Positive exchange-bias and giant vertical hysteretic shift in La0.3Sr0.7FeO3/SrRuO3 bilayers

The exchange-bias effects in the mosaic epitaxial bilayers of the itinerant ferromagnet (FM) SrRuO3 and the antiferromagnetic (AFM) charge-ordered La0.3Sr0.7FeO3 were investigated. An uncharacteristic low-field positive exchange bias, a cooling-field driven reversal of positive to negative exchange-bias and a layer thickness optimised unusual vertical magnetization shift were all novel facets of exchange bias realized for the first time in magnetic oxides. The successive magnetic training induces a transition from positive to negative exchange bias regime with changes in domain configurations. These observations are well corroborated by the hysteretic loop asymmetries which display the modifications in the AFM spin correlations. These exotic features emphasize the key role of i) mosaic disorder induced subtle interplay of competing AFM-superexchange and FM double exchange at the exchange biased interface and, ii) training induced irrecoverable alterations in the AFM spin structure.

T he discovery of exchange bias (EB) effect by Meiklejohn and Bean 1 has garnered enormous interest from the scientific community for its intriguing fundamental and technological aspects. Recent impetus on EB have resulted in diverse tantalizing avenues as the modern day electronic devices include its usage in spin valves, magnetic recording read heads, giant magnetoresistive sensors, etc 2,3 . The EB is usually characterized by an asymmetric shift in the magnetic hysteresis loop along the field axis when a ferromagnetic (FM)-antiferromagnetic (AFM) layered or a composite system is cooled in a static magnetic field through the Nèel temperature (T N ) of the AFM phase 4 . The magnitude of the loop shift (H EB ) depends on various factors such as the interfacial roughness, characteristics of the FM-AFM layers involved, the complex spin structure at the interface, the uncompensated moments at the interface, etc [4][5][6] . Usually for FM-AFM systems, the shift of the hysteresis loop is opposite to the cooling field (H CF ) direction and is termed as negative exchange bias (NEB). On the other hand, the shift of hysteresis loop along the same sign of H CF is termed as positive exchange bias (PEB) 5,6 . The PEB, a rarely observed phenomenon, was first reported for FeF 2 /Fe bilayer thin-films 5,6 . It is attributed to the AFM exchange coupling with its sign and magnitude strongly dependent on the H CF 5,6 . The AFM exchange coupling at the interface was also reported for two FM perovskite oxides, namely, La 2/3 Sr 1/3 MnO 3 and SrRuO 3 7 . The Cu 1-x Mn x /Co bilayers exhibited PEB in the vicinity of blocking temperature which subsequently vanishes at lower temperatures resulting in NEB due to the coexistence of FM and AFM interface coupling 8 . More recently, the PEB for Ni 81 Fe 19 /Ir 20 Mn 80 bilayers was observed and explained in the framework of meta-stable magnetic disorder at the FM-AFM interface induced by the magnetic training effect (TE) 9 .
Initially, most of the scientific quest to unravel the EB phenomenon was seen on metallic systems 1,3,4-11 . Recently, however, this phenomenon is also being explored and tuned in the magnetic perovskite oxides 7,[12][13][14][15][16] . Understanding the evolution of EB in perovskites oxide bilayers and multilayers is essential as these systems present a greater degree of freedom for tunability of EB at the interface via strain, orbital reconstruction, chargetransfer, etc. Their suitable combinations with structural compatibility at the FM-AFM interface might unveil many potent facets of EB. Observation of EB in the disordered-ordered magnetic interfaces, i.e., in paramagnetic (PM) LaNiO 3 and FM LaMnO 3 superlattice and the PM CaRuO 3 and AFM CaMnO 3 superlattices are clearly the recent important discoveries in this area 12,13 . More recently, strain engineered unexpected EB with the emergence of a self assembled spin glass like phase of LaSrMnO 4 at the film/substrate interface was reported for (La,Sr)MnO 3 single thin-films 17 . All endeavours are focussed on controlling and manipulation of EB by the interfacial interactions, thickness and number of layers of the FM and AFM phases, and the type of AFM order in the superlattice structures 14,15 . Overall the progress in EB has been two-fold. First, the EB has been addressed in unconventional heterostructures/bilayers with FM-PM, AFM-PM and collinear-noncollinear magnetic heterostructures 7,12,13,16 .
