Local magnetic behaviour of highly disordered undoped and Co-doped Bi2Se3 nanoplates: a muon spin relaxation study

Figure 1(a) shows the XRD patterns of the Co_x Bi_2−x Se₃ (where x = 0 and 0.1) samples, and the peak identifications on comparison with joint committee on powder diffraction standards data. Most of the peaks can be matched with the rhombohedral structure of Bi₂Se₃. The additional XRD peaks in Bi₂Se₃ sample correspond to insignificant Se and Bi₂O₃ impurities. For x = 0.1 sample, the XRD peaks are shifted to slightly higher 2θ values, indicating the substitutional doping of Co at Bi sites. Figure 1(b) shows an enlarged view of the (1010) peaks with their Gaussian fits to highlight the shift. The lattice constant c is calculated and plotted in figure 1(c). The lattice constant c of x = 0.1 is decreased to about ∼0.4% as compared to pure Bi₂Se₃ (x = 0) which further confirms the substitutional doping. As atomic radius of Co (0.125 nm) is smaller than atomic radius of Bi (0.163 nm), a decrease in c value is expected for substitutional doping. An impurity peak at 45.9°, corresponding to the (102) reflection of CoSe, emerges on doping, but it is also insignificant to affect the studied results to any considerable extent. Thus, almost phase-pure Bi₂Se₃ and Co_0.1Bi_1.9Se₃ samples are prepared. The segregation of CoSe phase already at x = 0.1 suggests that for any other x > 0.1 more of the Co atoms would be left undissolved (i.e. would not occupy the substitutional sites). Hence, taking x > 0.1 is undesirable. Figures 2(a)–(c) show the high-resolution XPS spectra and their deconvolutions in Bi 4f, Se 3d, and Co 2p regions. The Bi 4f spectra of both the samples have a major contribution from Bi₂Se₃ represented by the peaks at ∼157.4 eV for Bi 4f_7/2 [41], and a minor contribution from Bi₂O₃ represented by the peaks at ∼158.3 eV for Bi 4f_7/2 [42]. The Bi 4f_7/2 peaks are accompanied by the corresponding Bi 4f_5/2 peaks with a spin–orbit splitting of 5.3 eV. The Se XPS spectra of both the samples can be deconvoluted into a major Bi₂Se₃ component, 3d_5/2 and 3d_3/2 peaks appearing respectively at ∼52.9 and 53.7 eV [41], and a minor Se metal component with the 3d_5/2 and 3d_3/2 peaks at ∼54.9 and 55.7 eV [43]. The broad peak at ∼58 eV is attributable to loss features [43]. There are slight lower binding energy shifts in the Bi and Se peaks on Co doping, confirming the substitutional incorporation of Co at Bi sites [44], as also revealed by XRD. Figure 2(d) shows the variation of Bi and Se peak positions with x. The Bi 4f_7/2 and Se 3d_5/2 peaks in doped sample (x = 0.1) are shifted to lower binding energies with a shift of ∼0.04% compared to pure Bi₂Se₃ (x = 0). The shift further confirms substitutional incorporation of Co in Bi sites. The Co 2p spectrum of the Co-doped sample is deconvolutable into two spin–orbit doublets characteristic of Co²⁺ and Co³⁺, and two shake-up satellites [45].

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figures 3(a) and (c) show respectively the TEM images of the undoped and Co-doped samples, while the corresponding high-resolution images and selected area electron diffraction (SAED) patterns are shown in figures 3(b) and (d), respectively. From the images, the hexagonal morphology (∼200 nm lateral sizes) of the nanoplates, and their agglomeration on Co doping, can be seen. The lattice planes are clearly observable with lattice spacings of 0.20 nm corresponding to the (110) plane of Bi₂Se₃ for the undoped sample, and 0.22 nm corresponding to the (1010) plane of Bi₂Se₃ for the Co-doped sample. The SAED patterns of both the samples show weak and bright diffraction spots. The weak spots may have originated from either (i) the projections of diffractions from higher Lane zone(s) due to the large lattice parameter along the c axis and the low thickness of Bi₂Se₃ nanoplates (∼20 nm) along the c axis [46], or (ii) the presence of antisite defects or incomplete layers [47]. The clear lattice fringes in the high resolution TEM patterns, along with the spotty SAED patterns, confirm a good crystallinity of the samples.

Zoom In Zoom Out Reset image size

The temperature-dependent magnetizations measured in an applied field (H) of 500 Oe under zero-field-cooled (ZFC) and field-cooled (FC) conditions are shown in figure 4(a). For both the samples, the ZFC and FC curves start splitting from room temperature itself, which is an indication of the presence of a major magnetic component [44, 48]. Apart from the splitting, there is a broad shoulder near 250 K in the FC curves of both the samples, which is suggestive of the samples being superparamagnetic with a large nanoplate size distribution [44]. The upturns in both the ZFC and FC curves in both the cases suggest an additional paramagnetic (PM) phase that could be due to relatively disordered surface spins [44]. In line with our earlier report [44], each nanoparticle can be crudely modelled as having a relatively ordered core, and a relatively disordered shell with the exchange interaction J_s between the surface moments being less than the exchange interaction J in the core. The M–H curves recorded at various temperatures for the Bi₂Se₃ nanoplates are shown in figure 4(b). The occurrence of hysteresis loops and the non-saturation of the M–H curves indicate the presence of both ferromagnetic (FM) and PM phases in the sample, and thus corroborate the above picture.

