Post Deposition Interfacial Néel Temperature Tuning in Magnetoelectric B:Cr2O3

Boron (B) alloying transforms the magnetoelectric antiferromagnet Cr2O3 into a multifunctional single‐phase material which enables electric field driven π/2 rotation of the Néel vector. Nonvolatile, voltage‐controlled Néel vector rotation is a much‐desired material property in the context of antiferromagnetic spintronics enabling ultralow power, ultrafast, nonvolatile memory, and logic device applications. Néel vector rotation is detected with the help of heavy metal (Pt) Hall‐bars in proximity of pulsed laser deposited B:Cr2O3 films. To facilitate operation of B:Cr2O3‐based devices in CMOS (complementary metal‐oxide semiconductor) environments, the Néel temperature, TN, of the functional film must be tunable to values significantly above room temperature. Cold neutron depth profiling and X‐ray photoemission spectroscopy depth profiling reveal thermally activated B‐accumulation at the B:Cr2O3/ vacuum interface in thin films deposited on Al2O3 substrates. The B‐enrichment is attributed to surface segregation. Magnetotransport data confirm B‐accumulation at the interface within a layer of ≈50 nm thick where the device properties reside. Here TN enhances from 334 K prior to annealing, to 477 K after annealing for several hours. Scaling analysis determines TN as a function of the annealing temperature. Stability of post‐annealing device properties is evident from reproducible Néel vector rotation at 370 K performed over the course of weeks.


Introduction
Magnetic field and magnetization are axial or pseudovectors. 1 Manipulating the axial magnetization vector solely with the help of a polar electric field vector is a key challenge in the field of spintronics.However, electric field control of magnetization in the absence of dissipative electric currents is essential for energy efficient devices with applications in information technology.Of particular interest is energy-efficient, ultra-fast and non-volatile switching at temperatures which allow operation in a CMOS environment.Antiferromagnets, which avoid the slow (ns) magnetization reversal of ferromagnets, are candidates for ultra-fast spintronics.
Voltage-controlled antiferromagnetic (AFM) spintronics promise energy efficiency due to the absence of dissipative electric currents required in spin transfer torque or spin orbit torques alternatives.Recently, boron (B) doping of the prototypical magnetoelectric antiferromagnet Cr2O3 revealed new functionalities beyond the magnetoelectric effect of undoped Cr2O3 (chromia), i.e., induced magnetization (polarization) in the presence of an electric (magnetic) field.3][4] Below its antiferromagnetic ordering temperature, TN, spatial and time inversion symmetry are broken while the combined operation of parity and time inversion leave the system invariant.Under these conditions, the linear magnetoelectric effect becomes symmetry allowed.A diagonal magnetoelectric susceptibility emerges with distinct magnetoelectric response parallel and perpendicular to the three-fold symmetry axis of the system. 36][7] More surprisingly, in B:Cr2O3 a different type of magnetic response with an applied electric (E) field emerges.It enables isothermal voltage-controlled rotation of the Néel vector by π/2 in the absence of an applied magnetic field. 8180 degree switching of the Néel vector has been achieved in chromia when utilizing its magnetoelectric effect to lift the degeneracy between the two 180degree domain states.In pure Cr2O3 switching requires simultaneous application of an E-field (polar vector) and magnetic (H) field (axial vector) along the crystallographic c-axis.[11][12][13][14][15] Because voltage controlled Néel vector rotation in B:Cr2O3 takes place in H=0, the magnetoelectric effect, although still present in B:Cr2O3, is not causing the spin rotation.While details of the rotation mechanism are still under investigation, there is strong evidence from piezo force and magnetic force microscopy that B-doping breaks local spatial inversion symmetry.The local symmetry breaking creates polar nanoregions, which, in the presence of a homogenous Efield, give rise to uniform polarization.Piezo response accompanies the polarization, which strains the sample.Magnetoelastic coupling changes the anisotropy in response to the strain, which gives rise to non-volatile reorientation of the easy axis and reorientation of the Néel vector from in-plane to out-of-plane orientation and back. 16Magnetotransport measurements are sensitive to the orientation of the Néel vector.A heavy metal (Pt) Hall-bar in proximity of B:Cr2O3 films enables detections of a transverse Hall voltage, Vxy, in response to a current density j applied in the xdirection of the Hall bar where z points normal to the plane.The voltage signal Vxy can be used as a proxy for the boundary magnetization of the antiferromagnet.Boundary magnetization is an equilibrium property of insulating magnetoelectric antiferromagnets and is known from rigorous symmetry considerations 17 and the concept of magnetoelectric multipolization. 18It describes a roughness insensitive surface magnetization, which intimately couples to the orientation of the Néel vector.Magnetotransport measurements are sensitive to the orientation of the boundary magnetization and thereby the orientation of the Néel vector.Experiments suggest that spin Hall magnetoresistance associated with interfacial spin scattering provides the dominant contribution to Vxy. [19][20][21] Alternative mechanisms include proximity effects and interfacial chiral spin structures. 22Recent Hall measurements in large applied magnetic fields add to the notion that spin Hall magnetoresistance is not the sole contributor to the Hall signal. 23[13] In this work, we show that the operation temperature for reliable, voltage controlled Néel vector toggling, can be thermally tuned within a temperature range as wide as Δ ≈200 K via a post-deposition annealing protocol.First, we discuss data from cold Neutron Depth Profiling (cNDP) and x-ray photoemission spectroscopy (XPS) depth profiling which reveal that annealing transforms the B-concentration depth profile from its as-deposited virtually uniform profile into a peaked concentration profile with its maximum near the surface of the B:Cr2O3 film.These data are accompanied by magnetotransport measurements in B:Cr2O3/Pt Hall-devices.In agreement with the evolution of the concentration profile measured via cNDP and XPS, the transport data imply that the Néel temperature at the surface increases in response to annealing.We determine the dependence of the Néel temperature on the annealing temperature via a scaling analysis of the Vxy versus T data measured after various annealing protocols.

