Tuneable Vertical Hysteresis Loop Shift in Exchange Coupled La0.67Sr0.33MnO3‐SrRuO3 Bilayer

Harnessing extra degrees of freedom at the heterostructure interface is of crucial importance to bring additional functionalities in modern spintronic devices. Here, a vertical hysteresis loop shift (vertical bias) is demonstrated in an exchange biased system of ferromagnetic thin film heterostructure of La0.67Sr0.33MnO3 (10 nm)‐SrRuO3 (SRO) (20 nm), after field cooling with ±1 T below 100 K close to the Curie temperature (TC) ≈125 K of SRO and loop sweeping under ±1 T field. Besides, a positive exchange bias (HEB) is also observed below TC ≈125 K showing a maximum ≈11 mT at 2 K. The vertical shift is modeled closely using micromagnetic simulations and the layers’ thickness dependency is demonstrated. The reason for the shift is attributed to the simultaneous role of the interfacial antiferromagnetic interaction and the hard anisotropy of SRO against the Zeeman energy. Finally, from the experimental and simulation results, a generalized model of controllable and tunable vertical shift is proposed applicable for other material systems possessing glassy phases, uncompensated/canted spins, absent interfacial exchange coupling, etc., and hence can be informative for the use of vertical shift in future spintronic devices.


Introduction
Owing to the wide implications in both fundamental science and industrial applications, exchange bias (EB) has become an DOI: 10.1002/apxr.202300129integral part of spintronic devices such as spin valves, spin filters, tunnel junctions, magnetic random-access memories, etc., [1,2] The conventional EB manifests itself as the offset of the magnetic hysteresis (MH) loop in the horizontal or field (H) axis [3,4] due to the interfacial coupling between adjacent ferromagnetic (FM) and antiferromagnetic (AFM) layers.To exploit an extra degree of freedom, researchers have been curious to find the MH shift along the magnetization (M) axis, i.e., a vertical bias (VB) in continuation of the conventional EB for years.[7] The vertical shift behavior has been observed in systems including polycrystalline ceramics, [8] core-shell magnetic nanoparticles, [9] single-phase thin films, [5,10] bilayer heterostructures [11,12] manganite-based superlattices, [13] etc.13][14] For such exotic MH shift phenomenon, perovskite transition metal oxide systems are in particular fascinating and investigated for decades due to the strong interplay of spin, charge, lattice, and orbital degrees of freedom leading to strongly correlated d-orbital reconstruction effects.Tailoring the interfacial magnetic properties of the transition metal oxide heterostructures needs a quantitative and qualitative understanding of the system since the interfaces are extremely sensitive to the lattice structure, external strain, magnetic coupling, and magnetocrystalline anisotropy.20][21][22] In such a system, a rare positive EB shift (PEB: MH loop in the positive field direction for positive bias field (H FC )) is observed, despite both materials being FM.However, VB is still unaddressed in such an interesting system.LSMO is a popular soft FM having low magnetic anisotropy as well as low coercive field (H C ). Whereas, SRO has a relatively strong uniaxial magnetocrystalline anisotropy and a high H C (≈1 T).Having such contrasting yet intriguing properties, this system of LSMO-SRO with EB is suitable to study VB which can be applicable to any soft-hard magnetic material combination which further expands the use of VB in potential spintronic applications.
In this paper, we report a VB in an exchange-biased system (EB shift H EB ≈11 mT) of an FM-FM material heterostructure of LSMO-SRO (thickness ratio (t R = 1:2)) grown on SrTiO 3 (001) (STO) substrate.This system is particularly chosen as it shows EB wherein the magnetic anisotropies of the two materials are very different and hence magnetic switching happens at different fields which is required for the investigation.The VB is observed only below the Curie temperature (T C ) ≈125 K of SRO after cooling under H FC ≈±1 T and measuring MH loop with ±1 T loop tracing field range.Temperature (T) dependent measurements show the decrement of VB with increasing T. Field cooling (FC) dependent measurements show the increment in the amount of vertical bias (M VB ) till a threshold field and then saturates with increasing field.The PEB follows the same behavior as VB for both H and T variation.Object Oriented Micromagnetic Framework (OOMMF) micromagnetic simulations were performed to understand the mechanism of VB in the bilayer systems.The thickness (t) dependency model for the varying t of the hard layer (SRO) is also investigated through simulations.The origin of the AFM coupling in an FM-FM bilayer and an in-depth understanding of the VB and PEB is provided which was hitherto unexplored.We finally demonstrate the role of thicknesses and the competition of the anisotropies of the two films to obtain VB by a generalized model combining experimental and simulated results.

