Purely antiferromagnetic magnetoelectric random access memory

Magnetic random access memory schemes employing magnetoelectric coupling to write binary information promise outstanding energy efficiency. We propose and demonstrate a purely antiferromagnetic magnetoelectric random access memory (AF-MERAM) that offers a remarkable 50-fold reduction of the writing threshold compared with ferromagnet-based counterparts, is robust against magnetic disturbances and exhibits no ferromagnetic hysteresis losses. Using the magnetoelectric antiferromagnet Cr2O3, we demonstrate reliable isothermal switching via gate voltage pulses and all-electric readout at room temperature. As no ferromagnetic component is present in the system, the writing magnetic field does not need to be pulsed for readout, allowing permanent magnets to be used. Based on our prototypes, we construct a comprehensive model of the magnetoelectric selection mechanisms in thin films of magnetoelectric antiferromagnets, revealing misfit induced ferrimagnetism as an important factor. Beyond memory applications, the AF-MERAM concept introduces a general all-electric interface for antiferromagnets and should find wide applicability in antiferromagnetic spintronics.

I n the effort to develop low-power data processing and storage devices, nonvolatile random access memory schemes have received considerable attention 1 . Magnetic elements such as the magnetic random access memory (MRAM) (Fig. 1a) promise excellent speed, superior rewritability and small footprints, which has led to strong commercial interest in this technology for memory applications. In addition to ferromagnetic MRAM, two complementary approaches have recently emerged for advancing beyond conventional MRAM elements in terms of its writing power and data robustness. On the one hand, switching and reading the antiferromagnetic order parameter of metallic antiferromagnets with charge currents 2,3 has enabled purely antiferromagnetic MRAM (AF-MRAM), granting superior data stability against large magnetic disturbances and potentially even faster switchability. On the other hand, magnetoelectric random access memory (MERAM) promises energy efficient writing of antiferromagnets, by eliminating the need for charge currents through the memory cell and instead relying on electric fieldinduced writing. Reading out the antiferromagnetic state from MERAM has presented a challenge to date as magnetoelectric antiferromagnets (for example, BiFeO 3 or Cr 2 O 3 ) are dielectrics. Therefore, the readout signal of MERAM cells is conventionally acquired from a ferromagnet that is coupled with the magnetoelectric antiferromagnet by exchange bias [4][5][6][7][8] . While ferromagnets enable readability, their presence strongly interferes with the magnetoelectric selection of the antiferromagnetic order parameter 9 . This is related to exchange bias and ferromagnetic hysteresis, both of which need to be overcome in the writing process of MERAM with ferromagnets.
Here we put forth the concept of purely antiferromagnetic MERAM (AF-MERAM) (Fig. 1a), which avoids the issues associated with the presence of ferromagnets by instead using polarizable paramagnets, for example, Pt, to probe the order parameter of the magnetoelectric antiferromagnet. As shown schematically in Fig. 1b, the prototypical memory cell consists of an active layer of insulating magnetoelectric antiferromagnet, a bottom gate electrode for writing purposes and a top electrode that provides the readout interface via anomalous Hall measurements 10 . Using Cr 2 O 3 as an AF element, we demonstrate a complete working AF-MERAM cell, proving that this concept yields substantial improvements in terms of magnetoelectric performance over comparable MERAM realizations with ferromagnets. In particular, by removing the ferromagnetic component from MERAM, we reduce the writing threshold by a factor of about 50. These characteristics render AF-MERAM a promising new member to the emerging field of purely antiferromagnetic spintronics 3,11 . We show the magnetoelectric writing and all-electric reading operations of a cell at room temperature over hundreds of read-write cycles. While nonvolatile solid-state memory is one possible application of AF-MERAM cells, the concept is applicable to other fields of antiferromagnetic spintronics, such as logics, magnonics 12 and material characterization.

