Strain engineering is a powerful tool for manipulation of magnetism.^[56–58] The strain-mediated electrical control of magnetism is considered to be the first attempt at designing an ME coupling in artificial FM/FE particulates and phase segregated ceramics,^[59] and this approach has received renewed attention more recently.^[60,61] This type of ME coupling was also widely reported in magnetic thin films (e.g. Ni, CoFeB, LSMO, and CFO) grown on ferroelectric substrates (e.g. BTO, PMN-PT, and PZT).^{[17,18,33–38,62–75]} The external electric field alters the lattice or shape of the ferroelectric crystal by the converse piezoelectric effect, and then transfers the strain to the proximate magnetic layer, leading to changes in magnetic anisotropy, magnetization rotation, and coercivity through magnetostriction. In the FM/FE heterostructures, both (anti-)ferromagnetic oxides and metals are controlled by electric field.

2.1.1. Ferromagnetic oxides

In light of the rapid development of deposition technologies, such as oxide molecular beam epitaxy and reflection high-energy electron diffraction (RHEED)-assisted pulsed laser deposition (PLD), high-quality magnetic oxides can be epitaxially grown on ferroelectric substrates, constructing the cornerstone of electrical control of magnetism mediated by strain.^[76] In 2007, Eerenstein et al. found a giant change in the magnetic moment of epitaxial 40-nm LSMO (x = 0.33) on single crystal BTO substrate with FE switching.^[17] This variation in magnetization was attributed to the changes of magnetic anisotropy caused by strain coupling with non-180° BTO domain. The role of strain in this electrical manipulation was clearly demonstrated by Thiele et al. in the system of 20 nm–50 nm LSMO (x = 0.33) and LCMO (x = 0.33) on PMN-PT substrate.^[18] The dependence of magnetization on electric field follows the relationship between in-plane piezoelectric strain and electric field in a butterfly shape, as shown in Fig. 2. However, this work explained the modulated magnetization to the paramagnetic-ferromagnetic phase transition driven by strain as the FE switching alters the Curie temperature.

Fig. 2.

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	Fig. 2. (a) In-plane piezoelectric strain versus applied electric field (E ∥ [001]) recorded along a [100] edge of a 0.72PMN–0.28PT substrate. (b) Magnetization M ∥ [100] versus E ∥ [001] applied to the substrate for an LSMO/PMN-PT (001) heterostructure.[18]

Subsequently, strain-mediated electrical control of magnetism was observed in more and more oxide systems, with the realization of sharp and reversible changes in magnetization under electric field. Of course, the origins of strain-induced changes in magnetic properties have been vigorously pursued, with two mechanisms proposed to date: i) electrical control of electronic phase transition and ii) electrical modulation of magnetic anisotropy. The electronic phase transition driven by strain under electric field is supported by works using LSMO,^[17,18] LCMO,^[33] and Pr_0.6Ca_0.4MnO₃^[62] with a strong tendency toward phase separation in the ferromagnetic layer. In contrast, the changes of magnetic anisotropy under electric field was widely accepted in CoFe₂O₄^[34,63] and Fe₃O₄,^[35,36,64] where a magnetization orientation shift of 17° in Fe₃O₄/BaTiO₃ was observed.^[64]

2.1.2. (anti-)ferromagnetic metals

In addition to the successful epitaxial oxide-based ferromagnet, magnetic metal thin films, which are usually polycrystalline or amorphous, can also be tuned by electric field. The strain transferred from the substrate is proven to be able to alter the magnetic anisotropy of magnetic metal films. Compared with magnetic oxides, magnetic metal systems attract more attention due to their high T_C, flexibility, and ease of production. The FE control of magnetic metal was observed in many systems like Fe/BTO,^[65] Co/PMN-PT,^[66,67] Ni/BTO,^[38] CoFe/PMN-PT,^[68] CoPd/PZT,^[69] Fe-Ga/BTO,^[70] CoFeB/PMN-PT.^[71,72] The magnetic anisotropy, coercivity, magnetic moment, and magnetic switching were controlled by electric field in these systems. In a Co/PMN-PT heterostructure, both simulations and experiments demonstrated a macroscopically maneuverable and non-volatile 180° magnetization reversal at room temperature, as shown in Fig. 3(a).^[67] Zhao’s group applied the electrical control of magnetization rotation in CoFeB/PMN-PT^[71] in the CoFeB/AlO_x/CoFeB/PMN-PT magnetic tunnel junction, realizing a reversible, continuous magnetization rotation and manipulation of tunnel magnetoresistance (TMR) at room temperature by electric fields without the assistance of a magnetic field.^[72] These findings are significant for the practical application of electrical control of magnetism in spintronics.