Experimental Results
The X-ray diffraction (XRD) intensity versus 2 patterns of the bilayer film show epitaxially aligned (00l) peaks of LSMO and SRO on the (001) STO substrate (Figure S1, Supporting Information).
Figure 1a shows the MH curves for ±FC (±1 T) measurements for a bilayer system of LSMO (10 nm)-SRO (20 nm) films on STO (001) substrate at 2 K.[20][21][22] The bare SRO and LSMO films were grown to confirm their saturation fields and transition temperatures (Figure S2, Supporting Information).The shift in the ±FC loops for the saturation magnetization, M VB ≈±6.5 emu (3.55% of M S ).M VB was calculated as (M S+ + M S-)/2, where M S+ (M S-) corresponds to the positive (negative) saturation magnetization (M S ) values (signs are included).[20][21][22][23] H EB is calculated as (H C+ + H C-)/2, where H C+ and H C-are the cut-off points on the H axis for the ascending and descending branches of hysteresis loop, respectively.20][21][22][23] To study the evolution of VB with T, we carried out T dependent measurements.The magnetization versus temperature (MT) measurement at 10 mT in Figure 2a confirms the phase transitions of SRO and LSMO.The increasing slope around T C ≈310 K corresponds to the paramagnetic (PM) to FM transition of LSMO [24,25] followed by a slight kink around ≈125 K which is attributed to the T C of SRO. [26,27]From the MH curves recorded at different T for FC +1 T, a decreasing trend of M VB from low T (2 K) to ≈100 K is seen and it becomes zero at T higher than T C ≈125 K of SRO (Figure 2b), depicting the indispensable role played by the SRO in obtaining VB.Maximum VB is observed at the lowest T ≈2 K likely from the minimal thermal perturbations.EB increases in a similar way with decreasing T. We have also investigated the bias FC dependency on the system.For each measurement, the sample is cooled down from 350 K till 2 K under different H FC and measured with ±1 T loop sweeping range (Figure S5, Supporting Information).VB shows a rise with increasing H FC and then saturates after ≈4 T (Figure 2c).This could be due to the AFM coupling at the interface of FM-FM layers explained later.It is observed that H EB also follows the same behavior.In order to find the correlation of VB and EB, we studied another system of all FM-FM bilayer heterostructure of Ni 80 Fe 20 -SRO.SRO (5 nm) and Ni 80 Fe 20 (2 nm) bilayer film was grown by PLD and sputtering respectively on 5 mm × 5 mm STO substrate.The experimental results are given in SI.The t R of magnetic films is taken to be similar to the LSMO-SRO system for the sake of comparison.The observed VB ≈15 emu (33% of M s ) is found to be significant (Figure S4a).However, a nominal EB of 1.5-2 mT for ±FC loops is observed.T-dependent measurements also show a pronounced decrease in VB from 2 K till T C ≈135 K (SRO) and becomes negligible after 135 K (Figure S4c, Supporting Information).

