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H. Okabe, M. Hiraishi, A. Koda, [Y. Matsushita](https://orcid.org/0000-0002-4968-8905), [T. Ohsawa](https://orcid.org/0000-0001-7528-8940), [N. Ohashi](https://orcid.org/0000-0002-4011-0031), R. Kadono
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Nanoscale dynamics of hydrogen in ${\rm VO}_{2}$ studied by $\mu {\rm SR}$PHYSICAL REVIEW MATERIALS 8, 024602 (2024)Editors’ SuggestionNanoscale dynamics of hydrogen in VO2 studied by μSRH. Okabe ,1,2,* M. Hiraishi ,1,3 A. Koda ,1,4 Y. Matsushita ,5 T. Ohsawa ,5 N. Ohashi ,5 and R. Kadono 1,4,†1Muon Science Laboratory and Condensed Matter Research Center, Institute of Materials Structure Science, High Energy AcceleratorResearch Organization (KEK-IMSS), Tsukuba, Ibaraki 305-0801, Japan2Institute for Materials Research, Tohoku University (IMR), 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan3Graduate School of Science and Engineering, Ibaraki University 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan4Department of Materials Structure Science, The Graduate University for Advanced Studies (Sokendai), Tsukuba, Ibaraki 305-0801, Japan5National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan(Received 8 March 2023; revised 18 December 2023; accepted 3 January 2024; published 13 February 2024)Hydrogen dynamics in the nanoscale region of VO2 was investigated by muon spin rotation/relaxation(μSR) technique. Positively charged muon acts as a light radioisotope of protons and can be used as a probeto explore the inside of materials from an atomic perspective. By analyzing the muon hopping rate and thespatial distribution of the 51V nuclear magnetic moments, we have identified two types of diffusion paths in VO2(via oxygen-muon bonds or defects) and the potential of a high diffusion coefficient in the 10−10 cm2/s rangeat ambient temperature. Our results provide valuable information for developing hydrogen-driven VO2-relatedelectronic devices.DOI: 10.1103/PhysRevMaterials.8.024602I. INTRODUCTIONVanadium dioxide (VO2) has drawn the interest of nu-merous researchers due to its pronounced thermal-drivenmetal-insulator (M-I) transition at TMI (= 340 K) with anenticing V-V dimerization in the low-temperature phase [1].In parallel with the fierce debate on the M-I transition mech-anism, much effort has been attempted to explore its deviceapplications [2,3]. Since the resistance varies over severalorders of magnitude across the M-I transition and the tran-sition temperature can be tuned over a wide range by impuritydoping, various applications are being explored. One of theapplications is resistive random access memory (ReRAM) [4],which has the potential to realize next-generation nonvolatilememory devices with high-speed operation, high current den-sity, and high-density recording by using VO2 as a selector [5].Furthermore, ReRAM may apply to artificial neural networksdue to its multilevel, analog memory, and hysteretic current-voltage (I-V) characteristics [6].However, in recent years, Ji et al. pointed out that elec-trical switching behavior in VO2-based electric double-layertransistors (EDLT) arises from the electrochemically drivendoping of hydrogen ions [7]. It has been reported that impurityhydrogen in the ionic liquid used for the EDLT electrodemigrates into VO2 by the electric field and provides carriers,causing a change in resistance [8,9]. In general, hydrogen*Corresponding author: hirotaka.okabe.b4@tohoku.ac.jp†Corresponding author: ryosuke.kadono@kek.jpPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.readily penetrates metal oxide semiconductors and is a pos-sible source for unintentional carrier doping [10,11]. It hasalso been found that a considerable amount of hydrogen canreversibly enter and desorb from the VO2 film, significantlyaffecting its electrical properties [12,13]. Hydrogenation ofVO2 also induces structural modification; high hydrogencontent leads to orthorhombic HVO2 where intercalated hy-drogen accommodates in an oxygen (O) channel, formingtypical OH bonds [14]. Therefore, the physical propertiesof VO2 are strongly affected by hydrogen, and informa-tion on hydrogen dynamics is crucial for developing thesedevices.For hydrogen dynamics in VO2, diffusion coefficientsestimated from optical observations of the metal-insulator do-main boundary