Extraordinary Hall balance in ultrathin SrRuO3 bilayers

The correlated 4d transition metal oxide SrRuO3 (SRO) features an anomalous Hall effect that originates from momentum-space sources of Berry curvature and depends sensitively on the magnetization. Here, we exploit this sensitivity and realize an epitaxial extraordinary Hall balance device, consisting of two ultrathin layers of SRO, separated by an insulating SrTiO3 (STO) spacer. Our results highlight the potential of ultrathin SRO in the realization of oxide-based spintronic devices.


Introduction
Owing to its metallic properties, high chemical stability, and excellent compatibility with heteroepitaxy, SrRuO 3 (SRO) is a widely used material in oxide electronics [1][2][3]. One example is the synthesis of epitaxial supercapacitors, where two SRO electrode layers form atomically sharp interfaces with a high-k dielectric or ferroelectric material [4][5][6][7][8]. Another example is its use as a buffer layer in the growth of multiferroics [9,10]. In addition to its suitability as an epitaxial electrode, its itinerant ferromagnetic ground state has attracted significant attention over the past years [11][12][13]. One aspect that has been intensively studied is its intriguing anomalous Hall effect (AHE), which originates from a source of Berry flux in momentum-space, also known as a magnetic monopole [14]. Acting like an effective magnetic field, the Berry flux causes electrons with opposite spins to experience opposing anomalous velocities, creating a voltage transverse to the longitudinally applied current [15,16]. It was recently found that two-dimensional SRO is distinct from its three-dimensional counterpart as ultrathin films host not one, but multiple sources of Berry flux with distinct spin-orbital parity [17]. This translates to a topologically non-trivial character of bands at the Fermi level, which carry Chern numbers =   2 and constitute positive and negative contributions to the anomalous Hall effect, respectively. The magnetization is an important parameter, as it shifts the two bands with respect to the Fermi energy, thereby controlling the sign and magnitude of the anomalous amplitude R xy AH . Manipulation of the AHE in ultrathin SRO has been demonstrated through various approaches, such as electrostatic gating and interface engineering [17][18][19][20].
An essential feature of ultrathin SRO is its thickness-driven metal-insulator transition, which occurs in the vicinity of 4 unit cells (u.c.) [21,22]. As the thickness is decreased below this limit, confinement and structural effects deplete the density of states. This occurs simultaneously with a suppression of the Curie temperature and saturation magnetization. The thickness is therefore an effective tuning parameter for manipulating the AHE in ultrathin SRO and can be applied to realize spintronic devices. An application of this is the extraordinary Hall balance (EHB), which stacks two different ferromagnetic layers, creating a memory device with four states [23].
In this work, we synthesize a heterostructure consisting of two layers of ultrathin SRO, separated by an SrTiO 3 (STO) spacer. We tailor the SRO layer thicknesses such that they exhibit different magnetic properties, while retaining similar resistance values such that the current is divided roughly equally over the two layers. This results in an all-oxide EHB device that can be controlled by magnetic field and temperature. These results highlight the delicate nature of the AHE in ultrathin SRO and its potential in the realization of spintronic devices. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Synthesis
The heterostructure is grown by pulsed laser deposition (PLD) and the growth is monitored by in situ reflection high-energy electron diffraction (RHEED). During the deposition, the intensity of the first-order diffraction spot is recorded. To realize the EHB device, we synthesize two layers of SRO, separated by a 4 u.c. (insulating) STO spacer. The SRO thicknesses are chosen to be 4 u.c. and 5 u.c. for the bottom and top layers, respectively. In figure 1(a), we show the RHEED intensity during growth of the bottom SRO layer. The initial oscillation is associated with a termination conversion from RuO 2 to SrO [24], which results in an enhancement of the surface diffusion of the ablated species. At the appropriate substrate temperature (∼700°), this is usually followed by a step-flow growth mode, resulting in films with extremely low surface roughness [25]. A drawback however, is that it is more difficult to determine the number of layers grown due to the absence of layer-by-layer oscillations, particularly for substrates with large terrace widths [26]. We therefore opted for a slightly lower growth temperature (600°), for which RHEED oscillations are still faintly present. This allows for accurate determination of the layer thickness and growth rate, while maintaining a high surface quality. Discarding the initial oscillation [25], we stop the deposition at the fourth intensity maximum. We subsequently grow the 4 u.c. STO spacer, followed by the 5 u.c. SRO layer and finally a 10 u.c. protective STO capping layer. The RHEED patterns after completion of each layer are shown in figure 1(b). The well-defined spots of the SRO surfaces indicate that they are atomically smooth, whereas the slightly streaked spots of the STO surfaces are indicative of a shorther crystal coherence length compared to the SRO surfaces. Figure 1(c) shows an illustration of the SRO/ STO/SRO heterostructure.