Results
Room temperature operation of AF-MERAM. To realize the memory cell, we use an epitaxial layer stack of Pt(20 nm)/ a-Cr 2 O 3 (200 nm)/Pt(2.5 nm) that is prepared on Al 2 O 3 (0001) substrates. Similar stacks with a-Cr 2 O 3 have been extensively studied in the scope of traditional MERAM elements with ferromagnetic Co layers 4,5,[13][14][15] . The thicker bottom Pt film serves as the gate electrode and the thin Pt top layer is used to measure the AF order parameter all-electrically via zero-offset anomalous Hall magnetometry 10 (hereafter zero-offset Hall). This readout approach makes use of the uncompensated boundary magnetization of a-Cr 2 O 3 (0001), which is rigidly coupled to the AF bulk and creates proximity magnetization in the Pt film 16,17 .   An individual magnetoelectric element is obtained by patterning the top Pt layer. Figure 1c shows the protocol of an isothermal magnetoelectric switching experiment that was carried out at 19°C in a permanent magnetic field of HE þ 0.5 MA m À 1 along the film normal. The test sequence mimics random access operations comprising the three essential elements of any memory cell: writing, storage and reading. One of the key technological advantages is that the memory cell operates in static magnetic fields and writing operations are triggered by the application of a voltage. No energy input is necessary during the storage times. The reproducibility of this process is demonstrated over 300 write-store-read cycles in Fig. 1d, during which the cell reveals no performance degradation.
Two key material requirements must be satisfied to achieve reliable magnetoelectric reversal processes such as shown in Fig. 1. First, the order parameter has to be susceptible to the gate voltage via the linear magnetoelectric effect. Second, the cell has to exhibit thermal stability at the operation temperature, giving rise to stable remanent magnetic states. Both criteria can be directly probed in our system using the electrical writing and reading interfaces of the magnetoelectric cell. To reveal the exact influence of magnetic and electric field on the antiferromagnetic order parameter, it is mandatory to avoid the influence of magnetic anisotropy, which fixes the order parameter while below the ordering temperature, and instead carry out magnetoelectric field cooling through the ordering temperature. The map in Fig. 2a shows the resulting average antiferromagnetic order parameter in the cell after cooling from 30 to 7°C using the indicated combination of magnetic cooling field H cool and electric cooling field E cool ¼ V cool /t (t denotes the AF film thickness). For large EH fields, the order parameter selection is consistent with that expected in a-Cr 2 O 3 (refs 7,13,18,19) due to the linear magnetoelectric effect. However, for small writing voltages that are technologically desirable, the EH symmetry is disturbed, giving rise to magnetic field-induced selection of the order parameter. Strikingly, the EH symmetry is perfectly restored when accounting for a gate bias voltage V GB , which is about À 1 V for this system.
When applying a writing voltage to the cell at 19°C, the antiferromagnetic order parameter can be switched hysteretically with a coercive gate voltage V C of E1.5 V (Fig. 2b), completing the list of ingredients for the nonvolatile AF-MERAM prototype. The slightly asymmetric shape of the hysteresis loop is due to the gate voltage range being symmetric about The temperature window, in which magnetoelectric writing can be carried out, is limited at higher temperatures by the collapse of antiferromagnetic order and at lower temperatures by magnetic anisotropy 15 . It should be possible to widen this writability window considerably to 4100 K. The hightemperature limit can be enhanced by doping 20,21 , and the lowertemperature limit by applying higher writing voltages 4,5 or by intentionally reducing the anisotropy via doping 20 (Supplementary Note 1). Table 1 contains an overview of state-of-the-art studies of magnetoelectric functionality using magnetoelectric thin films [4][5][6]9,13 and single crystals 7 , but in both cases relying on interfacial exchange bias with a thin ferromagnetic layer. In addition, the AF-MERAM cell presented in this work is included for comparison. The metrics in the overview are the magnetoelectric film thickness t, the writing threshold (VH) C and the coercive gate voltage V C . For integration in microelectronics, the latter two are of particular relevance as the circuit voltage rating depends on them.
While exchange bias has traditionally been used to probe the antiferromagnetic state of Cr 2 O 3 , this leads to strongly increased magnetoelectric coercivities, especially for thin films of Cr 2 O 3 (refs 4,5). When judging the writing threshold, all the exchange bias systems require very large VH for isothermal magnetoelectric switching of the AF order parameter in Cr 2 O 3 . In contrast, the AF-MERAM approach provides a route to reduce both the coercivity and the resulting write voltage by a factor of about 50 over exchange-biased examples (Supplementary Note 2). In addition, AF-MERAM can be readout in permanent external magnetic fields, whereas exchange-biased MERAM requires the removal of the magnetic field for readout. Thus, the example here presented opens an appealing field of AF-MERAM with ultra-low 16   writing thresholds and superior stability and readability of the magnetic information in the presence of external magnetic fields.