Fig. 3.

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Fig. 3. (a) Pulsed electrical and magnetic operation and corresponding magnetic moments with a magnetic field of 3 Oe along [010] for Co/PMN-PT.[67] The different magnetization states are clarified as stage 1 (M ∥ [010]), stage 2 (M ∥ ), stage 3 (M ∥ ), and stage 4 (M ∥ ).[73] (b) Polarization-versus-voltage loop collected at 300Hz and room temperature for BTO. (c) Temperature dependence of the magnetization of FeRh/BTO measured at 20 kOe for various voltages.

With the fast development of antiferromagnetic spintronics, more attempts are made in the control of antiferromagnetic materials by electrical means. Cherifi et al. used ferroelectricity in BaTiO₃ crystals to tune the sharp metamagnetic transition temperature of epitaxially grown FeRh film and electrically drive a transition between AFM and FM order with only a few volts, just above room temperature [Figs. 3(b) and 3(c)].^[73] Such a strain-mediated phase transition in FeRh under FE switching also produces a giant electroresistance response.^[74]

In heterostructures where the magnetic properties are intimately linked to charge, a change in carrier doping level alters the magnetic performance. Two types of devices have been developed to realize the charge-mediated electrical control of magnetism: ferroelectric field effect transistors and multiferroic tunnel junctions.

2.2.1. Ferroelectric field effect transistor

The concept of field effect transistor (FET) could be taken as a reference here for designing artificial multiferroic structures to induce changes in the magnetic state. An induced or spontaneous electric polarization at the gate dielectric interface leads to charge accumulation or depletion and resulting magnetic property variations. For a ferroelectric material such as PZT, the charge carrier modulation is of the order of 10¹⁴ cm⁻², which is much larger than that made possible by using silicon oxide as the dielectric gate.^[77] More importantly, this effect is non-volatile after removing the electric field. The ferroelectric field effect transistor (FE-FET) has been used for a long time to modulate a variety of properties including superconductivity^[78,79] and metal–insulator transitions.^[80] In the past decade, the control of magnetism by FE-FET was reported, both in first-principles calculations and experiments, for a variety of systems, such as complex oxides, DMS, and metal ferromagnets.

In 2009, a dramatic magnetoelectric coupling mediated by the modulation of hole–carrier density was predicted in the La_1−xA_xMnO₃/BTO (001) (A = Ca, Sr, or Ba) system by the first-principles method, where the doping concentration x was 0.5, near the FM–AFM phase transition.^[81] The direction of BTO polarization was used to electrostatically manipulate the hole–carrier density in La_0.5A_0.5MnO₃ and the resulting FM–AFM phase transition at the interface. When the polarization points away from (toward) the interface, there is an upward (downward) shift of the local density of states, favoring a hole charge accumulation (AFM) (depletion (FM)) state. Also, a microscopic model based on the two-orbital double exchange was introduced to describe this FE screening effect in manganites. The model simulation confirmed that the charge accumulation/depletion near the interface could drive the interfacial phase transition, which gives rise to a robust magnetoelectric response and bipolar resistive switching.^[82]

The electric field control of magnetism mediated by charge modulation in FM oxide films was first observed by Molegraaf et al.^[39] The magnetic response of PZT (250 nm)/LSMO (4 nm) as a function of applied electric field exhibits a magnetoelectric hysteresis curve, as reflected by the magneto-optic Kerr effect (MOKE) at 100 K in Fig. 4(a). The changes in carrier density are proved by x-ray absorption near edge spectroscopy (XANES) in Fig. 4(b)^[40] and electron energy loss spectroscopy (EELS).^[83] Similar effects were observed or calculated in LSMO/BTO,^[84–86] LCMO/BFO,^[41] SRO/BTO,^[42,43] Fe₃O₄/BTO,^[44] CrO₂/BTO/Pt,^[45] PZT/Co:TiO₂,^[46] Fe/BTO,^[47,48,87] and Co₂MnSi/BTO,^[88] etc. The nature of the ME effect in these systems can be distinguished as follows: (i) modification in the electronic structure, like density of states near the Fermi level^[89] and electronic bonding^[47,87] at the interface; (ii) changes in the magnetic exchange interaction;^[46,90] (iii) changes in magnetic anisotropy.^[8,91] Sometimes more than one of the above processes occurs simultaneously in a single system.

