A hysteresis loop in electrical resistance of NbH_x observed above the $β−λ$ transition temperature

Metal hydrides have attracted considerable research interest for electronics applications involving superconductivity,^1,2 metal-insulator transitions,^3,4 photochromism,⁵ and magnetism.⁶ For electronics applications of hydrides, epitaxial thin film growth techniques are of crucial importance.^7–9 Since physical properties of metal hydrides in bulk strongly depend on hydrogen composition,^10–12 as demonstrated in thin films of YH_x^3,4 and PdH_x,^2,10,13 tuning the hydrogen content in thin films is important for controlling their physical properties.

Niobium hydrides exhibit structural and physical properties, which strongly depend on their hydrogen content.^14,15 For example, in bulk, β-NbH_x (0.7 < x < 1.1, orthorhombic, a = 0.484 nm, b = 0.492 nm, c = 0.347 nm)¹⁶ is a stable phase at room temperature, in which hydrogen atoms occupy interstitial tetrahedral sites (T-site) in an α-Nb (bcc, a = 0.330 nm)¹⁷ lattice. β-NbH_x shows a phase transition (β-ε transition for x < 0.75, β-λ transition for x > 0.75) at a transition temperature of approximately 200 K depending on the hydrogen content.¹⁴ A previous electron diffraction study of polycrystalline samples has revealed the formation of superstructures at low temperature: 2a × 2b × c in ε-phase (x ≈ 0.75), and 2a × 2b × (m/n) c in λ-phase (m/n = 14/3, 16/3, 18/3).¹⁴ At the boundaries of the transition temperature, the thermal conductivity and electrical resistivity as a function of temperature exhibit a hysteresis loop or shoulder structures.^15,18 Compared with such polycrystalline samples, epitaxial thin films open up ways to elucidate correlations between the hydrogen content, structures, and physical properties. Although hydrogen solubility and phase transition have been reported for Nb epitaxial films hydrogenated using a thin Pd overlayer,^19–24 there have been no reports on the direct growth of epitaxial thin films nor on the electrical resistivity of NbH_x epitaxial thin films.

Here, we report on the growth of epitaxial thin films of NbH_x and temperature-dependent electrical resistivity and structures of NbH_x epitaxial thin films with a variety of hydrogen contents. We observed a hysteresis loop in the resistivity at room temperature in epitaxial thin films with x ≥ 0.77. Notably, this hysteresis loop appeared above the phase transition temperature. Because the hydrogen content of x ≈ 0.77 coincides with the ε–λ phase boundary, this result suggests that the short-range order of the hydrogen rearrangement in the λ-phase (x > 0.75) remains locally in the β-phase, and is responsible for the hysteresis of the resistance.

Thin films of β-NbH_x were deposited on Al₂O₃(001) (Shinkosha Corp.) substrates by reactive magnetron sputtering. A Nb metal plate (purity: 99.9%, 2 inch diameter, Toshima Manufacturing Co., Ltd.) was used as the sputtering target. A mixture of pure Ar and H₂ gases was introduced into a vacuum chamber at a background pressure below 1×10⁻⁵ Pa during sputtering. The Ar partial pressure was fixed at 1.0 Pa in the growth chamber, and the hydrogen pressure (p_H2) was varied by adjusting the flow rate. The dc power supply at the Nb target was maintained at 50 W. The substrate temperature was varied from room temperature (RT) to 400°C. The typical film thickness was 65 nm for a growth time of 15 min; hence, the thin-film deposition rate was 260 nm/h. The structural properties of the thin films were characterized with an X-ray diffractometer (XRD, Bruker D8 DISCOVER) over the temperature range of 100–300 K. The hydrogen content (x) and depth profile of the thin films were ex-situ characterized by nuclear reaction analysis (NRA, Micro Analysis Laboratory, Tandem accelerator, the University of Tokyo).²⁵ The hydrogen contents were determined as an average in deeper regions at ∼5 nm away from the surface. The time scale of one NRA measurement was 30 minutes. The depth resolution of our NRA measurements was < 10 nm. The more detailed information about depth profile analysis of hydrogen is described in supplementary material. Electron transport properties were measured in a typical Hall-bar geometry using a Gifford–McMahon refrigerator with superconducting magnets (Niki Glass Co., Ltd., LTS205D-CM9T-TL-VT).