Discussion
The gate bias voltage of V GB % À1V (Fig. 2) presents a key challenge for achieving ultra-low voltage threshold switching and ultra-high data stability. It has a detrimental effect on both the required writing voltage and on the data stability at zero voltage as the antiferromagnetic state develops a susceptibility to magnetic fields, even in the absence of an electric field (V G ¼ 0). We find that the gate bias voltage is a material characteristic in thin films of magnetoelectric antiferromagnets, and in the following we reveal its physical origin and derive a means to control its value. When combining the large body of data on Cr 2 O 3 thin-film systems 4,5,7,9,13,15,17,[22][23][24][25][26][27][28][29] , a coherent picture emerges: the total magnetoelectric energy density exerting a selection pressure on the antiferromagnetic order parameter in thin-film magnetoelectric antiferromagnets is composed of three effects that act simultaneously: The first term describes the linear magnetoelectric effect with its coefficient a reported to be about 1 ps m À 1 in Cr 2 O 3 (refs 18,30). This is the only desired effect in the context of MERAM devices, while the other two effects are parasitic. The second term is the influence of the exchange bias coupling strength J EB on the antiferromagnet. While this term was typically the strongest contribution in previous studies (Supplementary Note 3), it is zero in AF-MERAM due to the lack of a ferromagnet. The last term arises from a non-zero areal magnetic moment density r m within the antiferromagnet itself, which renders the material ferrimagnetic. This term, due to emergent ferrimagnetism, cannot be excluded a priori. The gate bias voltage can now be calculated from equation (1): The gate bias voltage V GB is in an intimate relation with the magnetoelectric coefficient a and the areal magnetic moment density r m at the onset temperature of the thermal stability of the antiferromagnetic order. Equation (2) implies that the gate bias in magnetoelectric field cooling experiments vanishes for perfectly antiferromagnetic order (r m ¼ 0). Its non-zero value in our system can be used to estimate the approximate ferrimagnetic moment density at the ordering temperature of about 21°C, yielding a value of r m % 0:1m B nm À 2 . Conversely, achieving a low gate bias voltage requires that ferrimagnetism is averted. The presence of ferrimagnetism cannot be accounted for by any intrinsic effect within the Cr 2 O 3 antiferromagnetic film, as all magnetic moments, including boundary moments 10,16,17 , are intrinsically compensated when accounting for all boundaries (Supplementary Note 4; Supplementary Fig. 1). Therefore, extrinsic effects are necessary to break the sublattice equivalence and produce ferrimagnetism. In the following, we present an in-depth study of extrinsic thin-film phenomena and their influence on the emergent ferrimagnetism. Namely, we invoke different degrees of crystalline twinning, elastic lattice deformation, intermixing and misfit dislocation density in Cr 2 O 3 thin films, by preparing three distinct systems with epitaxial underlayers of Al 2 O 3 (0001), Pt(111) or V 2 O 3 (0001).
One striking result is that the gate bias voltage, and thus the emergent ferrimagnetism, can indeed be controlled by the choice of underlayer material. In particular, when Cr 2 O 3 thin films are grown on a V 2 O 3 underlayer, ferrimagnetism is almost entirely eliminated. Figure 3a shows a magnetoelectric field cooling map of the V 2 O 3 -buffered system exhibiting virtually perfect EH symmetry. As highlighted by the indicated line profiles (Fig. 3b,c), the selection preference for a particular antiferromagnetic state vanishes when either E ¼ 0 or H ¼ 0, as expected from the pristine action of the linear magnetoelectric effect (first term in equation (1)). The possibility to completely eliminate the gate bias is highly relevant for AF-MERAM applications, as the AF state can then be switched with lower voltages (Supplementary Note 5; Supplementary Fig. 2) and is completely stable once the gate voltage returns to zero. Overview of state-of-the-art isothermal magnetoelectric switching studies using either the linear magnetoelectric effect in Cr2O3 or the multiferroic coupling in BiFeO3. The value (VH)C gives the magnetoelectric writing threshold (product of magnetic field and voltage). The writing voltage VC allows to qualitatively compare Cr2O3-based systems and BiFeO3 systems in terms of the voltage at which the magnetization state switches. *Application of the writing voltage does not switch the ferromagnetic Co, but only the antiferromagnetic Cr2O3, implying that the magnetic field must be removed for readout from the ferromagnet. wFor comparability, the writing voltages are calculated for a magnetic field of H write ¼ 0.5 MA m À 1 as was used in the present study. The actual used writing voltages in these studies are similar to the normalized values, as the magnetic fields were also similar. To pinpoint the specific extrinsic effect that is responsible for the different degrees of emergent ferrimagnetism in Cr 2 O 3 thin films grown on different underlayers, it is instructive to correlate the observed areal magnetic moment density and the various growth-induced effects ( Table 2). The areal magnetization is determined via the slope of the dependence of the antiferromagnetic order parameter selection on the magnetic field ( Fig. 4c;  Supplementary Fig. 5). The gradual shape of these dependences results from a selection tendency of uniaxial antiferromagnetic domains according to their ferrimagnetism, averaged over the readout electrode area. To verify that the microscopic ordering is indeed a mixture of purely uniaxial domains, images of the surface magnetization states after zero-field cooling (Fig. 4d) and field cooling (Fig. 4b) were obtained by scanning nitrogenvacancy (NV) magnetometry [31][32][33] . This technique measures the stray magnetic field % 50nm above the sample surface, clearly indicating the equal presence of up-and down-domains in the zero-field-cooled state. In contrast, field cooling predominantly selects one of the two domain orientations that allows to calculate the degree of ferrimagnetism in the films.