Fig. 4.

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Fig. 4. (a) Magnetoelectric hysteresis curve of the PZT/LSMO at 100 K.[39] (b) Room temperature XANES results for the two polarization states of the PZT. The left top inset shows the difference in x-ray absorption for the two PZT polarization states. The right bottom inset is the variation of the x-ray light absorption as a function of the applied gate voltage at a fixed energy, E = 6549.7 eV.[40]

When we compare the strain- and charge-mediated cases, it is confusing that both the mechanisms of strain and carrier density appear in the same system, like in LSMO/BTO^[17,84,85] and Fe/BTO.^{[47,48,65,87]} It is noteworthy that modulation of carrier density induced by the electric field or polarization is mainly concentrated in the area near the interface, whose thickness is determined by the screening thickness (t_S) of the FM layer:^[6]

where ε is the dielectric constant, ℏ is the Planck constant, m is the electron mass, e is the electron charge and n is the carrier density. The t_S value is around 2 nm for common metallic FM material, resulting in a very thin FM layer in the charge-mediated cases. In contrast, the thickness of the FM layer is not limited by the t_S value, which is sometimes larger than 10 nm in the strain-mediated case. Moreover, the thick FE substrate in the strain-mediated case can produce a significant strain on the FM layer above, while the reduced FE thin film thickness in the charge-mediated case might weaken the clamping effect of FE-induced strain on the FM layer below. Additionally, the strain effect mainly comes from the lattice distortion between polarized and unpolarized states for the common (001) BTO or PMN-PT ferroelectric layer, but the polarization switching from positive to negative in the charge-mediated case changes little in lattices.^[30,38] Hence, the electrical control of magnetism mediated by strain follows the dependence of strain on electric field, while that mediated by carrier density follows the dependence of polarization on electric field.

2.2.2. Multiferroic tunnel junction

The electrical control of magnetism has also been realized in multiferroic tunnel junctions (MFTJs) where an FE (multiferroic) tunnel barrier is sandwiched between two FM (an FM and a normal metallic) electrodes.^[92–98] The interaction between ferroelectricity and ferromagnetism can be studied through transport measurement, which displays four distinct resistance states due to the TMR and tunnel electroresistance (TER) effects, as shown in Fig. 5(a). The four resistance states were first reported by Gajek et al. in LSMO/La_0.1Bi_0.9MnO₃ (LBMO)/Au MFTJ [Fig. 5(b)],^[94] but no obvious variation of the TMR with ferroelectric polarization has been observed, and multiferroic materials are very rare. Subsequently, artificial MFTJs with an FE barrier and FM electrodes were designed. Garcia et al. demonstrated that the TMR of −19% and −45% could be detected in LSMO (x = 0.33)/BTO (1 nm)/Fe MFTJ with FE layer in downward and upward states, respectively [Fig. 5(c)].^[95] In the work of Pantel et al. even the sign of the TMR was reversed in the LSMO (x = 0.33)/PZT (3.2 nm)/Fe MFTJ by the ferroelectric polarization; the TMR values were +4% and −3% when polarization pointed to LSMO (x = 0.33) and Co, respectively [Fig. 5(d)].^[96] Moreover, Yin et al. showed that inserting 0.8 nm interfacial LCMO (x = 0.5) in the LSMO (x = 0.3)/LCMO (x = 0.5)/BTO/LSMO (x = 0.3) MFTJ gave rise to a 500% variation of the TMR owing to the FM–AFM phase transition induced by the polarization-generated metal/insulator phase transition in LCMO (x = 0.5) [Fig. 5(e)].^[97] Such a resistive switching and phase transition with the hole modulation driven by FE polarization has also been predicted by the theoretical work of Tsymbal’s group.^[98] Unfortunately, all the aforementioned works of ferroelectric control of spin-polarization can be performed only below room temperature, and further efforts should be devoted to obtain efficient ferroelectric control of spin-polarization at room temperature.

Fig. 5.