Zoom In Zoom Out Reset image size

For the origin of magnetic moments responsible for the observed magnetism in pure Bi₂Se₃, which otherwise must be diamagnetic [18, 49], our recent paper [32] can be referred to. According to this, each of the Bi vacancies and Bi_Se anti-site defects carries a magnetic moment of 1.0 μ _B . After subtracting the linear (PM) component from the 10 K M–H curve of the Bi₂Se₃ sample, ∼0.16 emu g⁻¹ saturation magnetization can be obtained, which is equivalent to a magnetic moment of 0.018 μ _B /f.u. This is equivalent to a defect density of ∼10²⁰ defects/cm³, i.e. ∼1.8 atomic%. This is an order of magnitude higher than the defect density reported in the referred paper [32], which itself was considered to make the Bi₂Se₃ nanoplates highly disordered.

Figure 5(a) shows the M–H curves of the Co-doped sample, wherein the hysteresis (inset) and the non-saturation upto the maximum applied field suggest that both the FM and PM phases are retained on doping. The saturation magnetization obtained by subtracting the linear PM component at 10 K is ∼0.5 emu g⁻¹, which is more than three times the undoped value, and thus indicates an enhancement in magnetism on doping. This is equivalent to a magnetic moment of ∼0.06 μ _B /f.u. According to the DFT computations as represented by the Co 3d partial DOS in figure 5(b), each Co atom attains a moment of 2.28 μ _B , while there are no induced moments on Bi and Se atoms. This converts to 0.046 μ _B /f.u. contribution from Co. Adding the 0.018 μ _B /f.u. defect contribution because the defects are anyway also present, this leads to a total of 0.064 μ _B /f.u., which justifies the experimentally observed value ∼0.06 μ _B /f.u. Further, the 10 K hysteresis loop of the Co-doped sample is wider than the corresponding loop of the pure Bi₂Se₃ sample. This means, there is an overall enhancement in the magnetic order on Co doping. In terms of the magnetic core–shell picture presented above, the moments in both the core and the shell appear to get more ordered on Co doping.

Zoom In Zoom Out Reset image size

Figures 6(a) and (b) show the ZF μSR asymmetry A(t) spectra of pure and Co-doped Bi₂Se₃ samples at various temperatures; the insets show a comparison between the corresponding zero-field (ZF) and longitudinal field (LF) spectra at 2 K. For both the samples, there are following three common qualitative observations from the ZF spectra: (i) there is a successive loss in the initial asymmetry with decreasing temperature, (ii) there are no oscillations, and (iii) the asymmetry shows a qualitatively exponential decay with time. For long-range magnetic ordering when electronic static fields are present, an oscillatory signal with a frequency proportional to the local field at the muon site is, in general, expected. However, such oscillations, if present, might depolarize rapidly [50], and die before the occurrence of the first data point (0.22 μs) obtainable with the ISIS spectrometer. In this situation, the magnetic order will reflect as a loss in the initial asymmetry [51]. Therefore, the first two observations together signify the presence of a long-range magnetic order, although the corresponding electronic static field is not derivable from the present data. The full asymmetry achievable with the ISIS instrument is 0.22 for purely fluctuating moments, and the initial room temperature ZF asymmetry of the undoped sample is ∼0.23. So, at room temperature, the undoped sample has little static component. However, the corresponding value for the Co-doped sample is ∼0.20. This qualitative comparison is valid at all the temperatures. So, the Co-doped sample is magnetically more ordered and thus has more electronic static component. In the absence of electronic static moments, i.e. when only the nuclear static fields are present, a longitudinally applied 20 G field is typically sufficient to decouple the ZF and LF spectra [52]. So, a slightly incomplete decoupling of the 2 K ZF and LF spectra of the undoped sample (the inset of figure 6(a)) is an additional signature of the presence of static electronic moments in this sample at this temperature. The perception that the doped sample is more ordered is further strengthened by the even less incomplete decoupling of the 2 K ZF and LF spectra of this sample, as shown in the inset of figure 6(b).

