Zero-field topological Hall effect in BiSb/MnGa bi-layers as a signature of ground-state skyrmions at room temperature

We observe the signature of zero-field ground-state skyrmions in BiSb topological insulator / MnGa bi-layers by using the topological Hall effect (THE). We observe a large critical interfacial Dzyaloshinskii-Moriya-Interaction energy ( S C D = 5.0 pJ/m) at the BiSb/MnGa interface that can be tailored by controlling the annealing temperature Tan of the MnGa template. The THE was observed at room temperature even under absence of an external magnetic field, which gives the strong evidence for the existence of thermodynamically stable skyrmions in MnGa/BiSb bi-layers. Our results will give insight into the role of interfacial DMI tailored by suitable material choice and growth technique for generation of stable skyrmions at room temperature.

are meta-stable at zero magnetic field; they can be generated by applying external perturbation such as heating, 16 bipolar pulses of magnetic field, 11 or "blowing" through a narrow channel, 17,18 and can be erased by a large magnetic field. Such meta-stable skyrmions are suitable for race-track memories. On the other hand, stable (ground-state) skyrmions, which spontaneously emerge under zero magnetic field, are suitable for Brownian computing applications. Figure 1 shows the energy landscape of meta-stable and stable skyrmions under zero magnetic field as a function of the skyrmion number S. Here, S = 0,1 correspond to the ferromagnetic (FM) state and skyrmionic (SK) state, respectively. The energy of the meta-stable SK state is higher than that of the FM state, while that of the stable SK state is lower than the FM state. So far, stable SK state has been realized in artificial skyrmion lattices defined by lithography. 19,20 For practical applications, spontaneously emerging ground-state skyrmions at room temperature are strongly required.
In this work, we demonstrate room-temperature stable skyrmions in BiSb / MnGa bi-layers.
Here, BiSb is a topological insulator with high electrical conductivity 21 and strong spin Hall effect 22 , and MnGa is a ferromagnet with small magnetization and perpendicular magnetic anisotropy. 23 By tailoring the interfacial DMI, we can generate meta-stable and stable skyrmions at room temperature, which were detected by the THE. In a bi-layer with a large interfacial DMI (critical interfacial DMI constant DS = 5 pJ/m), the THE was observed at room temperature even under absence of external magnetic field, indicating the existence of thermodynamically stable skyrmions. Our results give insight into the role of interfacial DMI tailored by suitable material choice and growth technique for generation of stable skyrmion at room temperature.
The BiSb/MnGa bi-layers were grown by molecular beam epitaxy on semi-insulating GaAs(001) substrates with orientation of BiSb(012) // MnGa(001) // GaAs(001). Details of the growth procedure is shown in Fig. 2(a). After a thick GaAs buffer layer was grown at 550 o C, the substrate was cooled down to 50 o C to grow alternative monolayers of Mn-Ga-Mn-Ga as a template. 24 In order to modulate the interfacial DMI, we annealed the template at Tan = 350 o C (sample A) or 400 o C (sample B) for in 1 min to improve the MnGa surface morphology. Next, the samples were cooled down to 250 o C for growth of a thick MnGa thin film with a total thickness of 5 nm. Finally, a 10 nm BiSb (Sb 15%) thin film was grown at the substrate temperature of 200 o C.
The growth of BiSb/MnGa bi-layers was monitored in situ by reflection high energy electron diffraction (RHEED). Figure 2(b)-2(d) show the RHEED pattern of the as-grown MnGa template, and after annealing at 350 o C and 400 o C, respectively. The RHEED pattern changes from dim to bright streaky at higher annealing temperature, indicating that the atomic ordering and morphology of the template are improved by annealing. The surface roughness of the MnGa layers grown on top of the template was evaluated by atomic force microscope (AFM), which are shown in Fig.  2(e)-2(g).The root mean square of the surface roughness Rq of MnGa was reduced by annealing at higher temperatures, confirming that template annealing is effective.
To detect the signature of skyrmions in BiSb/MnGa bi-layers, we utilized the THE, which is the nondestructive electrical technique that can be incorporated to race-track memories or Brownian computer for readout of the skyrmion positions. The THE is easy to perform than using expensive tools such as the transmission X-ray holography, 25 X-ray microscopy, 26 or Lorentz force microscopy 27 with limited access. However, observation of the THE for interfacial DMIinduced skyrmions at room temperature is rare comparing with bulk DMI-induced skyrmions. The amplitude of the THE is proportional to the skyrmion density, and thus inversely proportional to the skyrmion size. The interfacial DMI-induced skyrmions are typically a few 100 nm to a few µm in diameter, for which the magneto-optical Kerr effect (MOKE) is the suitable detection technique.
As shown later, the skyrmions in our BiSb/MnGa bi-layers is predicted to be 55-80 nm in diameter, thus the THE is observable while the MOKE is not. In this case, the Hall resistivity can be expressed as ρxy = R0H + ρAHE + ρTHE, where the first, second and third term are the ordinary Hall effect, the anomalous Hall effect (AHE) and the THE, respectively. ρxy of the BiSb/MnGa bilayers was measured by using 50 µm-wide Hall bars fabricated by conventional ultraviolet photolithography and Ar ion milling. To extract the THE resistivity from ρxy, we estimate AHE resistivity by measuring the magnetic circular dichroism (MCD) intensity-magnetic field (MCD- , where R is the optical reflectivity, E is the photon energy, and ∆E is the Zeeman energy of the material. Because the magnitude of MCD is proportional to the magnetization (∆E ∝ M), this measurement reflects the hysteresis of the perpendicular magnetization Mz. 28 Because the light wavelength used in our MCD measurements (354 nm) is much larger than the atomic scale of the chiral spin texture of skyrmions, MCD can be used to estimate AHE but not THE. Note that an external magnetic field of 8 kOe is enough to saturate the magnetization of MnGa (See the supplementary information for the MCD hysteresis loops of MnGa measured at different maximum magnetic fields). The magnetization of the MnGa layer was also measured by superconducting quantum interface devices (SQUID). In sample A, the energy of the SK state is higher than the FM state at zero magnetic field ( Fig.   1(a)). Thus, it is necessary to apply a non-zero magnetic field oppositely to the magnetization direction to induce skyrmions. Note that these skyrmions are meta-stable in the sense that while they can survive when the field is swept back to zero (corresponding to the bipolar pulse technique reported in Ref.11), they can be easily erased by a large magnetic field. This behavior is demonstrated in a minor loop measurement shown in Fig. 3(c) for another BiSb (10 nm) / MnGa (5 nm) bi-layer (sample C) with the MnGa template annealed at Tan = 350°C. In contrast, the THE in sample B always re-emerges at zero magnetic field, indicating that they are stable skyrmions ( Fig. 3(b)). The existence of the THE in sample B under zero external magnetic field was observed in the hysteresis curves measured at different temperatures (see the supplementary material for full Hall resistance data at each temperature). The magnetic phase diagram of sample B as a function of the external magnetic field (H) and temperature (T) is shown in Fig. 3(d). The THE of sample B decreases with decreasing temperature and disappeared at about 125 K. The observed phase diagram of the THE is consistent with those reported for the temperature dependence of skyrmions. 27 For comparison, we also fabricated several reference samples; a MnGa (5 nm Landé factor, and Bohr magneton constant, respectively. 29 If the DMI constant D is larger than DC, skyrmions can emerge. Table 1 Fig. 4(a). The white dashed line indicates the Dc value for sample B.
One can see that the maximum Ku at this Dc for the Néel-like skyrmionic phase is around 3.