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Fig. 5. (a) Schematic diagram of the four resistance states in artificial MFTJS with two FM electrodes sandwiching an FE tunnel barrier. The white and black arrows represent the magnetic configurations and FE polarization, respectively. (b) Tunnel magnetoresistance curves at 4 K with Vdc. = 10 mV in an LSMO (x = 0.33)/LBMO(2 nm)/Au junction.[94] (c) Resistance versus magnetic field (R–H) curves for LSMO (x = 0.33)/BTO (1 nm)/Fe MFTJ (Vdc. = −50 mV, T = 4.2 K) after poling the ferroelectric barrier up or down, respectively.[95] (d) R–H curves measured at 50 K in the as-grown state of LSMO (x = 0.33)/PZT (3.2 nm)/Fe MFTJ.[96] (e) R–H curves for LSMO (x = 0.3)/LCMO (x = 0.5)/BTO/LSMO (x = 0.3) MFTJ.[97]

The exchange bias effect is known to be associated with the coupling between FM and AFM materials, where the exchange coupling gives rise to a shift of the magnetic hysteresis loop away from the center of symmetry at zero magnetic field. When the single phase multiferroic materials like Cr₂O₃,^[49–52] YMnO₃,^[53,99] LuMnO₃,^[100] and BiFeO₃^{[19,54,55,101,102]} (FE and AFM orders) serve as the FE layer, the exchange bias of heterostructure might be electrically reversed. The manipulation of exchange bias using intrinsic multiferroics allows the possibility of electric field switching of the direction of the magnetization.

Demonstration of exchange bias controlled by electric fields was first reported in perpendicularly magnetized [Co/(Pt or Pd)]/Cr₂O₃ heterostructures.^[49–52] Reversible switching of the exchange bias was observed at 303 K in a [Co/Pd]/Cr₂O₃ (0001) heterostructure by simultaneous application of a magnetic field and an electric field to switch the antiferromagnetic single domain state, which in turn switched the direction of the uncompensated spins at the Cr₂O₃ (0001) interface that biased the [Co/Pd] hysteresis loop.^[49] The electric field control of exchange bias in NiFe/YMnO₃ was reported by Laukhin et al.,^[53] who showed that the exchange bias, after cooling the system under a magnetic field, could be reduced to near zero by applying a voltage across the YMnO₃.^[99]

BFO is the most famous multiferroic materials with a ferroelectric T_C of ∼ 1100 K and G-type AFM Néel temperature of ∼ 640 K.^{[24,103–106]} The origin of exchange bias in G-type AFM BFO, with a fully compensated spin configuration at the interface, is related to the Dzyaloshinskii-Moriya interaction and FE polarization, which was theoretically demonstrated in the systems of BFO/LaMnO₃ ^[107] and SrMnO₃/SrRuO₃ by Dong et al.^[108] The FE polarization of BFO can point along any one of the eight degenerate [111] directions, permitting the possible formation of three types of domain walls (71°, 109°, and 180°).^[101,104] The domain structures could be controlled by the growth orientation, strain, and substrate.^[109–111] In 2006, Zhao et al. were first to demonstrate electrical control of antiferromagnetic domain structure in BFO at room temperature, wherein FE polarization switching induces AFM domain switching.^[101] Subsequently, it was shown that the exchange bias in a field-effect device with 600 nm BFO as the dielectric and 3 nm LSMO (x = 0.3) as the conducting channel can be caused to switch between two distinct states reversibly by poling the ferroelectric polarization of BFO, as in Fig. 6.^[19] Although the roles of strain and charge could not be fully excluded here, Wu et al. proposed that the electrical manipulation of exchange bias mainly arose from the induced interfacial magnetism in a few nanometers of the BFO layer. The interfacial magnetism in BFO was attributed to an electronic orbital reconstruction occurring at the BFO/LSMO interface.^[55,112]

Fig. 6.

