Planar Hall effect in c-axis textured films of Bi85Sb15 topological insulator

Measurements of the planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) in polycrystalline films of topological insulator Bi85Sb15 are reported. The observation of PHE and AMR in these films of carrier density ≈2 × 10 electrons/cm is like the behavior of in-plane field transport in thin films of metallic ferromagnets. However, the amplitudes of PHE (Δρ) and AMR (Δρxx) are at variance. Δρ and Δρxx also undergo a sign reversal near ≈160 K. We compare these results with the reported PHE of topological insulators and Weyl semimetals and discuss possible scenarios for anisotropic backscattering of charge carriers in this non-magnetic alloy. © 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0049577


I. INTRODUCTION
Bismuth-antimony alloys (Bi 1−x Sbx) are well-known thermoelectric (TE) materials. 1,2 Their TE characteristics emanate from a tunable electronic band structure achieved by adjusting the Bi/Sb ratio in the alloy. This material has attracted much attention in recent years on the recognition of a strong spin-orbit interaction (SOI) driven band crossing in the composition range of 0.03 < x < 0.22. 3,4 For x ≈ 0.03, it acquires a Dirac-like metallic state, which changes to a 3D Weyl semimetal on application of a magnetic field, with signatures of the chiral anomaly in longitudinal magnetoresistance (LMR). 5 For 0.09 < x < 0.22, (Bi 1−x Sbx) is a 3D topological insulator (TI), as established by angle resolved photoemission measurements on single crystals 6 and epitaxial thin films. 7 Electronic transport measurements on such crystals are characterized by a metal-like resistivity at low temperatures and the presence of weak Shubnikov-de Haas oscillations in the magnetic field dependence of longitudinal (ρxx) and Hall (ρxy) resistivity. 8 These features of electronic transport have been attributed to spin-momentum locked surface states. However, counter arguments suggesting subtle changes in bulk conduction at lower temperatures due to improved coherence and effectiveness of inadvertent doping have been given as well. The low effective mass of charge carriers and large dielectric function of Bi 1−x Sbx make the impurity conduction dominant at low temperatures. 9 The topological phase of (Bi 1−x Sbx) has been identified as an excellent spin-orbit torque (SOT) material for spintronic applications. [10][11][12][13] In epitaxial bilayers of BiSb and a ferromagnet (FM) like MnGa, the spin-momentum locked surface states of the former pump a large spin current into the FM layer under the action of a charge current driven Rashba-Edelstein effect (REE). 14 The REE torque on the magnetization of the FM layer has been established to be much larger than the spin Hall effect driven torque of a heavy metal like Pt. Interestingly, two recent studies 10,15 have indicated that the polycrystalline films of Bi 1−x Sbx made by a scalable process like sputtering are quite effective in producing spin currents to torque the magnetization of FeMn, FeCoB, and CoTb thin films. These observations have motivated us to undertake a detailed study of electronic transport in sputter-deposited polycrystalline films of BiSb. Although polycrystalline films of (Bi 1−x Sbx) alloys have been studied previously by a number of groups, [16][17][18] the focus of those studies has been their applicability as a thermoelectric material. Our objective here is to compare the low temperature (T ≥ 2 K) magnetotransport in polycrystalline films of Bi 85 Sb 15 with that of epitaxial films and single crystals where the existence of a topological phase has been established. We also seek to find the existence of the planar Hall effect (PHE) and anisotropic magnetoresistance (AMR), which have been seen earlier in several non-magnetic topological insulators [19][20][21][22][23][24] and the Dirac/Weyl family of semimetals. [25][26][27][28]