Simulation Results
To confirm our experimental results on VB, we performed the OOMMF simulations for both LSMO-SRO and Ni 80 Fe 20 -SRO systems. [28]Herein, the effect of EB coupling is excluded to understand the effect of VB only.We found that the loop swept in the range of ≈±1.1 T field shows VB for LSMO-SRO (Figure 3a) and ≈±0.9 T field for Ni 80 Fe 20 -SRO (Figure S6a, Supporting Information).The positive (negative) M shift of the MH loop is observed for positive (negative) bias confirming that VB is intrinsic to the system.On the contrary, the MH loop swept in the H range ±7 T shows no VB exactly homogenous to the experimen-tal curves (Figure 3b).Since t is analogous to M, we have varied t R (hard/soft) of the two layers to attain the VB dependence on the volume magnetization by simulations.It is found that the M VB increases with the initial increment in t R of two layers while it saturates at a very high t R (Figure 3).We have fitted the data points with the equation; ) where M VM refers to the maximum saturated shift of the loop and C explains the initial curvature of the fitted data points.The fitting parameters are obtained as M VM = 1.06 and C = 1.0.This is similar to the t dependency of the EB. [3]

Discussion
With the preceding discussion of the magnetic properties, the system can now be modeled to understand the mechanism involved.LSMO carries 70% Mn 3+ and 30% Mn 4+ ions from the Sr hole doping in which the Mn 3+ t 2g 3 e g 1 -Mn 4+ t 2g 3 e g 0 orbitals interact through a double exchange (DE) mechanism mediated by O-2p orbital electrons. [29]SRO is a rare example of itinerant FM with Ru 4+ t 2g 4 three majority and one minority spin polarized states. [30]SRO Ru 4+ has empty e g orbitals due to dominating crystal field splitting over Hund's coupling. [30]The half-filled t 2g electrons of Mn 4+ 3d orbitals couple antiferromagnetically with the Ru 4+ 4d electrons with three majority spin states and one minority spin state (t 2g 3↑1↓ ) (Figure 4a), while the Mn 3+ couple  ferromagnetically with Ru 4+ orbitals according to the Goodenough Kanamori rules. [31]The schematic in Figure 4 shows the Mn 4+ -Ru 4+ interactions only for the sake of simplicity.The O down spin jumps to the empty orbital of Mn 4+ and the Ru 4+ down spin replaces the vacant orbital of O.This suggests DE AFM interaction between the Ru4d 4 -Mn3d 3 at the FM-FM interface which is an essential requirement for EB in FM-FM LSMO-SRO bilayer. [32,33]This is a unique feature of ruthenite-manganite systems.Under +FC, H FC aligns all the LSMO and SRO interfacial spins in the H direction above T C .This will bring the system into a high positive interfacial magnetic energy (E im+ ) (Figure 4b).However, below the T C of SRO, the energetically favorable AFM coupling at the interface of LSMO and SRO competes with the stabilized spin states formed after FC.This may leave the interfacial AFM spins partially reversed (Figure 4c).The DE AFM interaction between the Mn 4+ and Ru 4+ at the interface favors the exchange coupling which results due to the pinning of the LSMO FM spins with the interfacial AFM spins of LSMO and SRO. [34]Therefore, the AFM interaction along with the hard anisotropy of SRO spins play a significant role in obtaining VB.However, for Case II, when |H m-| > |H S |, all the spins will have enough Zeeman energy to rotate in the opposite direction with negative interfacial magnetic energy |E im-| ∼ |E im+ |.This leads to a symmetrical hysteresis loop (Figure 4d).Thus, the VB results from the interplay of both H FC and loop tracing field.
