X-ray magnetic circular dichroism study of Dy-doped Bi 2 Te 3 topological insulator thin ﬁ lms Journal of Magnetism and Magnetic Materials

Magnetic doping of topological insulators (TIs) is crucial for unlocking novel quantum phenomena, paving the way for spintronics applications. Recently, we have shown that doping with rare earth ions introduces large magnetic moments and allows for high doping concentrations without the loss of crystal quality, however no long range magnetic order was observed. In Dy-doped Bi 2 Te 3 we found a band gap opening above a critical doping concentration, despite the paramagnetic bulk behavior. Here, we present a surface-sensitive x-ray magnetic circular dichroism (XMCD) study of an in situ cleaved ﬁ lm in the cleanest possible environment. The Dy M 4,5 absorption spectra measured with circularly polarized x-rays are ﬁ tted using multiplet calculations to obtain the effective magnetic moment. Arrott – Noakes plots, measured by the Dy M 5 XMCD as a function of ﬁ eld at low temperatures, give a negative transition temperature. The evaporation of a ferromagnetic Co thin ﬁ lm did not introduce ferromagnetic ordering of the Dy dopants either; instead a lowering of the transition temperature was observed, pointing towards an antiferromagnetic ordering scenario. This result shows that there is a competition between the magnetic exchange interaction and the Zeeman interaction. The latter favors the Co and Dy magnetic moments to be both aligned along the direction of the applied magnetic ﬁ eld, while the exchange interaction is minimized if the Dy and Co atoms are antiferromagnetically coupled, as in zero applied ﬁ eld. CC BY license


Introduction
Magnetic doping of topological insulators (TIs) [1], resulting in the breaking of time-reversal symmetry (TRS), is crucial for unlocking novel quantum phenomena [2]. In three-dimensional TIs, the topological surface state (TSS) is protected by TRS, and magnetic doping leading to long-range ferromagnetic order with outof-plane anisotropy is one possibility to open a gap in the TSS [3]. Such a magnetically induced band gap was first experimentally confirmed in Mn-doped Bi 2 Se 3 using angle-resolved photoemission electron spectroscopy (ARPES) [4]. Long-range ferromagnetic ordering was induced in the prototypical 3D-TIs Bi 2 Se 3 and Bi 2 Te 3 upon Mn [5,6] and Cr doping [7][8][9].
Recently, we have shown that doping Bi 2 Te 3 thin films with rare-earth (RE) ions, such as Gd, Ho, or Dy, introduces large magnetic moments and allows for high doping concentrations, however, no long-range magnetic order was observed [10][11][12][13]. In Dy-doped Bi 2 Te 3 we found a band gap opening above a critical doping concentration using ARPES [14], persisting up to a temperature of 300 K, despite the paramagnetic bulk behavior [13]. However, the question of the origin of this band gap remains unanswered.
Despite the paramagnetic bulk behavior of Dy-doped films, there is the possibility of surface ferromagnetic ordering via the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the localized Dy moments and the TSS [1,3,15,16]. However, recent reports have also shown different scenarios, e.g., a band gap arising from magnetic surface clusters in the case of Cr-doped Bi 2 Se 3 [17], or hybridization causing a temperature-independent gap of ∼100 meV in Mn-doped Bi 2 Se 3 [18]. As the intricate details of the interplay between the competing magnetic interactions depend critically on the chemical potential of the material [19], only surface-sensitive experiments on ultra-clean surfaces can determine the effective magnetic order in a given materials system.
Here, we present a surface-sensitive x-ray magnetic circular dichroism (XMCD) study of the structural and magnetic properties of an in situ cleaved film of Dy-doped Bi 2 Te 3 in the cleanest possible UHV environment [20]. The magnetic order is investigated using the Arrott-Noakes criterion, which yields an estimate of the critical temperature of the sample. No ferromagnetic ordering was found at the surface of a cleaved sample, which is identical to the one that showed a gap opening in ARPES [14]. Next, we attempted to introduce ferromagnetic order via proximity-coupling of Co adatoms. Instead of finding increased ordering, we measured a decrease of the critical temperature of the Dy-doped sample [21], which may be due to antiferromagnetic alignment between the Dy and Co atoms at the interface.

