Polarity reversal of the charge carrier in tetragonal TiH x ( x = 1 . 6 − 2 . 0) at low temperatures

We present a combined experimental and theoretical study of the charge transport properties of TiH x ( x = 1 . 6–2 . 0) epitaxial thin ﬁlms. We found that the Hall coefﬁcient of TiH x strongly depends on hydrogen content and unit-cell volume: Nearly stoichiometric TiH x ( x ≈ 2 . 0) ﬁlms with large unit-cell volumes showed positive Hall coefﬁcients at 4 K, whereas TiH x samples with x < ∼ 1 . 7 and small unit-cell volumes showed negative Hall coefﬁcients at 4 K. Our density functional theory calculations reveal that the volume change leads to the change in the aspect ratio of the tetragonal lattice, thereby lifting the degeneracy of Ti t 2 g states, and alters the contributions of electrons and holes at the Fermi surface and the sign of the Hall coefﬁcient. The present study clariﬁes the important role of the lattice symmetry in determining the charge carrier polarity, and we suggest that electronic properties of metal hydrides can be tuned by the lattice parameters via the hydrogen contents.


I. INTRODUCTION
Metal hydrides have attracted considerable attention from the viewpoint of energy device applications, including hydrogen storage systems and fuel cells [1,2].In recent years, fast ionic conduction of metal cations (Li + , Na + , Mg 2+ ) [3] and hydride (H − ) ions [4,5], as well as high transition-temperature superconductivity in H 3 S [6] and LaH x [7,8], have attracted broad research interest in electrochemical and condensed matter physics communities.In addition, the successful growth of epitaxial thin films has advanced the applications of hydrides in electronics [9][10][11][12].Accordingly, metal hydrides have become one of the key materials in energy and electronics fields to exploit their exotic physical properties and functionalities.
Despite the importance of hydrides in electronic device applications, understanding of the electronic structures and electron transport properties of hydrides is limited.Although a few photoemission studies have been performed on rareearth hydrides to clarify their electronic structures [13][14][15][16], their charge transport properties including carrier polarity and carrier density remain elusive [17][18][19].Titanium dihydride (TiH 2 ) is an archetypal metal hydride with interesting electron transport properties.In particular, the sign of its Hall coefficient in the polycrystalline form of TiH 1.86 depends on temperature: n-type conduction appears at low temperatures below 200 K, while p-type conduction appears near room temperature [17].Although the cubic-to-tetragonal phase transition occurs at 313 K in TiH 2 [20], the temperature region for the sign change is different, and the dominant factor determining the carrier polarity still remains unclear.We have recently succeeded in the epitaxial growth of single-phase TiH x (x ≈ 2) (111) thin films on an insulating Al 2 O 3 (001) substrate [21].The use of epitaxial thin films should allow precise control of the hydrogen content, growth orientation, and structural deformation of these hydrides and thus improve our understanding of their electron transport properties.
Here, we investigated the structures, compositions, and electronic properties of TiH x epitaxial thin films.We grew TiH x thin films with different hydrogen compositions and then evaluated their electron transport properties.While a positive Hall coefficient was observed in TiH 1.91 (100) and TiH 1.75 (110) epitaxial thin films at 4 K, the Hall coefficient was negative for a TiH 1.67 (111) film.Structural and compositional analyses showed that the Hall coefficient values were scaled well in that the unit-cell volume correlated with the hydrogen content.Density functional theory (DFT) calculations predict that the aspect ratio of the tetragonal lattice (tetragonality) associated with the unit-cell volume plays a crucial role in tuning the carrier polarity of TiH x at low temperatures.