Zoom In Zoom Out Reset image size

If there are also dynamic moment fluctuations, they result in an exponential decay of asymmetry at longer times [50]. The third observation, i.e. the qualitative exponential decay of all the asymmetry spectra, thus, suggests that there are also dynamic moment fluctuations in both the samples, apart from the (unquantifiable) static fields. This conjecture is further assisted by the fact that ZF μSR spectra of both the samples can be best fitted using an exponential function plus a constant background of the form:

$$\begin{eqnarray}&&A(t)={A}_{0}\,{e}^{-\lambda t}+{A}_{B},\end{eqnarray} \tag{ 1 }$$

where A₀ is the effective initial asymmetry, λ is the electronic relaxation rate, and A_B is the temperature independent background that would appear when a fraction of muons cross the sample and stop in the Ag sample holder. The relaxation rate is given by λ = $2{{{\rm{\Delta }}}_{{dyn}}}^{2}/\nu$, where Δ_dyn /γ_μ (γ_μ = 2 π × 135.5 MHz T⁻¹ is the muon gyromagnetic ratio) is the dynamic field distribution width and ν is the frequency of fluctuation of the electronic moments [53].

The temperature dependence of A₀, as obtained from the fittings, is shown in figure 6(c) for both the samples. We analyze the two curves one by one. In the case of undoped Bi₂Se₃, starting from 300 K, the curve appears to have a constant (saturation) value of ∼0.180 till ∼265 K, then decreases monotonically to ∼0.124 at ∼65 K, and then remains roughly constant down to 2 K. The maximum (saturation) in A₀ occurring near 300 K is indicative of the presence of purely dynamic moments at these temperatures. In the ideal situation of a PM (completely disordered) to FM (completely ordered) phase transition, A₀ is expected to drop to A₀/3 sharply at the transition temperature [53]. A reduction in A₀ is a qualitative measure of the spin fluctuation frequency ν that is supposed to have a high value in the disordered state and become zero in the ordered state. There are two deviations in the present data from the ideal: (i) A₀ does not drop to A₀/3 = 0.06 at low temperatures; it is 0.124–0.06 = 0.064 higher than for a single-component magnetically ordered (like FM) material. This indicates that there is another more disordered component, the spin fluctuations of which do not get arrested at the lowest measured temperatures [53]. This substantiates the conjecture that the sample is composed of a relatively ordered core (with a relatively large exchange interaction J) and a relatively disordered shell (with a relatively small exchange interaction J_s ). (ii) The transition is very broad (65–265 K). This is a signature of the high structural disorder [53], as has been inferred earlier. In the case of Co-doped sample, however, the following three observations can be noted: (i) the room temperature initial asymmetry has not reached the corresponding value obtained for the undoped sample. This means, the sample has a larger ordered (static) component than possessed by the undoped sample even at 300 K. This additional order is brought in by the larger Co moments over and above the smaller defect moments. This appears to have strengthened both the exchange interactions J and J_s to some J⁺ > J and ${{J}_{s}}^{+}\gt {J}_{s}$, respectively. This is the reason for the A₀ value of the doped sample to be systematically smaller than the corresponding undoped value at all the temperatures. (ii) The 2 K initial asymmetry is still way above the ideal 0.062 value. This means, the dynamically fluctuating spins corresponding to the shell have not been arrested even at this temperature, although they are now slower than those in the undoped sample because of the enhanced exchange interaction. (iii) A₀ decreases essentially monotonically from 300 to 2 K without any saturation. This is likely due to the additional structural disorder that has been generated on Co doping.

The λ versus T curves for the two samples are shown in figure 6(d). If we ignore the kinks occurring at ∼135 K to avoid any over-interpretation of the results obtainable with the present limited data, both the curves appear to increase monotonically on temperature reduction. If we further assume that Δ_dyn has a rather weak temperature dependence, this monotonic rise in λ signifies decreasing moment fluctuation (rate) on decreasing the temperature. This is in line with the inference made from the A₀ versus T curves. Further, the systematically higher λ for the doped sample than for the undoped sample at all the temperatures gives an additional support to the earlier conjecture that the doped sample has more order (less moment fluctuations) than the undoped one.

To summarize the μSR results, both the pure and Co doped Bi₂Se₃ nanoplates comprise of two magnetically separate regions: (i) a core with both static fields and dynamically fluctuating moments, typical of an FM materials, and (ii) a shell with purely dynamically fluctuating moments, akin to a PM material. This is in agreement with the macroscopic observations of both FM and PM states in the samples. The fluctuations slow down with temperature reduction. In the core, this results in a gradual enhancement of the static component. In this volume, the fluctuations are apparently arrested fully at the lowest temperatures, giving way to a fully static field (ordered state) at these temperatures. The transition between the fully static and (nearly) fully dynamic states is broad due to the high structural disorder arising from the defects. The moment fluctuations of the shell also slow down with decreasing temperature, but are still present at the lowest temperatures as in a PM material. The Co doped sample has slower fluctuations (more magnetic order) than the undoped sample at all temperatures, and the transition between the fully static to fully dynamic states could not take complete in the measured temperature range. It can be conjectured that the high concentration of magnetic moments associated with the defects in highly disordered Bi₂Se₃ nanoplates act as normal magnetic dopants; magnetic (Co) doping enhances the magnetism further. So, it would perhaps not be wrong to say that highly disordered TI's could act as magnetic materials even without any magnetic ions, and their magnetic properties can be engineered by magnetic impurity doping.