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Fig. 6. (a) Schematic of the BFO/LSMO field-effect device. (b) Magnetic coercivity of the LSMO with respect to gate voltage (VG) at 5.5 K. The arrows show the direction of the pulse sequence. (c) Electric-field control of exchange bias. From top to bottom: the VG-pulse sequence used for the measurements; the measurements of normalized exchange bias and peak resistance for the gate-pulse sequence obtained in negative and positive remanent magnetization; examples of individual MR curves from the upper and lower resistive states where the exchange-bias values were determined.[19]

Although multiferroic materials, e.g., BFO, typically serve as the FE layer for exchange bias-mediated electrical control of magnetism, it is inaccurate to consider that all the electrical control of magnetism in the systems including BFO originates from exchange bias. For instance, an electrically driven change in FE polarization, and thus AFM order, in BFO can switch the magnetization of a thin metal film (e.g., CoFe) lying above.^[54] The mechanical strain produced by ferroelasticity can also modify the preferred orientations of the magnetic domains and therefore the macroscopic magnetization. When a material near the FM–AFM phase transition point, like LCMO (x = 0.5), is combined with BFO, the modulation of carrier caused by ferroelectric polarization might play a dominated role in the electrical manipulation of magnetism with competition between FM and AFM phases.^[41]

According to the conventional understanding from the capacitor model, the electric field only changes the carrier density (Δn_S ∼ CV_G/e) in the system by an electrostatic doping mechanism. Dhoot et al. studied electrostatic field-induced doping in LCMO (x = 0.2) transistors using electrolyte (EMIM-TFSI) as a gate dielectric, as shown in Fig. 8(a). For positive gate bias, electron doping drives a transition from a ferromagnetic metal to an insulating ground state.^[123] The thickness of the electrostatically doped layer depends on bias voltage but could extend to 5 nm, requiring a field doping of 2 × 10¹⁵ charges per cm² equivalent to 2.5 electrons per unit cell area. In contrast, negative gate voltage enhances the metallic conductivity by 30%. In Pr_1−xSr_xMnO₃ (x = 0.5) thin film, the doping level x was controlled by gate voltage, accompanied by the modulation of Curie temperature and resistance, realizing a phase transition similar to the classic phase diagram.^[124]

Fig. 8.

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	Fig. 8. (a) Sheet resistance versus temperature for 5-nm LCMO (x = 0.2) at VG = 0 (black line), −3 (red line), and +3 V (blue line).[123] (b) Magnetic field dependence of the anomalous Hall conductivity σAH at 300 K for Co: TiO2, measured at different VG. The values of electron density n at each VG obtained from the ordinary Hall effect are shown in parentheses.[125]

In another system, magnetic oxide semiconductor of Co:TiO₂, Yamada et al. realized electric field–induced ferromagnetism at room temperature by means of EDL gating with high-density electron accumulation (> 10¹⁴ per square centimeter).^[125] By applying a gate voltage of a few volts, a low-carrier paramagnetic state was transformed into a high-carrier ferromagnetic state, thereby revealing the considerable role of electron carriers in high-temperature ferromagnetism and demonstrating a route to room-temperature semiconductor spintronics, as shown in Fig. 8(b). The carrier density, resistance, and magnetoresistance were also tuned by EDL gating in the 5d iridate, Sr₂IrO₄ with large spin-orbit coupling.^[126]

Although the electrostatic doping mechanism successfully accounts for the changes in carrier density in some systems, it cannot explain the non-volatile electric-field effect in the whole bulk of film. Thus another mechanism base on electrochemical reaction is then proposed: the electric field applied on ionic liquid could bring about redox in the channel material, which could induce the creation and migration of oxygen vacancies.^[127] The introduction of oxygen vacancies makes the non-volatile and in-depth effect reasonable.

For example, the electrically reversible control of ferromagnetic phase transition based on oxygen vacancy migration in manganite film was reported by Cui et al.^[20] The formation of an insulating, magnetically hard phase induced by the migration of oxygen in the magnetically soft matrix was directly observed in the magnetoresistance [Fig. 9(a)] and Fourier-filtered [Fig. 9(b)] images. It randomly nucleated and grew across the film instead of initiating at the surface and spreading to the bottom. This discovery provides a conceptually novel vision for the electric-field tuning of phase transition in correlated oxides. The realization of a reversible metal-insulator transition in colossal magnetoresistance materials will also further the development of four-state memories, which can be manipulated by a combination of electrode gating and the application of a magnetic field [Fig. 9(c)]. The reversible control of charge transport, metal-insulator crossover and magnetism in field-effect devices were also realized based on EDL gated SRO.^[128] In these thin-film devices, the metal-insulator crossover temperature and the onset of magnetoresistance could be continuously and reversibly tuned in the range 90 K–250 K and 70 K–100 K, respectively, by application of a small gate voltage. A reversible diffusion of oxygen ions in the oxide lattice dominates the response of these materials to the gate electric field.

Fig. 9.

