Exchange Bias Modulated by Antiferromagnetic Spin‐Flop Transition in 2D Van der Waals Heterostructures

Abstract Exchange bias is extensively studied and widely utilized in spintronic devices, such as spin valves and magnetic tunnel junctions. 2D van der Waals (vdW) magnets, with high‐quality interfaces in heterostructures, provide an excellent platform for investigating the exchange bias effect. To date, intrinsic modulation of exchange bias, for instance, via precise manipulation of the magnetic phases of the antiferromagnetic layer, is yet to be fully reached, owing partly to the large exchange fields of traditional bulk antiferromagnets. Herein, motivated by the low‐field spin‐flop transition of a 2D antiferromagnet, CrPS4, exchange bias is explored by modulating the antiferromagnetic spin‐flop phase transition in all‐vdW magnetic heterostructures. The results demonstrate that undergoing the spin‐flop transition during the field cooling process, the A‐type antiferromagnetic ground state of CrPS4 turns into a canted antiferromagnetic one, therefore, it reduces the interfacial magnetic coupling and suppresses the exchange bias. Via conducting different cooling fields, one can select the exchange bias effect switching among the “ON”, “depressed”, and “OFF” states determined by the spin flop of CrPS4. This work provides an approach to intrinsically modulate the exchange bias in all‐vdW heterostructures and paves new avenues to design and manipulate 2D spintronic devices.


Introduction
With the emergence and extensive research on 2D van der Waals (vdW) magnetic materials, [1,2] heterostructures comprising vdW magnets exhibit a particularly rich variety of novel phenomena, such as chiral spin textures, [3,4] magnetic proximity effect, [5,6] quantum anomalous Hall effect, [7] exchange bias effect, [8] etc.In particular, in the vdW magnets constituted ferromagnet/antiferromagnet (FM/AFM) heterostructures, perfect interfaces without dangling bonds or interfacial defects, are capable of investigating the interface-related effect, especially for the exchange bias effect.Moreover, interfacial magnetic interactions play a prominent role in vdW heterostructures due to the weak interlayer coupling of the vdW magnets.Therefore, exchange bias is highly expected in vdW FM/AFM heterostructures and its underlying mechanism can be well explored.
For spintronic devices based on exchange bias, great efforts are paid to optimize the strength of exchange bias field (H ex ).Besides, effective modulation of exchange bias is also urgently necessary for practical applications.Recently, some external methods, such as proton intercalation, [18,27] gate voltage, [19] pressure engineering, [12,28] and surface oxidization, [16,17,29] have been conducted to tune the exchange bias effect in 2D vdW heterostructures.Although these extrinsic stimuli have enriched the application scenario of exchange bias, intrinsic modulation of exchange bias, for instance, via the manipulation of the precise magnetic phases of the AFM layer, is still in demand for integration.Inspired by the easily accessible spin-flop transition between A-type AFM state and canted AFM one of CPS at relatively low fields, the concern of whether the spin-flop transition could modulate the exchange bias is intriguing and worthwhile.
Herein, the exchange bias effect has been observed in both FGT/CPS and (Fe 0.74 Co 0.26 ) 3 GeTe 2 (FCGT)/CPS, archetypes of all-vdW FM/AFM heterostructures.Negative exchange bias is evidenced in both heterostructures due to the ferromagnetic coupling at the interfaces.Proper cooling field (H CF ) and thickness of FGT are required for FGT/CPS heterostructures to gain the expected exchange bias.The depressed coercivity (H C ) of FCGT via doping, smaller than the spin-flop field (H SF ) of CPS, is capable of achieving the effective modification of the exchange bias in FCGT/CPS by the spin-flop transition.Adopting a H CF surpassing the H SF , CPS turns from A-type AFM to canted AFM, thus the exchange bias effect is depressed or even eliminated.In this way, we can select the desired states of exchange bias by an intrinsic approach of the convenient field-cooling process.This work offers a deep understanding of the spin-flop-modulated exchange bias in all-vdW heterostructures.This understanding facilitates the design and manipulation of spintronic devices on the basis of 2D vdW magnets.

