Colossal Magnetoresistive Switching Induced by d0 Ferromagnetism of MgO in a Semiconductor Nanochannel Device with Ferromagnetic Fe/MgO Electrodes

Exploring potential spintronic functionalities in resistive switching (RS) devices is of great interest for creating new applications, such as multifunctional resistive random‐access memory and novel neuromorphic computing devices. In particular, the importance of the spin‐triplet state of cation vacancies in oxide materials, which is induced by localized and strong O–2p on‐site Coulomb interactions, in RS devices has been overlooked. d0 ferromagnetism sometimes appears due to the spin‐triplet state and ferromagnetic Zener's double exchange interactions between cation vacancies, which are occasionally strong enough to make nonmagnetic oxides ferromagnetic. Here, for the first time, anomalous and colossal magneto‐RS (CMRS) with very high magnetic field dependence is demonstrated by utilizing an unconventional RS device composed of a Ge nanochannel with all‐epitaxial single‐crystalline Fe/MgO electrodes. The device shows colossal and unusual behavior as the threshold voltage and ON/OFF ratio strongly depend on a magnetic field, which is controllable with an applied voltage. This new phenomenon is attributed to the formation of d0‐ferromagnetic filaments by attractive Mg vacancies due to the spin‐triplet states with ferromagnetic double exchange interactions and the ferromagnetic proximity effect of Fe on MgO. The findings will allow the development of energy‐efficient CMRS devices with multifield susceptibility.


Introduction
[4][5][6][7][8] RS is a phenomenon in which a device switches between a high-resistance state (HRS) and a low-resistance state (LRS) depending on the applied voltage.Generally, RS is observed in metal/insulator/metal structures, where metallic conductive filaments form along defects that are moved and aligned by an electric field applied to the insulating layer, thus greatly changing the resistance.[13][14][15][16][17][18][19][20] Thus, using the spin states in conductive d 0 -ferromagnetic filaments allows us to explore new possibilities for the spintronic applications of RS, such as multifunctional resistive-random access memories.However, little research has been conducted on spin states in RS devices.There are only a few studies on manipulating RS by an external magnetic field, in which tunneling magnetoresistance, [21] the magnetic field dependence of ferroelectricity, [22] and a spacecharge-limited current are used. [23]However, no study has utilized the spin states of vacancies in insulating materials to control RS.
For the first time, we demonstrate anomalous and colossal magnetoresistive switching (CMRS) with substantial magnetic field dependence using an unconventional RS device composed of a Ge nanochannel and all-epitaxial single-crystalline Fe/MgO electrodes.In the same device structure that involves Al/MgO electrodes instead of Fe/MgO, switching behavior does not appear, indicating the vital role of the Fe electrodes.We can attribute this new phenomenon to d 0 -ferromagnetic filament formation via the spin-triplet states of Mg vacancies in MgO, which become ferromagnetic due to Zener's double exchange interactions between the Mg vacancies and the proximity effect of the Fe electrodes.Our result demonstrates a novel method for using spin states of d 0 ferromagnetism in oxide vacancies, enabling energyefficient devices with ultrahigh multifield susceptibility.

Preparation of the Ge Nanochannel Device with Fe/MgO Electrodes
We grow an epitaxial single-crystal ferromagnet/insulator/semiconductor heterostructure composed of Fe (17 nm)/MgO (1 nm)/Ge:B (34 nm, B concentration: 1 × 10 15 cm −3 )/Ge (51 nm) on an n − -Ge (001) substrate using molecular beam epitaxy (see Section 5 and Figure 1a-e).During growth, the in situ reflection high-energy electron diffraction shows streaky patterns, indicating that the Ge:B, MgO, and Fe layers grow epitaxially on the substrate (Figure S1, Supporting Information).This feature is confirmed in the lattice image taken by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), as shown in Figure 1e.After growth, we partially etch the Fe layer to a thickness of ≈2 nm by Ar-ion milling.The two-terminal device structure with a drain electrode (3 × 20 μm 2 ) and a source electrode (1 × 20 μm 2 ) is patterned using electron beam lithography and Ar-ion milling (Figure 1a-d).These electrodes are separated by a Ge:B channel with a width of ≈20 nm (Figure 1d, Figure S10, Supporting Information).This device structure is similar to that of ref. [24] which involves Au electrodes and a GaAs channel; in that structure, RS is observed, but it disappears in a magnetic field.As a reference device, we prepare a device with the same structure; however, we use Al electrodes instead of Fe electrodes.We implement the same procedure described above to prepare this reference device, but the Al layer is deposited by sputtering after growth (Section 5).For the sample used for the device with the Fe electrodes, we see a magnetization hysteresis loop for the perpendicular and in-plane magnetic field directions due to the small thickness of Fe (≈2 nm, see Figure S2, Supporting Information).This result indicates that the thin Fe electrodes have both perpendicular and in-plane magnetic anisotropy components.We ground the source electrode and apply a bias voltage V DS to the drain electrode to measure the drain-source current I DS .We obtain the drain-source resistance R(H) = V DS /I DS with an external magnetic field H, as described below.