II. METHODS
Thin films of TiH x were fabricated on Al 2 O 3 (001), MgO(100), and (110) substrates (Shinkosha Corp.) using reactive magnetron sputtering.A Ti metal plate (purity: 99.99%, 2 in.diameter, Toshima Manufacturing Co., Ltd.) was used as a sputtering target, and a mixture of pure Ar and H 2 gases was introduced into a vacuum chamber (background pressure <2 × 10 −4 Pa) for sputtering.During the depositions, the Ar partial pressure was fixed at 1.0 Pa with a constant flow rate of 20 SCCM (cubic centimeter per minute at STP) in the growth chamber, and the flow rate of H 2 gas was varied from 0.6 to 3.0 SCCM on Al 2 O 3 (001) and MgO(100) and (110) substrates.The dc power supply at the Ti target was maintained at 100 W. The substrate temperature during growth was fixed as 150 °C.The typical film thickness was 100 nm with a growth rate of 400 nm/h.The structural properties of the thin films were characterized using commercial x-ray diffraction (XRD, Bruker D8 Discover) and synchrotron XRD (SPring-8, BL13XU).Electron transport measurements were carried out in a typical Hall-bar geometry using a Gifford-McMahon refrigerator with superconducting magnets (Niki Glass Co., Ltd., LTS205D-CM9T-TL-VT). Hydrogen composition and depth profiling of the thin films were evaluated using nuclear reaction analysis (NRA, Micro Analysis Laboratory, Tandem accelerator, the University of Tokyo) [22,23].X-ray absorption spectroscopy (XAS) measurements were conducted at room temperature at the undulator beamline BL-2 MUSASHI at Photon Factory, KEK.XAS spectra were recorded in total electron yield (TEY) mode using the sample drain current and in transmission (TM) mode using x-ray-excited optical luminescence from Al 2 O 3 or MgO substrates.
DFT calculations were performed using the projector augmented wave (PAW) method [24] as implemented in the QUANTUM-ESPRESSO package [25,26].Electron-ion interactions were described by the PAW potentials adopted from PSLIBRARY [27].The PBEsol [28,29] generalized gradient approximation was employed for the exchange-correlation functional.Wave functions and augmentation charge were expanded in terms of a plane-wave basis with kinetic energy cutoffs of 80 and 640 Ry, respectively.Brillouin zone sampling was performed with a uniform 16 × 16 × 16 (16 × 16 × 12) k-point grid for the primitive (conventional) body-centered tetragonal cell and the Fermi surface was treated using the Hermite-Gaussian function [30] of the order of 1, with a smearing width of 0.01 Ry.With this setting, the calculated lattice constant for the cubic phase  [31].The Hall coefficient was calculated based on the semiclassical Boltzmann theory as implemented in the BOLTZTRAP code [32].Fermi surfaces were visualized using the FERMISURFER code [33].Photon energy (horizontal axis) was calibrated using the spectrum of a Ti 0.996 Nb 0.004 O 2 single crystal (green).For reference, spectra of metallic Ti (Ref.[34]   The depth profile of hydrogen content x obtained using NRA indicated uniform distributions in all the films (Fig. 2).Furthermore, the x values depended on the orientations of the films; in particular, the (111)-oriented film was the most hydrogen deficient.The values of x were 1.91 ∓ 0.08, 1.75 ∓ 0.05, and 1.64 ∓ 0.08 for the (100)-, (110)-, and (111)oriented films, respectively.Subsequently, we investigated the valence states of Ti in TiH 1.90 /MgO(110) and TiH 1.66 /Al 2 O 3 (001) epitaxial films using XAS.Spectra obtained in TEY mode were similar to that of Ti 4+ in TiO 2 [Fig.3(a)].As these TEY spectra were sensitive to surface conditions (probing depths of only a few nanometers from the surface were employed), it is reasonable to consider that film surfaces are oxidized to form TiO 2 .In contrast, the spectra of both films recorded in the TM mode, a bulk-sensitive technique providing characteristic spectra, showed similar characteristics for the intermediate state between Ti 4+ and Ti 0 [Fig.3(b)] [34].Accordingly, the valence states of Ti are similar in TiH 1.90 /MgO(110) and TiH 1.66 /Al 2 O 3 (001) films, which in turn were different from metallic Ti and TiO 2 .