Sample preparation
Pulsed Laser Deposition (PLD) in ultra-high vacuum with a base pressure of ≈ 5x10 -9 Torr (≈ 7 × 10 −7 Pa) is used to grow (0001)-oriented films of the sesquioxides V2O3 and subsequently, B-doped chromia.The V2O3 film, which is grown on the c-plane of a sapphire single crystalline substrate, serves as bottom electrode in a gated Hall bar structure, to be used in magnetoelectric transport studies.The sapphire substrates were cleaned using a modified Radio Corporation of America protocol. 24The substrates were heated to 820 • C during V2O3 deposition.A KrF excimer laser with pulse energies of 200 mJ, a spot size of ≈ 6 mm 2 , and a pulse width of 20 ns (at a repetition rate of 10 Hz) was used to ablate a V2O3 target.The target-to-substrate distance was kept at about 9 cm and the substrate rotation rate was at 4 rpm.Cr2O3 was then grown on the resulting substrates (described above) using PLD, in the presence of a decaborane (B10H14) background gas.
The pulse energy was 190 mJ and the frequency was 10 Hz for Cr2O3 target.The temperature of the substrate was maintained at 800 °C during deposition of the chromia films.The growth rate of Cr2O3 (V2O3) was about 0.025 nm/s (0.017 nm/s), and the thickness was maintained at 200 nm (20 nm).For the neutron depth profile experiments, 300 nm B-doped Cr2O3 were grown directly on sapphire substrates as these samples did not require bottom electrodes.The structural properties were characterized using X-ray diffraction and the surface roughness was confirmed to be below a root mean square value of 0.25 nm (see Figs. 1S and 2S in supplementary information).We also performed XPS depth profiling.This destructive method required growth of an additional sample which was fabricated to be comparable to the sample used for transport measurements.To this end a 200 nm thick Cr2O3 film on a 20 nmV2O3 bottom layer supported on a (0001) sapphire substrate was fabricated.Further details of growth and characterization are provided in our earlier studies. 16r electrical transport measurements, a 5 nm thick Pt film was deposited on Cr2O3 film via DC magnetron sputtering in a vacuum chamber with base pressure of 1 × 10 -8 Torr (1.33 × 10 -6 Pa) and a process pressure of 5 mTorr (0.667 Pa) with an applied power of 30 W. The heterostructure thus consists of a Pt thin film on top of 200 nm B-doped Chromia film grown on a back gate V2O3 film (20 nm).Pt was then patterned into 1 µm x 8 µm sized star-shaped Hall bar structures using e-beam lithography.Additional details of device fabrication are provided in the supplementary information of Ref. [16].We note that samples of different thicknesses have been grown specifically for the different measurement techniques.For transport measurements, our routine chromia layer thickness is 200 nm, that serves to apply a relatively lower voltage pulse for switching experiments.For XPS measurements we used a similar sample, i.e., a 200 nm of B:Cr2O3 on 20 nm V2O3, supported on sapphire substrate.In the case of cNDP measurements, the instrument resolution required the Cr2O3 layer to be a few hundred nm and hence 300 nm was chosen to be a nominal value.As the target was to measure B distribution in the sample, it was decided to confine ourselves with using the B:Cr2O3 directly grown on sapphire to keep the experimental observations straightforward.