Results and Discussion
Figure 1a illustrates the vdW heterostructure of FGT/CPS (or FCGT/CPS), where vdW gaps without dangling bonds provide a high-quality interface.Different from the cases of traditional exchange bias effect in thin-film heterostructures, where interfacial defects and diffusions normally play a pronounced role, perfect interfaces among vdW heterostructures allow us to investigate the intrinsic magnetic coupling mechanisms of the exchange bias effect.FGT/CPS (and FCGT/CPS) vdW heterostructures were fabricated as depicted in Figure 1b.FGT (FCGT) flakes with different thicknesses (11.8-52 nm) were mechanically exfoliated from the bulk crystal and transferred onto electrodes using a dry transfer method with polydimethylsiloxane (PDMS), and the CPS flake (the thickness range of CPS is 10.7-148 nm.Note that the thickness of most CPS flakes we chose is ≈120 nm due to its easy accessibility and sufficient pinning of antiferromagnetism) was then transferred onto the FGT flakes, followed by encapsulation of the entire heterostructure with h-BN to prevent oxidation and contamination.Recently, the exchange bias has been observed in FGT with surface oxidization, [16] however, the intrinsic magnetic couplings between FGT and CPS are more desired in this work.In order to distinguish the genuine exchange bias of FGT/CPS from the oxidized-FGT/FGT (Figure S3, Supporting Information), the device (with two standard 6-electrode Hall-bar configurations) of a large-area FGT (52 nm of the thickness) partially covered by CPS, as shown in Figure 1c of the optical image, was fabricated to measure the individual FGT and the heterostructure, separately.Moreover, the cross-sectional scanning transmission electron microscope (STEM) images and corresponding energydispersive X-ray spectroscopy (EDS) mappings were employed to further validate the quality of the FGT/CPS heterostructure.The annular bright-field (ABF)-STEM image (Figure 1f) gives a picture of the FGT/CPS heterostructure encapsulated by h-BN on the SiO 2 /Si substrate with pre-deposited Au electrode, displaying flat and homogeneous interfaces.High-resolution high-angle annular dark field (HAADF)-STEM images (Figure 1d,e) show the high-quality crystal structures of CPS and FGT, respectively.Moreover, the EDS mappings demonstrate a clear distribution of different elements in corresponding regions, further signifying the clean and homogeneous interface of the FGT/CPS heterostructure.
To explore the exchange bias in FGT/CPS heterostructure, magnetotransport measurements are employed to record the Hall resistance (R xy ) with the anomalous Hall effect (AHE).Hall signal of the individual FGT region was initially measured without field cooling, then standard measurement methodology of the exchange bias effect with field cooling was conducted on the heterostructure.As shown in Figure 2a, at a typical temperature of 2 K, Hall resistance of the pure FGT region (black dashed line) is oddly symmetric relative to the zero point, manifesting no exchange bias in pure FGT and further excluding the possibility of the oxidization induced exchange bias in our samples.More transport results of individual FGT region can be referred to in Figure S2 (Supporting Information).In contrast, for the FGT(52 nm)/CPS(120.2nm) heterostructure, obvious lateral shifts of the AHE loop are observed under both the negative field cooling (NFC) of −0.5 T and positive field cooling (PFC) of +0.5 T. In the case of NFC, the shift is toward the positive magnetic field, while the opposite shift is toward the negative one for the PFC.This indicates a negative exchange bias exhibits at the interface of FGT/CPS, which is typically found in most vdW magnetic heterostructures. [11,13,14] , where H C + and H C − are the positive and negative coercivity, respectively.Figure 2c shows the temperature dependence of H ex from 2 to 30 K. The magnitude of these H ex induced by the PFC and NFC is identical within experimental error and decreases with increasing the temperature.The exchange bias effect disappears at 20 K, signifying a blocking temperature (T B ) for this FGT(52 nm)/CPS(120.2nm) heterostructure.