Characteristics of Our Device
Our device shows I DS -V DS curves that are typical of conventional RS devices; we see a threshold voltage (V th ) with a steep increase in I DS from the HRS to the LRS at a temperature T = 3 K (Figure 2a).As shown in Figure 2b, hysteresis exists in the I DS -V DS characteristics; the V th value obtained when V DS is swept from low to high is larger than that when swept from high to low.This behavior is typical of RS.Thus, filament formation via vacancies is the most likely conduction mechanism in our device, which is similar to conventional RS devices.The striking difference of our device is the strong magnetic field response.In Figure 2a, we observe a large shift in V th of 1.87 V by changing μ 0 H from 0 T to 1 T (from 7.12 V to 8.99 V).Furthermore, the ON/OFF ratio defined as (R ON − R OFF )/R OFF , where R ON and R OFF are the values of R(H) at V DS = V th + 0.03 V and V DS = V th − 0.03 V, respectively increases from 3000% to 8500% when changing μ 0 H from 0 to 0.7 T, as shown in Figure 2c, where H is applied along the [110] direction in the film plane.This is unusual behavior for RS.The strong magnetic field dependence suggests that the spin states in the filaments are crucial for transport.Another important feature is that the large H dependence of V th disappears when the temperature increases to 20 K, although RS continues, as shown in Figure 2d.At 20 K, V th hardly moves when the magnetic field changes.As shown in the temperature dependence of the resistance under various magnetic fields, this anomalous magnetic field dependence appears at temperatures lower than 10 K (Figure 2e).This result suggests that this unusual magnetic field responsivity originates from some spin ordering emerging at low temperatures (in Supporting Information, we show the temperature dependence of the I DS -V DS characteristics in Figure S6, the MR curves at 20 K in Figure S8, and the endurance test results in Figure S9). [14,16]he magnetoresistance (MR) curves show large switches between the HRS and LRS (Figure 3a); threshold magnetic fields (H th ) are observed in these curves, with steep jumps of R to values more than two orders of magnitude larger.The shapes of the MR curves are susceptible to the V DS values, and H th monotonically increases with increasing V DS (from violet to yellow in Figure 3a).The MR ratio, which is defined as axis in the film plane (Figure 3b).We observe similar MR curves when H is applied perpendicular to the film plane (along [001]) (Figure 3c), with an MR ratio reaching 11 000% [= (1650 MΩ − 15 MΩ)/15 MΩ] at V DS = 9.0 V (Figure 3d).Moreover, similar behavior appears when H is applied along [110] in the film plane (Figure 3e), although the signal is unstable.Thus, this phenomenon does not strongly depend on the magnetic field orientation.This result indicates that this phenomenon is fundamentally different from the previously observed magnetic field dependence of the RS due to the Lorenz force, which disappears when the magnetic field direction is along the current direction, observed in RS devices with a long oxide channel of 5 μm. [23]As shown in Figure 3f, for the reference device with Al electrodes, MR is apparent.However, we do not see any steep switching; we see a monotonous and much smaller change in MR (see Figure 3f and Figure S3, Supporting Information, for the I DS -V DS characteristic), which is known to appear in Ge. [25] This result indicates the vital role of the Fe electrodes in the CMRS with high magnetic field responsivity observed in this study.