and from measurements of transient electronictransport properties during proton intercalation have been re-ported [15,16]. Since these reports focus on the micron-orderVO2-HVO2 transition process, a proton-relay hydrogen dif-fusion mechanism (Grotthuss mechanism [17]) with a highhydrogen concentration seems dominant. In contrast, VO2 inelectronic devices is typically a thin film of several tens ofnm, and therefore the hydrogen content is small and may havea different diffusion mechanism than the above. However, ob-serving the dynamics of trace amounts of hydrogen in devicesis extremely difficult and remains unexplored.Here, we report on the dynamics of hydrogen at a di-lute concentration in VO2 investigated by muon spin rotation(μSR) spectroscopy. Positively charged muon (μ+) is a sub-atomic particle that acts as a light radioisotope of proton,simulating the local state of hydrogen in the matter on anatomic scale while simultaneously probing one’s own envi-ronment [18]. In addition, muons are injected directly intothe material as a pulsed ion beam generated by an accelerator(about 103/cm2 per pulse), so there is no need to fabricate the2475-9953/2024/8(2)/024602(6) 024602-1 Published by the American Physical Societyhttps://orcid.org/0000-0001-7170-0117https://orcid.org/0000-0002-7750-6937https://orcid.org/0000-0002-4453-4472https://orcid.org/0000-0002-4968-8905https://orcid.org/0000-0001-7528-8940https://orcid.org/0000-0002-4011-0031https://orcid.org/0000-0002-0915-2727https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevMaterials.8.024602&domain=pdf&date_stamp=2024-02-13https://doi.org/10.1103/PhysRevMaterials.8.024602https://creativecommons.org/licenses/by/4.0/H. OKABE et al. PHYSICAL REVIEW MATERIALS 8, 024602 (2024)FIG. 1. Zero-field μSR time spectra in VO2 measured at varioustemperatures (5 K ∼ 380 K). The solid lines represent the result ofleast squares fitting by Eq. (1). All spectra were measured in thetemperature increasing process.sample into a thin film or device. The clarification of hydrogendynamics in VO2 in the nanoscale region using muons isexpected to provide valuable insights into the developmentof next-generation electronic devices such as ReRAM andhydrogen-driven devices.II. EXPERIMENTAL DETAILSWe used a powder sample (M180μm pass) of VO2 (99.9%purity, Kojundo Chemical Lab. Co., Ltd.). The crystal struc-ture and phase purity were checked using the powder x-raydiffractometer (SmartLab, Rigaku Co.) from 300 to 400 K(see Figs. S1–S3 in the Supplemental Material [19]). Thestructural transition from the low-temperature orthorhombicphase to the high-temperature tetragonal (rutile) phase via theintermediate phase was observed around 340 K, as reportedpreviously [20]. Considering the possibility that the samplealready contained hydrogen, the hydrogen content was ob-served by thermal desorption spectrometry (TDS1200, ESCO)(Fig. S4). The amount of desorbed hydrogen was 1.14 ×1019 cm−3 (corresponding to H0.00034VO2) upon increasingthe temperature to 1073 K. The magnetic susceptibility wasmeasured using the SQUID magnetometer (MPMS, QuantumDesign, Inc.) from 5 to 400 K. No magnetic anomalies wereobserved in this temperature range, except for the M-I transi-tion of VO2 [Fig. 2(a)]. Vanadium oxides have many analogswith slightly different oxygen ratios that exhibit differentmagnetic transition temperatures [21]. Based on these results,our sample quality is adequate for studying the nature ofVO2. μSR experiments were performed using the ARTEMISspectrometer installed in the S1 area at the Muon ScienceEstablishment (MUSE), Japan Proton Accelerator ResearchComplex (J-PARC).III. RESULTS AND DISCUSSIONFigure 1(a) shows zero-field μSR time spectra at severaltemperatures from 5 K to 380 K. These spectra above ∼200 Kshow the Gaussian-like line shapes mainly attributed to therandom local fields from the nuclear magnetic moment of51V (5.148 μN). However, below 150 K, it can be seen thatFIG. 