Magnetic interactions in BiFe0.5Mn0.5O3 films and BiFeO3/BiMnO3 superlattices

The clear understanding of exchange interactions between magnetic ions in substituted BiFeO3 is the prerequisite for the comprehensive studies on magnetic properties. BiFe0.5Mn0.5O3 films and BiFeO3/BiMnO3 superlattices have been fabricated by pulsed laser deposition on (001) SrTiO3 substrates. Using piezoresponse force microscopy (PFM), the ferroelectricity at room temperature has been inferred from the observation of PFM hysteresis loops and electrical writing of ferroelectric domains for both samples. Spin glass behavior has been observed in both samples by temperature dependent magnetization curves and decay of thermo-remnant magnetization with time. The magnetic ordering has been studied by X-ray magnetic circular dichroism measurements, and Fe-O-Mn interaction has been confirmed to be antiferromagnetic (AF). The observed spin glass in BiFe0.5Mn0.5O3 films has been attributed to cluster spin glass due to Mn-rich ferromagnetic (FM) clusters in AF matrix, while spin glass in BiFeO3/BiMnO3 superlattices is due to competition between AF Fe-O-Fe, AF Fe-O-Mn and FM Mn-O-Mn interactions in the well ordered square lattice with two Fe ions in BiFeO3 layer and two Mn ions in BiMnO3 layer at interfaces.

which is expected to facilitate the study of the Fe-O-Mn interaction. In this paper, BFMO films and BFO/BMO superlattices (simply denoted as BFO/BMO) were grown on (001) STO substrates. Spin glass behavior were observed in both samples. The Fe-O-Mn interaction has been confirmed to be AF by X-ray magnetic circular dichroism (XMCD) measurements. Spin glass in BFMO can be categorized as cluster spin glass, while spin glass in BFO/BMO results from competing AF and FM interactions at interfaces. Figure 1(a) shows the X-ray diffraction (XRD) patterns of BFMO and BFO/BMO with LaNiO 3 (LNO) as buffer layer in Bragg-Brentano geometry using a D/teX Ultra detector (1D detector). Only (001) and (002) diffraction peaks can be observed, indicating the high (001) orientation, which is due to well matching of lattice constant of BFO (3.96 Ǻ ), BMO (3.95 Ǻ ) and LNO (3.838 Ǻ ) to STO (3.905 Ǻ ) 12,[17][18][19] . The out-of-plane lattice constants are calculated to be 3.96 Ǻ for BFMO and 3.93 Ǻ for BFO/BMO, respectively. The epitaxial growth of BFO/BMO was further confirmed by a high resolution transmission electron microscope (HRTEM), as shown in Fig. 1(b). However, due to the same crystal structure and similar atomic number of Fe and Mn for the epitaxial layers of BFO and BMO, the interface in the superlattice structure cannot be clearly resolved in the HRTEM images. Considering the pseudo-cubic lattice constant of BFMO of 3.93 Ǻ 13 , the slightly larger c lattice constant of BFMO is due to inplane compression from the STO substrate, and strain relaxation possibly happened in BFO/BMO. The strain due to the lattice mismatch could introduce the contrast variation at the interface between BFO/BMO and STO, shown in Fig. 1(b). According to the phase diagram, BFMO displays predominated orthorhombic structure 20 . The h-2h XRD patterns of BFMO and BFO/BMO were carefully measured in parallel beam geometry using a scintillation detector (the inset of Fig. 1(a)). Due to the close atomic scattering factors of Fe 31 and Mn 31 , the (001) superlattice diffraction peak was hardly resolved. The (002) superlattice peak of BFO/BMO, marked by an arrow, can be clearly seen in the inset, which is absent in the XRD pattern of BFMO. The scintillation detector in parallel beam geometry is much less sensitive than the D/teX Ultra detector in Bragg-Brentano geometry which should reveal the impurity phases. Thus, this superlattice peak cannot be due to impurity phases since it was absent when we used Bragg-Brentano geometry as shown in the main frame of Fig. 1(a). On the other hand, compared with Bragg-Brentano geometry, the parallel beam geometry is more sensitive for the reflection from surfaces and interfaces of films. As shown in the inset of Fig. 1(a), clear observation of the superlattice peak confirms the high concentration of BFO/BMO interfaces. The period of superlattice was calculated using Bragg equation to be about 0.91 nm, which is slightly larger than the designed period (0.79 nm). This is due to the limitation of our PLD system that the layer