It should also be noted that measuring the gate bias voltage V GB (Equation (2)) provides a second route to quantify the areal magnetization r m absolutely, which is however restricted to conducting underlayers and suffers from the uncertainty of the value of a. Therefore, magnetization values determined via the gate bias will not be used for the comparison of the different underlayer materials.
Based on these data, we conclude that elastic film strain, twinning and cation intermixing in epitaxial Cr 2 O 3 films cannot account for the observed degree of ferrimagnetism, as none of these properties are correlated to the areal magnetization (Table 2). Instead, the results suggest that the lattice mismatch is the cause of the emergent ferrimagnetism.
The scaling relationship between the measured areal magnetic moment density and the linear lattice misfit between Cr 2 O 3 and its underlayer is shown in Fig. 4a. When taking into account the data of the three investigated systems, we find that the data align tightly to a quadratic scaling relation (red line). Such a relationship hints at the number of the misfit dislocations per area being the key property determining the areal ferrimagnetic moment density. This result leads to a picture in which the population of the two antiferromagnetic sublattices is unbalanced by the presence of misfit dislocations.
Such dislocations arise due to the heteroepitaxial film growth (Fig. 4f)   Underlayer material Twinning ratio (%) c axis compression (%) Expected miscibility Linear misfit (%) Areal magnetization q m (a.u.) The values for the structural properties are derived in detail in the (Supplementary Note 6; Supplementary Fig. 3; Supplementary Fig. 4). The ferrimagnetic moment density values are relative values obtained by zero-offset Hall (Supplementary Note 7; Supplementary Fig. 5; Supplementary Fig. 6). They are normalized to the approximate value for Pt/Cr 2 O 3 /Pt obtained via the gate bias voltage as of equation (2).   Fig. 4e, the dislocations (orange boxes) can contain unequal populations of spin 'up' and spin 'down' atoms if the dislocation terminates after an odd number of atomic layers. These surplus spins are all aligned within one domain due to the layered sublattice structure in a-Cr 2 O 3 (0001). While the magnetic moment of atoms near dislocations might be different from atoms in the relaxed lattice, this picture serves to illustrate that misfit dislocations do indeed unbalance the atomic populations in each of the two sublattices.
Remarkably, the lattice misfit not only correlates with the magnitude of the emergent magnetization, but also with its sign with respect to the antiferromagnetic order parameter. This sign change of the ferrimagnetic behavior in the case of tensile misfit for the V 2 O 3 -buffered sample emerges naturally from the previously introduced picture. Tensile misfit results in atoms being skipped from the bottom boundary sublattice instead of atoms being added. Therefore, tensile misfit results in the top boundary magnetization being aligned along the cooling field, while compressive misfit results in the top boundary magnetization being aligned opposite to the magnetic cooling field.
To quantify ferrimagnetism, we investigate the magnetic fieldinduced antiferromagnetic order parameter selection with no electric field applied (Fig. 4c), which is influenced exclusively by the last term of equation (1). The Al 2 O 3 buffered films are clearly more susceptible to the magnetic field than the V 2 O 3 -buffered films, which is in line with the substantially larger lattice misfit of the former over the latter. Moreover, a magnetic field of the same sign selects opposite antiferromagnetic states in the two systems, which corresponds to the opposite sign of the lattice misfit.
