Giant g -factors of Natural Impurities in Synthetic Quartz
GGiant g -factors of Natural Impurities in Synthetic Quartz Maxim Goryachev, a) Warrick G. Farr, and Michael E. Tobar ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia, 35 Stirling Highway,Crawley WA 6009, Australia (Dated: 13 November 2018)
We report the observation of g -factors of natural paramagnetic impurities in a pure synthetic quartz crystalat milli-Kelvin temperatures. Measurements are made by performing spectroscopy using multiple high- Q Whispering Gallery Modes sustained in the crystal. Extreme sensitivity of the method at low temperaturesallows the determination of natural residual impurities introduced during the crystal growth. We observe g -factors that significantly differ from integer multiples of the electron g -factor in vacuum, and with values ofup to 7 .
6, which reveals much stronger coupling between impurities and the crystal lattice than in previousstudies. Both substitutional and interstitial ions are proposed as candidates for the observed interactions.Crystalline quartz is very important material exten-sively used in different areas of science and technologyincluding optics, acoustics and device physics. In par-ticular, unprecedented acoustic quality factors both atliquid helium and milli-Kelvin temperatures have beenrecently demonstrated . To further progress these ar-eas, ultra-pure materials are required, which depend onefficient refining and identification of residual impurities.These impurities are believed to be responsible for lim-itations in quality factors and generation of the flickernoise as well as nonlinear effects at low temperatures .In addition to applications of quartz itself, this materialserves as a case study for understanding different defectsin other silica-based materials.Quartz is one of the most widely used materials dueto its exceptional purity. This originates in the stableatomic configuration, which allows only few elementsfrom the periodic table to be present in the quartzcrystalline structure as an impurity . Nevertheless, theElectron Paramagnetic Resonance (EPR) studies of thismaterial are relatively easy due to the very narrowlinewidths which increase the method sensitivity. Verynarrow linewidths are explained by the fact that noneof the host constitutive nuclei (most abundent isotopes)have a spin moment . This makes quartz crystal a goodcandidate as a host material for Cavity Quantum Elec-trodynamics experiments, which interact spin ensembleimpurities to microwave frequency photons .The imperfection of quartz crystals are related to sub-stitutional and interstitial impurity ions (Al, H, Cu, Ag,Ge, P, Ti, Fe, etc) as well as vacancy centres (E (cid:48) ) asso-ciated with oxygen ions missing in the crystal structure.Trivalent substitutional ions such as Al , Fe , Ge and Ti are typically accompanied by monovalent im-purity ions, such as H + , Li + , Na + , which are interstitiallypositioned in the crystal as charge compensators. Thereis a large number of experimental and theoretical studiesdedicated to different representatives of these impuritiesand corresponding bonds .Quartz has been extensively studied in optical a) Electronic mail: [email protected] domain using various methods such as InfraredSpectroscopy, dielectric relaxation spectroscopy andthermoluminesence , etc. In contrast, microwave spec-troscopy has been limited mostly to studies of naturalquartz for geological purposes or intensionally doped orirradiated synthetic samples. Thus, more sophisticatedresearch of synthetic quartz properties at microwave fre-quencies is required. In this paper, we demonstrate re-sults of synthetic pure quartz spectroscopy in X and Kubands (8 −
22 GHz) and at milli-Kelvin temperatures.The microwave spectroscopy has been performed us-ing Whispering Gallery Modes (WGM) of a cylindricalshaped crystal. Due to non-negligible coupling to param-agnetic imperfections, microwave photons of such modesexhibit interaction with certain transitions of ion impu-rities or possibly other paramagnetic centres in a realcrystal. As an effect of this coupling, WGMs exhibitconsiderable broadening, frequency shift or total disap-pearance when a transition energy of some impurity istuned to a photon energy. The interaction is clear atlow temperatures when the population of higher energystates is lower. By sweeping a DC magnetic field alongthe quartz cylinder symmetry axis, impurity transitionenergies change due to the Zeeman effect allowing ob-servations of multiple interactions between matter andfield. This spectroscopic approach has been already ap-plied to ultra-pure sapphire crystals where naturallyoccurring ions of Fe , Cr and V are identified withgood agreement with theoretical predictions.The crystal under study is undoped crystalline quartzcylinder with the diameter of 49 . . a r X i v : . [ c ond - m a t . m t r l - s c i ] D ec is the bandwidths of WGMs. The higher the quality fac-tors of electromagnetic modes, the lower the impurityconcentrations that could be detected. Although crys-talline quartz exhibits significantly higher dielectric lossesin the microwave region at low temperatures thansapphire, the achieved quality factors of WGMs are suffi-cient to observed a number of interactions between thesemodes and various impurities. The typical values of qual-ity factors of excited WGM are of the order of 10 witha maximum Q of 2 · at 20 .