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Fig. 9. (a) Channel magnetoresistance acquired by sweeping the magnetic field along the channel (left axis) and the normalized magnetization curves measured with the magnetic field applied in-plane along the (100) direction of the substrate at 10 K under VG = + 3 V. (b) Fourier-filtered images of LSMO with VG = + 3.0 V. The ⊥ and dashed ovals mark the dislocation and estimated areas with high dislocation density, respectively. (c) Channel resistance versus VG with H = 0 kOe and 5 kOe.[20]

Electrical manipulation of lattice, charge, and spin are realized respectively by the piezoelectric effect, field-effect transistor, and electric field control of ferromagnetism, bringing about dramatic promotions both in fundamental research and industrial production. However, it was generally accepted that the orbitals of materials were impossible to alter once they have been made. EDL gating was used to dynamically tune the orbital occupancy and corresponding magnetic anisotropy of LSMO thin films in a reversible and quantitative manner.^[21] Positive gate voltage increases the proportion of occupancy of the orbital and the magnetic anisotropy that were initially favored by strain (irrespective of tensile versus compressive), while negative gate voltage reduces the concomitant preferential orbital occupancy and magnetic anisotropy (Fig. 10).

Fig. 10.

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	Fig. 10. Normalized x-ray absorption spectroscopy (XAS) [photon polarization parallel (E ∥ a) and almost perpendicular (E ∥ c) to the sample plane] and x-ray linear dichroism (XLD) signals of (a) tensile and (b) compressive strained LSMO.[21]

The electrochemical reaction mechanism was also demonstrated in the Co/GdO_x, where the redox at the interface was controlled by the migration of oxygen ions under electric field.^[129,130] The Co films could be reversibly changed from an optimally oxidized state with a strong perpendicular magnetic anisotropy to a metallic state with an in-plane magnetic anisotropy or to an oxidized state with nearly zero magnetization, depending on the polarity and time duration of the applied electric fields. Yuan et al. figured out a “phase diagram” to distinguish the electrostatic or electrochemical nature of EDL gating: the high work frequency and the low temperature together favor the electrostatic doping, while low frequency and high temperature favor the electrochemical reaction.^[131] Nevertheless, various factors determine the mechanism of EDL gating, e.g. strain state, oxygen diffusion ability, etc., all of which need more in-depth investigation.

The two-dimensional electron gas (2DEG) or two-dimensional electron liquid (2DEL) that forms at the interface between the two insulating non-magnetic oxides LaAlO₃ (LAO) and SrTiO₃ (STO) has sparked widespread research interest due to its possession of a remarkable variety of emergent behaviors including superconductivity,^[132,133] strong Rashba-like spin-orbit coupling^[134] and ferromagnetism.^[135–138] From a fundamental perspective, interfacial ferromagnetism could be a leading example of truly emergent phenomena; while it is true that bulk SrTiO₃ can be doped to be metallic and superconducting, neither constituent in bulk form exhibits ferromagnetism.^[138] The first signatures of magnetism at the LAO/STO interface were reported in magnetotransport measurements by Brinkman et al.^[139] Direct current scanning quantum interference device (SQUID) magnetometry measurements by Ariando et al.^[140] showed ferromagnetic hysteresis extending to room temperature. Torque magnetometry measurements by Li et al.^[136] showed evidence for in-plane magnetism with a high moment density. Scanning SQUID microscopy by Bert et al.^[137] revealed inhomogeneous micron-scale magnetic ‘patches’ x-ray circular dichroism measurements by Lee et al.^[138] indicated that the ferromagnetism is intrinsic and linked to d_xy orbitals in the Ti t_2g band. Despite this variety of evidence, the existence and nature of magnetism in LAO/STO heterostructures has remained controversial. Since most of the exotic properties depend strongly on carrier density that can be tuned easily by electric field,^[134] the nature of 2DEG or 2DEL can be readily explored by an electric field — back-gating^[141] or top-gating^[142] — or via nanoscale control using conductive atomic force microscope (AFM) lithography.^[143]