II. EXPERIMENTAL DETAILS
Bi 85 Sb 15 films were deposited on thermally oxidized silicon wafers by magnetron sputtering of a stoichiometric 2-in. diameter alloy target in a laser deposition/sputtering hybrid load-lock chamber with a base pressure of ∼7 × 10 −8 Torr. The Bi 85 Sb 15 alloy has a low melting temperature (Tm ∼ 300 ○ C) 29 and high sputtering yield. 30 The sputter gun was operated at low power (≈25 W) to avoid surface melting of the target and to ensure a low growth rate (∼0.15 nm/s). Films were deposited at ambient temperature and at 100 and 150 ○ C. It was noticed that the higher deposition temperature and excessive growth rates result in rough films. This is a perennial issue with the growth of thin films of low melting point alloys and elements. 30 The crystallographic structure of these films has been evaluated with x-ray diffraction. For measurements of magneto-transport, films were deposited through a shadow mask in a Hall bar geometry with the bar dimensions of 300 × 3000 μm 2 . Transport measurements were carried out in a physical property measurement system in the temperature and field ranges of 2-300 K and 0 to ±9 T, respectively. The use of a vertical sample rotator allowed in-plane and out-of-plane rotation of the film for measurements of anisotropic magnetoresistance and planar Hall effect.

III. RESULTS
The binary equilibrium phase diagram of (Bi 1−x Sbx) shows complete solubility of the two elements for all values of x, leading to a single-phase material of rhombohedral structure. 31 However, due to the low melting points of Bi and Sb, the growth or annealing of BiSb films at T > T Liquidus may result in phase separation; therefore, we have deposited the films at only T < 150 ○ C. Figure 1 compares the Θ-2Θ x-ray diffraction profiles of the two films grown at 35 and 100 ○ C. The x-ray profile of the film deposited at 35 ○ C shows diffraction peaks corresponding to several allowed hkl-indices with (001) reflections being most prominent. The higher intensity of such reflections suggests a predominantly c-axis oriented growth along the c-axis of the rhombohedral cell. This preferential growth becomes prominent at 100 ○ C as indicated by the suppression of the intensity of reflections corresponding to non-zero values of h and k indices. These observations are consistent with the results of Rochford et al. 16 on Bi 80 Sb 20 films deposited on thermally oxidized silicon by cosputtering of elemental targets. Films of Bi 85 Sb 15 deposited by radio frequency sputtering of the alloy target on (0001) sapphire reveal a preferential c-axis growth due to a better c-plane lattice match between sapphire and BiSb. 31 Here, we focus on electron transport in the BiSb films deposited at ≈ 35 ○ C. Ambient temperature growth of the TI film is preferred when it is deposited on amorphous ferromagnets like FeGaB, FeCoB, and Fe-Gd alloys to avoid their crystallization. The inset of Fig. 2 shows the zero-field longitudinal resistivity of the film between 2 and 300 K. The resistivity first rises on lowering the temperature down to ∼180 K, and then, this rise tapers off, leading to a resistivity of ∼2.0 mΩ cm at 2 K. This behavior of resistivity is comparable to that reported by Fan et al. 31 for sputter-deposited films on (0001) sapphire.
It is also worth comparing the resistivity of these films with those made by molecular beam epitaxy. The data of Cho et al. 2 for films grown by MBE on CdTe crystals reveal a resistivity of ∼0.2 mΩ cm at 300 K, which rises to ∼2.5 mΩ cm at 2 K. While the resistivity ratio ρ(2 K)/ρ(300 K) of the MBE grown films is the same (∼1.2) as that of the sputter-deposited films reported here, the temperature dependence of resistivity is strikingly different in the two cases. The resistivity of sputtered polycrystalline films first rises and then tapers off, while for the MBE films, 2 the rise is faster at lower temperatures. Interestingly, the ρxx(2 K)/ρxx(300 K) ratio for Bi 1−x Sbx single crystals with x = 0.09 is ≈ 1.8, 8 with a ρxx(300 K) of ∼0.16 mΩ cm. The temperature dependence of ρxx is similar to that of the sputtered film, barring some signatures of a metallic conduction at T < 50 K, which is presumably due to well-defined conducting surface states in single crystal samples.
The main panel of Fig. 2 shows the Hall resistivity (ρxy) of the ambient temperature deposited film measured between 2 and 20 K as a function of magnetic field. ρxy is linear in field for μ 0 H ≤ 3 T and does not show any temperature dependence. In the framework of a simple Drude model, it yields a carrier density of 1.97 × 10 19 electrons/cm 3 and carrier mobility of ∼203 cm 2 V −1 s −1 . The slight upward curvature of ρxy vs H at the higher fields suggests a

FIG. 2.
Hall resistivity (ρxy) of the Bi 85 Sb 15 film measured between 2 and 20 K as a function of magnetic field. The linear portion of ρxy vs μ 0 H has been used to calculate the carrier concentration. The Hall resistivity shows a very weak temperature dependence at high fields. The inset of the figure shows the resistivity (ρxx) of the film in zero-field measured between 2 and 300 K.