To deeply understand the magnetic couplings of this vdW heterostructure, the magnetic properties of the antiferromagnetic CPS are investigated.Figure 2d shows the temperaturedependent susceptibility of the CPS.Upon cooling, the susceptibility initially increases and then decreases sharply, forming a predominant peak in this curve.T N is manifested to be ≈38 K as defined from the peak of this magnetic susceptibility, consistent with previous studies. [24,25]Magnetization as a function of the applied out-of-plane field including the backward-forward sweeps at different temperatures is displayed in Figure 2e.It should be noted that the backward-and forward-sweeps are fully overlapped, distinct from the cases of monolayer or odd-layer CrI 3 or CPS. [30,31]For temperatures below T N , magnetizations increase faintly as the field increases in the low magnetic field region, which is a typical AFM feature.Distinctively, increasing the magnetic field to a critical one (namely H SF ), magnetizations increase sharply and nonlinearly, which is the field-driven spin-flop phase transition. [24]Undergoing this phase transition, the A-type AFM ground state of CPS transforms into a canted AFM one, of which magnetic moments are aligned antiferromagnetically perpendicular to the applied field but with small net moments along the easy axis.The insets of Figure 2e illustrate the alignments of magnetic moments before and after the spin-flop transition.The H SF decays with increasing temperature and the spin-flop transition vanishes when the temperature is higher than 35 K. Figure 2f summarizes the magnetic phases diagram of CPS under different temperatures and applied magnetic fields.When the temperature is below T N , CPS turns from the paramagnetic (PM) phase to the AFM one.In a low field region below T N , CPS is in its ground state of A-type AFM.When the magnetic field surpasses the H SF (the solid purple line in Figure 2f), the spin-flop transition begins and the CPS becomes canted AFM.
Besides the magnetic properties of CPS, H C or saturation fields (H S ) of FGT also play a key role in exchange bias.For FGT with strong PMA, [32] H C is nearly the same as the H S .As shown in Figure 2f, thickness-dependent H C of FGT with three different thicknesses is plotted.H C exhibits an apparent thickness dependence, i.e., the thinner of the thickness, the larger of the H C .The field required for the spinflop of CPS is relatively low, which is comparable to or even smaller than the H C of FGT, especially for the thinner ones.Generally, to generate the unidirectional anisotropy and thus the exchange bias, the AFM/FM heterostructure is cooled down below the T N with a H CF a few times larger than the H C . [33]For AFM/FM systems, a larger H ex is expected when the FM sample is thinner while the AFM one is thicker, resulting from the enhanced proximity effect at the interface. [14]Indeed, the H ex of FGT(29.3 nm)/CPS(117.7 nm) is larger than that of FGT(52 nm)/CPS(120.2nm) (Figure S6a, Supporting Information).However, for the 11.8 nm-FGT-based het-erostructure, the H C of FGT is extremely large (≈8700 Oe at 4 K).The energy barrier for this large H C during the moments switching could overwhelm the unidirectional anisotropy, as is normally required for the effective exchange bias. [13,18]Consequently, the corresponding exchange bias of FGT(11.8 nm)/CPS(119.1 nm) is irregular and the magnitude of H ex induced by PFC and NFC is distinct (Figure S6b, Supporting Information).In addition, given the required H CF is already larger than the H SF , CPS has already undergone the spin-flop transition.In this vein, a reliable and comprehensive field-cooling-dependent exchange bias research cannot be reached due to the large H C of thin FGT and the low H SF of CPS.Therefore, it is necessary to choose a suitable FM material with a relatively lower H C to fully explore the modulation of the exchange bias via the spin-flop transition.