2. Temperature dependence of (a) the magnetic susceptibil-ity χ , (b) the asymmetry A, (c) the relaxation rate λ, (d) the nucleardipole-field width �, and (e) the hopping rate ν. The inset in (e)shows the Arrhenius plot of ν as a function of 1/T with a line ofbest fit from 200 K to 280 K. The temperature dependence of ν iswell explained by a thermal activation process, ν = ν0exp(−Ea/kT ),where ν0[= 24(3)μs−1] is the prefactor (preexponential) dependenton the dipole-dipole coupling between muon and nuclear spins, andEa[= 0.11 (1) eV] is the activation barrier for muon diffusion.a fast exponential relaxation with partial loss of asymmetryappears in the initial time region (t �∼ 1 μs). This suggeststhe gradual development of microscopic magnetic order ofvanadium electron spins in parts of the sample, which mayresult from lattice imperfections [22]. Based on the aboveobservation, we analyzed the time spectra using the following024602-2NANOSCALE DYNAMICS OF HYDROGEN IN VO2 … PHYSICAL REVIEW MATERIALS 8, 024602 (2024)curve-fit function:GZ(t ) = AGKT(�, ν, Bext, t )e−λt + Abg. (1)A is a signal amplitude called asymmetry, which reflectsthe volume fraction of the sample. The first term on theright-hand side is the product of the dynamic GaussianKubo-Toyabe function GKT(�, ν, Bext, t ) [23] which repre-sents the relaxation due to random local fields exerted fromnuclear magnetic moments (described by nuclear dipole-fieldwidth �, hopping rate of the muon ν, longitudinal field Bext),and the exponential relaxation component due to hyperfineinteraction with electron spins (relaxation rate λ). The secondterm on the right-hand side (Abg) represents the T -independentbackground term from the surrounding sample holder andcryostat walls. When � � ν, the muon spin depolarizationcan be quenched by applying Bext ≈ 2 − 3 × �/γμ, so aglobal fit of the spectra at different Bext (0, 5, 10 G) usingEq. (1) can determine � and ν reliably at each tempera-ture (Fig. S5). The longitudinal field dependence of the timespectrum is clearly observed even after 10μs. This fact sug-gests that the high-flux pulsed muon at J-PARC has enabledone to separate ν and � in VO2 clearly. Figure 2 shows thetemperature dependencies of the magnetic susceptibility χand the μSR fitting parameters A, λ, �, and ν. χ exhibitsa paramagnetic-nonmagnetic transition at TMI with a thermalhysteresis of 10 K, while there is no indication of any mag-netic anomalies below TMI [Fig. 2(a)]. While this is seeminglyinconsistent with the decrease of A (reflecting the volume frac-tion of the nonmagnetic component) and associated increasein λ below ∼150 K (indicating the emergence of the local fieldfrom unpaired electron spins) [Figs. 2(b) and 2(c)], our previ-ous study indicates that this is due to the coexistence of thesinglet state and microscopic magnetic ordered states causedby structural imperfections, such as lattice defects [22]. Theincrease in λ above 180 K is due to two possible reasons: (i)unpaired electrons are located adjacent to the defect wheremuons are trapped, forming a polaronlike state [24–28], and(ii) λ and nuclear relaxation are not completely separated (λis affected by changes in ν) in the high-temperature regionwhere ν � �. (A discussion of magnetism is beyond thescope of this paper and will be omitted).� shows a gradual decrease with increasing temperature,markedly above 200 K [Fig. 2(d)]. Note that the spectra couldnot be reproduced by Eq. (1) with � fixed to a constant(Fig. S6). This is not expected unless the 51V distributionvaries due to changes in crystal structure or muon sites [seeEq. (2) below]. Considering that the fluctuation rate ν in-creases in the relevant temperature range [Fig. 2(e)], thedecrease in � can be attributed to the change of the muon siteby diffusion; it is unlikely that the diffusion of V ions (∼500times heavier than muons) sets in at such low temperatures.The activation energy Ea of the hopping motion estimatedfrom the slope of the line in the Arrhenius plot for ν theinset of Fig. 2(e) is approximately 0.11 eV in the temperaturerange from 200 K to 280 K. This value is comparable to theactivation energy for hydrogen diffusion (0.08–0.12 eV) inSr/BaTiO(3−x)Hx hydride conductors [29,30]. The increasein ν begins to be observed around 180 K and reaches about0.15μs−1 around 250 K, which is similar to that reportedfor other oxides as a result of μ+ diffusion [31,32]. On theother hand, ν is suppressed in the high-temperature side above∼250 K and saturated at 280 K. This also correlates witha decrease in �, suggesting that the diffusion pathway maychange near the structural phase transition. Thus, the preex-ponential coefficients obtained by fitting the data, including280 K with the