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Observation of a Charge-Neutral Muon-Polaron Complex in Antiferromagnetic Cr2o3

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Observation of a Charge-Neutral Muon-Polaron Complex in Antiferromagnetic Cr2o3 PHYSICAL REVIEW X 10, 011036 (2020) Observation of a Charge-Neutral Muon-Polaron Complex in Antiferromagnetic Cr2O3 † M. H. Dehn ,1,2,3,* J. K. Shenton,4 S. Holenstein ,5,6 Q. N. Meier ,4 D. J. Arseneau ,3 D. L. Cortie,1,2,7, ‡ B. Hitti,3 A. C. Y. Fang,1, W. A. MacFarlane,2,3,7 R. M. L. McFadden ,2,7 G. D. Morris,3 Z. Salman ,6 H. Luetkens,6 N. A. Spaldin ,4 M. Fechner,4,8 and R. F. Kiefl1,2,3 1Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada 2Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada 3TRIUMF, Vancouver, BC V6T 2A3, Canada 4Department of Materials, ETH Zurich, CH-8093 Zürich, Switzerland 5Physik-Institut der Universität Zürich, CH-8057 Zürich, Switzerland 6Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 7Department of Chemistry, University of British Columbia, Vancouver, BC V6T 1Z1, Canada 8Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany (Received 1 September 2019; revised manuscript received 6 November 2019; accepted 26 November 2019; published 14 February 2020) We report a comprehensive muon spin rotation (μSR) study of the prototypical magnetoelectric þ antiferromagnet Cr2O3. We find the positively charged muon (μ ) occupies several distinct interstitial sites and displays a rich dynamic behavior involving local hopping, thermally activated site transitions, and the formation of a charge-neutral complex composed of a muon and an electron polaron. The discovery of such a complex has implications for the interpretation of μSR spectra in a wide range of magnetic oxides and opens a route to study the dopant characteristics of interstitial hydrogen impurities in such materials. We address implications arising from implanting a μþ into a linear magnetoelectric and discuss the challenges of observing a local magnetoelectric effect generated by the charge of the muon. DOI: 10.1103/PhysRevX.10.011036 Subject Areas: Condensed Matter Physics, Magnetism, Materials Science I. INTRODUCTION polarization is observed, providing an accurate measure- ment of the magnetic coupling of the muon spin with its Positively charged muons implanted into semiconduc- þ − environment [1]. Mu centers have been studied in a wide tors and insulators often form muonium (Mu ¼½μ e ), a range of materials, providing direct information about the hydrogenlike charge-neutral bound state. It is convention- electronic structure of hydrogen defects as shallow or deep- ally referred to as a paramagnetic center as the bound level dopants [2–5]. So far, the study of such charge-neutral electron is unpaired and its spin is decoupled from all the muon states has been limited to nonmagnetic materials, other electrons. Since the electronic structure of Mu in a since paramagnetic Mu is widely assumed to be subject to solid is virtually identical to that of hydrogen, Mu has been μ strong depolarization in the presence of magnetic moments studied extensively using muon spin spectroscopy ( SR) to 3þ learn about interstitial hydrogen, one of the most ubiquitous such as those on Cr [3], and, with the exception of MnF2 defects in semiconductors. In a μSR experiment, spin- [6], no Mu has been confirmed in magnetic materials. polarized muons (μþ) are implanted into the sample of Here, we present strong evidence for a charge-neutral interest, and the subsequent time evolution of the spin muon state in the antiferromagnet Cr2O3. In particular, our data, in conjunction with detailed density-functional-theory (DFT) calculations, make a compelling case for the exist- *[email protected] † ence of a muon-polaron complex, where the positive muon Institute for Superconducting and Electronic Materials, is bound to an oxygen, and an excess electron localizes on a Australian Institute for Innovative Materials, University of 2þ 3 4 Wollongong, North Wollongong, NSW 2500, Australia. nearby Cr ion, changing its valence to Cr ( d ). The ‡ Department of Physics, Simon Fraser University, Burnaby, degeneracy of the now occupied eg orbital is lifted via a BC V5A 1S6, Canada. lattice distortion, leading to a Jahn-Teller (JT) polaron [7–9] on the Cr ion. Crucially, the resulting JT-stabilized muon- Published by the American Physical Society under the terms of polaron complex is not paramagnetic and therefore distinct the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to from Mu, since the bound electron is strongly coupled to the the author(s) and the published article’s title, journal citation, 3d electrons of the Cr host ion. Therefore, no signatures and DOI. conventionally associated with a charge-neutral state are 2160-3308=20=10(1)=011036(18) 011036-1 Published by the American Physical Society M. H. DEHN et al. PHYS. REV. X 10, 011036 (2020) displayed, concealing its existence. However, despite its muons undergoing locally restricted hopping and muons