Discussion of the Transport Mechanism
Similar to conventional RS, the origin of the steep jump in I DS (Figure 2a) and the hysteresis (Figure 2b) in the I DS -V DS characteristics can be attributed to the formation of conductive filaments.In our system, the possible constituents of the filaments are vacancies of Mg and O atoms in MgO, [11,12,[14][15][16]18] diffused Fe atoms in MgO, and B atoms in Ge. RS as been widely observed for MgO.[21,[26][27][28] Our spatially resolved electron dispersive X-ray (EDX) analysis shows slight Fe diffusion into the MgO layer (Figure S7, Supporting Information).However, diffused Fe atoms are relatively dispersive.Fe atoms would have to replace onsite Mg atoms for filament formation by the electric field.Meanwhile, Mg vacancies can move much more easily. Mg defectsseem relatively concentrated in the blurred-lattice regions where strain will be strong, as shown in Figure 1e.Thus, the strong magnetic field responses of our device and the necessity of the Fe electrodes suggest that this phenomenon is related to the spin state in the d 0 -ferromagnetic conduction filaments formed by Mg vacancies, where attractive forces work between those vacancies (Figure 4a).In the HAADF-STEM crosssectional lattice image shown in Figure 1e, regions exist where Mg atoms (white dots) are not discernible in the MgO layer; these regions result from the imperfect compatibility between Ge and MgO.In the EDX mapping (Figure S7, Supporting Information), one can see a slight diffusion of Mg atoms into the Ge:B layer, which may cause the formation of Mg vacancies.In this sample, the MgO layer is overly thin (=1 nm), preventing full recovery of defects during growth.The Mg vacancies provide holes with a spin-triplet state and sometimes make MgO ferromagnetic due to Zener's double exchange interactions between the vacancies.[11][12][13][14][15][16][17][18][19]29] When V DS increases, the attractive Mg vacancies migrate and create ferromagnetic conduction filaments, resulting in the LRS (Figure 4b).When V DS decreases to a value lower than that when the filaments form, they collapse and hysteresis appears.
Although there may be several possible scenarios for CMRS in a magnetic field, the most likely case is as follows.The Mg vacancies in MgO provide two localized O-2p holes around the oxygen atoms adjacent to each vacancy. [30]Due to the localized nature of O-2p orbitals, these holes, which take a spinsinglet state when they are in the same orbital in general cases, repel each other through strong on-site Coulomb interactions and then form a spin-triplet state in different orbitals to decrease Coulomb repulsion.][33][34][35][36][37][38] Thus, the O-2p holes exhibit large exchange splitting in Mg vacancies.When Mg vacancies are adjacent, holes hop between Mg vacancies and are spin-polarized by exchange splitting, forming partially occupied impurity bands and reducing the band energy.6]18] This ferromagnetic exchange interaction is strong yet short-range.Therefore, ferromagnetic ordering is very weak when the film is thin (≈1 nm), as in our case.According to first-principles calculations, an attractive chemical potential exists between Mg vacancies with ferromagnetic exchange interactions, [36,37,43] supporting the formation of conductive filaments in MgO.The Curie temperatures of these filaments are es-timated to be low because of their one-dimensionality.However, in our device, the wavefunctions of the adjacent Fe electrodes can enter MgO, inducing a ferromagnetic-proximity effect that stabilizes the weak ferromagnetism.The ferromagnetism may be partially caused by Fe diffusion into the MgO layer or the stray field from the Fe layer due to the atomic-level roughness [44] of the Fe/MgO interface.Due to the extremely thin Fe layer in our device, we can easily change the magnetization direction in any orientation due to interfacial perpendicular anisotropy, [45] resulting in the relatively isotropic magnetic field direction dependence (Figure 3a,c,e).
When a magnetic field is applied, the spin states of the Mg vacancies are aligned, and the ferromagnetism becomes stable; however, this effect drastically increases the local exchange field (exchange splitting) around the vacancies.This phenomenon localizes the hole wavefunctions because of the Pauli exclusion principle, reducing the hopping probability of holes between Mg vacancies and weakening the ferromagnetism of MgO, which In (b), wavefunctions of the Mg vacancies are connected due to the electric field, forming a conduction filament.Here, the connected wavefunctions are expressed by bright spheres.In the filament, weak d 0 ferromagnetism is realized due to Zener's double exchange interaction and the proximity effect due to the adjacent Fe layer.Thus, spins in filaments are roughly aligned.In (c), when a magnetic field is applied, spins are aligned more strongly.However, due to the Pauli exclusive principle, holes cannot overlap, and thus, the wavefunctions shrink.Then, the conduction filament is broken.