Arrhenius formula, are about an order ofmagnitude smaller than for other oxides, which also supportssuch a change in the diffusion mechanism.Above room temperature, the increase in ν shows a sharpdrop around TMI [Fig. 2(e) and Fig. S7(e)]. This behaviormay attribute to the trapping effect by lattice defects andphase boundaries. The muons, which diffuse rapidly due to thetemperature rise, are easily trapped in the lattice defects thatrequire considerable activation energy to escape [33]. Further-more, since three phases coexist during the M-I transition ofVO2, the distribution of Ea is expected to be larger at the phaseboundary due to structural disorder associated with tweedy orglassy textures of mixed phases with characteristic correla-tion lengths of ∼5 nm observed in VO2 epitaxial films [34].In addition, the carrier mobility measurement has inferred astrong scattering of electrons at the boundaries of metallic andinsulating domains in the inhomogeneous transition of VO2[35]. Given the above facts, the strong lattice inhomogeneityin the coexisting state inherent to the first-order phase tran-sition contributes to the sharp drop of ν around TMI. This isalso supported by the fact that the dropping temperature of νroughly coincides with the appearance of the coexisting state(Fig. S7).To discuss the crystallographic sites of muon (or hydrogen)in VO2, we performed the theoretical calculation of � versusmuon position. Since muon is an ultrahigh sensitivity probeof local magnetic fields, we can estimate the muon sites usinga spatial configuration of 51V nuclear magnetic moments asa guide. In polycrystals under zero magnetic field, �2 canbe evaluated as the second moment of internal field distri-bution exerted from nuclear magnetic moments (I = 7/2 in51V, which is subject to quadrupole interaction) using thefollowing formula [36]:�2 ≈ 49γ 2μ(μ04π)2 ∑ μ2ir6i, (2)where γμ (= 2π × 13.553 kHz/G) is the muon gyromagneticratio, ri is the distance from the ith nuclear magnetic momentμi, and μ0 is the vacuum permeability. Figure 3 shows thecalculated spatial distribution of � for the cross-sectionallayers parallel or perpendicular to the oxygen channels in thetetragonal and the monoclinic structures. Comparison of thecalculated results for both structures shows that there is nosignificant difference in the � distribution within each oxygenchannel. The value of �/γμ is just under 4 G (� ∼ 0.34 μs−1)at the center of the oxygen channel and has similar valuesalong the channel direction. The maximum value of �/γμdetermined from experiments is about 3.2 G (� ∼ 0.27 μs−1)at 4 K, indicating that the muons are located near the center ofthe oxygen channel at low temperatures. This result is in in-teresting agreement with the muon/hydrogen case in β-MnO2which has a similar structure to VO2 and is presumed to be acommon property of rutile-type oxides [37].024602-3H. OKABE et al. PHYSICAL REVIEW MATERIALS 8, 024602 (2024)FIG. 3. Calculated distribution of � for the cross-sectional layersparallel or perpendicular to the oxygen channels in the tetragonaland the monoclinic VO2. The values of � (numerical values in thecontour map, unit: Gauss) are calculated by using Dipelec code[39] with reported lattice parameters [40]. Crystal structures werevisualized using the VESTA program [41].As the temperature increases, � decreases rapidly to aboutone-fifth of its low-temperature counterpart (� ∼ 0.05 μs−1)above TMI. The muon sites corresponding to such a small valueof � are not found for the interstitial position, even consider-ing a lattice distortion caused by hydrogen intercalation in therutile structure. Therefore, it is highly likely that implantedmuons are trapped in vacancies at high temperatures. Sincethe crystallite size of this sample is 50 ∼ 80 nm (Fig. S3),FIG. 4. (a) The reduction rate of � as a function of the numberof removed vanadium N . The inset shows the spatial arrangement ofmuon (Mu) and surrounding vanadium, the first (V1), second (V2),and third (V3) nearest neighbors. (b) Temperature dependence of theexperimental � with the simulation result. The dotted lines indicatethe reduction rate of � at each stage of removing V1, V2, and V3.the surface contribution is expected to be small. However,muons might have diffused to the grain boundaries at hightemperatures considering the saturation of ν above 