Cold Neutron Depth Profiling
Cold neutron depth profiling experiments were completed at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR). 25Within this facility cold neutrons are provided by a 20 MW nuclear reactor equipped with a liquid hydrogen cold source. 26perimental data were collected at Neutron Guide-5 (NG-5) at the NIST cold neutron depth profiling station (see Ref. [ 27 ] for instrument description -note that the instrument location and neutron fluence rate has changed since the publication of this cited manuscript).cNDP experiments were conducted by mounting a sample behind a ≈ 5.0 mm (diameter) opening in a ≈ 5 mm thick Teflon (fluorinated ethylene propylene) circular aperture.This aperture was mounted onto a large Al disk with a ≈ 30 mm (diameter) hole in its center, which was aligned to face a circular transmission-type silicon surface barrier detector (Ametek).The detector was located ≈ 120 mm from the sample surface.NDP results are the average distribution of 10 B across the surface area of ≈ 5.0 mm aperture opening. 10 All four charge particle products of the 10 B(n,α) 7 Li reaction were measured, but only the 4 He particle profile from the 93.57% branching ratio reaction was utilized to calculate final concentration values. 28This is due to the high counting statistics of this profile as compared to the other three profiles, as well as the low profile overlap with the low energy background spectrum.
Each sample was measured for ≈ 30 h.Profiles of a non-borated chromia film (experimental blank), a 10 B concentration standard (in-house, N6 series), and a 10 B energy reference material (NIST SRM93a) were also collected using the same experimental setup.Each area analyzed was irradiated at a near constant cold neutron fluence rate of 1.2× 10 9 neutrons cm 2 sec -1 , with any variations in the fluence rate being corrected via data collected from a neutron monitor.The data was binned to the approximate resolution of the detector (≈ 20 keV).
The 10 B atom cm -2 concentration was calculated using where [a] and [b] are the concentrations ( 10 B atoms/cm 2 ) of isotopes a and b being measured in the sample and standard, respectively, and 0 is the thermal neutron cross-sections for the charged-particle emissions (≈3600 barns, 1 barn = 1x10 −28 m 2 ).Concentration uncertainty is reported to 1σ and is based on experimental counting statistics.
Conversion of data to depth profiles was completed via construction of a channel vs. energy (keV) and an energy (keV) vs. depth (nm) calibration curves.The data in the channel vs. energy (keV) curve were collected experimentally using a similar setup to that described above.The data in the energy (keV) vs. depth (nm) calibration curve were acquired by modeling α particle transport and interaction with the device's chromia layer in TRIM, a subprogram of SRIM (2008). 29An assumed theoretical density of 5.22 g cm -3 for the chromia (Cr2O3) layer was used in all modeling along with an initial α particle energy of 1472.42 keV and mass of 4.0015 u (1.6605x10 −27 kg). 27ofiles shown in Fig. 1a have the depth scale reported relative to Cr2O3.The sapphire layer and vacuum were not modeled.
Samples were heat-treated using a top-loading closed-cycle refrigerator (CCR, Janis) and a temperature controller (Lakeshore 340).Only one (1) sample was heat-treated at a time to prevent cross-sample contamination.For heating, a sample was loaded into a clean aluminum holder and then enclosed in the CCR vacuum chamber, which was subsequently evacuated to a pressure of ≈ 0.001 Pa.This pressure was maintained over the course of the heat-treatment.Samples were heated to either 500 K or 400 K depending on the experimental guidelines using a heating rate of 5 K/min.
The samples were held at their respective treatment temperatures for ≈ 18 h, after which they were cooled to room temperature using a cooling rate of 5 K/min.Samples were immediately loaded into and measured by NDP following completion of their heat-treatments.
Fig. 1a shows the measured B-concentration profile of the as-deposited sample prior to heat treatment.The concentration profile is virtually constant and, as expected, decreases at the interfaces to vacuum (depth = 0 nm) and sapphire (depth ≈ 300 nm) respectively.The concentration depth profile after 18 hours of annealing at 500 K (circle) and a second annealing cycle of 18 hours with total exposure time of 36 hours at 500 K (triangles) are also presented in Fig. 1a.The two In the case of diffusion, particle currents are driven by concentration gradients.The evolution of a system towards equilibrium is associated with a reduction of the concentration gradient, which causes the particle current.Fig. 1 shows cNDP data sets taken after annealing for 18 hours and 36 hours.These two data sets are virtually identical indicating that the B-concentration increase in the 50 nm surface layer region is a thermodynamic equilibrium feature.A process solely driven by a concentration gradient would have progressed as long as a concentration gradient can drive a particle current.This has not been observed.Rather a stable equilibrium profile evolved.The measured profile, which shows a sizable concentration gradient in thermal equilibrium, is rather the result of a surface segregation process.Surface segregation describes the enrichment of an element (here B) in an alloy at the surface with respect to the bulk.The concentration profile resulting from surface segregation is an equilibrium property and has been extensively studied in metal alloys. 30It is determined by the temperature dependent Gibbs surface free energies of the constituents.That implies on one hand that the annealing temperature controls the surface segregation and, in contrast to solely concentration drive diffusion, leads to a concentration profile with a gradient near the surface.Although the overall amount of B, integrated over the volume of the sample, might very well be reduced on annealing, it appears from Fig. 1a that the Bconcentration in the 50 nm subsurface layer increased as a result of annealing.In this context it is worth to remember that diffusion, as described by Fick's laws, reduces concentration gradients in accordance with Le Chatelier's principle.Surface segregation is a process which, once equilibrium is reached, ensures that the chemical potential across the sample and between bulk and surface of the sample is homogeneous.Although the chemical potential depends on concentration, and a concentration gradient typically contributes to a non-uniform chemical potential, the difference between bulk and surface free energy compensates the concentration dependent contribution to the chemical potential and stabilizes a concentration gradient near the surface.This concentration gradient is necessary to establish homogeneity of the chemical potential and thus thermodynamic equilibrium.
The thermodynamics of surface segregation bears similarities to the thermodynamics of an ideal gas of particles of mass, m, at constant temperature, T, subject to a gravitational field of constant gravitational acceleration g.When defining the particle density, n, at the bottom h = 0 of the column of gas as (ℎ = 0), one can introduce the elevation dependent particle density (ℎ) = (ℎ = 0) −ℎ/   .The h-dependent particle density implies the particle density gradient, (0,0, The final concentration profile in our sample is stable over time because it is associated with the equilibrium state determined by the minimum of the total Gibbs free energy.The phenomenon of surface segregation (as depicted in Fig. 1b) is not limited to metallic alloys but also is well-known in materials with an electronic band gap such as the III-V semiconductor alloys and transition metal oxides. 31,32Because it is known that the B-concentration in B:Cr2O3 determines its Néel temperature, 5,7 it is expected that the B-rich surface layer has a strongly increased Néel temperature compared to Cr2O3.

