Optical spectroscopy of single- and two-ion transitions in an antiferromagnetic stoichiometric rare-earth crystal

TL;DR

The paper addresses how optical transitions in Nd3+-doped antiferromagnetic NdGaO3 respond to magnetic fields up to 3 T. It uses a mean-field single-ion crystal-field Hamiltonian, augmented by a pair Hamiltonian to capture two-Nd transitions, to reproduce observed spectra. Key findings include the identification of three magnetic phases (antiferromagnetic, intermediate, paramagnetic), the existence of single-Nd and two-Nd absorptions, and satellite lines; the two-ion model aligns with observed field dependences and selection rules. The work provides a framework for interpreting spectra in stoichiometric rare-earth magnets and has implications for microwave-to-optical transduction and quantum technologies.

Abstract

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.

Figures (6)

• Figure 1: Magnetic structure of NdGaO$_3$ below the Néel temperature with zero external magnetic field, using the conventions in Refs. Marti1995Luis1998.
• Figure 2: Energy level diagram of the Nd3+ ions in an antiferromagnetic NdGaO3 crystal. The red and blue arrows indicate allowed transitions of $\pi$ and $\sigma$ polarised light. Irreducible representations are from Ref. Koster_1963. $\bm{B}_{0}$ is the applied static magnetic field and $\bm{B}$MF is the mean magnetic field. These magnetic fields are along the $c$ axis.
• Figure 3: (a) A photograph of the thinned down NdGaO$_3$ sample attached on a quartz wafer substrate used for optical measurements. (b) Setup of optical measurements. Solid and dashed arrows represent, respectively, optical and electric lines. PBS denotes Polarised Beam Splitter cube; ND, neutral density filter; BS, unpolarised Beam Splitter cube; PC, fibre Polarisation Controller; Ref. Cav. , Reference Cavity; GT, Glan–Taylor polariser; DR, Dilution Refrigerator; PD, Photodetector; NGO, NdGaO$_3$ sample; $\lambda/2$, half-wave plate.
• Figure 4: Optical transmission spectra with the external static magnetic fields along the $c$ axis and the (a) $\pi$- and (b) $\sigma$-polarised electric field. Solid, dotted, and dashed lines represent main, in-plane-pair ($\perp$ NN), and out-of-plane-pair ($\parallel$ NN) lines, respectively, which are calculated using the Hamiltonian in Eq. \ref{['eq:pairham']}, with $J_\perp/k_B = \qty{-0.65}{\kelvin}$, $J_\parallel/k_B=+\qty{0.07}{\kelvin}$, and $J_\parallel'=J_\perp'=\qty{-0.1}{\kelvin}\times k_B$. Calculated transition frequencies are shown, with energy level diagrams showing their physical mechanisms, for the polarisation that the calculated selection rules allow. There is a global frequency offset for all lines as the crystal-field model, which was not trained on any optical data, gives a different transition frequency. An example set of satellite lines are shown dash-dotted, and these are simply calculated as main lines, frequency offset by 250. All spectra were measured by the PMT at the base temperature of the DR, below 40 mK.
• Figure 5: Magnetic field dependence of the satellite line spectra with (a) $\pi$, (b) $45^\circ$, and (c) $\sigma$ optical polarisations. Panels (a) and (c) are details from Fig. \ref{['Fig: Opt B parallel c-axis']}. In panel (c), a white vertical line at 0.89 T represents an experimental error that is irrelevant to the absorption. (d) A diagram of an optical polarisation angle and the crystal axes. (e) Black solid dots show extracted absorption frequencies from panels (a) and (c), with the same lines as in Fig. \ref{['Fig: Opt B parallel c-axis']}.