III. RESULTS AND DISCUSSION
Figure 4(a) shows the longitudinal resistivity (ρ xx ) of TiH x epitaxial thin films as a function of temperature, which suggests that all the films are metallic.Note that the observed resistivity of ∼10 −4 cm at 300 K is ten orders of magnitude smaller than the estimated H ionic resistivity in TiH x (∼10 6 cm, 1.65 x 2.02) [35], indicating the negligible contribution of ionic motion.In addition, we found that the sign of the Hall coefficient at 4 K strongly depends on    [21]; we speculate that this film was hydrogen deficient at x < 1.70.
It is worth stressing that the Hall coefficient at low temperature scales with the unit-cell volume [Fig.4(d)].For simplicity, here we define the unit cell as the size of the cubic structure.Each unit-cell volume was experimentally obtained using two asymmetric scans during XRD measurements (Tables I-III).As the unit-cell volume increases, the Hall coefficient at 4 K increases linearly, and the sign changes from negative to positive.The unit-cell volume in bulk TiH x is known to increase with increasing x [36].Indeed, a linear relationship was observed between unit-cell volume and x for our epitaxial thin films (Table IV and Appendix B), which suggests that the correlation between the unit-cell volume and hydrogen content of the TiH x film affects the sign of their Hall coefficient.
We performed DFT calculations to investigate the mechanism that determines the sign of the Hall coefficient.The calculations revealed that the sign depends significantly on the aspect ratio of the TiH 2 tetragonal unit cell, namely, tetragonality.We calculated the total energy of tetragonal TiH 2 as a function of lattice constant a, while the lattice constant c is optimized for each value of a.We found that optimized unit-cell volume (V cal ) monotonically increases as a increases [Fig.5  detailed unit-cell volume dependence near the Fermi level is shown in Fig. 5(c).
We then analyzed the electronic structures in detail to understand the sign change of the Hall coefficient, revealing that both electrons and holes contribute to the Fermi surface and that a subtle change in the band structure determines the polarity of the charge carrier.Under the conditions of small volume and large tetragonality, the c/a value is considerably larger than unity, and the contribution of electrons to the Fermi surface becomes dominant [Fig.6 When the hydrogen content x deviates from 2, TiH x may be electron doped.We examined the doping effect using the rigid band model for the structure close to the high-symmetry one (a = 4.37 Å and c/a = 1.01), which shows the p-type conduction with no doping.We calculated the Hall coefficient as a function of charge [Fig.7(a)].We found that at doping of about 0.2 electron per formula unit, there is a sign change in the Hall coefficient, i.e., polarity change from p to n type.Further, using the same high-symmetry unit cell, we explicitly doped electrons/holes with the neutralizing background charge and obtained similar results [Fig.7  We also studied the electron doping effect from hydrogen vacancies.We constructed a model (1 × 1 × 1) conventional tetragonal cell (Ti 2 H 4 ) based on the same high-symmetry structure (a = 4.37 Å and c/a = 1.01) as above, and introduced a hydrogen vacancy.We found that the introduction of a hydrogen vacancy dopes electrons, but the Hall coefficient remains positive even at low hydrogen content (x = 1.5) (Fig. 8) as long as the high symmetry (i.e., cubic symmetry) is retained.This result suggests that the content of hydrogen vacancy does not necessarily correspond to the amount of electron doping, and that the positive Hall coefficient is robust as long as the crystal symmetry is high.Thus, although electron doping by hydrogen vacancy plays some role in the shift of the Hall coefficient, especially at low hydrogen content, the symmetry breaking is the dominant factor governing the polarity change of the charge carrier of TiH x from p type to n type.To discuss the effect of doping by the hydrogen vacancy quantitatively, we may need to consider random hydrogen vacancies using a larger unit cell, but this deserves further investigation.

IV. CONCLUSIONS
In summary, we have investigated the charge transport properties of TiH x epitaxial thin films at 4 K, revealing that TiH 1.91 (100) and TiH 1.75 (110) films showed positive Hall coefficients, whereas negative values were observed for the TiH 1.67 (111) film.Structural and compositional analyses showed that the Hall coefficient values were scaled by the FIG. 8. Hall coefficient of TiH 2 as a function of energy calculated by using the high-symmetry structure (a = 4.37 Å and c/a = 1.01) in the conventional tetragonal unit cell (Ti 2 H 4 ) with and without a hydrogen vacancy (V H ). For the system with V H , the effect of the atomic relaxation was also considered.The origin of the energy is set to the Fermi level (E F ). unit-cell volume, which in turn correlated with the hydrogen content.Density functional theory calculations revealed that the unit-cell volume and the resulting tetragonality play an important role in determining the carrier polarity of TiH x .These results showed that electronic structures in metal hydrides can be tuned via lattice parameters through control of hydrogen content.MgO(110) substrate.A 55-nm-thick polycrystalline AlN film was deposited as a protective layer using magnetron sputtering.The out-of-plane XRD pattern shows Laue fringe structures reflecting a smooth interface (Fig. 9).This fringe structure is consistent with an atomically abrupt interface at TiH 2 (111)/Al 2 O 3 , as previously reported in a study using scanning transmission electron microscopy [21].
FIG. 2. Hydrogen content measured on TiH x thin films grown on (a) MgO(100), (b) MgO(110), and (c) Al 2 O 3 (001) substrates as a function of depth using nuclear reaction analysis.Note that close-tosurface hydrogen-deficient regions observed in (110)-oriented films are artifacts originating from 15 N beam misalignment.