Figures 1(a) and (b) show the out-of-plane XRD patterns of the films deposited on Al₂O₃(001) at a variety of p_H2 (T_s = 400°C). All the fabricated films were single phase, and the lattice parameters depended on the p_H2 value. As p_H2 was increased, the peaks at approximately 38° and 82° shifted to lower angles indicating that the films gradually changed from α- to β-phase NbH_x [Fig. 1(b)]. The peak at 2θ ≈ 36.4° observed in the film prepared at p_H2 = 0.17 Pa, which matched that of β-NbH 020 (bulk).¹⁶ Note that the hydrogen content of the film (p_H2 = 0.17 Pa) was x = 0.77, as described in later.

Pole figure measurements revealed that the β-NbH_x films were epitaxially grown on the substrates. The pole figure of the film prepared at p_H2 = 0.17 Pa (β-NbH_0.77) featured peaks of Al₂O₃ 116 (2θ = 57.5°, χ = 42.3°) and β-NbH_0.77 220 (2θ = 53.1°, χ = 45.5°) appear at the same φ-angles [Figs. 1(c) and (d)], demonstrating the in-plane epitaxial relationship of [110]_Al2O3//[100]_NbH0.77 [Fig. 1(e)]. Note that the six diffraction spots for β-NbH_0.77 220 indicate the formation of three rotational domains. The films deposited at p_H2 = 0.10 and 0.16 Pa also showed a similar in-plane epitaxial relationship (not shown in figure). We also succeeded in controlling the growth orientation of β-NbH_x epitaxial thin films with MgF₂(110), MgO(110), and Al₂O₃(012) substrates [Fig. S1 and S2].

We subsequently evaluated the hydrogen content of the films. We performed NRA measurements to quantitatively determine the depth profile of the hydrogen content in NbH_x(010) on Al₂O₃(001) substrates [Fig. 2(a)].²⁵ Although hydrogen is slightly deficient near the surface (∼5 nm) possibly due to surface oxidation, the depth profiles showed a uniform distribution in the films. We consider that the hydrogen composition in the films is intact in air, because XRD and resistance (shown later) are unchanged within half a year at least. We confirmed that the hydrogen content increased as p_H2 was increased.

To investigate the relationship between the hydrogen content and physical properties, we performed four-probe electrical resistivity measurements on NbH_x epitaxial films deposited on Al₂O₃(001) [Fig. 2(b)]. Note that the resistivity in the figure was normalized to the value at 300 K. The typical resistivity at 4 K was 6.7×10⁻⁵ Ωcm for NbH_0.80. The NbH_0.15 film showed a large residual resistance ratio (RRR) and exhibited superconductivity at ∼8 K. As the value of x increased, the RRR values decreased and superconductivity was not observed above 4 K in samples with x ≥ 0.71.

Notably, we found a shoulder and hysteresis in the temperature dependence of the resistance. The NbH_0.71 film exhibited a shoulder structure at ∼220 K, which has previously been argued to be related to a phase transition.¹⁸ Furthermore, in NbH_0.77 and NbH_0.83 films, we observed a hysteresis over a wide temperature range (200–300 K). The samples showed larger and lower resistances in heating and cooling processes, respectively. To our knowledge, hysteresis over such a wide temperature range (over room temperature) has not been reported before.