15 GHz.The results of actual measurements are presented asdensity plots depicting transmission through the crystalas a function of frequency and external magnetic field.An example of interactions between a crystal WGM andparamagnetic impurities is shown in Fig. 1. The brightline at zero detuning frequency, the WGM, has field de-pendence only at certain values of the field correspondingto energies of some impurity transitions. A collection ofWGMs gives a map of interactions in the frequency-fieldaxes shown in Fig. 2. This figure demonstrates inter-actions denoted as (A)-(D) in Fig. 1. The dashed linedenotes a WGM shown in Fig. 1. Solid lines, fitted de-pendencies of transition energies on magnetic field, revealthe Zeeman effect for a certain impurity. These lines areused to identify corresponding g -factors assuming energylevels belong to the electron. Application of the externalmagnetic field in the opposite direction (negative field)leads to a symmetric picture around the field-axis B = 0.Interpretations of the experimental results are given inTable. I. The observed Zeeman-lines are attributed tothree paramagnetic ions that are the natural impuritiesin the synthetic quartz crystals. Firstly, line (a) couldbe attributed to either lithium or nitrogen for which ahyperfine-like structure is observed (see transition (A) inFig. 1). This structure is shown in Fig. 3 demonstratingthree absorption dips. Such three-level system impliesthat the nuclear spin number of the corresponding im-purity ion to be I = 1. The only two stable isotopeswith such nuclear spin are N and Li. Li (7 .
6% natu-ral abundance) and Li (92% natural abundance) are themost suitable candidates. Another argument in favour ofthese interstitial ions is relatively low zero field splittingoriginating in week coupling to the crystal lattice.Secondly, (b)-(d) form a transition structure that istypical for ions with electron spin S ≥ (transitions in-volving higher order states could be out of the observablerange) and nuclear spin I = 0, such as Fe , Cr ions .ESR of Fe ions have been observed in synthetic brownquartz as well as studied in intentionally doped α -quartz . The most common substitutional impurity ofquartz, Aluminium, also has suitable electron spin S = ,although nonzero nuclear spin ( I = ) suggests the exis-tence of hyperfine splitting that is not observed experi-mentally.Thirdly, line (e) has the almost same slope as line(d) that correspond to a two-photon transition of apreviously-discussed ion with S ≥ (either Fe orCr ). Although unlike in the previous case, the ion DC M agne t i c F e il d , m T −100 −50 0 50 100481216 Offset Frequency, kHz (A)(B)(C)(D) FIG. 1: Absolute value of the transmission through theWGM quartz resonator as a function of the excitationmicrowave signal and DC external magnetic field. Thecentral frequency is 20 . I = since transition (B) in Fig 1 demonstrates splitting intwo. Existence of this splitting does not allow us to at-tribute this line to (cid:12)(cid:12) − (cid:11) → (cid:12)(cid:12) − (cid:11) of the previous type of
40 80 120 160 200510152025
External DC Magnetic field, mT F r equen cy , G H z (A)(B)(C)(D) Measured WGM-ESR interactionline of fit (a)line of fit (b)line of fit (c)line of fit (d)line of fit (e)
FIG. 2: Map of interactions between cavity WGM andparamagnetic defects. Solid lines show fittedZeeman-like splitting lines. Parameters of the curves areshown in Table I.TABLE I: Possible interpretation of fitted impuritytransitions fitted in Fig. 2 with fitted g -factors and zerofield splittings (ZFS).Ions Transition g -factor ZFS, GHz(a) Li + / Li + , N + (cid:12)(cid:12) − (cid:11) → (cid:12)(cid:12) + (cid:11) .
612 0 . , Cr (cid:12)(cid:12) − (cid:11) → (cid:12)(cid:12) − (cid:11) − .
883 20 . (cid:12)(cid:12) + (cid:11) → (cid:12)(cid:12) + (cid:11) .
173 20 . (cid:12)(cid:12) + (cid:11) → (cid:12)(cid:12) − (cid:11) − .
609 24 . , Y (cid:12)(cid:12) + (cid:11) → (cid:12)(cid:12) − (cid:11) − .
726 20 . S ≥ . The only stableisotopes of such nuclear spin are Y, Ag and
Agthat cover all 100% of corresponding chemical elementsfound in nature. Traces of Ag has been determined pre-vious in germanium-doped synthetic quartz . Anotherexplanation for line (e) is that the double line structurearises from substitution of Oxygen on two different citeswith I = 0 impurity ion.Regardless of the above discussion, all Zeeman linesdemonstrate anomalous values of electron g -factors. In-deed, all experimentally identified g -factors varying from4 . .
5% and are significantly different from the closestinteger multiple of the electron g -factor in vacuum. Typ-ically such discrepancies do not exceed 1% . The valuesof g -factors observed in this work has been never reportedby any of theoretical or experimental studies except forCu ( g ≈ . .
7) and Ni + ( g ≈ . . . Although neither of thesetwo impurities fit into the observations seen here as theassociated electron and nuclear spin numbers are differ- ent. The difference from the electron g -factor is causedby much stronger influence of the crystal lattice field onthe paramagnetic impurities. The study also reveals aparamagnetic impurity with extremely large g -factor of7 .
176 180 184 188 192 T r an s m i ss i on t h r ough t he c r ys t a l , a . u . Magnetic Field, mT
FIG. 3: Transmission through the crystal at the WGMresonance near the interaction (A).The present study demonstrates new experimental ob-servations of g -factors in synthetic quartz spectroscopy.These results have not been predicted by any of the the-oretical studies. The uniqueness of the experiment is inthe extreme sensitivity of the method allowing to dis-cover new phenomena in pure crystals at extreme lowtemperatures. ACKNOWLEDGMENTS
This work was supported by the Australian ResearchCouncil Grant No. CE110001013 and FL0992016.
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