Sample fabrication and magnetic properties
3 thin films, with x denoting the substitutional Dy concentration, were grown by molecular beam epitaxy (MBE) on c-plane sapphire substrates [13]. The rhombohedral films were prepared using a two-step growth recipe with a final substrate temperature of 300°C. The films are free of secondary phases as confirmed by x-ray diffraction and transmission electron microscopy [14]. The growth recipe and the structural properties of the films are described in detail in Refs. [13,14]. The films investigated in this study have a Dy concentration of x¼ 0.055 and 0.113. For the lower concentration the TSS band structure remains intact and shows a linear dispersion, whereas for the higher concentration a sizeable gap was observed in ARPES [14], suggesting a possible change in magnetic properties.
The bulk magnetic properties of ( ) − Dy Bi Te 3 thin films was measured using a superconducting quantum interference device (SQUID) magnetometer with the field applied in-plane; the data is shown in Ref. [13]. No hysteretic behavior is observed. As discussed in detail in Ref. [13], the saturation magnetization of Dydoped samples is doping concentration-dependent-much different from Gd-and Ho-doped Bi 2 Te 3 samples [11,12]. The inverse susceptibility χ = H M 1/ / of the samples can be fitted by a straight line, as expected from a paramagnetic system following the Curie-Weiss law.

Experimental
X-ray absorption spectroscopy (XAS) and XMCD measurements were performed on beamline I10 at the Diamond Light Source, UK, and beamline ID32 at the European Synchrotron Radiation Facility (ESRF), France. XAS was detected simultaneously in bulk-sensitive fluorescence yield (FY) and total-electron-yield (TEY) mode. TEY is surface sensitive giving a probing depth of ∼4 nm at the Co L 2,3 edge [20], increasing to ∼6 nm at the Dy M 4,5 edge [22]. The XMCD was obtained as the difference between two XAS spectra recorded with the helicity vector antiparallel and parallel to the applied magnetic field μ μ ( − ) − + , where μ is the absorption coefficient.
Measurements were performed with the x-ray beam, which is parallel to the applied magnetic field, impinging at 20°grazing incidence on the sample.
XAS and XMCD measurements were performed on the ( ) − Dy Bi Te x x 1 2 3 samples after in situ cleaving in the UHV environment ( ≤ − 10 9 Torr) of the superconducting magnet chamber. The XAS and XMCD spectra for the x ¼0.055 sample are shown in Fig. 1 (a) and (b), respectively, measured in both TEY and FY mode. The maximum of the Dy M 5 edge is located at 1292.9 eV photon energy [22]. There are considerable differences in line shape between the TEY and FY spectra that are not due to saturation and self-absorption effects, which are small for low concentrations. A comparison for the Dy M 5 XMCD shows that the positive peak at ∼1289 eV is smaller, but the negative peak at ∼1293 eV is larger in FY than in TEY. This behavior is in agreement with the multiplet spectra calculated by van Veenendaal and Benoist [23]. The reason for the discrepancy is that, in contrast to the TEY, the FY is not proportional to the absorption cross-section because it also depends on the decay rate. The latter varies with the intermediate (XAS) state, where states at higher photon energies normally have higher fluorescence decay rates [20].
Ferromagnetic Co was evaporated onto the pristine surface of the x ¼0.055 sample, with the goal of introducing or enhancing the ferromagnetic order through proximity coupling [21], using an electron beam-evaporator mounted in the XAS measurement chamber. The sample was kept at 10 K during this process to inhibit reactions between the incident Co atoms and the clean sample surface [24]. The base pressure during evaporation was < × − 1 10 9 Torr. The XMCD measurements were performed in regular intervals during the deposition to check lineshape and remanent magnetization. This way, the final thickness of the Co layer was determined to be ∼3 nm. Fig. 1(c) and (d) shows the XAS and XMCD for the thin Co layer deposited onto the cleaved sample. The spectra show no evidence of alloying between Co and the underlying sample.
The magnetic proximity effect in the Dy-doped TI is measured using the surface sensitive TEY signal, which only probes the region close to the Co capping.