At the LAO/STO interface, the electron gas is inherently sandwiched between two insulators. It is thus rather natural to try and explore the system’s ground states by modulating the carrier density with an electric field. In a standard field-effect device, an electric field is applied between a metallic gate and a conducting channel across a dielectric. SrTiO₃ substrate is chosen as the dielectric because it is characterized at low temperatures by a large dielectric constant. The metallic gate is a gold film sputtered opposite to the channel area onto the back of the substrate. A typical sketch of the back-gated field-effect device is shown in the inset of Fig. 11(a). A series of experiments, using the STO substrate as the gate dielectric, has revealed a complex phase diagram [shown in Fig. 11(a)].^[134,144] A superconducting dome appears within a certain range of carrier densities modified by electric field. By reducing the carrier concentration from the largest doping level (V ∼ 320 V), critical temperature T_BKT is at first increased, reaches a maximum at around 310 mK and then decreases to zero. This critical line ends at V_C < −140 V, where the system undergoes a quantum phase transition. Transport measurements have proved the existence of a very large perpendicular magnetoresistance (MR), interpreted as evidence of weak (anti)localization effects. Close to V_C, the magnetoconductance switches from positive to negative, as displayed in Fig. 11(b). It was proposed that this evolution is tied to the steep rise of a Rashba spin-orbit interaction upon increasing the gate voltage.^[144]

Fig. 11.

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Fig. 11. (a) Electronic phase diagram of the LAO/STO interface, obtained through field-effect modulation of the carrier density.[144] The inset shows a schematic view of a field-effect device, showing the source (S), drain (D), longitudinal voltage (V+ and V−), Hall voltage (VH), and gate voltage (G) contacts. (b) Modulation of the magnetoconductance s with gate voltage for an LAO/STO interface.[134] The change from a weakly localized regime (positive Δs) to a weakly anti-localized regime (negative Δs) reveals the increase in strength of the spin-orbit coupling. (c) Magnetoresistance (MR) at Vg ∼ 100 V at different temperatures.[145]

Since the electronic properties of LAO/STO interfaces are extremely sensitive to growth conditions, some other samples prepared under higher oxygen pressure display coexistence of superconductivity and ferromagnetism.^[145] Figure 11(c) shows the MR of the sample at a few different temperatures at V_g ∼ 100 V (not in the superconducting regime). The magnitude of the resistance–change and the sharpness of the resistance-dip near zero field both increase with decreasing temperature, consistent with a phase coherence length that increases with decreasing temperature. A closer look at the low-field MR reveals an additional resistance dip near zero field that is related to weak localization. The MR also shows a hysteretic butterfly pattern similar to that seen in T_C (H) (not shown here), indicating that local magnetic fields arising from magnetic order also modulate quantum interference in the carrier gases.

Aside from back-gating, there is also top-gating of 2DEG by employing the dielectric of LAO film, which is often as thin as several unit cells and needs a much lower gating voltage. A two-terminal capacitor device is used to electrically gate the LAO/STO interface [Figs. 12(a) and 12(b)]. The top circular electrode is grounded, and a voltage V_dc is applied to the annular interface contact. Decreasing V_dc depletes the interface of mobile electrons, while increasing V_dc leads to electron accumulation and results in a conductive interface. By using a top-gated LAO/STO interface with different voltages, interfacial magnetism as a function of mobile interfacial carrier density can be detected by magnetic force microscopy (MFM). As shown in Fig. 12(c), the first MFM image, taken at V_dc ∼ 4 V (‘state 1’), shows a strong-contrast electrode in the frequency channel, clearly signaling an out-of-plane ferromagnetic domain. As the voltage goes to −2 V, the domain contrast has nearly vanished, with new horizontal bands appearing parallel to the fast scan axis until the contrast is absent at 0 V. The phenomena clearly indicate the emergence of an in-plane ferromagnetic phase as electrons are depleted from the interface.

Fig. 12.

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Fig. 12. (a) Experimental set-up: the MFM tip is mechanically driven by a piezoelectric transducer near its resonant frequency and kept at a constant height above the surface. The top electrode and the MFM tip are both grounded, and a DC bias is directly applied to the interface.[135] (b) Kelvin-probe force microscopy measurement of a region that includes the area for which MFM measurements are made.[134] The top gate is grounded, and voltage bias to the interface (Vdc) is 3 V. The topography is shown as height, while the colour maps onto the measured surface potential (the work function is already subtracted). (c) MFM frequency images over a 3 mm×3 mm area indicated by the black dashed line-enclosed region in panels (b). The MFM tip is magnetized horizontally parallel to the [010] sample direction.[135] MFM frequency images for Vdc increasing from −4 V to 0 V then decreasing to −4 V. Magnetic domain features are clearly observed for Vdc < − 2 V. The final state 2, obtained after cycling the voltage to Vdc = 0, is uncorrelated with the initial state 1. The regions enclosed by dashed lines give examples of where magnetic contrast is unchanged (region 1) or reversed (region 2) after voltage cycling.