With H FC increment, the SRO spins will be more anisotropic, and interfacial LSMO spins more oriented toward H FC direction.This will further enhance VB with increasing H FC .This competition between H FC and AFM coupling causes different H C in both descending and ascending branches which is attributed to the PEB trend with H FC .This explains the VB and PEB trend with FC (Figure 2c).The field dependency emphasizes the importance of AFM coupling at the FM-FM interface.This is similar to having an FM-AFM heterostructure where H FC dependency over partially reversed AFM spins states holds enormous importance in EB variation with field.At this point, it can be well understood that the lowest T of measurement will freeze the spins, which thus increases VB and PEB for a suitable intermediate loop tracing field.The appearance of VB below T C of SRO therefore is viable (Figure 2b).
To further understand if VB always accompanies EB, another system of very different anisotropies Ni 80 Fe 20 -SRO was investigated which shows a nominal EB but significant VB.To analyze both the systems, i.e., LSMO-SRO and Ni 80 Fe 20 -SRO, we manually removed the vertical MH shift and kept the horizontal shift intact and vice versa from the experimental MH data (Figure 5).We observe that removing the horizontal shift from the LSMO-SRO system, vertical shift remains same.Similarly, if M VB is made zero, horizontal shift remains unaffected.On the other hand, Ni 80 Fe 20 -SRO shows interesting behavior.When horizontal shift is made zero, M VB stays unaffected, whereas when M VB is removed, the nominal H EB vanishes.This implies the EB ≈1.6 mT in Ni 80 Fe 20 -SRO was caused by the shift in the M S only and not the inherent property of this material system.This implies VB cannot be always associated with EB and it can have its own origin.
To understand the origin of VB, the vertical shift was modeled by OOMMF simulations.VB is observed without considering EB coupling in the simulation.The t dependency is studied for these two systems (LSMO-SRO and Ni 80 Fe 20 -SRO).With increasing t of the hard layer (SRO), the overall exchange interactions among the hard layer spins increase further making it difficult to rotate them for loop reversal field.Therefore, M VB gradually increases with increasing t R and at very high t R , it saturates (Figure 3c).Not only that, varying t reduces the H C and distorts the loops as seen by simulations (Figure S7, Supporting Information).We also tried different hard-soft material combinations (LSMO-Co, LSMO-CoSm, etc.) to validate the proposed model (Figure S8, Supporting Information).We realize that any soft-hard material combination even after providing with intermediate loop tracing field cannot give the VB.This implies the right choice of material combination with their optimum thickness and the compatible anisotropies should be taken into account to obtain a significant VB.
An intuitive description of the origin of VB is now offered.An additional anisotropy appears at the EB-coupled interface.(i.e., LSMO-SRO).The hard interfacial anisotropy (from the pinning) and the adjacent layers' anisotropies together can shift the loop in the vertical direction and EB further helps in obtaining VB.This can also be imprinted in a material heterostructure by having strongly competitive anisotropic hard-soft layers to obtain the novel VB, as in the case of Ni 80 Fe 20 -SRO.So, the VB observed in the previous reports actually originates from an additional anisotropy created at the interface either from frozen, uncompensated/canted spins or EB coupling.If this additional anisotropy is not strong enough, it may not lead to VB. [13] Our generalized model can thus be applied to understand systems having spin glass structures, uncompensated/canted spins in any system spanning from ceramics to superlattice films to achieve a tuneable vertical shift of the MH loop, hence extending its applicability to wider materials range and micromagnetic devices.