by layer growth with each layer thickness of 1 unit cell cannot be strictly fulfilled in our work. However, alternative growth of BFO and BMO layers with thickness of roughly 1 pseudo-cubit unit cell provides high concentration of BFO/BMO interfaces and a high interface/bulk ratio, which might facilitate the characterization of Fe-O-Mn superexchange interaction. It has been theoretically predicted the possible checkerboard superstructure in BFO/BMO, which is (110)-oriented superlattice 21 . However, due to the (001) growth direction of our films with alternative (001) BFO and BMO layers, the checkerboard superstructure seems unlikely to be formed. Figure 2 shows the X-ray photoelectron spectroscopy (XPS) core level spectra of Fe 2p and Mn 2p in BFMO and BFO/BMO, calibrated by the C 1s line (284.8 eV) binding energy 22 . The binding energy of Fe 2p 3/2 is at 710.3 eV for BFMO and 710.1 eV for BFO/ BMO. The valence states of Fe in both samples are almost the same after considering the XPS accuracy of 60.1 eV. However, the decomposition of Fe 2p 3/2 spectrum into a superposition of symmetric components is questionable, thus it is complicated to obtain the exact concentration of Fe 21 and Fe 31 23 . A satellite peak can be observed at 8.7 eV for BFO/BMO and 8.6 eV for BFMO above the corresponding principal peak. Due to the different d orbital electron configuration, Fe 21 and Fe 31 show satellite peak at 6 eV or 8 eV above their 2p 3/2 principle peaks, respectively 14 . The Fe 2p core level spectra of BFMO and BFO/BMO are similar to those previously reported BFO, confirming that Fe is mainly in 13 valence state 14 . The binding energy of Mn 2p 3/2 is at 641.8 eV for BFMO and 641.6 eV for BFO/BMO, respectively. A shoulder peak marked by arrow below this energy can be observed in both samples, which originates from a small concentration of Mn 21 14 .

Results
BFO is a well known multiferroic material with ferroelectricity above room temperature. However, leakage current is a big obstacle for observation of ferroelectric hysteresis loops for both samples. The ferroelectric nature of BFMO and BFO/BMO was characterized at room temperature using piezoresponse force microscopy (PFM), as shown in Fig. 3. The clear local PFM hysteresis loops for both samples suggest their ferroelectricity. It was recently pointed out that similar PFM hysteresis loops were observed in soda-lime glass due to dipoles induced by ionic motion under external electric field 24 . We measured the phase hysteresis loops with various maximum voltages, as shown in Fig. 3(a) and (e), and coercivity of both samples shows little variation. Furthermore, we measured the amplitude hysteresis loops with different frequencies, as shown in Fig. 3(b) and (f). The observed amplitude hysteresis loops for both samples are insensitive to the time periods. Thus, the ferroelectricity in both BFMO and BFO/BMO can be inferred from the PFM results 24 . We further studied the retention of domains written by the PFM tip, as shown in Fig. 3(c), (d), (g) and (h). After 10 hours, negligible changes were observed in domain patterns for both samples. Figure 4(a) shows the field dependent magnetization (M-H) curves of BFMO measured at different temperatures. As can be seen, a clear soft FM hysteresis loop can be observed at 300 K, indicating  room temperature ferromagnetism. Similar phenomenon has been reported by Choi et al., which was explained by larger strain in ultrathin film 12 . However, others reported only negligible weak ferromagnetism 14 . It should be noted that magnetic properties of pure (001) STO substrate have been checked, the observed weak ferromagnetism is much smaller than the magnetization values of both samples, and can be neglected. The observed magnetization is smaller than that reported by Choi et al. 12 , but much larger than that by Bi et al. 14 . With decreasing temperature, not only the magnetization increases, but also the coercivity increases drastically, especially below 200 K 25 . The M-H curves measured at different temperatures for BFO/BMO show similar behavior. The M-H curves are superposition of paramagnetism and weak ferromagnetism. With applying a maximum magnetic field of 40 kOe, the total magnetization of BFO/BMO is almost the same as that of BFMO, but the FM magnetization of BFO/BMO is much smaller than that of BFMO.