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scitation.org/journal/adv two-carrier scenario for electron transport in this system. The high field data also reveal a very weak temperature dependence in the temperature range of 2-20 K. While there is a lack of carrier concentration and mobility data on epitaxial and polycrystalline films of Bi 85 Sb 15 , the carrier concentration in our films is ∼2 orders of magnitude higher than that reported by Taskin and Ando 8 for x = 0.09 BiSb single crystals and the carrier mobility of these films is smaller by the same factor. The measurements of the electrical resistivity of 3D topological insulators and Dirac/Weyl semimetals in a configuration where the current density, magnetic field, and induced electric field are in the same plane have generated considerable interest due to the presence of anisotropic magnetoresistance and planar Hall effect, [19][20][21][22][23][24][25][26][27][28] which have traditionally been the signatures of electronic transport in a magnetically ordered metal. 32 We carried out the measurements of the electrical resistivity of BiSb thin films in a field-in-plane geometry. Here, the transport current Jx (=25 A/cm 2 ) flows in the x direction, and the induced electric fields Exx and Exy in the x and y directions, respectively, are measured as the magnetic field is rotated in the xy plane from −90 ○ to 270 ○ . The angle ϕ = 0 corresponds to the situation where H and Jx are parallel. The induced electric field in the direction of Jx yields magnetoresistivity, whereas the orthogonal field Exy results in the planar Hall effect.
The components of the resistivity tensor are expressed as 20,32 where Δρ = ρ −ρ † , with ρ and ρ † corresponding to H perpendicular to Jx and H parallel to Jx, respectively. The anisotropic magnetoresistance (Δρ) and ρ PHE are characteristic features of spin-orbit scattering dominated electronic transport in magnetic alloys due to coexisting s and d bands near the Fermi energy. 32 Interestingly, however, PHE and anisotropic magnetoresistance have been found in non-magnetic 3D topological insulators like Bi 2 Te 3 and Bi 2 Se 3 , [19][20][21][22][23][24] including the observation of a nonlinear response at higher current densities in epitaxial films of Bi 2 Se 3 , which depends on the direction of current with respect to the crystal axis of the monolayer. 23,24 Appreciable values of AMR and PHE have been observed in Dirac and Weyl semimetals as well. [25][26][27][28] While in the latter class of semimetals, this anisotropic transport has been attributed to breaking of chiral symmetry, which results in a large negative longitudinal magnetoresistance (NLMR), varied interpretations have been proposed for PHE in 3D TIs where no NLMR is seen. Bi 1−x Sbx is one of the first reported 3D TIs. While the measurements of the Hall resistivity and orbital MR in single crystals and epitaxial films of Bi 1−x Sbx have been reported earlier, 6,8,9 data on PHE and AMR are lacking. Figure 3(a) shows the variation of ρxx and ρxy at 2 K and +9 T as the sample is rotated to change the angle between magnetic field and current density directions from −90 ○ to 270 ○ . A similar measurement of ρxx and ρxy at 2 K with the field direction reversed is shown in Fig. 3(b). We note that the positions of extrema in ρxx and ρxy data of Figs. 3(a) and 3(b) are consistent with Eqs. (1) and (2). However, there is a noticeable asymmetry in the behavior of ρxy for the two field orientations. There are two factors that contribute to this asymmetry. First is a normal Hall voltage that results from a non-zero out-of-plane component of the magnetic field due to a misalignment of the film plane and the plane of rotation. This contribution is antisymmetric in field and can be eliminated on symmetrization of the (+H) and (−H) data. Second is a zero-field misalignment voltage across the Hall contacts, which will add to the