is caused by Zener's double exchange interactions (Figure 4c).Thus, a relatively high V th is needed for the formation of conductive filaments because of the reduced attraction between the Mg vacancies (Figure 2a,b). [43]With increasing temperature, the weak ferromagnetism of MgO greatly weakens.The abovementioned repulsion of the wavefunctions by the magnetic field application decreases in effectiveness.This reduced effectiveness may explain why the magnetic field dependence disappears at temperatures as low as 10 K (Figure 2e).When Al electrodes are used for the device, the ferromagnetic proximity effect is absent.In this case, filaments do not form because the attractive chemical potential is weak in nonmagnetic MgO.Thus, the resistance remains high even with a large V DS , and RS does not occur (Figure 3f).
To confirm this scenario, we calculate the electronic state of MgO with a Mg vacancy concentration of 5% using the first-principles calculation.As shown in Figure 5a, the calculated density of states reveals exchange splitting between the up-spin and the down-spin states, meaning that the ferromagnetic state is stable due to the presence of Mg vacancies.The calculated exchange coupling constant shown in Figure 5b demonstrates that the ferromagnetic state is stable between oxygen atoms.The calculated chemical pair interaction in Figure 5c shows that an attractive force exists between nearestneighbor Mg vacancies (their distance is ≈0.7 of the lattice constant), which is the origin of the conductive filament formation.
We simulate the crystal structure of MgO with Mg vacancies after layer-by-layer growth using the Monte Carlo method (Figure 5d-f).In Figure 5d, Mg vacancies are found to be agglomerated due to the attractive forces between nearest-neighbor Mg vacancies.In Figure 5e, due to the gathering of Mg vacancies, the surrounding oxygen atoms are connected in a filamentary form.In Figure 5f, due to the network of oxygen atoms with ferromagnetic bonds, ferromagnetism prevails in entire conductive filaments.Thus, the ferromagnetic filaments are formed.This picture is consistent with our experimental results.
Our large MR may appear similar to the space charge effectinduced MR, [25,46] in which a magnetic field can largely modulate the current-voltage characteristics.However, neither steep RS nor hysteresis appears in the space charge effect-induced MR.Moreover, in our case, the current is not proportional to the voltage square (Figure S4, Supporting Information), differing from the space charge effect.To eliminate the role of hydrogen atoms in RS, [47,48] we carry out secondary ion mass spectrometry (SIMS) measurements.The obtained hydrogen concentration in the MgO layer is estimated to be ≈0.7% of the MgO host atoms.This value is smaller than that reported for all SiO 2 samples in ref. [47], suggesting that hydrogen atoms in our film have little or almost no effect.Our results may be similar to the electrical breakdown in semiconductors with impact ionization, in which the breakdown voltage largely depends on the doping concentration. [49]However, we have nearly the same switching voltage of less than ≈10 V when using the B concentration of 10 18 cm −3 for the Ge:B buffer layer (not shown).Therefore, we cannot explain our results using this phenomenon.
From the discussion above, the aforementioned scenario, in which conductive, weak d 0 -ferromagnetic filaments form via spin-triplet states of Mg vacancies in MgO because of the ferromagnetic proximity effect from the Fe electrodes, is the most likely explanation for our experimental results.Further microscopic investigations should elucidate detailed mechanisms of CMRS.Although our demonstration is performed at low temperatures, there are several possible methods for increasing the operating temperature.One technique is to form thick self-organized Konbu-phase nanorods instead of the thin Mg vacancy filaments in the MgO layer. [36,37,43]In this case, we can increase the volume of percolation paths with double exchange interactions, thus increasing the Curie temperatures of the conduction filaments.Other possible approaches involve using different oxide materials with strong ferromagnetism, large vacancy concentrations, or strong on-site Coulomb interactions.This unique method of using vacancies in oxides may pave a novel path for creating energy-efficient devices with high multifield susceptibility.