280 K.We performed a simulation of the relationship between �and the size of the vacancy based on Eq. (2). The virtualelement muon (Mu) was fixed at the center of the oxygenchannel, and � was calculated for a variety of situations wherethe V ions at the first, second, and third nearest neighbors(V1,V2, and V3) were removed sequentially. Note that struc-tural distortions due to the vacancy was not taken into account.Figure 4(a) shows the reduction rate of � as a function ofthe number of removed vanadium N . One can see that �decreases almost linearly as N increases within the each Vshell (V1–V3), down to about 20% when the V ions in the V3shell (the third nearest neighbors) are removed. Figure 4(b)compares the simulation result and the experimental �. Theexistence of the vacancy of a radius of ∼0.38 nm (the distancebetween center Mu and V3) can explain the magnitude of �above TMI. The discrepancy in � between our result and thatreported in the previous μSR study [38] can be interpreted asdue to the difference in the oxygen ratios between samples.According to their μSR result, some magnetic order wasobserved even in the nonmagnetic state below TMI. Whilethe details of the sample quality in Ref. [38] are unknown,magnetic secondary phases may have formed during the bulksintering process. In any case, our results strongly suggest thatmuons at high temperatures spend most of their life in a dif-fusive process of repeated “capture and release” by vacancies.The μSR study in a similar trapping mechanism has been dis-024602-4NANOSCALE DYNAMICS OF HYDROGEN IN VO2 … PHYSICAL REVIEW MATERIALS 8, 024602 (2024)cussed in semiconductors [33,36]. These two different muons(interstitial and vacancy) also exist in β-MnO2 and correspondto two other hydrogens called Ruetschi and Coleman protonsin battery materials [42–44]. Finally, to gain further insightinto the interstitial hydrogen dynamics in VO2, we discussmuon diffusion in the oxygen channel at intermediate temper-atures. The diffusion coefficient of muon Dμ is approximatedby the following equation [45]:Dμ =n∑i=11NiZis2i ν, (3)where Ni is the number of muon hopping sites in the ith path,Zi is the vacancy fraction, and si is the hopping distance. Theinterstitial hydrogen diffusion pathway is one-dimensional-like along the O channel in VO2, and the diffusion transverseto the channel can be negligible [15,47]. Assuming thatmuon diffusion via the O-Mu bond is dominant below roomtemperature, a muon jumps to one of the four neighboringoxygen atoms (Ni = 4, the average O-O distance si = 0.271nm). Additionally, neglecting the existence of other muonsor hydrogen (Zi = 1) and taking the experimental value ofthe hopping rate at 280 K [ν = 0.20(2)μs−1] to Eq. (3) yieldsDμ = 1.47(2) × 10−10 cm2/s. This value is on the same orderof magnitude as the reported diffusion constants of hydrogenDμ = 0.46 × 10−10 cm2/s at 300 K [16] and Dμ = 6.7 ×10−10 cm2/s at 373 K [15], indicating that the result of ourhydrogen simulation by muon is reliable; the mass differ-ence (the muon’s mass is one-ninth that of the proton) isunimportant at high temperatures where only moderate iso-tope dependences, e.g., Dμ = 4.7(9) × 10−4 cm2/s and Dμ =7.5 × 10−4 cm2/s above 300 K in iron [46], are expected.Interestingly, it is about three orders of magnitude larger thanDμ (= 1.8 × 10−13 cm2/s at 298 K) in TiO2, which has thesame crystal structure [47]. Based on the above results, weconclude that the interstitial hydrogen in VO2 has the potentialto diffuse at a sufficient rate (i.e., ∼10−10 cm2/s) even atroom temperature, suggesting that it is suitable for applica-tions requiring a fast response, such as ReRAM. However,high-quality VO2 thin films are required to fabricatehigh-reliability devices because defect/vacancy-mediatedmuon diffusion is observed even below room temperature[Fig. 4(b)].IV. SUMMARYIn summary, we have provided nanoscale information onthe hydrogen dynamics in VO2 using muon as pseudohy-drogen. The temperature dependence of the muon hoppingrate and the spatial distribution of the 51V nuclear magneticmoments indicates the existence of two types of muon dif-fusion (via O-Mu bonds and defects/vacancies) and that ahigh-quality thin film can have a diffusion coefficient of theorder of 10−10 cm2/s around room temperature. 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