According to recent work, [34,35] Co-doped FGT shares the same crystal structure with FGT, but has a smaller H C , typically not exceeding 2000 Oe.This depressed H C is due to decreased magnetic anisotropy with the Co dopant, [35,36] making FCGT suitable for investigating the influence of spin flop on exchange bias through the field-cooling dependence.Figure 3a shows Hall resistance of FCGT(51.1 nm)/CPS(123.4nm) under the PFC and NFC of 0.5 T. Similar to the results of FGT/CPS (Figure 2a), negative exchange bias with |H ex | ≈50 Oe is observed.We note the smaller |H ex | compared with the one of FGT(52 nm)/CPS(120.2nm) is ascribed to the depressed ferromagnetism of FCGT.The magnitude of the H ex decreases with increasing temperature, and the T B is ≈20 K, as shown in Figure 3b.Keeping CPS in the A-type AFM state with a moderate H CF of 0.4 T, we explore the exchange bias as a function of the thickness of both the FCGT (t FM ) and the CPS (t AFM ) (Figure 3c).When exploring the t FM -dependent exchange bias, the t AFM is fixed at ≈120 nm.While for the t AFM -dependent one, the t FM is fixed at ≈40 nm.It can be seen that the |H ex | of FGT(≈40 nm)/CPS(t AFM ) increases from ≈2.5 to ≈140 Oe when the t AFM increases from 10.7 to 120 nm, and the |H ex | saturates at ≈140 Oe with further increasing the t AFM .For the thickness of CPS below 10 nm, the exchange bias effect disappears due to the reduced anisotropy energy in CPS, which is not large enough to pin the spins in FGT during the magnetization reversal.Meanwhile, the |H ex | of FCGT(t FM )/CPS(≈120 nm) initially increases from 25 to 142 Oe as the t FM increases from 13.8 to 40.3 nm and then decreases to 30 Oe when the t FM is 51.1 nm, contrary to the conventional exchange bias of |H ex | ∝ 1/t FM (i.e., |H ex | consistently decreases as increasing the t FM ). [16]This divergence between H ex and 1/t FM has also been observed in other vdW systems, such as FGT/CrCl 3 , [13] FGT/Oxidized-FGT, [16] FGT/CoPc, [14] and Fe 5 GeTe 2 /FePS 3 , [18] possible due to the weak interlayer coupling [16] or the lower volume magnetization of the thin FM flake cannot activate the AFM order sufficiently. [14]Subsequently, we selected the FCGT(40.3 nm)/CPS(119.2nm) device due to its largest H ex among these heterostructures to investigate the cooling field dependence of exchange bias.Figure 3d summarizes the exchange bias under different field cooling processes, of which the H CF can span the field required for the spin-flop transition.We note that the H ex and T B are different for each field cooling process and we only plot the AHE loops for the temperature range of T ≤ T B in Figure 3d.With the H CF of +0.4 T, the shifted AHE loop disappears until 22 K.By contrast, under the H CF of +1 T, the exchange bias nearly vanishes at 4 K.These differences determined by various H CF imply that the spin-flop transition indeed modulates the exchange bias effect.
To further analyze the modulation of spin flop on exchange bias, a contour map of the |H ex | as a function of temperature and H CF is plotted in Figure 4a.Note that when the H CF = 0.2 T, the exchange bias of FCGT(40.3 nm)/CPS(119.2nm) undergoes a rapid degradation as increasing the temperature and disappear at ≈10 K.These depressed H ex and T B under the H CF of 0.2 T are predominately due to the relatively small H CF . [33]Moreover, for the H CF > 0.4 T, the area representing exchange bias shrinks in Figure 4a, indicating that T B decreases with increasing the H CF .Specifically, T B of 22 K is the largest one when H CF = 0.4 T and decays upon increasing the H CF .This H CF -modulated T B is determined by the spin-flop transition of CPS, which will be discussed later.Besides T B , we further explore the H ex tailored by H CF , especially when H CF surpasses the H SF .At a fixed temperature, it is obvious that the magnitude of H ex does not increase and then saturates with the increasing H CF , as expected in FM/AFM systems. [9,15]However, |H ex | increases as the H CF increases until the H CF exceeds the H SF, at which point the |H ex | starts to decrease.For instance, at 4 K, |H ex | increases from 130 to 177 Oe as the H CF increases from 0.2 to 0.8 T. When the H CF is larger than 0.8 T, at which field the spin-flop transition of CPS occurs at 4 K, therefore, the CPS becomes a canted AFM.Correspondingly, magnetic moments begin to tilt and antiferromagnetically align perpendicular to the field.The uncompensated moments at the interfaces get weakened, thus the exchange bias effect is depressed.Further increasing the H CF exceeding 1 T, moments of CPS have completely antiferromagnetically aligned in-plane with small net moments along the c axis, suppressing the interfacial magnetic coupling as well as the exchange bias effect.During this spin-flop process, the canted AFM phase reduces the interface magnetic coupling, leading to a degradation of the strength of the interfacial exchange coupling, J FM-AFM , thereby suppressing the exchange bias (Figure S11, Supporting Information).Therefore, when the H CF is larger than the H SF , the exchange bias ef-fect is degraded or even washed out.Under this circumstance, if one applies a H CF of 0.4 T, despite a rapid decrease of H SF (from ≈0.8 to ≈0.4 T) in the temperature range of 10-20 K, H SF is larger than the H CF all along.CPS does not experience the spin flop and exchange bias is not influenced in the whole temperature range.Therefore, FCGT(40.3 nm)/CPS(119.2nm) has the largest T B when H CF = 0.4 T. For the increased H CF in other cases, H CF generally goes beyond the H SF , especially at high temperatures.Exchange bias is depressed or eliminated at this temperature, thus leading to a lower T B for the H CF > 0.4 T. To sum up, the spin flop can effectively modulate the exchange bias of FCGT/CPS vdW heterostructure on both T B and H ex .
