Evidence of a topological Hall effect in Eu_1−xSm_xTiO₃ Free

The topological Hall effect (THE) is a hallmark of topologically nontrivial (chiral) spin textures such as skyrmions and can be observed as a distinct, additional contribution in Hall measurements which is superposed on the ordinary and anomalous Hall effects.^1,2 It arises from the Berry phase that the conduction electrons acquire when moving in the topologically protected spin texture.^3–5 Skyrmions are a result of the Dzyaloshinskii-Moriya interaction in chiral magnets with a non-centrosymmetric crystal structure, such as MnSi,⁶ and they have generated significant interest for applications in nonvolatile memories.² The topological Hall effect has also been observed in centrosymmetric crystals such as SrFe_1−xCo_xO₃ and pyrochlores,^7,8 where helical structures form as a result of magnetic frustration, and in thin films, where inversion symmetry may be lifted by interfaces and surfaces.^9,10 Oxide films and interfaces that support topologically nontrivial spin textures and whose carrier density can be manipulated are interesting because of the potential for control by electric field effects and because proximity effects can be utilized to realize other exotic states within all-epitaxial heterostructures.

Doped EuTiO₃ films are attractive for such approaches. In its stoichiometric form, EuTiO₃ is a quantum paraelectric with the cubic perovskite structure at room temperature, similar to SrTiO₃.^11,12 The Eu magnetic moments [4f⁷ (S = 7/2)] order in a G-type antiferromagnetic pattern below the Neel temperature of 5.5 K.^13–15 Strained EuTiO₃ films can become simultaneously ferromagnetic and ferroelectric at low temperatures.¹⁶ Chemical doping, i.e., substitution of Eu⁺² with a trivalent rare earth ion, introduces itinerant electrons into the Ti 3d t_2g derived conduction band states. The material then becomes a ferromagnetic metal due to Ruderman-Kittel-Kasuya-Yosida (RKKY) type interactions between the localized 4f and itinerant 3d t_2g electrons.^17,18 La-doped EuTiO₃ films exhibit a strong anomalous Hall effect (AHE) whose sign can be manipulated by the carrier density.¹⁸ Here, we investigate Eu_1−xSm_xTiO₃ thin films grown by hybrid molecular beam epitaxy (MBE). We show that in addition to a positive AHE, a topological Hall effect (THE) component appears in the Hall measurements at temperatures below 5 K.

Epitaxial, 50-nm-thick Eu_1−xSm_xTiO₃ layers were grown by MBE on (001) (La_0.3Sr_0.7) (Al_0.65Ta_0.35)O₃ (LSAT) single crystals. Elemental Eu and a metalorganic compound, titanium tetra isopropoxide (TTIP), were used to supply Eu, Ti, and oxygen. The MBE approach is similar to that previously used for SrTiO₃,^19,20 except that no extra oxygen was supplied. X-ray diffraction (XRD) showed that the films were of single-phase, and thickness fringes indicated smooth films of high structural quality (see supplementary material). Electron beam evaporation through a shadow mask was used to deposit Au/Ti (400/40 nm) contacts for Hall and longitudinal (magneto-)resistance measurements using square Van der Pauw structures that were contacted via Au wire bonds. Temperature (T) dependent magnetotransport measurements were carried out using a Quantum Design Physical Property Measurement System (PPMS) with an excitation current of 20 μA. A dilution refrigerator was used for some of the data shown in the supplementary material.

Figure 1(a) shows the sheet resistance R_s as a function of temperature for Eu_1−xSm_xTiO₃ thin films with x = 0 and x = 0.045. The nominally undoped EuTiO₃ film is highly resistive and quickly exceeds the measurement limit below room temperature, while the doped sample shows metallic (dR_s/dT > 0) behavior. Figure 1(b) shows the temperature dependence of the carrier concentration for the Eu_0.955Sm_0.045TiO₃ film as determined from the ordinary Hall effect. The room temperature carrier concentration is 9 × 10²⁰ cm⁻³, close to the expected carrier density (8 × 10²⁰ cm⁻³) from the nominal doping concentration. It shows some temperature dependence, which may indicate some carrier trapping and can also be a result of the particular behavior of Hall and resistance scattering rates, typical for these oxides, as discussed elsewhere.^21,22

Figure 2(a) shows the temperature dependence of R_s under various magnetic fields (B) applied normal to the film (B = 0, 1, 3, 6, and 9 T) at low temperatures (2 K–50 K) for the Eu_0.955Sm_0.045TiO₃ film. Without B, an upturn in R_s emerges at 20 K followed by a sharp drop at ∼6 K. The magnetic field suppresses the upturn systematically until it almost vanishes at 9 T. A similar behavior was reported previously for La¹⁷ and Nb²³-doped EuTiO₃ and is due to the alignment of the localized spins under the magnetic field, which reduces the resistance. Figure 2(b) shows R vs. B (magnetoresistance) for the Eu_0.955Sm_0.045TiO₃ film at 2 K, 5 K, 10 K, and 15 K, respectively. Here, B was swept from −9 T to +9 T and back. All samples show negative magnetoresistance, which peaks at 5 K, consistent with Fig. 2(a). Hysteresis in the magnetoresistance can be noticed at 5 K and below [see also Fig. 2(c)]. The hysteresis confirms the ferromagnetism reported in the literature.^17,18