Experimental Section
Sample Preparation: An epitaxial single-crystal heterostructure composed of Fe (17 nm)/MgO (1 nm)/Ge:B (34 nm, B concentration: 1 × 10 15 cm −3 )/Ge (51 nm) was grown on an n − -Ge (001) substrate using molecular-beam-epitaxy (MBE) with a base pressure of 5 × 10 −9 Pa (Figure 1).Here, n − -Ge means a lightly doped n-type Ge with a doping concentration of ≈10 17 cm −3 .Before growth, the Ge substrate was chem-ically cleaned with ultrapure water, ammonia water, and acetone, and it was etched with ultrapure water and buffered hydrogen fluoride (HF) in a cyclical manner for 40 min.Then, the substrate was installed in the ultrahigh-vacuum MBE growth chamber through an oil-free load-lock system.Initially, the Ge substrate was degassed at the substrate temperature T S = 300 °C for 30 min and thermally cleaned at T S = 700 °C for 30 min.After the thermal treatment, the Ge:B layer was grown on the Ge substrate at T S = 300 °C.The MgO layer was deposited by electron beam evaporation at T S = 80 °C with a deposition rate of 0.1 nm s −1 , followed by Fe layer growth at T S = 80 °C in the same MBE chamber.After growing each of the MgO and Fe layers, the sample was annealed at T S = 200 °C for 10 min to improve the flatness of each interface.During growth, in situ reflection high-energy electron diffraction (RHEED) showed streaky patterns, indicating that the MgO and Fe layers were epitaxially grown on Ge:B (Figure S1, Supporting Information).No apparent Fe oxidization was seen in the heterostructure (Figure S5, Supporting Information).After growth, the Fe layer was partially etched to a thickness of ≈2 nm by Ar-ion milling.The two-terminal device structure with a drain electrode (3 × 20 μm 2 ) and a source electrode (1 × 20 μm 2 ) was patterned using electron beam lithography and Ar-ion milling.In the first lithography and etching processes, the Ge:B layer was etched off, except for the mesa region (Figure 1a-c).In the subsequent lithography and etching processes, the Fe and MgO layers in the channel region were etched off.The Ge:B layer in this region was left unetched as a channel (Figure 1a-c).As a reference, a similar device was made using Al electrodes instead of Fe.By using the same growth conditions as those used for the device with the Fe electrodes, MgO (1 nm)/Ge:B (10 nm, B concentration: 1 × 10 15 cm −3 )/Ge (51 nm) was grown on an n − -Ge (001) substrate.After growth, a 50-nm Al layer was sputtered and a two-terminal device was made using the same process.
First Principles Calculation: The first-principles calculations of electronic structures for MgO with Mg vacancies were performed using the AkaiKKR code, [50] which was based on the Korringa-Kohn-Rostoker Green's function method. [51,52]The randomness of atomic configurations was treated using the coherent potential approximation (CPA). [53,54]Here, the charge screening effect, which can be a problem in a single-site approximation, was taken into account in the calculations.To describe the O-2p states correctly, the variational pseudo-self-interaction correction method [55] was employed for the exchange-correlation potential.
To investigate the origin of ferromagnetism quantitatively, the Heisenberg exchange coupling constant was calculated based on Liechtenstein's formula. [56]This method considers the total energy change due to perturbations caused by the rotations of magnetic moments following the force theorem. [57]Chemical pair interactions between Mg vacancies were calculated using the generalized perturbation method. [58]In this method, the configuration-dependent energy, which was the deviation from a perfectly disordered CPA system, was expanded in concentration fluctuations.During these calculations, the concentration of Mg vacancies was assumed to be 5%, and the lattice constant was fixed to the experimental value of MgO: 4.21 Å.
Seike et al. proposed that Mg vacancies form "self-organized nanowires (Konbu phase)" by layer-by-layer crystal growth. [36]In the present study, to investigate the effect of such nanostructures on ferromagnetism, the formation of filaments was simulated using the Monte Carlo (MC) method with the calculated exchange coupling constant.The concentration of Mg vacancies was fixed at 5% in the simulation box, consisting of the 20 × 20 × 20 conventional cells.100 000 MC steps and scaled temperature k B T/|V 01 | = 0.01 were employed to simulate the structure of MgO with Mg vacancies, where k B is the Boltzmann constant and V 01 is the chemical pair interaction between nearest-neighbor Mg vacancies.
Statistical Analysis: No statistical analysis was adopted in the experiments.