Calculated spectra
Electric-dipole transitions from the d 3 core level in REs are allowed to empty f 4 states, but forbidden to d 5 and s 6 valence states. For the multi-electronic configuration of the 9 1 0 transitions can be calculated using atomic multiplet  [25][26][27].
Following the standard procedure to account for interatomic interactions [22], the parameters of the Slater integrals for the Coulomb and exchange interactions were reduced to 65%, while the spin-orbit interaction was kept at 100%. The Dy M 5 (M 4 ) line spectra were convoluted by a Lorentzian of Γ¼0.25 eV (0.5 eV) for intrinsic lifetime broadening and a Gaussian of σ = 0.35 eV for instrumental broadening. The intrinsic lifetime at the M 4 is broader than at the M 5 edge due to Coster-Kronig decay [22].
The calculated spectra I q are shown in Fig. 2 ; for sign convention see Ref. [20].
Sum rules relate the integrated intensities of the XAS and XMCD M 4,5 spectra to the ground state expectation values of the orbital and spin moments [28,29], and were used for the L 2,3 edges of Mn, Fe, and Co dopants and adatoms in TIs [9,24].
For the REs the sum rule analysis is less straightforward [30] because of (i) the large jj mixing between the d 3 5/2 and d 3 3/2 , which requires a correction factor, (ii) the linear dichroism, which has to be taken into account in the sum spectra for the normalization per hole, and (iii) the presence of a usually large magnetic dipole term T z .
Under the condition that the f 4 crystalline electrostatic field is small compared to the f 4 spin-orbit interaction, the spin and orbital moments remain parallel, so that their ratio is fixed [31]. Then, as a function of the magnetization, M, the XMCD intensity scales with M, while the isotropic intensity remains constant. Thus the scaling factor for the magnetic moment is directly obtained from the reduction in the asymmetry 1 . This method has been used in Refs. [6,11].
Here, we will employ an alternative method to determine the magnetic moments. This method is based on the fact that for most heavy REs the multiplet structure has distinct peaks that can be assigned to left-and right-circular polarization [22]. The Dy M 5 absorption structure is well suited to determine the relative contributions of the three fundamental spectra, I À 1 , I 0 , and + I 1 , since their respective peaks are well separated in photon energy by ∼2 eV each. Fig. 2(a) shows that the main peak at 1292.9 eV is almost purely + I 1 with only a few percent of I 0 . Likewise, the lowenergy peak is almost purely I À 1 . On the other hand, the M 4 intensity is much lower and less suitable for polarization analysis. Nonetheless, also here the measured XAS and XMCD is in good agreement with the calculation [22,32].
The experimental Dy M 4,5 spectra, μ À and μ þ , for the cleaved sample with x¼ 0.055 at 7 T and 6.2 K at grazing incidence were fitted using the calculated I À 1 , I 0 , and + I 1 spectra from Fig. 2(a). Results are shown in Fig. 2(b which gives polarization scaling factors for the magnetic moment of 0.545 and 0.427, respectively. The polarization factor for μ + is lower due to the extra intensity in the experimental spectra around 1296 eV, which is less pronounced in the calculation. Since the μ À spectrum shows no such deficiency, its result is more accurate. Hence we take the somewhat higher polarization factor for μ À .
The LS-coupled Hund's rule ground state, . Assuming that the x-ray beam is fully polarized, the μ À spectrum gives a magnetic moment that is 54.5% of the Hund's rule ground state value. Hence, from the XMCD on our sample, we obtain an effective magnetic moment of μ μ = 5.8 /Dy eff B . SQUID magnetometry of this sample yielded a saturation magnetization of μ μ ≈ 8.3 /Dy eff B , which is also less than the free ion Hund's rule value. While the XMCD measures only the f 4 moment on the Dy atoms, SQUID measures all moments including also the Dy d 5 moment and any induced magnetization on the Te atoms.
These results show that the Dy atoms are far from completely magnetized. However, the observed dichroism is similar in size as was seen for other polarized Dy spectra in the literature [33][34][35]. We expect that the common cause of the reduced moment is the Experimental μ þ and μ À spectra (solid red lines) of the cleaved sample with x ¼0.055 at 7 T and 6.2 K at grazing incidence, and their sum and difference spectra compared with the calculated spectra (dash-dotted blue lines). The experimental spectra were fitted with the calculated spectra I À 1 , I 0 , and + I 1 from (a), yielding the relative intensity ratios given in Eq. (1). Spectra have been offset for clarity. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.) presence of a small crystal field on the Dy f 4 electrons. Crystal-field effects might play an important role in explaining the reduction of the effective magnetic moment observed for Dy dopants since the Dy atoms are substituting Bi in the Bi 2 Te 3 lattice, which are in an octahedral environment of Te atoms. The importance of crystal field effects at low temperatures is well established in the literature, but difficult to quantify theoretically [36].