To understand the structural contribution to the emergence of this hysteresis, we measured XRD patterns at low temperatures. Figures 3(a) and (b) show the temperature dependence of the out-of-plane XRD patterns of NbH_0.71 (no hysteresis) and NbH_0.77 (hysteresis) thin films, respectively. For both films, additional 010 (2θ ≈ 18°) and 030 (2θ ≈ 56°) superlattice reflections were observed on reducing the temperature (<220 K) [top panels of Figs. 3(c) and (d)], indicating that both films exhibited phase transitions from the β-phase. Since the formation of superlattice and its transition temperatures are in good agreement with those reported in bulk,¹⁴ we discuss the structures and physical properties of films following the phase diagram of bulk.

However, the low-temperature phases were different in the two films. As shown in the lower panels of Figs. 3(c) and (d), the slope of the 020 lattice spacing observed in the NbH_0.71 thin film greatly changed on the phase transition, whereas only a slight change in the slope was observed in the NbH_0.77 thin film. This result indicated that a different type of phase transition occurred in the two samples: considering the phase diagram, a β-ε transition occurred in NbH_0.71 and a β-λ transition occurred in NbH_0.77.

We observed hysteresis in samples with x ≥ 0.77. Figure 4(a) summarizes the presence or absence of hysteresis for films with a variety of x values. The samples with x ≥ 0.77 exhibited hysteresis [shown in red in Fig. 4(a)]; however, samples with x < 0.77 showed no hysteresis. The value of x ≈ 0.77, is consistent with the boundary of the ε- (x < 0.75) and λ- (x > 0.75) phases, as discussed in the above structural analyses. Thus, the hysteresis in electrical resistance is likely related to the β–λ phase transition. However, we note that the hysteresis was observed above the β–λ transition temperature of ∼220 K [Figs. 3(c) and (d)].

Finally, we discuss the origin of the hydrogen-content-dependent hysteresis observed above the β-λ transition temperature. On the basis of the phase diagram of bulk, we speculate that the hydrogen content plays an important role in the hysteresis and highlights the contribution of the λ-phase (x > 0.75) distinct from the ε-phase (x < 0.75). In terms of the structure, as the hydrogen content increases from x < 0.75 to x > 0.75, the c-axis order evolves in the λ-phase; according to electron diffraction studies,⁸ a peculiar long-range periodicity of 14/3 c, 16/3 c and 18/3 c appears. This long-range c-axis order originates from a redistribution of the hydrogen density, similar to charge density waves.¹⁴ In the case of charge density waves, it is discussed that the electronic transition temperature could be higher than the structural transition temperature, because of the persistence of short-range order (order parameter fluctuation) above the structural transition temperature.^26,27 Accordingly, the short-range order of the hydrogen density might remain locally above the β–λ structural transition, thus leading to the hysteresis in the electrical resistance.

In summary, we have successfully deposited β-NbH_x epitaxial thin films with different hydrogen contents by a magnetron sputtering method. The temperature dependence of the electrical resistivity showed a hysteresis over a wide temperature range of 200–300 K. The hysteresis appeared only in films with a hydrogen content of x ≥ 0.77, indicating that the hysteresis was related to the β–λ phase transition. Interestingly, the hysteresis was observed above the β–λ phase transition temperature, suggesting that the short-range order remained locally above the β–λ transition temperature.

See supplementary material for the orientation control of NbH_x epitaxial films, the depth profile analysis of hydrogen content using nuclear reaction analysis, and XRD analysis at low temperatures.

R. S. acknowledges funding from JSPS Kakenhi Grant No. 17H05216, and JST-PRESTO Grant No. JPMJPR17N6, Japan. T. H. acknowledges funding from JSPS Kakenhi Grant Nos. 26246022, 26106502, 26108702, 26610092, 18H03876, 18H05513, 18H05514, and 18H05518, and JST-CREST (JPMJCR1523) program. This work was also performed under the Inter-university Cooperative Research Program of the Institute for Materials Research, Tohoku University (proposal No. 17K0060). The authors thank Prof. Hiroyuki Matsuzaki and Mr. Yuya Komatsu for assistance with NRA measurements. The authors thank Mr. Ryo Nakayama for fruitful discussions.