Figure 1 .
Figure 1.a) Top view, b) bird's eye view, and c) side view of the Ge-nanochannel device made from an epitaxial single-crystalline heterostructure composed of Fe (2 nm)/MgO (1 nm)/Ge:B (34 nm; B concentration of 1 × 10 15 cm −3 )/Ge (51 nm) on an n − -Ge (001) substrate.d) Scanning electron microscopy top view near the channel region of the sample.e) Scanning transmission electron microscopy lattice image of the grown sample taken with the electron beam azimuth along the [100] axis of Ge.

Figure 2 .
Figure 2. I DS -V DS characteristics at various H values at 3 K a) when V DS is increased from zero and b) when V DS first increases from zero and then decreases.c) ON/OFF ratios at various H values at 3 K. d) I DS -V DS characteristics at various H values at 20 K when V DS increases from zero.e) Temperature dependence of R for μ 0 H = 0, 0.5, and 1 T applied along the [110] direction in the film plane when V DS is 7 V.In (a), (d), and (e), the color of the curves corresponds to the magnetic field shown in the color bars.The arrows represent the sweep direction of V DS .

Figure 3 .
Figure 3. a) MR curves for various V DS and b) MR ratios as a function of V DS when H is applied along the [110] direction of Ge in the film plane at 3 K. c) MR curves for various V DS and d) MR ratios as a function of V DS when H is applied perpendicular to the film plane of Ge (the [001] direction) at 3 K. e) MR curves for various V DS when H is applied along the [ 110] direction in the film plane at 3 K. f) MR curves for various V DS obtained for the reference device with Al electrodes with various H values applied perpendicular to the film plane at 3 K.In (a), (c), (e), and (f), the thick (thin) curves represent the results obtained when H is swept from plus to minus (minus to plus).In (a), (c), and (e), the arrows represent the sweep direction of H.In (a), (c), and (f), the color of the curves corresponds to the V DS value shown in the color bars.

Figure 4 .
Figure 4. a-c) Schematic pictures of the conduction mechanism in our device.(a) shows the case when V DS and H are overly small, preventing the formation of conduction paths (HRS).(b) shows the case when V DS is sufficiently large to form conduction paths (LRS).(c) shows the case when H > H th with the same V DS as (b).In (c), due to V th being increased by H, V th becomes larger than V DS .The conduction paths disappear due to the localization of holes (HRS) due to the magnetic field application.In (a-c), the small pale blue spheres represent O-2p holes, and the arrows represent the spins of holes.The transparent white spheres express hole wavefunctions.The red spheres represent Mg vacancies.Due to the strong confinement of holes around the Mg vacancies, they take a spin-triplet state in each Mg vacancy.The gray region expresses the background of the paramagnetic MgO layer.In (b), wavefunctions of the Mg vacancies are connected due to the electric field, forming a conduction filament.Here, the connected wavefunctions are expressed by bright spheres.In the filament, weak d 0 ferromagnetism is realized due to Zener's double exchange interaction and the proximity effect due to the adjacent Fe layer.Thus, spins in filaments are roughly aligned.In (c), when a magnetic field is applied, spins are aligned more strongly.However, due to the Pauli exclusive principle, holes cannot overlap, and thus, the wavefunctions shrink.Then, the conduction filament is broken.

Figure 5 .
Figure 5. a-c) Calculated electronic states for MgO with a Mg vacancy concentration of 5%.In (a), the black and blue lines express the total density of states and the partial density of states of oxygen p-orbitals, respectively.(b) shows the exchange coupling constant between oxygen atoms as a function of their distance, where the positive and negative values express the ferromagnetic and antiferromagnetic interactions, respectively.(c) shows the chemical pair interaction between Mg vacancies as a function of their distance, where the positive and negative values express repulsive and attractive interactions, respectively.d-f) Simulated crystal structure of MgO after layer-by-layer growth obtained by the Monte Carlo method.(d) shows Mg vacancies.(e) shows Mg vacancies and the surrounding oxygen atoms.(f) shows Mg vacancies and ferromagnetic bonds between oxygen atoms.Here, red spheres represent Mg vacancies, white spheres represent oxygen atoms, and gray lines represent ferromagnetic bonds between nearest-neighbor oxygen atoms.