X-ray Photoemission Depth Profiling
Experiments dependent on neutrons generated in a nuclear reactor are expensive and, as such, completed under time limitations.Fig. 1a shows cNDP data for the as prepared sample and depth profiles after annealing at 500 K for 18 hours and 36 hours.
In order to elucidate the role of the annealing temperature in the continuous evolution of the B-concentration profile we independently performed table-top experiments measuring depth profiles with the help of X-ray photoemission spectra (XPS) taken after annealing the sample at increasing temperatures.A sapphire (0001)/V2O3 (20 nm)/Cr2O3 (200 nm) sample was grown specifically for the destructive depth profiling measurements.
Figure 2 shows the results of subsequent XPS measurements using a ThermoFisher K-Alpha Photoelectron Spectrometer.Specifically, we measured the binding energies of the 1s electrons of B and the binding energies of the 2p1/2 and 2p3/2 electrons of Cr.Squares, circles, up and down triangles represent XPS data taken at room temperature after annealing the sample at 320, 380, 450 and 550 K.Each data point represents an XPS spectrum taken at a particular depth of the sample with a probing depth of 1nm.For each annealing temperature, the first spectrum is taken at the surface (depth=0).Subsequent spectra are taken after Ar-ion etching a local region of 5 mm x 2mm (representative XPS spectra are provided in the supplementary material) for 30 seconds at ion energies of 3 keV.The relation between etching time and depth is assumed to be linear and corrects for the fact that the transmission of a hemispherical analyzer changes with the electron kinetic energy of the photo electrons. 33early, a very significant gradual increase of B-concentration within a surface layer of about 50 nm width is seen in the XPS spectra in agreement with the neutron data and in agreement with the interpretation of the transport data.In addition to the evolution of the pronounced peak near the surface, the XPS depth profiles also reveal a gradual increase in B-concentration from the interface with the substrate to the surface.We interpret this gradual increase as B-migration taking place during the growth process of the sample.A similar observation holds for the cNDP data of the as prepared sample where B-concentration gradually increases from the sapphire interface at d ≈ 300 nm to its maximum value at d≈ 200 nm.In contrast to Fig. 1a Despite the qualitative agreement between the cNDP and XPS depth profiling measurements regarding the formation of a B-concentration increase in a 50 nm layer near the surface, there are striking differences which ask for an interpretation.The cNDP data in Fig. 1 show a clear difference in the Boron concentration in the 100-200 nm range for the as deposited and annealed sample.In the XPS depth profiling data of Fig. 2 this difference is far less pronounced.Both XPS and neutron capture techniques have different probing depths and thus can provide similar trends but cannot provide identical depth profiles.Neutron depth profiling is based off 10 B capture and can be considered as more sensitive than XPS because of low cross-section of B1s core in XPS.
Moreover, during XPS measurements, a small rectangular area of the sample was sputtered each time, prior to taking the XPS data.This is a key difference compared to the cNDP.The sputtering creates defects and intermixing as it removes material.The information obtained by XPS at each depth is coming from a 1 nm thick layer where the aforementioned layer mixing can make the experimental error more pronounced at greater depths.Furthermore, the sputtering removes different species at different rates because boron has a higher sputtering cross-section than chromia. 34In addition, it makes a difference to have a thermodynamically stable surface segregation layer as in the case of the cNDP measurements or a freshly created surface where segregation did not happen and boron can possibly escape.
To take into account the differences in resolution of the two methods, we employed a convolution technique followed by the work by J.F. Ziegler et.al. 35We display and discuss the result in the supplementary material (Figs.9S and 10S).Next, VG = -55 V is applied prior to the 201 st data point.This pulse brings the AFM back to the   ≈ 0 state.Evidence for the polarity dependence of the rotation is provided by applying again a pulse of VG = -55 V prior to the 301 st Hall measurement.Because the system is already in the   ≈ 0 state, the pulse of identical polarity to the previous one leaves the AFM in the   ≈ 0 state.

