectively, including the dispersion of both states. The single-ion transition-moment operator is transformed to a basis in the crystal eigenstates and the resulting absorption line shape is shown to depend on a $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-dependent transition-moment operator weighted by a combined exciton-magnon density of states and the magnon occupation number. The magnon dispersion is calculated from the known ground-state exchange interactions while the exciton dispersion is varied to give a best fit to the observed line shapes. The resulting excited-state exchange parameters are shown to be reasonable. The exciton dispersion is found to be quite significant (up to 2 ${\mathrm{cm}}^{\ensuremath{-}1}$) for one of the excited states. These two materials thus represent the first examples for which the exciton dispersion of the electronically excited states of a rare-earth salt have been directly observed.

DOI
10.1103/physrevb.6.264

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Physical review. B, Solid state•Sep 15, 1977•3 citations
The high-resolution optical-absorption spectra of the magnetic insulators GdCl3{\mathrm{Cl}}_{3}Cl3​ and Gd(OH)3{(\mathrm{OH})}_{3}(OH)3​ in a 35-kG magnetic field are used to demonstrate, for the first time, the influence of the magnon dispersion on the line shapes of single-ion-induced optical transitions. The absorption line shapes for transitions from the first thermally populated spin state to several single-ion states of the 6P72^{6}P_{\frac{7}{2}}6P27​​ and 6P52^{6}P_{\frac{5}{2}}6P25​​ manifolds of the Gd+3{\mathrm{Gd}}^{+3}Gd+3 ion are calculated. The initial and final states are properly treated as a magnon and exciton, respectively, including the dispersion of both states. The single-ion transition-moment operator is transformed to a basis in the crystal eigenstates and the resulting absorption line shape is shown to depend on a k\ensuremath→\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}k\ensuremath→​-dependent transition-moment operator weighted by a combined exciton-magnon density of states and the magnon occupation number. The magnon dispersion is calculated from the known ground-state exchange interactions while the exciton dispersion is varied to give a best fit to the observed line shapes. The resulting excited-state exchange parameters are shown to be reasonable. The exciton dispersion is found to be quite significant (up to 2 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1) for one of the excited states. These two materials thus represent the first examples for which the exciton dispersion of the electronically excited states of a rare-earth salt have been directly observed.
We report the observation of a magnon sideband in the 6P7/2 ⇐ 8S7/2 optical absorption spectrum of Gd+3 in the ferromagnetic insulator GdCl3. The transition energy and its dependence on magnetic field demonstrate this to arise from the simultaneous excitation of a magnon and optical exciton. The decrease in its intensity with increasing magnetic field suggest the source of its intensity is directly connected with the zero‐point spin deviations which occur in a ferromagnet possessing significant magnetic dipolar interactions. The magnitude of the intensity is shown to be consistent with a single‐ion transition mechanism which because of the zero‐point spin deviations allows a small probability for a double‐excitation process. This transition mechanism is distinct from that responsible for the previously observed magnon sidebands in the transition‐metal magnetic insulators.
Elucidating magnetic structure with optical dopants: erbium-doped Gd2_22​SiO5_55​
The narrowness of the optical transitions of rare-earth-ion dopants makes them highly sensitive probes of their environment. We measured the optical transitions Er3+^{3+}3+ dopants to determine the previously unknown magnetic ordering of Gd2_{2}2​SiO5_{5}5​ -- a promising host for quantum applications of rare-earth dopants. By measuring the transitions' magnetic-field dependence we determined an antiferromagnetic ordering with spins oriented along or slightly canted from the crystal's a∗a^*a∗ axis. The optical transitions are narrower than the coupling to gadolinium spins revealing information about the coupling strengths. We further optically measured a Néel temperature of 1.86±0.01stat.±0.07syst.1.86\pm0.01_\mathrm{stat.}\pm0.07_\mathrm{syst.}1.86±0.01stat.​±0.07syst.​ K, and assembled a phase diagram in applied field and temperature showcasing a triple point where two gadolinium sites order semi-independently from each other. At high applied field the erbium dopants show long optical coherence times up to 0.4 ms at 3 T; at low fields these are probably limited by three low-frequency magnon modes below 10 GHz, observed directly. This study can be used to benchmark a method of magnetic structure determination.
The authors report a detailed analysis of the intensity and polarisation dependence of the 8 S 7/2 to 6 P 7/2 two-photon transition Stark components of Gd 3+ in the concentrated magnetic insulator Gd(OH) 3 under an applied magnetic field (up to 3.5 T) at very low temperature (2 K). The experimental technique consisted of detecting the ultraviolet 6 P 7/2 to 8 S 7/2 one-photon fluorescent emission resulting from two-photon excitation in the 6 P 7/2 states, using a single pulsed dye-laser beam. The standard second-order theory of Axe is shown to fail in explaining the relative intensities of the Stark components. This is especially true in the case of the Delta M=0 transitions for which strong disagreements are observed. It is shown that the introduction of the third-order contribution involving the spin-orbit interaction within the 4f 6 5d states allows the experimental spectra to be reproduced in a correct way. Finally the effects of ion-ion interactions on the two-photon line profiles are discussed.