Based on the temperature-and H CF -dependent T B and H SF , the exchange bias effect modulated by spin-flop transition is depicted in Figure 4b.When the H CF is applied smaller than the H SF , the exchange bias is not influenced, displaying an "ON" state.However, once the conducted H CF goes beyond the H SF , the spin-flop transition begins where magnetic moments tilt and antiferromagnetically align perpendicular to the field.Consequently, exchange bias is depressed and the T B is reduced, which is regarded as a "depressed" region.Moreover, further increasing the H CF much exceeding the H SF , CPS has already become a canted AFM.In this vein, the interfacial magnetic coupling is eliminated and the exchange bias effect vanishes.It turns an "OFF" state.Therefore, by tuning the spin-flop phase transition of CPS, we can select the desired exchange bias effect switching among the "ON", "depressed", and "OFF" states via setting up the appropriate cooling fields.Due to the fact that the AFM state of 2D vdW CPS has a relatively weak interlayer exchange coupling, it allows the low-field switching between the A-type AFM and canted states.It provides a perfect laboratory for studying exchange bias based on 2D antiferromagnetism.This spin-flop modulated exchange bias effect has also been reproduced in different FCGT/CPS heterostructures with various CPS thicknesses (Figure S12, Supporting Information).

Conclusion
In summary, we have demonstrated the exchange bias effect modulated by AFM spin-flop phase transition of CPS in 2D vdW magnetic heterostructures.Via AHE measurements, thickness-and cooling field-dependent exchange bias effect is exhaustively investigated in both FGT/CPS and FCGT/CPS heterostructures.With the typical characteristic of CPS at a relatively low magnetic field, the spin-flop transition can effectively depress the exchange bias of FCGT/CPS vdW heterostructure on both T B and H ex .It allows one to select the desired exchange bias effect switching among the "ON", "depressed", and "OFF" states via conducting the appropriate cooling fields.This work provides an intrinsic approach, vi precisely setting up the magnetic phases of AFM materials to manipulate the exchange bias effect, showing great promise for spintronic devices based on vdW magnets.

Experimental Section
Device Fabrication: Single-crystal FGT, FCGT, and CPS were grown using the chemical vapor transport method, as previously. [21,23]Electrodes of Ti/Au (5 nm/25 nm) with standard Hall-bar configuration were initially deposited on SiO 2 /Si substrates via electron beam lithography and electron beam evaporation.vdW heterostructures were fabricated using the dry transfer method.Thin flakes were mechanically exfoliated from the bulk using the scotch tape, and then suitable flake was picked up using PDMS.The thin layers of FGT or FCGT, followed by CPS, were sequentially transferred onto the pre-patterned electrodes.Finally, the entire heterostructure was covered with a large-area h-BN to prevent oxidation and contamination during subsequent measurements.All device fabrications were conducted in a glovebox.
Magnetism and Transport Measurements: Magnetic properties of CPS with an out-of-plane geometry were measured by the superconducting quantum interference device (SQUID).Transport properties were conducted via a cryogen-free refrigeration system.Hall resistance and longitudinal resistance were measured simultaneously via a standard lock-in technique with an applied current of 100 μA and a reference frequency of 13 Hz.