In conclusion, we demonstrated reliable room temperature magnetoelectric random access memory cells based on a new scheme that relies purely on antiferromagnetic components and does not require a ferromagnet for readout. This AF-MERAM provides substantially reduced writing thresholds over conventional MERAM prototypes, enabling further improvements in the energy efficiency of nonvolatile solid-state memory and logics. Since a permanent magnetic writing field does not interfere with readout in AF-MERAM, this new approach extends voltage driven writing to magnetoelectric antiferromagnets such as Cr 2 O 3 , whereas such functionality has previously been feasible only in multiferroic antiferromagnets such as BiFeO 3 (Table 1). It should be noted that the advantages of omitting the ferromagnet from MERAM cells likewise apply to multiferroic antiferromagnets, opening an appealing field of AF-MERAM with ultralow writing thresholds and superior stability of the magnetic order parameter. The concept also provides an important new building block for the emerging field of antiferromagnetic spintronics. While we did not investigate the speed of the actual writing process, first prototypes of conventional MERAM could be switched within a few tens of nanosecond 5 .
We use thin films of magnetoelectric antiferromagnetic Cr 2 O 3 as the core material and find that this material becomes ferrimagnetic when grown as epitaxial thin films. Emergent ferrimagnetism in thin films of magnetoelectric antiferromagnets can be desirable 34 . For the application to purely antiferromagnetic magnetoelectric elements, however, ferrimagnetism should be minimized. Through an in-depth structural characterization, we find that the observed degree of ferrimagnetism is correlated with the square of the linear lattice misfit between Cr 2 O 3 and its underlayer. This finding provides both a fundamental mechanism for the phenomenon of emergent ferrimagnetism and suggests a readily available tuning knob to enhance or eliminate the magnetic field coupling of magnetoelectric antiferromagnets.

Methods
Sample preparation. Oxide films were grown by reactive evaporation of the base metal in high vacuum onto c-cut sapphire substrates (Crystec GmbH) heated to 700°C initially and to 500°C after the first few monolayers. The background gas used was molecular oxygen at a partial pressure of 10 À 5 mbar. Chromium was evaporated from a Knudsen cell, vanadium was evaporated from a block target using an electron-beam and platinum was sputtered from a d.c. magnetron source. Deposition of the oxides was carried out using rates of about 0.4 Å s À 1 and was monitored in situ by reflection high-energy electron diffraction. Oxide layers were subjected to a vacuum annealing process at 750°C and residual pressure of 10 À 7 mbar directly after growth. The thin Pt top layers were deposited at lower temperatures of E100°C using a higher rate of 1.0 Å s À 1 to maintain layer continuity. Hall crosses were patterned from the top Pt layers, by SF 6 reactive ion etching around a photoresist mask.
Transport experiments. Transport was measured using zero-offset Hall 10 . Typical current amplitudes were on the order of 500 mA. RAM operation was carried out in a permanent magnetic background field of H % þ0:5MA m À 1 along the film normal.
To obtain the average AF order parameter dependence on the magnetic cooling field, the data of the spontaneous Hall signal after cooling under a range of field values were fitted by an expression that provides the normalization and the absolute magnetic moment distribution of individual domain pieces within the Cr 2 O 3 films (Supplementary Note 7). The relative domain sizes of films with different buffer layers were determined using zero-offset Hall by evaluating the statistics of the domain selection within the finite-size Hall crosses (Supplementary Note 7).
The structural properties of the Cr 2 O 3 films on different buffer layers were characterized by x-ray diffraction and channeling contrast scanning electron microscopy as shown in detail in (Supplementary Note 6).
NV magnetic microscopy. Scanning NV magnetometry was performed with a tip fabricated from single-crystal, o1004-oriented diamond that was implanted with 14 N ions at 6 keV, and annealed at 800°C to form NV centres 35 .An external field of 2.2 kA m À 1 was applied along the NV axis (diamond o1114 crystal direction) to induce Zeeman splitting of the NV electronic ground-state spin. A microwave driving field was then locked to the spin transition at E2.864 GHz to track the additional Zeeman shift due to the stray field of the magnetic film surface 36 . Magnetic field values for each pixel were obtained by averaging the microwave lock frequency for 7 s. Data availability. The data underlying the present work are available upon request from the corresponding authors.