PHE voltage on symmetrization of ρxy [{(ρxy(+H) + ρxy(−H)}/2].
This constant resistance can be subtracted from the measured ρxy(H) provided its value is small such that the AMR induced change in it is insignificant compared to the true ρxy(H). In addition to these two factors, another contaminant of ρxy comes from the orbital

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scitation.org/journal/adv magnetoresistance (OMR) of the misaligned section of the transverse contacts when the sample is tilted with respect to the plane of rotation. This would add a cos 2 ϕ term in Eq. (2). The misalignment of the plane of rotation and the plane of the sample adds an error in the value of AMR as well. If the OMR of the sample is large, then the normal component of the field will add an OMR contribution to ρ xx and ρ // xx. We address these errors by first symmetrizing the ρxx(ϕ) and ρxy(ϕ) data of Figs. 3(a) and 3(b). The result of this procedure is displayed in Fig. 3(c), along with the fits of ρxx(ϕ) to Eq. (1) and of ρxy(ϕ) to a function of the type ρxy(ϕ) = A + B sin(ϕ) cos (ϕ) + C cos 2 (ϕ). The last term of this equation considers the error in ρxy due to OMR of the misaligned section, as discussed earlier. The magnitude of this error [C cos 2 (ϕ)] and the antisymmetric contribution to ρxy are displayed in Fig. 3(d). Comparing the peak amplitude of ρxy in Fig. 3(c) and the peak amplitude of the C cos 2 (ϕ) term in Fig. 3(d) shows that the maximum error introduced by this term in the measurement of ρxy is ≤±3.5%. Moreover, a comparison of the peak value of antisymmetric ρxy (≈3 μΩ cm) at 9 T in Fig. 3(d) with the Hall resistance data shown in Fig. 2 linearized in field (slope ≈ 70 μΩ cm/T) yields a tilt angle of ≈0.6 ○ with respect to the plane of the sample. The angular dependencies of the symmetrized ρxy and ρxx at 2 K for several values of field are shown in Figs. 4(a) and 4(b), respectively. In the plot of Fig. 4(a), the constant offset value of Δρxy at zero-field has been subtracted, whereas Fig. 4(b) displays the variation of ρxx(ϕ) with respect to the average value of ρxx at ϕ = ± 90 ○ . The dominant sin(ϕ) ⋅ cos(ϕ) and cos 2 (ϕ) dependencies of these quantities are evident in Figs. 4(a) and 4(b), respectively. The variation of the peak amplitudes of Δρ PHE and Δρxx (ρxx // − ρxx ) extracted from these plots as a function of magnetic field is shown in Fig. 5. The two important conclusions that can be drawn from these data are: (1) the longitudinal magnetoresistance is positive with a field dependence of the type Δρxx ∼ H α (α = 1.5) and (2) the PHE amplitude is larger than Δρxx.
In the inset of . Two noteworthy conclusions that can be drawn from these data are: (1) the LMR is larger than OMR and (2) the AMR is small but positive, indicating the absence of any chiral anomaly. The resistance tensor of a two-dimensional magnetic film for an in-plane magnetic field predicts that the amplitudes of Δρ PHE and Δρxx should be the same. The large difference seen in the values of Δρ PHE and Δρxx in this case points toward some subtle differences in the origin of these components in the resistance tensor. One might argue 20 that in systems with large orbital magnetoresistance, the out of film plane magnetic field due to sample misalignment may significantly change the value of Δρxx. An estimation of this error can be made by looking at the results of the orbital MR measurements shown in Fig. 5 and the estimated tilt of 0.6 ○ from the antisymmetric ρxy in Fig. 3(d). This much tilt at 9 T would result FIG. 5. Amplitudes of Δρ PHE (ϕ) and Δρxx(ϕ) at 2 K plotted as a function of magnetic field. The inset shows the variation of out-of-plane and in-plane field magnetoresistance and anisotropic magnetoresistance as a function of applied field.