Magnetotransport measurements
Similarly, VG = +55 (-55) V applied prior to the 400 th (500 th ) point brings the AFM in a state of non-zero (zero)   while a pulse of unchanged negative polarity prior to the 600 th point leaves the AFM state unchanged at   ≈ 0. Thus, a completely deterministic polarity dependent voltage switching is demonstrated.A VG = +55V pulse applied prior to the 700 th measurement selects the   ≈ 7mV state associated with out of plane orientation of boundary magnetization and Néel vector.Immediately after application of this pulse and without exposure to annealing, the temperature is increased from T1= 295 K to  1  =305 K and Hall measurements are taken.temperature  <   .Qualitatively, this holds not only near the critical temperature but for all 0 <  ≤   .

Scaling analysis and evolution of the surface TN on annealing
The T-dependent surface segregation of boron and the associated TN -runaway effect, i.e., The scaling analysis utilizes the solution of the mean-field equation which approximates the Tdependence of spontaneous order below a critical temperature.In contrast to the power-law  ∝ ( −   )  , which describes critical behavior with the help of the universality class dependent critical exponent, , the mean-field approximation is independent of dimensionality and symmetry of a spin-Hamiltonian.It does not discriminate between universality classes but has the advantage of being a meaningful approximation outside the critical region, i.e., away from the critical point.
Microscopic details, such as the number of nearest neighbor spins and their interaction strength, can be absorbed in the critical temperature as a single parameter.In the absence of an applied conjugate field the mean-field equation reads 37 where  0 = 1 in case  describes a normalized order parameter. 0 ≠ 1 considers a saturation value when  refers to a quantity proportional to the order parameter such as Vxy.
The solid line in Fig. 5a shows the numerical solution of Eq.( 2).When plotted in the format / 0 vs. /  , each data set that can be approximated by Eq.( 2), will fall onto this universal curve (line in Fig. 5a) regardless of the specific value of TN.The position of the data on the universal curve uniquely determines the critical temperature   associated with a data set.We utilize the scaling approach to estimate   (   ) from the collapse of the Vxy vs. T data on the mean-field master curve.For quantitative optimization of the data collapse we set up the functional It assigns the positive number ( 0, ,   ) to the n th data set, which contains Kn data points   (  ) within  1 ≤   ≤    =    .( 0, ,   ) quantifies the deviation of   (  ) from perfect collapse (S=0) on the master curve.Minimization of ( 0, ,   ) with respect to  0, and   determines the critical temperature   (   ) =    0, .When plotting , the best possible data collapse based on the least square criterion of Eq.( 3) is achieved.
Fig. 5 a shows the virtually perfect data collapse of all Vxy vs. T data sets.The legend in Fig. 5a provides the values of    =    while  1 = 295 .This is the case for all data sets with the exception of the solid blue circles extending down to /  = 0.2.Here data taken between 100 K and 295  are combined with data taken between 295  and 370 K and ( 0, ,   ) is minimized for the combined data.Note that the data between 100 K and  1 have been measured after the sample has been exposed to 370 K. Once the sample has been annealed at temperatures above (2) which serves as master curve for a data collapse of Vxy vs. T data.The legend displays symbols associated with Vxy vs. T and their    (see text for details).The inset shows a complete Vxy vs. T data set which includes data for T>TN.Data were taken three months after the sample has been exposed to Tmax=335 K. Vertical line marks TN as determined from scaling analysis.(b) Plot of   vs.    (squares) where the respective   -value has been determined by minimizing the functional of Eq.(3).Circles show data experiments taken with a time delay of weeks after the annealing procedure.Uncertainty bars are determined by repeating the analysis for data sets with variable sampling size of data points.The uncertainty bar of a respective TN-value indicates the standard deviation determined from 5 data sets of different sampling sizes.345 K,   vs.    saturates (see Fig. 5b).The saturation value    ≈ 477  becomes independent of subsequent temperature protocols.The main goal of this work is to demonstrate qualitative effects.The transport data, the neutron data, and the XPS data had to be taken at different samples due to the fact that all experiments alter the sample irreversibly.One cannot expect perfect quantitative agreement when comparing the results of three different samples.As can be seen from the analysis of the transport data in Fig. 5b, the annealing effects set in gradually but speed up dramatically in a rather narrow temperature window.It can be expected that this temperature window varies from sample to sample due to factors including variation in doping concentration and defect concentration.Within this context we find the agreement between the three very different methods satisfactory but acknowledge that they remain on a qualitative level.