inconspicuous signal, the presence of such a complex has that remain static in their site. In order to explain this a significant impact on the location and stability of muon surprising behavior, we turn to DFT to identify candidate stopping sites, and the local fields experienced there. muon sites for all three environments and conclude that the This discovery of a charge-neutral muon-polaron com- coexistence of site-stable and dynamic muons can be plexinCr2O3 suggests that neutral-charge states could explained with the formation of a charge-neutral Jahn- form in other insulating magnetic materials as well, which Teller–stabilized muon-polaron complex (Sec. V). Finally, has implications for the interpretation of a wide range of in Sec. VI, we discuss the implications of charge-neutral μSR data. Furthermore, analogous to Mu in semiconduc- states in Cr2O3 and its relevance for other magnetic oxides, tors, the study of muon-polaron complexes in magnetic as well as possible consequences arising from implanting oxides may provide detailed information on the dopant positively charged muons into a linear magnetoelectric. characteristics of interstitial hydrogen, a good understand- ing of which is crucial for a precise control of charge II. EXPERIMENTAL DETAILS carriers in such materials. The μSR experiments we report here are carried out at Cr2O3 is of additional interest due to its magnetoelectric the Centre for Molecular and Materials Science at TRIUMF properties. Being the first material predicted [10] and (Vancouver, Canada), although initial spectra were taken at measured [11,12] to exhibit an induced linear polarization the GPS instrument at PSI (Villigen, Switzerland). The (magnetization) in response to a magnetic (electric) field, it is zero- and low-magnetic-field measurements are taken in the widely regarded as the prototypical linear magnetoelectric LAMPF spectrometer, and the high-magnetic-field data are [13,14] and remains the subject of active research [15], acquired in the NuTime spectrometer. All data are acquired directed primarily at exploiting its magnetoelectric properties P – with the initial muon spin polarization i perpendicular to for device applications [16 18]. In addition, there are the beam direction (zˆ). unresolved fundamental questions raised by the recent In a μSR experiment, spin-polarized, positively charged prediction that an electric charge within a linear magneto- muons are implanted into the sample, where they decay with electric is surrounded by a monopolar magnetic field dis- a lifetime of τμ ¼ 2.2 μs. The resulting decay positron is tribution, and thus is subject to a magnetic force in an external μ emitted preferentially along the muon spin direction and can magnetic field [19]. SR is a unique way to investigate such be detected in a time-resolved manner with plastic scintil- predictions since the spin-polarized muon acts both as a test lators placed in pairs around the sample. This anisotropic charge and a sensitive probe of the local magnetic field. positron emission introduces a spin-dependent imbalance in μ However, as indicated by studies from the early days of SR the count rate, causing the asymmetry signal SðtÞ, the count- – [20 23], the spectra in Cr2O3 are complex, and their normalized difference of a counter pair, to be directly interpretation was inconclusive. Furthermore, given theweak proportional to the spin polarization PðtÞ along the detector magnetoelectric coupling in Cr2O3, only subtle changes to axis. A detailed description of the μSR technique can be the local magnetic environment in response to the muon found in Ref. [1]. In the presence of a magnetic field B, the charge are expected, and a thorough understanding of the muon spin precesses about the field direction with frequency interaction between the implanted muon and its host material f ¼ γμ=2π · jBj, where γμ ¼ 2π × 135.5 MHz=T is the is required as a prerequisite for the search for any muon- muon gyromagnetic ratio. Thus the precession frequency induced magnetoelectric effects. is a direct measure of the local magnetic field experienced by The paper proceeds as follows. In Sec. II, we briefly the muon. μ introduce the SR technique and summarize the exper- In a crystal lattice, the charged muon usually stops in one imental conditions. Next, in Sec. III, we report the results of or more distinct sites that minimize the overall energy. At a a comprehensive μSR study of Cr2O3 under zero-field (ZF) given temperature, several crystallographically distinct conditions and in applied magnetic fields. The data are sites may be populated, each of which causes a different presented in three parts: (1) In ZF, up to three spin- time evolution of the spin polarization. For example, in precession frequencies are observed, indicating three dis- magnetic materials, muons may experience different inter- tinct muon environments with different internal magnetic nal fields at inequivalent sites, causing spin precession at B B ð≪ B Þ fields int.
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