The discovery of electrically controlled ferromagnetism at the LAO/STO interface provides a new and surprising route to a wide range of spintronic applications. Nevertheless, the nature of the ferromagnetic state at the intriguing LAO/STO interface remains unexplored, and many effects such as spin-torque transfer, spin-polarized transport, and electrically controlled spinwave propagation and detection are expected but not demonstrated. Thus, there is plenty of space to employ the electric control in controlling interfacial ferromagnetism for the versatile application of the intriguing LAO/STO interface.

Controlling magnetization switching by an electric field without the assistance of a bias magnetic field may enable new data-storage spintronic devices requiring only low electric power. The modification of the correlated oxide interface may offer an avenue to explore this new strategy. In the experiments by Cuellar et al.,^[146] the manipulation of interfacial magnetic Cu states with electric field in La_0.7Ca_0.3MnO₃/PrBa₂Cu₃O₇/La_0.7Ca_0.3MnO₃ magnetic tunnel junctions [Fig. 13(a)] realized the electrical switching of magnetization without an applied magnetic field. As shown in Fig. 13(b) both high and low resistance states, corresponding to two different magnetic configurations, are stable in zero magnetic field, in other words, using only electrical means, two different magnetic states can be stabilized at very low power.

Fig. 13.

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Fig. 13. (a) Sketch of the LCMO (x = 0.3)/PrBa2Cu3O7/LCMO (x = 0.3) magnetic tunnel junctions and the test setup. Magnetic field was directed in-plane along the [110] direction (easy axis of the harder top layer), as according to drawing.[146] (b) At low bias (100 mV, blue symbols) the minor loop shows the saturation state 1, the high resistance state 2 (which is due to misalignment of magnetic moments of top and bottom layers), and the low resistance 1’ where magnetic moments are aligned along the easy axis of the bottom layer. Notice that high 2 and low 1’ resistance states are stable in zero magnetic field at a temperature of 94 K.[147] (c) Heterostructure and test setup schematics. (d) Spin asymmetry of Sample A after cooling in 700 mT without a bias and with a bias of −400 V, respectively.[147]

Direct electric field control of magnetization without multiferroics or magnetoelasticity may also induce magnetoelectric coupling. Grutter et al. demonstrated an electric field dependence of the emergent ferromagnetic layer at CaRuO₃/CaMnO₃ interfaces [Fig. 13(c)].^[147] The application of a −400 V bias voltage on CaMnO₃/CaRuO₃ heterostructures induced an increase of the magnetization by a factor of 2.86 ± 0.4 [Fig. 13(d)], ascribed to driving the conduction electrons from the CaRuO₃ across the interface into the CaMnO₃, which enhanced the interfacial double exchange interaction.

Current information storage devices are based on two different aspects of solid state materials, spin and charge. Generally, spin and charge of electrons are employed separately. In magnetic recording and magnetoresistive random access memories (MRAM), a magnetic field (H) or a high-density current is used to write or read the information stored in the magnetization. Differently, the recording of two logic states (high resistive state HRS and low resistive state LRS) in resistive random access memories (RRAM) is on the basis of resistance switching modulated by electrical stimuli. The quest for higher data density in information storage is motivating researchers to study how to manipulate magnetization without the need of cumbersome H and achieve a new paradigm wherein spin and charge act on each other. Thus with a simple RRAM architecture, electrical control of magnetism in RRAM with the medium of diluted magnetic oxides,^[148,149] antiferromagnet,^[150,151] manganites^[152,153] and ferrimagnets^[154] has attracted extensive attention. The orderly migration of oxygen vacancies (V_O) is considered to be the origin of the resistive switching (RS) behavior in these systems. Considering that such structures not only show stable bipolar RS characteristics, but also exhibit magnetic modulation with the alternation of set and reset processes, it is expected to obtain four logic states by encoding information in both RS and magnetic manipulation and even to achieve the dream of storing information magnetically and switching it electrically. Interestingly, magnetoresistance measurements indicate spin transport through an electrochemically formed copper nano-filament in LRS, in contrast to the disappearance of spin transport in HRS at the same temperature.^[155]