Transport
The longitudinal resistance of the heterostructure is shown as a function of temperature in figure 2(a). The derivative (dR/dT) is shown in the inset, where a sharp peak is observed at approximately 130 K. While a slight difference has been reported in the dR/dT behavior between bulk crystals and thin films [27][28][29], in both cases the peak is suggested to be caused by a logarithmic divergence of the specific heat due to short-range spin fluctuations across the magnetic phase transition [3,30,31]. As such, the peak at 130 K in the dR/dT identifies the Curie temperature of one of the SRO layers. Careful inspection reveals a shoulder at~115 K, identifying the magnetic phase transition of the second SRO layer. Considering the thickness-dependent suppression of T c discussed prior, we attribute the high and low Curie temperatures to the 5 u.c. and 4 u.c. layers, respectively. This confirms a different temperature evolution of the magnetizations of the two layers, resulting in two distinct spinpolarized conduction channels. The temperature dependence of the Hall effect is shown in figure 2 3 ), the ordinary Hall component for the 50 mT fields is in the order of tens of mΩ and therefore much smaller than the anomalous component, which is in the order of several Ω. We can therefore neglect R xy ord such that R R xy xy AH  . At~120 K, we observe a sign change, which is characteristic of the intrinsic topological contribution to the AHE [17,32]. This temperature corresponds to the magnetization value where the topological =   2 bands compensate one another and the total anomalous amplitude is zero [17]. Above this temperature, the positive contribution dominates up until the Curie temperature, where the magnetization vanishes.
In figure 2(c), we show the magnetic field dependence of the (top) longitudinal (MR) and (bottom) Hall resistance. Both the MR and Hall data show that two magnetic transitions take place at different B c . This provides a further indication of the presence of two spin-polarized conduction channels. From the Hall measurement we clearly recognize that the magnetization of one channel switches very abruptly, while that of the other channel switches more gradually. We attribute the channel that switches abruptly to the bottom SRO layer, as it is likely more ordered due to the growth on the atomically flat surface of the STO substrate. This is consistent with the abrupt switching observed for a single SRO layer. We expect the second SRO layer to be more disordered as it is grown on top of the SRO/STO stack, which has accumulated some surface roughness, as indicated by the RHEED patterns in figure 1. The concomitant variations in surface topography could give rise to magnetic domains with switching fields having a broader distribution than those of the bottom layer, resulting in a shallower slope at B c .
For an EHB device, it is required that the two layers have different coercive fields. While this property has been established in figure 2(c), there are no field values at 10 K where the magnetic state is perfectly stable i.e. plateaus where *R B 0 xy AH  . We therefore proceed to study temperature dependent magnetic field sweeps to identify a regime where multiple magnetic states can be stabilized. A particularly interesting region is in the vicinity of the sign change observed in figure 2(b). Considering the different temperature evolutions of the two channels, it is likely that in this range, one channel exhibits a positive AHE while the other remains negative. Accordingly, we can expect a variety of different magnetic and electronic configurations. In figure 3(a), we show magnetic field sweeps in the temperature range < < T 90 K 130 K. Figure 3(b) gives an enlarged view of sweeps recorded at 110, 115, and 120 K. In agreement with figure 2(b), we find that with increasing temperature, the overall sign of the AHE changes from negative to positive between 115 and 120 K. In addition, we find that for several temperatures-particularly for 90 and 110 K-three plateaus are present with a stable magnetic state. Remarkably, for 90 K the first plateau has a higher R xy value than the second plateau, whereas the situation is inverted at 110 K. To gain more insight in the behavior of the two channels, it is necessary to separate the signal into its two individual components. We first remark that in general, two Hall resistances cannot be added to give the total Hall resistivity. However, it can be shown (see the supplementary information available online at stacks. iop.org/JPMATER/3/025005/mmedia) that in the small Hall angle limit (R R xy xx  ), the summation of two Hall channels R xy a and R xy b is given by i.e. the two resistances (voltages) are scaled by the fraction of the total current they carry. Since in ultrathin SRO films the longitudinal resistance is about three orders of magnitude larger than the Hall resistance, this expression is valid and the total Hall resistance is a linear sum of the two individual channels. Using the empirical relation  experimentally observed behavior. Both AH components show a sign change, as well as a decrease of B c with increasing temperature, consistent with the behavior of single SRO layers. Channel 1 (red) changes sign at 100 K and channel 2 (blue) at~120 K. Additionally, the coercive fields of the two channels are well separated, which is essential for an EHB device. This further confirms the different temperature evolution of the magnetization in figure 2(a). In the right panel of figure 3(c) are labeled (i), (ii) and (iii), respectively. The table below summarizes the signs of the anomalous coefficients (R s ), the orientation of the magnetization (M) and the resulting AHE amplitude (R xy AH ) for channels 1 and 2 (red and blue). The key difference between the two temperatures is the sign of channel 2, which is negative at 90 K, but positive at 110 K. This causes the different behavior in state (ii) between the two temperatures, resulting in a step down of R xy AH at 90 K, but a step up at 110 K. As a result, the EHB properties can be controlled with temperature, which adds a tuning parameter to the device.