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scitation.org/journal/adv in a ≈95 mT perpendicular field. From Fig. 5, we conclude that the effect of this misalignment of field on the measurement of Δρxx is negligible.
We have also considered the possibility of contamination of Δρxx by the large thermoelectric power of BiSb alloys. 1,2 This effect may get accentuated by the large distance (≈2000 μm) between the Vxx pads compared to the distance (≈300 μm) between Vxy pads if any thermal gradients across the length of the sample are produced by uneven cooling. However, this speculated thermoelectric contribution to the longitudinal voltage will lead to an asymmetry in Vxx at ϕ = 0 ○ and ϕ = 180 ○ , which we do not see. Clearly, the difference in the amplitudes of Δρxx and Δρxy PHE does not appear to be a spurious effect emerging from any misalignment or thermal gradients.  Δρxx are plotted in Fig. 7. The change in the sign of these two quantities appears to correlate with the inflection point in the temperature dependence of ρxx, as can be seen in the inset where we have plotted dρxx/dT vs T.

IV. DISCUSSION
The noteworthy features of the in-plane magnetoresistance of these Bi 85 Sb 15 thin films are: (1) observation of a planar Hall effect, (2) a difference in the amplitudes of Δρ PHE and Δρxx, and (3) a sign reversal of these two quantities in the vicinity of 150 K. Although BiSb is non-magnetic, this first observation of PHE in BiSb is consistent with the recent reports of PHE in non-magnetic semimetals like (Bi 1−x Sbx) 2 Te 3 , 20 bismuth, 31 and MoTe 2 25,26 with non-trivial band topology. The observation of PHE in (Bi 1−x Sbx) 2 Te 3 has been attributed to scattering by magnetic impurities present in the sample. 20 The anisotropy of the Fermi surface and the resulting large difference in the magnetic field dependence of ρ xx and ρ // xx have also been argued to be the source of PHE in some systems. 26,33 We have analyzed the field dependence of ρ xx and ρ // xx at 2 K. The resistance rises as ∼ H α , with α as 1.46 and 1.51 for the and // measurements, respectively. A treatment of electron transport in the framework of a semiclassical Boltzmann transport equation attributes PHE in topological insulators to orbital magnetism of Bloch electrons, which is non-zero because of the symmetry breaking in-plane magnetic field. 22,27 This model, however, does not predict a difference in the value of Δρ PHE and Δρxx. The experimental data of Taskin et al. 20 on the (Bi 1−x Sbx) 2 Te 3 crystal show a large difference in ΔR PHE and ΔRxx, which the authors have attributed to a contamination of the signal by an OMR contribution arising from the misalignment of the sample plane and the plane of rotation. However, this scenario does not apply in the present case as we have shown that the difference in Δρ PHE and Δρxx cannot be attributed to a tilt of the sample plane. Similarly, a change in the sign of planar Hall and anisotropic magnetoresistance at higher temperatures is difficult to explain based on misalignment and/or impurity scattering.
A plausible description of this difference in the amplitudes of Δρ PHE and Δρxx as well as of the sign change has been given by

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Zheng et al. 28 where they consider the tilt of Dirac cones in the TI induced by the in-plane magnetic field. This tilt contributes to anisotropic backscattering, which is enhanced further by impurity resonant states and may lead to a sign change in AMR. The change in the sign of AMR of our BiSb films is consistent with this picture.

V. CONCLUSIONS
In summary, we have addressed the behavior of longitudinal and Hall resistivities of highly oriented thin films of the Bi 85 Sb 15 topological insulator, which has been established as a superior spin torque material for spintronic applications. [11][12][13][14][15] The overall features of the out-of-plane magnetic field transport are comparable to earlier reports on MBE grown films. The in-plane field transport reveals a striking planar Hall effect whose magnitude is larger by a factor of ≈2 as compared to the magnitude of AMR. Moreover, both PHE and AMR undergo a sign change on raising the sample temperature beyond ∼150 K. These new features of the in-plane magnetic field transport presumably arise due to anisotropic scattering of Dirac electrons in a planar magnetic field.