Robust post-annealing switching behavior
The stabilization of the post-annealing surface Néel temperature at    ≈ 477  suggests that annealing improves and stabilizes device properties.To confirm this expectation, we perform post annealing isothermal voltage-controlled rotation of the Néel vector.Rather than rotating the Néel vector near room temperature as shown in Fig. 3, we perform the Hall measurements at 370 K.In addition, to provide evidence that the device is not degrading over time, we perform the postannealing switching experiments with a time delay of weeks after the annealing procedure.In pure chromia, magnetoelectric switching can be brought about at lower temperatures by applying higher voltage pulses at a fixed magnetic field. 13,14There are competing mechanisms causing the temperature dependence of the switching field product in pure Cr2O3.On one hand, the magnetic anisotropy, which determines the energy barrier for switching, increases with    The XPS depth profile spectra were taken by annealing the sample in heating furnace at temperatures of 320 K, 380 K, 450 K and 550 K for every 2 hours.The data was analyzed by using CasaXPS software.The intensity for every induvial peak was calculated after fitting the data by subtracting the background using the Shirley approach.Figure 7S-a (a-f) & Figure 7S-b (g-l) shows the fitted XPS spectra for B 1s peaks after background subtraction for the sample annealed at 550 K.

Fig. 1 :
Fig.1: (a) B-concentration depth profile of the as-deposited and heated samples measured via cNDP.Depth = 0 nm is the B:Cr2O3/vacuum interface and depth ≈ 300 nm is the interface between the as-deposited B:Cr2O3(0001) film and the Al2O3(0001) substrate (diamonds).Postannealing B-concentration depth profiles measured at room temperature after 18 hours (circles) and 36 hours (triangles) annealing at 500 K. Data represented to one standard deviation and are based on experimental counting statistics.(b) Schematic depicting surface segregation of B because of annealing.Grey regions are those where B resides in the as-prepared or increased concentration range.Blue regions resemble B-depleted regions.
̂.It is the non-zero component of this gradient which ensures that the chemical potential  =    ln (ℎ)   + ℎ fulfills  ℎ = 0.This analogy shows that, for a gas in a gravitational field, the equilibrium condition of a constant chemical potential is realized due to the presence of the concentration gradient.The presence of the gravitational field in the gas plays a similar role as the presence of a surface in B:Cr2O3 films.The surface creates a contribution to the chemical potential which enables the presence of a B-concentration profile in B:Cr2O3.The B-concentration profile gives rise to a depth invariant chemical potential and thus thermal equilibrium.
, which shows only the difference in the B-concentration between the as prepared sample and the B -concentration profile after annealing at 500 K, the XPS depth profiling displays the gradual effect of annealing on the concentration profile.Note that the sample prepared for XPS measurements has a 20 nm V2O3 bottom layer resembling the structure of the sample used for better comparison with the transport measurements.The absence of an increased B-concentration at the V2O3/B:Cr2O3 interface originates from the structural and dielectric similarity between V2O3 and Cr2O3.The same holds for Al2O3 and Cr2O3.The similarity in structure and dielectric properties between these three sesquioxides and the epitaxial growth of the films minimizes the interface contribution to the chemical potential and hence eliminates the stabilizing effect of the concentration gradient observed near d=0 at the vacuum or metallic interface.
Fig. 3a shows Vxy for 800 sequential Hall measurements taken at T = 295 K with voltage pulses of positive or negative polarity applied every 100 data points.The applied voltage creates an Efield (≈ ±55 / 200  = ±275 /) across the B:Cr2O3-film of the device which gives rise to electrically controlled spin manipulation in the AFM film.