Statistical Analysis: The Hall resistance in Figure 2b, Figures S3-S7 (Supporting Information) were offset for clarity.

Figure 1 .
Figure 1.Basic characterization of 2D vdW FM/AFM heterostructures.a) Schematic diagram of the FGT (FCGT)/CPS magnetic heterostructure.b) Fabrication process of the FGT (FCGT)/CPS nanodevice.c) Optical image of the FGT/CPS vdW heterostructure.d,e) HADDF-STEM images of CPS and FGT, respectively.The scale bar is 2 nm.f,g) Cross-sectional ABF-STEM image and corresponding EDS mappings of the FGT/CPS heterostructure encapsulated by h-BN on the SiO 2 /Si substrate with pre-deposited Au electrode.The scale bar is 20 nm.

Figure
Figure2bsummarizes Hall resistance at different temperatures under a PFC and an NFC process, respectively.It is seen that the shifts degrade as increasing the temperature.Exchange bias field, H ex , is defined asH ex = (H C + + H C − )/2, where H C + and H C − are the positive and negative coercivity, respectively.Figure2cshows the temperature dependence of H ex from 2 to 30 K. The magnitude of these H ex induced by the PFC and NFC is identical within experimental error and decreases with increasing the temperature.The exchange bias effect disappears at 20 K, signifying a blocking temperature (T B ) for this FGT(52 nm)/CPS(120.2nm) heterostructure.To deeply understand the magnetic couplings of this vdW heterostructure, the magnetic properties of the antiferromagnetic CPS are investigated.Figure2dshows the temperaturedependent susceptibility of the CPS.Upon cooling, the susceptibility initially increases and then decreases sharply, forming a predominant peak in this curve.T N is manifested to be ≈38 K as

Figure 2 .
Figure 2. Exchange bias effect in FGT(52 nm)/CPS(120.2nm) heterostructure and the magnetic properties of CPS.a) Typical magnetic field dependence of Hall resistance, R xy , measured at 2 K for FGT(52 nm)/CPS(120.2nm) under both PFC and NFC and the individual FGT without field cooling.b) Magnetic field dependence of R xy of FGT(52 nm)/CPS(120.2nm) at various temperatures under a H CF of 0.5 T adopted in positive and negative fields, respectively.c) Temperature-dependent H ex of FGT(52 nm)/CPS(120.2nm).d) Magnetic susceptibility of CPS as a function of the temperature, showing a T N of ≈38 K.The magnetic field of 1000 Oe is applied along the c-axis.e) Field dependence of the magnetization of CPS at various temperatures with H//c-axis.The insets schematically show the spin textures of the A-type AFM state and the canted-AFM one, respectively.f) Magnetic phase diagram of CPS and the temperature dependence of H C of FGT with different thicknesses.The purple solid line indicates H SF of CPS at different temperatures.

Figure 3 .
Figure 3. Thickness and field-cooling dependence of the exchange bias effect in FCGT/CPS heterostructure.a) Field dependence of the Hall resistance R xy measured at 4 K for FCGT(51.1 nm)/CPS(123.4nm) heterostructure with applying the H CF of +0.5 and −0.5 T, respectively.b) Temperature dependence of the |H ex | of FCGT(51.1 nm)/CPS(123.4nm).c) Thickness dependence of the |H ex | at 4 K with the H CF of +0.4 T of the FGT(≈40 nm)/CPS(t AFM ) and FCGT(t FM )/CPS(≈120 nm).d) H CF -dependent exchange bias effect of FCGT(40.3 nm)/CPS(119.2nm) heterostructure.For clarity, we only plot the AHE loops for the temperature range of T ≤ T B in each field cooling process.

Figure 4 .
Figure 4. a) The magnitude of |H ex | of FCGT(40.3 nm)/CPS(119.2nm) as a function of the temperature and cooling field, H CF .b) The modulation of the exchange bias in FCGT/CPS heterostructure through CPS spin-flop transition.