Zero field cooled (ZFC) and field cooled (FC) temperature dependent magnetization (M-T) curves were measured under 100 Oe from 5 K to 300 K with cooling field of 10 kOe for FC curves, as shown in Fig. 4(b) (BFMO) and (d) (BFO/BMO). A broad peak at around 243 K can be observed in the ZFC M-T curve for BFMO, but only a kink has been observed in the FC M-T curve (inset of Fig. 4(b)). With increasing doping concentration of Mn, T N of BFO continuously decreases 26 . T N of BFMO ceramics decreases to 440 K 27 . Due to positive formation enthalpy of ordered structure of Mn and Fe, the distribution of Mn and Fe is inhomogeneous 14 . As a result, Fe-rich and Mn-rich clusters will form. Three exchange interactions exist in the system, namely Fe-O-Fe, Mn-O-Mn and Fe-O-Mn with different ordering temperature. T N of 440 K has been attributed to Fe-O-Fe ordering, which is above the measuring limit of our system. T N of BFMO prepared in high pressure with ordered Mn and Fe structure is 270 K 25 , and Du reported the second ordering temperature at 260 K 27 . Thus, we attribute the observed peak at 243 K in M-T curves to the onset of Fe-O-Mn interaction. It is interesting to note that the deviation of FC magnetization from ZFC one at the freezing point (temperature at which ZFC peak occurs) for both samples has been observed. This is a feature, but not exclusive, for the spin glass system 28,29 . In both cases of superparamagnet and spin glass, finite dipolar interaction between the spins results in the deviation of FC-ZFC curves at temperature lower than blocking or freezing temperatures and FC magnetization increases continuously as the temperature is lowered 28 . One of the important characteristic features of spin glass is the phenomenon of aging. To confirm the spin glass behavior in BFMO and BFO/BMO, thermoremnant magnetization (TRM) depending on time was measured at various temperatures below 350 K by cooling the sample in a field of 10 kOe from 350 K to the final temperature, abruptly decreasing field to 500 Oe to measure the time-dependent magnetization. For the magnetic relaxation in spin glass, a stretched exponential decay is expected 28,30 , where the glassy component M r mainly contribute to the observed relaxation effects. The time constant t and exponent n are related to the relaxation rate of spin glass. For 0,n,1, it stands for spin glass system 28,31 . In equation (1), M 0 is added to account for the nonrelaxed magnetization responding to the applied field of 500 Oe 30 . Figure 5(a) and (c) show typical relaxation curves measured at 5 K for BFMO and BFO/BMO, respectively. Solid curves are the best fitting with equation (1), and fitting parameters are shown. It can be clearly seen that the fitting to experimental data is very well. The parameter of n is 0.40 for BFMO and 0.53 for BFO/BMO, which is close to the other spin glass systems 28,31,32 . Spin glass is generally due to site disorder and lattice frustration, leading to frustrated interactions 33 . Furthermore, if FM clusters are  considered as macroscopic spins with competing interactions, spin glass behavior can be observed, termed to cluster spin glass 34 . These spin systems qualitatively exhibit similar and characteristic variations of magnetizations 35 . Thus, XMCD measurements were performed to further clarify the magnetic ordering at low temperatures. Figure 6 shows X-ray absorption spectroscopy (XAS) and XMCD spectra recording at Fe and Mn L 2,3 edges for BFMO and BFO/BMO measured at 4.2 K under a magnetic field of 10 kOe. The line shape of Fe XAS spectra for both BFMO  In contrast to the similar line shape of Fe and Mn XAS spectra in BFMO and BFO/BMO, XMCD spectra are obviously different. As can be seen in Fig. 6, Fe XMCD spectrum for BFMO is very close to that of c-Fe 2 O 3 , i.e., having two opposite peaks at O h and T d sites, respectively 36  doping on structure distortion of FeO 6 octrahedra with antiparallel alignment of spins leads to opposite signs of XMCD signal at different photon energy. Thus we try to correlate Fe XMCD spectrum to site disorder of Fe ions, since similar XMCD spectrum of Fe L edge has been observed in BFO film with high density of domain walls 39 . As shown in Fig. 6(b), a strong peak can be observed in Mn XMCD spectrum, which is much similar to that in BMO film grown on (001) STO substrate 40 , suggesting the formation of Mn-rich clusters with FM Mn-O-Mn interactions. In comparison with weak Fe XMCD signal, the relatively strong Mn signal implies that the enhanced ferromagnetism in BFMO at low temperature is mainly from Mn, instead of Fe.