Fig. 3b visualizes
Fig.3bvisualizes the pulse train applied during the 800 Hall measurements.Vertical dashed lines correlate E-pulses with the Vxy-signal shown in Fig.3a.Unlike our previous work,16 here we go beyond a scheme of pulses with periodically alternating polarity.The more intricate protocol applied here allows to provide evidence for the polarity dependence and deterministic nature of the Néel vector rotation.Initially, a pulse of VG = -55 V is applied.The subsequent 100 Hall measurements show that a state with   ≈ 0 has been initialized where Néel vector and boundary magnetization are oriented in-plane.Prior to the 101 st Hall measurement, a pulse of VG = +55 V is

Fig. 3 :
Fig. 3: Electric field driven manipulation of the AFM order parameter and the Néel vector orientation.(a) Vxy switching between a higher and zero voltage at 295 K, corresponding to the application of gate pulse voltage as shown in (b).(c) Vxy measured as a function of increasing temperature after the application of VG = +55 V at 700 th measurement.Dashed horizontal line indicates that the T-dependent measurement starts at the Vxy-value set by the last gate pulse.Uncertainty bars represent the standard deviation calculated for each set of 100 Vxy measurements at each temperature.(d) Cartoon of Hall bar device showing V2O3 back gate, B-doped Cr2O3 film with AFM spin structure, Pt Hall cross with Au electrodes, current density j flowing in direction of black arrow causing signal Vxy controlled by gate voltage VG (adapted from Mahmood et al., 2021[ref 16], not to scale).

Fig. 3c showsFig 4 :
Fig. 3c shows Vxy versus T measured on increasing the temperature from T1 to  1  .Vxy(T1) coincides with the value of Vxy set by the last gate pulse and decreases with increasing temperature.The horizontal dashed line between the ordinates of Fig. 3a and Fig. 3c highlights the fact that the T-dependent measurement starts at the Vxy value associated with out of plane orientation of the Néel vector.The decrease of Vxy vs. T is in accordance with the expected T-dependence of the AFM order parameter and the associated boundary magnetization, which both vanish at TN. Qualitatively, this T-dependence is well-known from Cr2O3-based Hall-bar structures where it is straightforward to measure Vxy vs. T at temperatures near and above TN. 12,21,36The situation changes in Hall-bar structures based on B: Cr2O3.Here annealing alters the B-concentration profile whenever the sample is exposed to a new maximum temperature for the first time.The increase in B-concentration at the B: Cr2O3/Pt interface increases the surface layer Néel temperature.To keep the change in the B-concentration in a given measurement cycle small and to systematically map the evolution of TN on annealing, the maximum temperature,    , of the n th measurement within [295 K,    ] is kept significantly below the surface Néel temperature,   ( −1  ), induced by the previous measurement within [295 K,  −1  ] where  −1  <    .  (   ) is determined from a scaling analysis outlined in detail below.Within a single temperature sweep, the data can be modeled in good approximation with the help of one constant value of TN.Because of the T-induced change in the B-concentration profile, the virgin Vxy vs. T

Fig 5 :
Fig 5: (a) Scaling analysis of T-dependent magnetotransport data.Uncertainty of these data sets are displayed in Fig. 4 and the inset.Line shows the numerical solution of the mean-field Eq.(2) which serves as master curve for a data collapse of Vxy vs. T data.The legend displays symbols associated with Vxy vs. T and their    (see text for details).The inset shows a complete Vxy vs. T data set which includes data for T>TN.Data were taken three months after the sample has been exposed to Tmax=335 K. Vertical line marks TN as determined from scaling analysis.(b) Plot of   vs.    (squares) where the respective   -value has been determined by minimizing the functional of Eq.(3).Circles show data experiments taken with a time delay of weeks after the annealing procedure.Uncertainty bars are determined by repeating the analysis for data sets with variable sampling size of data points.The uncertainty bar of a respective TN-value indicates the standard deviation determined from 5 data sets of different sampling sizes.