Conclusion
In summary, we demonstrate the origin of vertical bias in an unconventional exchange coupled ferromagnetic-ferromagnetic heterostructure of LSMO-SRO.We propose a model combining both experimental and micromagnetic simulation results to elucidate the importance of strong interfacial anisotropy and optimum loop tracing field range to achieve both the vertical bias and the positive exchange bias below the Curie temperature of the SRO.Due to the Ru4d 4 -Mn3d 3 double-exchange interaction at the FM-FM interface of LSMO-SRO, an AFM interfacial coupling is generated which leads to the positive exchange bias.The additional anisotropy from the pinning effect at the interface of LSMO with SRO further leads to the vertical bias.With the right choice of magnetic materials, a significant vertical bias can be obtained due to extra anisotropy generated at interfaces in other systems possessing uncompensated spins/canted or frozen glassy spins which was so far unaddressed quantitatively and qualitatively.This is an important step forward to a comprehensive understanding of tuneable vertical bias and therefore has important implications in future spintronic devices.

Experimental Section
Thin Film Growth: The epitaxial thin films of SRO (20 nm) and LSMO (10 nm) were grown successively by multi-targeted pulsed laser deposition technique on a 5 mm × 5 mm SrTiO 3 (STO) substrate.LSMO was deposited at 750 °C and 100 mTorr oxygen partial pressure whereas SRO was deposited at 700 °C and 100 mTorr oxygen partial pressure, respectively, from the chemical stoichiometric ceramic targets by using the KrF excimer laser (248 nm) at a laser fluence of 2 J cm −2 .
Structural Characterization of the Films: The crystal structure was characterized using a Panalytical Empyrean vertical diffractometer with Cu K radiation ( = 1.54Å).
Study of Magnetic Properties: The detailed magnetic measurements were carried out in a Quantum Design MPMS3 magnetometer with maximum H range of ±7 T and T range of 2-350 K.The sample was demagnetized at room temperature by a proper demagnetization protocol and the magnet was reset before the measurement to ensure that there was no trapped flux present in the sample or the superconducting coils of the magnetometer. [35]MT for FC, ZFC, and remanence were performed to identify the phase transitions in the sample.Positive and negative FC MH measurements were carried out at different H FC and loop sweeping fields to explore their effect on VB.

Figure 1 .
Figure 1.MH loop for LSMO-SRO measured at 2 K after FC. a) Under H FC ≈±1 T for loop tracing field ±1 T. b) Under H FC ≈+7 T for loop tracing field +7 T showing full saturation with no EB and VB.

Figure 2 .
Figure 2. a) Zero filed cooling (ZFC), FC, and remanence MT measurements show the phase transitions at the T C ≈310 K and ≈125 K for LSMO and SRO respectively, confirming the onset of FM from PM phase with decreasing T. b) Evolution of EB and VB for a range of T across 200 K to 2 K under FC = +1 T. c) for FC change from 20 mT up to 6 T at 2 K.

Figure 3 .
Figure 3. Simulation results of VB similar to the experimental results for LSMO-SRO under loop tracing field range of a) ≈±1.1 T. b) 7 T. Inset shows the zoomed version.c) Dependence of the t R over the VB shows a gradual increase and saturation eventually.

Figure 4 .
Figure 4. a) Interfacial AFM coupling between Mn 4+ and Ru 4+ mediated by O 2p electrons in LSMO-SRO system under equilibrium.b) Spin alignment towards the positive direction under positive FC above T C leading to high E im+ .c) Case I: The interfacial partially reversed AFM spin states due to less loop tracing field applied in the opposite direction causing VB and PEB.d) Case II: The spins reverse on the application of the reversal loop tracing field |H m-| ≥|H S | leading to E im-of similar magnitude of E im+ and broken AFM coupling.No VB and PEB observed.
The angle of the interfacial spins relies on the amount of external H FC .Now for Case I, when the reversal measuring field (|H m-|) lower than the saturation field of SRO (|H S |) is applied, i.e., |H m-| < |H S | of the hard layer, the soft layer spins away from the interface will align in the negative H direction, though the SRO spins will remain magnetically uncompensated owing to their high anisotropy.However, the interfacial LSMO-SRO spins maintain the AFM coupling for the favorable low interfacial magnetic energy configuration (E im-); |E im-| < |E im+ | since the interfacial interaction energy (|E im |) dominates the Zeeman energy due to insufficient H m-. In this scenario, LSMO interfacial spins stay partially reversed and do not fully rotate under the influence of the H FC .The SRO spins projected in the H FC direction along with partially rotated interfacial LSMO spins contribute less than usual to the M S-during loop reversal.This leaves only the rotated LSMO spins away from the interface aligned in the opposite direction to contribute to the M S-.This suppresses the M S-and leads to the total M S+ being greater than the M S-manifesting VB from additional strong anisotropy at the interface (Figure4c).Thus, the H FC influences not only the hard SRO spins but the interfacial LSMO spins as well.At the same time, we observe PEB (|H C-|<|H C+ |) too due to preserved two-sublattice AFM symmetry during field reversal.

Figure 5 .
Figure 5. MH loops after removing a) horizontal shift and b) vertical shift from LSMO-SRO MH c) horizontal shift and d) vertical shift from Ni 80 Fe 20 -SRO MH obtained experimentally.The green text is to show the manual removal of the EB/VB.