Figures 3(a) and 3(b) show the Hall results for the Eu_0.955Sm_0.045TiO₃ film at T = 2 K (a) and 5 K (b), respectively. The Hall data were antisymmetrized to eliminate the magnetoresistance contribution, i.e., $Rxy=Rxyraw+B−Rxyraw−B/2$⁠, where the superscript indicates the raw data. A linear fit to R_xy at high B (6 T–9 T) yields the ordinary Hall component (R₀B) and is also shown. Comparing the two curves shows that at low fields, R_xy deviates from linearity. In the presence of an AHE and/or a THE, R_xy is given by $Rxy=R0H+RAHE+RTHE$⁠, where $RAHE$ and $RTHE$ are the anomalous and topological effects, respectively.^1,2 Figures 3(c) and 3(d) show the data after subtraction of R₀B from R_xy at T = 2 K (c) and additional temperatures (d), respectively. At 5 K and above, the monotonic increase in the resistivity with B is characteristic of the conventional AHE, described as $RAHE=αMRxx0+βMRxx02+γMRxx2$⁠, where $α, β, and γ$ are the coefficients of skew scattering, side jump, and intrinsic components, respectively, and $Rxx0$ is the residual resistance.²⁴ In these films, it is expected that the high resistivity (∼10⁻⁴ Ω cm) causes the AHE to be dominated by the intrinsic, Berry phase contribution.²⁵ 

At 2 K [Fig. 3(c)], peaks appear in addition to the AHE. The peak at ∼0.8 T (stronger in upward than downward sweep) is near the field at which the closure of the hysteresis is seen in the magnetoresistance data shown in Fig. 2(b). A second, more pronounced peak at ∼2 T has no corresponding feature in the magnetoresistance. These general features are very similar to the THE signal found in a wide range of other materials with magnetic skyrmions.^1,2,9 Their origin is magnetic as the peaks only appear below the Curie temperature. Therefore, nonmagnetic phenomena such as multicarrier Hall response cannot be the origin. Furthermore, they can be suppressed with an in-plane field (see supplementary material), which indicates that a two-dimensional spin texture gives rise to the THE.⁹ It is interesting that the THE only appears at 2 K, whereas the AHE and magnetoresistance hysteresis are already pronounced at 5 K, which may indicate a possible phase transition to a topological non-trivial spin structure. Preliminary measurements at 40 mK indicate that the features assigned here to the THE persist to very low temperatures (see supplementary material). This indicates that the THE can be associated with a non-collinear structure. The persistence to low temperatures can be contrasted with that of helical MnSi, where thermal fluctuations are required to stabilize the skyrmion state.⁶ It is important to note, however, that chiral magnetic textures with zero topological charge can exhibit Hall effects that are quite similar to the THE of magnetic skyrmions.^26,27 Therefore, future experiments should focus on an independent measurement that could confirm a topologically non-trivial spin structure.

In conclusion, undoped and Sm-doped EuTiO₃ films were grown by MBE. The Sm-doped sample is an itinerant ferromagnet below 5 K which exhibits the AHE. At 2 K, signatures of a THE are observed which are indicative of a non-trivial spin structure. Further investigations of the spin texture and determining the space group of compressively strained films, which may be non-centrosymmetric,¹⁶ should allow for insights into the origin of the spin structures that give rise to the THE. The results open a wealth of possibilities for future investigation. Because the carrier density can be tuned, this may allow for studies of a quantized THE.²⁸ Interfaces with other rare earth titanates may allow for interfacial electron systems due to the polar discontinuity, in analogy with GdTiO₃/SrTiO₃ and SmTiO₃/SrTiO₃,²⁹ introducing charge carriers without chemical doping and reducing disorder. Finally, EuTiO₃ is perfectly lattice matched with SrTiO₃, which can be superconducting, and their combination in epitaxial structures may be of interest for novel superconducting states.^30,31

See supplementary material for XRD data and measurements of the THE as a function of the magnetic field orientation and at 40 mK.

We acknowledge support from the U.S. Army Research Office (No. W911NF-14-1-0379) and FAME, one of the six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA. The dilution fridge used in the measurements was funded through the Major Research Instrumentation program of the U.S. National Science Foundation (Award No. DMR 1531389). This work made also use of the Central facilities supported by the MRSEC Program of the U.S. National Science Foundation under Award No. DMR 1121053.