This has challenged our present understanding of EB which is generally observed in conventional FM-AFM heterostructures 14,15 . The second focus has been to tune and realize the novel EB properties beyond NEB. For instance, the realization of PEB and its reversal to NEB with critical role played by both the extrinsic and the intrinsic factors in controlling PEB, are essential components yet to be explicitly realized and understood.
In this communication, we report a novel and unique set of EB properties in orthoferrtite-ruthenate bilayers La 0.3 Sr 0.7 FeO 3 /SrRuO 3 (LSFO/SRO) fabricated on mosaic and non-mosaic SrTiO 3 (STO) (111) substrate. These samples, henceforth will be referred to as LS Mosaic and LS Non-mosaic , respectively. The proximity of the magnetic transition temperatures of the G-type AFM LSFO (T N , 190 K) and the FM SRO (T C , 160 K) makes them a suitable combination for investigation of EB properties in bilayer thin-film [18][19][20][21] . The (111) orientation of STO was chosen as it presents opportunity for increased interactions at the interface as compared to the conventional (100) STO substrate. This occurs as the [Fe 31 /Fe 51 ] ions in the AFM LSFO will be surrounded by three of the same type and three of the other type i.e. Ru 41 ions of the FM SrRuO 3 12 . We observe a low-field PEB, its sign reversal by both extrinsic and intrinsic factors and achieved a gigantic vertical magnetization shift. In this bilayer system, G-type AFM structure of LSFO coupled with FM SRO present an opportunity to control the EB by intriguing intrinsic factors such as nearest neighbour spin compensation, spin-flop coupling and competing superexchange (SE) interactions between FM and AFM resulting in a spin glass like interface. Whereas, the mosaicity of the substrate introduces external factors such as modulated spin structure at domain walls, random defects, and interface roughness to control and manipulate the EB. Formation of LSFO/SRO bilayers on both the mosaic and non-mosaic STO (111) substrate helps extract the contribution of extrinsic and intrinsic factors responsible for novel features of EB. A unique exhibition of diverse EB properties in LSFO/SRO observed here has been explained in the framework of modulation of the interfacial AFM spin structure with H CF and training induced subsequent runs. . Three peaks in w-scans with a separation of 120 degrees are observed for LSFO, SRO and STO which is expected to arise from the three fold symmetry of the STO (111) substrate. The mosaicity of the LS Mosaic is distinctly evident in the reciprocal space map (RSM) scans around the asymmetric (330) peak. It shows that the STO substrate peak is split into multiple spots [figure 2(c) and supplementary S1]. This typically depicts that the substrate surface consists of several small crystalline blocks and each block corresponds to one of the reflection of the substrate in the RSM map as shown in figure 2(c). Further, corresponding to each substrate reflection there exists a reflection of the coherently strained LSFO and SRO epitaxial layers for the LS Mosaic . Such exhibition of multiple epitaxial peaks is absent in the LS Non-mosaic sample which is formed on non-mosaic STO substrate [figure 2(d)]. The bulk pseudo-cubic lattice parameter of the LSFO is 3.87 Å , SRO is 3.93 Å and the STO is 3.905 Å . The out-of-plane lattice constant for the LSFO is 3.85 Å and the SRO is 3.945 Å . This suggests that the LSFO is under tensile strain, whereas, the SRO is under compressive strain. Overall, we can recognize qualitatively different crystal structures of the same substrate on which the LSFO/SRO bilayers namely, LS Mosaic and LS Non-mosaic , were fabricated and their respective implications on the EB properties studied.

Results
Magnetization (M) versus temperature (T) at a magnetic field (H) of 500 Oe in the field cooled cooling (FCC) protocol shows a T C , 150 K for LS Mosaic and LS Non-mosaic [inset figure 3(a)]. This is slightly lower than the bulk T C , 160 K of the SRO, presumably, due to strain in the thin film 14,15 . The M versus H loops at 2 K for zero-field cooling (ZFC) and in different H CF for LS Mosaic are shown in  Overall, the EB properties of LS Mosaic are novel and unusual, whereas, the EB for LS Non-mosaic is rather conventional and is commonly observed for FM-AFM systems.