Fig. 5b
Fig. 5b shows   vs.    as obtained from the scaling analysis.Uncertainty bars are determined by repeating the analysis for data sets with variable sampling size of data points.The uncertainty bar of a respective TN-value indicates the standard deviation determined from 5 data sets of different sampling sizes.For the as-deposited sample we find   ≈ 334  (uncertainty barsmaller than the plot symbol).On annealing, that is with increasing    ,   (   ) increases

Fig. 6a shows
Fig.6ashows deterministic switching at T = 370 K, as it follows the voltage pulse application in the same order as the 295 K experiment.The high voltage state of the transverse Hall signal of   ≈ 4  is measured after application of a gate pulse of   = +45  (+225MV/m).The zero state is set after application of   = −45  (-225 MV/m).Note that a lower switching voltage of ± 45V achieves switching at 370 K compared to   = ± 55V required for switching at 295 K.
decreasing temperature.On the other hand, the parallel magnetoelectric susceptibility,  ∥ , of Cr2O3 has a pronounced temperature dependence.It peaks around 280 K and becomes small for temperatures far below the Néel temperature and very close to the Néel temperature.As a result, the magnetoelectric change in the free energy, Δ = 2 ∥ , which must overcome the magnetic anisotropy energy on switching, becomes strongly temperature dependent and particularly small at low temperatures and very close to the Néel temperature.In B: Cr2O3 the mechanism of Néel vector rotation is different.Rotation takes place in zero applied magnetic H-field and the temperature dependence of  ∥ becomes irrelevant.The reduced switching voltage solely reflects the reduced magnetic anisotropy associated with increased temperature.Reduced switching voltages are highly beneficial for applications.Further reduction of the switching voltage can be achieved by reducing the thickness of the B: Cr2O3 because the electric field scales inversely proportional to the film thickness.In pure Cr2O3, the authors achieved switching of the Hall signal via magnetoelectric

Fig. 6 :Figure
Fig. 6: (a) Isothermal voltagecontrolled switching between high and zero Hall voltage signals at 370 K, corresponding to the application of gate pulse voltage as shown in (b).

Figure
Figure 5S (a-d) shows the XPS depth profile data for B 1s peak after annealing the sample at a

Figure
Figure6S (a-d) Shows the Boron 1s peaks of the B:Chromia sample after annealing it at a temperature of 320 K for 2 hours.The shaded grey region shows the B 1s peaks that appear in the binding energy range of 192.6 eV.

Figure
Figure 7S-a (a-f): Figure shows the XPS data for B 1s peaks (black solid lines), Shirley

Figure
Figure 7S-b (g-l): Figure shows the XPS data for B 1s peaks (black solid lines), Shirley

Figure
Figure 8S-a (a-f): Figure shows the XPS data for Cr 2p3/2 peaks (black solid lines), Shirley

Fig. 10S :
Fig.10S: (a) B-concentration depth profile of the as-deposited and heated samples measured via cNDP.Depth = 0 nm is the B:Cr2O3/vacuum interface and depth ≈ 300 nm is the interface between the asdeposited B:Cr2O3(0001) film and the Al2O3(0001) substrate (diamonds).Post-annealing Bconcentration depth profiles measured at room temperature after 18 hours (circles) and 36 hours (triangles) annealing at 500 K. Data represented to one standard deviation and are based on experimental counting statistics.The line (right axis) shows the result of a convolution procedure of the XPS depth profiling data.XPS depth profiling measurements are discussed in the subsequent section.
(   ) >   ( −1  ), make it challenging to measure Vxy vs. T near   .To determine   in the absence of data near   , we employ a scaling approach.It allows to estimate   (   ) from Vxy vs. T data taken within  1 = 295 ≤  ≤    where    is significantly below   (   ).
and the subsequent history independence of    corroborate the interpretation of the depth profiling in terms of surface segregation and exclude a B-diffusion mechanism.The latter would continue as time progresses and intensify with increasing annealing temperature until the B-concentration is depleted.Instead, stabilization of a high surface Néel temperature is observed with beneficial implication on device applications.