Figure 1 (
Figure 1(a) shows out-of-plane XRD patterns of the TiH x thin films, showing the successful fabrication of orientationcontrolled TiH x epitaxial thin films.Depending on the crystal orientations of the substrates, TiH x (100), (110), and (111) thin films (described in a cubic setting) were grown on MgO(100), MgO(110), and Al 2 O 3 (001) substrates, respectively.The rocking curve full width at half maximum values of the TiH 2 200, 220, and 111 peaks were 1.2°, 1.6°, and 1.1°, respectively.Note that the 5-nm-thick ultrathin TiH 2 film deposited on a MgO(110) substrate also showed a crystalline 220 peak from synchrotron XRD (Appendix A), suggesting that the TiH x film crystalizes from the initial growth process.All films were epitaxially grown and showed tetragonal lattices with slight expansion in the out-of-plane direction and contraction in the in-plane directions [Fig.1(b)] at room temperature.
FIG. 3. X-ray absorption spectroscopy (XAS) measurements.Spectra obtained in (a) in total electron yield (TEY) mode and (b) in transmission (TM) mode.Red and blue plots relate to TiH 1.90 /MgO(110) and TiH 1.66 /Al 2 O 3 (001) thin films, respectively.Photon energy (horizontal axis) was calibrated using the spectrum of a Ti 0.996 Nb 0.004 O 2 single crystal (green).For reference, spectra of metallic Ti (Ref.[34] in (a)) and TiO 2 [green spectrum in (b)] are given as black dashed lines.Spectra are shifted for clarity.

FIG. 4 .
FIG. 4. (a) Temperature dependence of longitudinal resistivity (ρ xx ).(b) Magnetic-field dependence of transverse resistance (R xy ).(c) Hall coefficient observed at 4 K in thin films with variable hydrogen content x.The x values were obtained using nuclear reaction analysis measurements.The error bars in (c) are standard deviations.(d) Plots of Hall coefficient at 4 K as a function of unit-cell volume.
(a), lower panel], and the value of a strongly correlates with the unit-cell volume.Note that c/a monotonically decreases as a increases [Fig.5(a), upper panel].We then calculated the Hall coefficient as a function of unit-cell volume and found that at the Fermi level, small unit-cell volumes result in negative Hall coefficients, whereas large unit-cell volumes result in positive Hall coefficients [Fig.5(b)].The

FIG. 5 .
FIG. 5. (a) Optimized c/a value (upper panel) and unit-cell volume (V cal ) (lower panel) as functions of the lattice parameter a.(b) Calculated Hall coefficient at the Fermi level as a function of unit-cell volume.(c) Energy (E) dependence of the calculated Hall coefficient for different lattice parameters a.The origin of the energy is set to the Fermi level (E F ).
(a)].In contrast, at larger volumes with c/a ≈ 1 (small tetragonality), the contribution of holes is dominant [Fig.6(b)].The variation in the Hall coefficient sign originates from the lift of the degeneracy of Ti t 2g states (d xy , d yz , and d zx orbitals) at c/a ≈ 1 [Fig.6(c)]. (b)].

FIG. 6 .
FIG. 6.(a) Fermi surface at a = 4.30 Å (V cal = 79.5 Å 3 ).(b) Fermi surface at a = 4.37 Å (V cal = 83.5 Å 3 ).Blue and red surfaces indicate electron and hole contributions, respectively.(c) Partial density of states for Ti d states.The energy origin is set to the Fermi level (E F ).

FIG. 7 .
FIG. 7. (a) Hall coefficient of TiH 2 at the Fermi level as a function of charge per formula unit calculated by using the high-symmetry structure (a = 4.37 Å and c/a = 1.01) and the rigid band model.(b) Hall coefficient of TiH 2 as a function of energy (E) calculated by using the high-symmetry structure (a = 4.37 Å and c/a = 1.01) with additional charge with the neutralizing background charge.e is the elementary charge, and positive (negative) charge indicates hole (electron) doping.The origin of the energy is set to the Fermi level (E F ).

FIG. 10 .
FIG. 10.Unit-cell volume of TiH x thin films as a function of hydrogen content (x).

TABLE I .
Asymmetric-scan results for TiH x (100) thin films.

TABLE III
. Asymmetric-scan results for TiH x (111) thin films.

TABLE IV .
Summary of growth orientations, hydrogen contents, unit-cell volumes, and Hall coefficients.thevalue of x.Magnetic-field dependence of the transverse resistance (R xy ) is shown in Fig.4(b).The slope is negative in the TiH 1.67 (111) thin film, while the slope is positive in the TiH 1.75 (110) and TiH 1.91 (100) thin films.Figure4(c) summarizes the values of Hall coefficient at 4 K as functions of x as measured using NRA.As x increases, the Hall coefficient increases monotonically, and the sign of the Hall coefficient switches from negative to positive at x ≈ 1.70.Namely, the polarity of charge carrier is switched from electron to hole at x ≈ 1.70.Note that we have previously reported negative Hall coefficients at 4 K, as observed in a TiH x (111) thin film on an Al 2 O 3 (001) substrate