In the LS Mosaic sample the mosaicity of the substrate induces topographic modulations which results in randomly oriented AFM easy axis of AFM grains in LSFO layer with a FM SRO layer coupled on to it. These sporadic distributions of magnetic inhomogeneities, having imperfections and defects at the interface result in various spin frustrated ensembles with a mixture of FM, AFM and spin flop coupling regimes 22,23 figure 4(b)]. This indicates that the pinning defects in the AFM layer are undergoing changes not only with training runs but have H CF sensitivity as well.
The disorder induced in the LS Mosaic is quite intriguing, as training causes H EB to traverse from PEB (LS Mosai A-B) to NEB (LS Mosaic C-D) regime, whereas its counterpart LS Non-mosaic exhibits NEB regime only. The TE is essential signature and can unveil the microstructural spin rearrangements along with the possible mechanisms driving the H EB . To understand the underlying intricacies, we compared the influence of training in the NEB regime of LS Mosaic C with that of the LS Non-mosaic . The training leads to irreversible changes in the interfacial domain configurations, which causes the magnetization of the LSFO pinning layer to be nonconserved 26 . Such relaxation effects in the nonconserved order parameters can be addressed using Landau-Khalatnikov expression which was successfully employed to describe the TE in LSMO/SRO heterostructures 26 . The phenomenological expression used to model the cycle dependence (n) with H EB is, where, K and H e EB~H EB (n??) are the crucial fitting parameters, H EB (1) is the first loop H EB value. The equation (1) can also be written as H EB (nz1)~(Kz1)H EB (n){KH e EB 26 . The value of K usually lies in the range 21 # K # 0 26 . When K 5 0, it yields H EB (n 1 1) 5 H EB (n) implying no training, whereas for K 5 21, it is H EB (nz1)~H e EB which yields a step like change in H EB between the first two data points with no TE for n . 2 26 . Equation (1) was successfully fitted to both LS Mosaic C and LS Non-mosaic , with the values of K as 20.52 and 20.97, respectively. For n $ 2, the H EB for LS Mosaic C keeps on decreasing with n, whereas, the H EB for LS Non-mosaic exhibits a negligible change.
The contrasting training behaviour for LS Mosaic C and LS Non-mosaic , plausibly indicates different training mechanisms governing both the samples. We attribute the initial large decrease in H EB for both the samples to a 'Hoffmann' like behaviour, where the major changes after the first reversal can be ascribed to a transformation from an initial noncollinear arrangement of the AFM spins to a more relaxed collinear arrangement 27 . Furthermore, as per Hoffmann's model, the TE should cease for n $ 2 27 . This is displayed by LS Non-mosaic , whereas, LS Mosaic C shows a continuous decrease in H EB even beyond n $ 2. This decrease in H EB (n $ 2) for LS Mosaic , typically indicates that along with the Hoffman's component (which largely trains out after the first cycle), a second contribution to training may be present. This seems to arise from the thermally activated depinning of the uncompensated AFM spins 28,29 . Thus, the LS Mosaic and the LS Non-mosaic can explicitly be distinguished via field training, as the former exhibits a combination of a Hoffman and thermally activated depinning mechanism, whereas, the later trains out via 'Hoffman' mechanism 27,28 .
We also observed a positive vertical magnetization shift in the hysteresis loop along the same sign as of the H CF for both the samples   H C and M av for LS Mosaic sample. We observed an enhanced overall M av for LS Mosaic D, as compared to that of LS Mosaic (A-C) in the entire temperature range [ figure 6(b,c and d)]. This suggests that the training causes a temperature independent retention of the irrecoverable permanent spin rearrangements in the AFM layer for the LS Mosaic D.

Discussions
In this section we will discuss the key observations of the LS Mosaic sample, in the following sequence, i) competing exchange interactions at the LSFO/SRO interface and the possible EB model for the observed PEB, ii) dynamics of the training induced dissimilar hysteresis loop shape transitions, and iii) the vertical magnetization shift.
