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Extraordinary magnetoresistance (EMR) is a geometric magnetoresistance effect occurring in hybrid devices consisting of a high-mobility material joined by a metal. The change in resistance can exceed 107% at room temperature when a magnetic field of 5 T is applied. Magnetic field sensors based on EMR hold the potential formeasuring weak magnetic fields with an unprecedented sensitivity, yet, to date this potential is largely unmet. In this work, we provide an extensive review of the current state-of-the-art in EMR sensors with a focus on the hybrid device geometries, the constituent material properties and applications of EMR. We present a direct comparison of the best devices in literature across magnetoresistance, sensitivity and noise equivalent field for different materials and geometric designs. The compilation of studies collected in this review illustrates the extremely rich possibilities for tuning the magnetoresistive behavior varying the device geometry and material properties. In addition, we aim to improve the understanding of the EMR effect and its interplay with geometry and material properties. Finally, we discuss recent trends in the field and future perspectives for EMR.

Heterostructures and crystal interfaces play a major role in state-of-the-art semiconductor devices and play a central role in the field of oxide electronics. In oxides the link between the microscopic properties of the interfaces and bulk properties of the resulting heterostructures challenge our fundamental understanding. Insights on the early growth stage of interfaces and its influence on resulting physical properties are scarce -- typically the information is inferred from post growth characterization. Here, we report on real time measurements of the transport properties of SrTiO3-based heterostructures while the crystal heterostructure is forming. Surprisingly, we detect a conducting interface already at the initial growth stage, much earlier than the well-established critical thickness limit for observing conductivity ex-situ after sample growth. We investigate how the conductivity depends on various physical processes occurring during pulsed laser depositions, including light illumination, particle bombardment by the plasma plume, interactions with the atmosphere and oxygen migration from SrTiO3 to the thin films of varying compositions. Using this approach, we propose a new design tool to control the electrical properties of interfaces in real time during their formation.

The metallic interface between two oxide insulators, such as LaAlO3/SrTiO3 (LAO/STO), provides new opportunities for electronics and spintronics. However, due to the presence of multiple orbital populations, tailoring the interfacial properties such as the ground state and metal-insulator transitions remains challenging. Here, we report an unforeseen tunability of the phase diagram of LAO/STO by alloying LAO with a ferromagnetic LaMnO3 insulator without forming lattice disorder and at the same time without changing the polarity of the system. By increasing the Mn-doping level, x, of LaAl1-xMnxO3/STO, the interface undergoes a Lifshitz transition at x = 0.225 across a critical carrier density of nc= 2.8E13 cm-2, where a peak TSC =255 mK of superconducting transition temperature is observed. Moreover, the LaAl1-xMnxO3 turns ferromagnetic at x >=0.25. Remarkably, at x = 0.3, where the metallic interface is populated by only dxy electrons and just before it becomes insulating, we achieve reproducibly a same device with both signatures of superconductivity and clear anomalous Hall effect. This provides a unique and effective way to tailor oxide interfaces for designing on-demand electronic and spintronic devices., Comment: 18 pages and 6 figures

The two-dimensional metal forming at the interface between an oxide insulator and SrTiO3 provides new opportunities for oxide electronics. However, the quantum Hall effect, one of the most fascinating effects of electrons confined in two dimensions, remains underexplored at these complex oxide heterointerfaces. Here, we report the experimental observation of quantized Hall resistance in a SrTiO3 heterointerface based on the modulation-doped amorphous-LaAlO$_{3}$/SrTiO$_{3}$ heterostructure, which exhibits both high electron mobility exceeding 10000 cm$^{2}$/Vs and low carrier density on the order of ~10$^{12}$ cm$^{-2}$. Along with unambiguous Shubnikov-de Haas oscillations, the spacing of the quantized Hall resistance suggests that the interface is comprised of a single quantum well with ten parallel conducting two-dimensional subbands. This provides new insight into the electronic structure of conducting oxide interfaces and represents an important step towards designing and understanding advanced oxide devices.

Oxide interfaces provide an opportunity for electronics. However, patterning of electron gases at complex oxide interfaces is challenging. In particular, patterning of complex oxides while preserving a high electron mobility remains underexplored and inhibits the study of quantum mechanical effects where extended electron mean free paths are paramount. This letter presents an effective patterning strategy of both the amorphous-LaAlO$_3$/SrTiO$_3$ (a-LAO/STO) and modulation-doped amorphous- LaAlO$_3$/La$_{7/8}$Sr$_{1/8}$MnO$_3$/SrTiO$_3$ (a-LAO/LSM/STO) oxide interfaces. Our patterning is based on selective wet etching of amorphous-LSM (a-LSM) thin films which acts as a hard mask during subsequent depositions. Strikingly, the patterned modulation-doped interface shows electron mobilities up to ~8,700 cm$^2$/Vs at 2 K, which is among the highest reported values for patterned conducting complex oxide interfaces that usually are ~1,000 cm$^2$/Vs at 2 K.

With infrared ellipsometry we studied the response of the confined electrons in a $\gamma$-Al$_2$O$_3$/SrTiO$_3$ heterostructures in which they originate predominantly from oxygen vacancies. From the analysis of a so-called Berreman mode, that develops near the highest longitudinal optical phonon mode of SrTiO$_3$, we derive the sheet carrier density, ${N_{s}}$, the mobility, $\mu$, and also the depth profile of the carrier concentration. Notably, we find that ${N_{s}}$ and the shape of the depth profile are similar as in LaAlO$_3$/SrTiO$_3$ heterostructures for which the itinerant carriers are believed to arise from a polar discontinuity. The main differences concern the higher mobility and a relatively stronger confinement of the electrons in $\gamma$-Al$_2$O$_3$/SrTiO$_3$, Comment: 12 pages, 2 figures