We characterise optical transitions of neodymium ions (Nd3+) in antiferromagnetic neodymium gallate (NdGaO3) with applied fields up to 3 T. The magnetic phase of this material has not previously been studied with the field along its magnetisation axis. The measured optical spectra indicate three magnetic phases -- antiferromagnetic, intermediate, and paramagnetic -- where the intermediate phase likely forms a different magnetic structure from typical spin-flop phases. The observed absorptions were classified into two distinct families of optical transitions: single-Nd and two-Nd absorptions. We demonstrate that the optical transitions in the antiferromagnetic and paramagnetic phases can be modelled using a standard single-ion crystal-field Hamiltonian that interacts with a mean magnetisation from the rest of the lattice, and we expand that model to encompass pairs of ions, explaining the origins of the two-Nd transitions. This study offers a deeper understanding of the optical transitions in rare-earth antiferromagnetic crystals, which have been recently attracting significant interest for microwave-to-optical quantum transduction, despite being relatively unexplored to date.
Microwave and optical transitions of rare-earth ions enable microwave-to-optical frequency transduction. This transduction is a coherent process; therefore, the narrow linewidths and long coherence times of rare-earth ions are crucial for achieving efficient frequency conversion. Particularly long coherence times can be achieved with small-spin materials, as unpaired electronic and nuclear spins introduce magnetic noise, serving as a decoherent source of the transitions. However, complete spin-free rare-earth materials cannot exist without charge compensation. Consequently, residual spins in existing rare-earth materials act as a bottleneck, limiting both their spin and optical coherence times. Rather than focusing on nearly spin-free materials, this thesis investigates the microwave and optical transitions of rare-earth ions in materials that are fully concentrated with electronic spins. Recent studies on rare-earth magnetic materials have demonstrated narrow optical linewidths resulting from magnetic ordering and a particularly strong coupling between microwave cavity modes and the collective excitations of rare-earth ions. Although these recent studies are noteworthy, the energy-level transitions, especially optical transitions, of rare-earth ions in magnetic materials remain largely unexamined. In this thesis, various spectroscopic studies are employed to characterise their transition properties and to develop a model of energy levels. The model presented is expected to be applicable to other rare-earth magnetic materials, thereby opening avenues for further investigation in this class of systems. Two types of rare-earth magnetic materials are investigated: neodymium gallate with a stoichiometric concentration of neodymium ions, and gadolinium vanadate doped with a low (ppm) concentration of erbium ions. Microwave and optical transmission spectroscopy are employed under externally applied magnetic fields to characterise the energy-state transitions of the rare-earth ions in both materials. The magnetic phases and corresponding spin configurations influence the observed spectra, making conventional approaches to spectral simulation inadequate. To address this challenge, mean field and magnon-coupled crystal-field models are developed in this thesis to predict magnon and optical transition spectra. These simulations exhibit good agreement with experimental results, allowing for the characterisation of transition properties. Following the characterisation of the material, a new transduction approach is introduced, developed, and implemented using doped rare-earth ions in a magnetic material. In this scheme, coherent conversion between microwave and optical modes is achieved by exciting an optical transition of the doped ions.
The theory of the coherent pairing of Frenkel excitons in the presence of a resonant electromagnetic field is generalized to include the effect of the electron spin. It is shown that at high exciton densities and when the electromagnetic field is at resonance or near resonance, the removal of the spin degeneracy of the exciton pairs results in generating two fields, the singlet and the triplet biexciton fields, respectively. The gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ due to the singlet and triplet biexciton fields, respectively, are calculated and they are found to be independent of one another only in the limit when the exchange interactions between the charges disappear. In this limit, the energy modes for singlet and triplet biexciton fields have well-defined meaning and propagate through the crystal independently. A dielectric gap is induced by the electromagnetic field, which produces the energy splitting in the singlet biexciton spectrum, and it must be less than that of ${\ensuremath{\Delta}}_{+}$ for the singlet biexciton state. For finite values of the exchange interaction, the gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ depend strongly on each other and consequently the singlet and triplet biexciton fields are strongly mixed together. Optical transitions to the singlet and triplet biexciton states are considered and the corresponding expressions for the absorption coefficient are derived. The ground-state energy describing the binding energy arising from the singlet and triplet biexciton fields is calculated and discussed. Numerical estimates indicate that at high exciton densities, namely, for exciton concentrations 1018{10}^{18}1018-1019{10}^{19}1019 ${\mathrm{cm}}^{\ensuremath{-}3}$ and when the ratio of the average exciton-exciton interaction over the average kinetic energy is between 0.7 and 2 (strong-coupling limit), the energy gap due to the singlet biexciton state is in the range 40-650 ${\mathrm{cm}}^{\ensuremath{-}1}$, the corresponding transition temperature is 33-534 \ifmmode^\circ\else\textdegree\fi{}K, while the binding energy is 22-684 ${\mathrm{cm}}^{\ensuremath{-}1}$.