Conclusion
The sensitive relationship between the AHE and the layer thickness in ultrathin SRO is a powerful element in synthesizing films with tailored properties. By controlling the thickness on an atomic scale, this sensitivity can be harnessed and the AHE can be controlled. We demonstrated this by creating an all-oxide EHB device, consisting solely out of two separated SRO layers with slightly different thicknesses. We further showed that, due to the intrinsic sign change of the AHE in SRO, the EHB functionality can be controlled by temperature. These results highlight the delicate nature of the AHE in SRO, as well as its potential for application in spintronic devices.

Additional information Methods
The heterostructure was grown on a TiO 2 -terminated SrTiO 3 substrate. The deposition was done by PLD, using a 248 nm KrF excimer laser at a 1 Hz repetition rate and a laser fluence of -1.7 J cm 2 . The growth temperature and pressure were  600 C and 0.1 mbar O 2 , respectively. The sample was capped by a 10 u.c. crystalline STO layer to impose symmetric boundary conditions [17] and to prevent degradation due to exposure to ambient conditions [33]. Heating is performed with an infrared diode laser. The temperature was measured with a pyrometer and the growth is monitored with in situ RHEED. After growth, the sample was annealed for 1 h in 300 mbar O 2 at 550°, minimizing the oxygen vacancies that might have formed, and subsequently cooled down to room temperature at  20 C min −1 in the same pressure. Transport measurements were performed in an Oxford flow cryostat with a base temperature of 1.5 K and equipped with a 10 T superconducting magnet. Ohmic contacts to the the two SRO layers were established by ultrasonic Al wedge bonding. A~15 Hz m 10 A current was sourced in a four-point van der Pauw geometry and the resulting longitudinal and transverse voltages were measured with a lock-in amplifier. Longitudinal and transverse resistances were subsequently obtained by dividing by the current.