Arrott-Noakes analysis
In order to investigate the magnetic order on the surface of the pristine ( ) − Dy Bi Te 3 thin film, the critical behavior was analyzed using the Arrott-Noakes plot criterion. This leads to an estimation of the critical temperature, T C , of a transition from a non-magnetic to a magnetically ordered system. The criterion consists of plotting the isothermal variations of M 2 as a function of H M / , with M being the magnetization and H the applied field, which should yield straight lines according to [21,37] where T is the temperature, and A and B are constants. The intercept of the isotherms with the H M / axis, i.e., where = M 0 2 , is positive (negative) for > T T C ( < ) T T C , so that T C is equal to that temperature for which the intercept is zero.
Arrott and Noakes [38] generalized this criterion to express the equation of state for a magnetic system near its critical temperature in terms of the critical exponents β and γ, as where C 1 and C 2 are constants. In the long-range mean-field model, these exponents are β = 0.5 and γ = 1, which yields Eq. (2).
In the nearest-neighbor 3D Heisenberg model, the corresponding values are β = 0.36 and γ = 1.386. Fig. 3 (Fig. 3(b) and (e)) do not yield linear behavior, which indicates that the mean-field model does not appropriately describe this material. Instead, we applied the Arrott-Noakes criterion which uses the values of β and γ for the 3D Heisenberg model. These curves are shown in Fig. 3 (c) and (f). By fitting parallel straight lines to the high-field regions (forcing the gradient of all lines to the same value) we obtain the ( ) γ H M / 1/ intercepts, collected in Fig. 5(a). The zero points of these intercepts give = ( − ± ) T 14 1 C K and ( − ± ) 9 2 K for the TEY and FY data, respectively.
Similarly, M vs H, Arrott, and Arrott-Noakes plots for the x¼ 0.055 sample are shown in Fig. 4. A comparison of the M vs H plot obtained for the as-cleaved sample and that with the Co overlayer measured at 14 K is depicted in Fig. 4(a). The fact that the latter curve lies underneath the as-cleaved sample indicates a decrease in M, which, at the same time, suggests a decrease in T C for the Dy atoms at the interface of the Dy-doped sample and the Co layer.
The full set of Arrott-Noakes plots, measured in TEY mode, for the x ¼0.055 sample with an Co overlayer are shown in Fig. 4(d). The ( ) γ H M / 1/ -intercepts obtained from the linear fits of the highfield region of each isotherm are plotted in Fig. 5(b). T C extracted from the zero point of the intercept yields a value of ( − ± ) 2.0 0.8 K. Note that this value is greater than that found for the x¼0.113 sample ( − ± ) 14 1 K , but given the different Dy doping concentrations for the two samples resulting in different magnetic properties [13], only the relative trends can be compared.
These results show that the Co top layer has an adverse effect on the magnetic ordering of the Dy dopants in the Bi 2 Te 3 sample in that T C is decreased. This suggests antiferromagnetic coupling between the Co and Dy atoms at the interface. Even though the Co L 2,3 XMCD measured in remanence does not indicate antiferromagnetic coupling, one has to bear in mind that, at the temperatures measured, the ( ) − Dy Bi Te 3 film is paramagnetic so that the exchange interaction between Dy and Co atoms is weak. Furthermore, the remanent field of the superconducting magnet of ∼30 mT may be enough to align the Dy and Co atoms.
In RE-transition metal (TM) compounds, the TM d 3 orbitals are hybridized with the RE d 5 orbitals with an antiferromagnetic coupling between the spins. In the RE atom, the localized f 4 electrons couple parallel to the d 5 spins, so that the resulting indirect f 4d 3 exchange coupling is antiferromagnetic [39]. This has been experimentally confirmed for Dy/Fe and Dy/FeCo amorphous alloys [40] and − Dy Co compounds [41]. This mechanism also holds for RE-TM interface layers, such as Gd/Fe [42], Gd/CoFe, Tb/ NiFe [43], and Dy/CoFe [44]. While magnetically doped TIs do not necessarily behave the same as the aforementioned alloys, compounds, or layer systems, it indicates that an antiferromagnetic coupling is possible.
Clearly, our experimental results show that there is a competition between the magnetic exchange interaction and the Zeeman interaction. The latter favors the Co and Dy magnetic moments to be both aligned in the direction of the applied magnetic field, whereas the atomic exchange interaction is minimized if the Dy and Co atoms are antiferromagnetically aligned, i.e., in zero applied field. However, in order to measure the magnetic moments an applied field is needed to align them. This dilemma is broken by using Arrott plots, where extrapolation to zero field evidences an antiferromagnetic coupling.

Summary and conclusions
In summary, we studied the magnetic properties of the surfaces of Dy-doped Bi 2 Te 3 in greater detail using surface-sensitive XMCD on in situ cleaved thin films. We determined the effective magnetic moment for the x¼ 0.055 sample in 7 T field at 6.2 K from multiplet calculation fits to the circularly polarized Dy M 4,5 spectra to μ ∼5.8 /Dy B . Co adatoms were deposited in an attempt to introduce ferromagnetic long-range order in the films. Using XAS, no change in the chemical state of the Dy atoms was observed as is, in principle, ideal for proximity coupling to the Dy-doped films. The magnetic order on the surfaces was studied in detail using the Arrott-Noakes analysis of the XMCD hysteresis plots as a function of temperature. Using the nearest-neighbor 3D Heisenberg model, the intercepts yield a transition temperature of about À 14 K in surface-sensitive TEY mode of the as-cleaved film (x ¼0.113). For the x ¼0.055 film, the proximity-coupling to the Co layer gave a lowering of the transition temperature, which suggests an antiferromagnetic ordering scenario. In conclusion we have addressed the outstanding question of ferromagnetism in Dy-doped Bi 2 Te 3 , finding no evidence of it down to 5 K. This means that another mechanism is responsible for the gap opening seen in these films in ARPES [14]. Our data provides weak indications of an interaction scenario consistent with antiferromagnetic ordering. Recently, it has been reported that antiferromagnetically ordered surfaces could (locally) break TRS, leading to a gap opening [45], which is an interesting concept to explore in the future.