The subtle interplay of FM-SE and AFM-SE interactions at the LSFO/SRO interface drives the PEB R NEB transition in the LS Mosaic sample. The transition may be attributed to a potential crossover from AFM to FM exchange coupling [ figure 3(b)]. This occurs as the mosaicity induces a disorder at the LS mosaic interface, thus, inducing the competition between FM-AFM exchange interactions. On one hand, LSFO grain boundaries exhibit FM-SE interaction in  44,45 . Presently, IDW can manifest between different crystallite ensembles, consisting of independent AFM grain boundaries with a coupled FM layer on to it. The IDW can provide AFM coupling at the interface which will yield PEB for LS Mosaic A. Also, IDW shows training and H CF sensitivity. Thus, as the H CF is increased thickness of IDW may decrease due to domain wall compression, yielding a complete NEB regime for LS Mosaic C-D 44,45 .
At this point, it is imperative to discuss the possibility of charge transfer at the LSFO-SRO interface. Charge transfer was found to be associated with the observed unidirectional anisotropy in LSMO/ YBCO 46,47 . In contrast, for the La 2 CuO 4 /LSMO bilayers, it was demonstrated that charge transfer is not a key factor, as the H C was found to exhibit a AFM thickness dependence [keeping FM thickness constant]. In the present case too, the H C was found to vary with the LSFO thickness for the LSFO/SRO bilayers on nonmosaic STO substrate [unpublished data]. This further bolsters the dominant role of SE interaction at the LSFO/SRO spin-glass like interface.
The  On the other hand, this coherent reversal of the SRO spins is hindered at H C2 for the LS Mosaic C-D and the loop closes at H C3 . This emergence of H C2 can be associated with the domain wall depinning processes which may be training or thermally assisted 28,29,50,51 . Further the TE largely alters the pinned spin concentration from LS Mosaic A to LS Mosaic D. This is evident as the relative changes in H C1 with temperature are quite pronounced for LS Mosaic A and LS Mosaic C. In contrast, the LS Mosaic D exhibits a negligible change in H C1 . This indicates that the pinning defects concentration have been drastically reduced for LS Mosaic D with subsequent training runs. Furthermore, the H C1 was found to decrease from 20. Finally, we comment on another important observation, which is the vertical magnetization shift [inset figures 4(c) and 4(d)]. The observation of vertical shift along the same sign as of the H CF usually indicates FM coupling at the interface 5,6 . We observed a positive vertical shift for LS Mosaic A and LS Non-mosaic which suggests FM coupling at interface. But, interestingly, LS Mosaic A also exhibits a PEB, which point towards the AFM coupling at the interface. Nevertheless, similar contrasting scenario was well addressed by Fritzimmons et al., as they showed that a microscopic AFM coupling at the interface is likely possible and can manifest along with a positive vertical shift 30 . This is seen for LS Mosaic A sample. Moreover, a giant vertical shift of about 35% for our optimized sample suggests that a large number of uncompensated AFM spins exists when the bilayer is grown along (111) orientation of STO [figure 4(d)]. This may occur as LSFO is known to exhibit an intriguing quasi-2D charge ordering on STO (111) rather than a perfect 3D charge ordered regime with a charge-disproportionate Fe 31 and Fe 51 ions along (111) 19 . The latent defects and imperfections in the film may give rise to uncompensated spins in the bulk along with the surface AFM spins resulting in massive EB.
To summarize, we report a novel method of mosaicity induced disorder to obtain a rare phenomenon of PEB, magnetic annealing and H CF induce PEB R NEB transition and accompanying loop shape transitions. While the mosaic-disorder induces AFM exchange coupling at the interface which causes PEB, the uncompensated spins arising from the intrinsic nature of the magnetic order of LSFO yield the huge vertical shift. These studies open up new avenues for obtaining the otherwise elusive PEB for FM/AFM systems and an innovative way to tune giant vertical shift in magnetic oxides.

Methods
The bilayers of LSFO as bottom layer and SRO as top layer were fabricated on STO (111) single crystal substrates by pulsed laser deposition (PLD) technique using a 248 nm KrF excimer laser. Deposition was carried out at a repetition rate of 4 Hz with laser energy of 1.7 J/cm 2 at the target with a substrate temperature of 700uC, oxygen partial pressure of 25 Pa and a post-deposition annealing for 5 minutes in 1.5 kPa of O 2 . Thickness of the bilayers with LSFO (37 nm) and SRO (20 nm) for LS Mosaic and LS Non-mosaic were measured using a surface profiler. The X-ray diffraction (XRD) measurements were carried out using PANalytical Empyrean. Magnetization measurements were performed on a SQUID magnetometer (Quantum design, USA).