In contrast to BFMO, BFO/BMO exhibits a small peak in Fe XMCD spectrum, suggesting a weak magnetic contribution from Fe in BFO layers. Previous reports have shown that 4% XMCD signal in BFO/La 0.7 Sr 0.3 MnO 3 bilayers, which corresponds to a magnetic moment of about 0.6 m B /Fe 15 , and 1% XMCD signal in BFO/ La 0.5 Ca 0.5 MnO 3 corresponding to that of around 0.1 m B /Fe 16 . Accordingly, the observed 1.8% XMCD signal in BFO/BMO can be roughly estimated as 0.2 m B /Fe, which is much larger than the canted moment (0.03 m B /Fe) in bulk BFO 15 . This suggests that the observed 1.8% XMCD does not originate from spin canting in BFO due to the Dzyaloshinskii-Moriya (DM) interaction, while is more likely attributed to the induced spin canting by exchange coupling between Fe and Mn at interfaces 15,16 . The weakening of antiferromagnetism and induced weak ferromagnetism in BFO layer at interface have also been observed in BFO/CoFe and BFO/CoFeB due to exchange coupling 41,42 . For Mn XMCD spectrum in the BFO/BMO, we have found a splitting at L 3 edge, different from the single peak observed in BMO 40 . This discrepancy could be explained as that BMO layer is not strictly one unit cell thick, thus Mn ions have different neighboring environments. For instance, Mn ions inside BMO layer have only the nearest neighboring Mn ions, while Mn ions at interfaces have the nearest neighboring Fe ions, leading to various distortion on MnO 6 octahed-   ral. These two different locations of Mn ions possibly lead to the splitting at L 3 edge. The same sign of split XMCD peaks suggests that Mn spins tend to align parallel, confirming the FM interaction of Mn-O-Mn. Comparing Fe and Mn XMCD spectra in BFO/BMO, their opposite sign suggests an antiparallel alignment of the corresponding magnetic moments, confirming the AF exchange interaction of Fe-O-Mn at interfaces. The Mn spins in BMO layer tend to align parallel to each other due to FM interaction between Mn ions. Thus the spins of neighboring Fe ions in BFO layer will be forced to align parallel through the AF interaction of Fe-O-Mn at interfaces. Together with AF interaction between neighboring Fe ions in BFO layer, spin canting might be enhanced, leading to enhanced weak ferromagnetism.

Discussion
The XMCD results on BFMO clearly demonstrated the formation of FM Mn-rich clusters in AF Fe-rich matrix, indicating the cluster spin glass 34 , as the schematic diagram shown in Fig. 5(b). Considering the layered growth structure of BFO/BMO, a square lattice has been formed at interface with two Fe ions in BFO layer and two Mn ions in BMO layer, as shown in the schematic structure in Fig. 5(d). Due to AF exchange interaction, the spins of two neighboring Fe ions, Fe1 and Fe2 in BFO layer, align antiparallel. The AF exchange interaction between neighboring Fe and Mn at interface will force the spins of Mn ions to align antiparallel to the neighboring Fe ions, thus the spins of neighboring Mn ions will be forced to align antiparallel to each other. However, FM exchange interaction between neighboring Mn ions will force the spins to align parallel to each other, leading to high frustration. Geometrical frustration is generally observed in triangle lattices without disorder that has AF exchange interaction between the nearest neighboring magnetic ions. Magnetic frustration might also be realized in the well ordered square lattice with finely tuned AF and FM interactions 33 . The spin glass in BFO/BMO can be understood by the competing AF (Fe-O-Fe in BFO, Fe-O-Mn at interface) and FM (Mn-O-Mn in BMO) exchange interactions at interfaces with well ordered square lattices similar to geometrical frustration in triangle lattices 33 .
In summary, comparative structural and magnetic studies have been performed on multiferroic BFMO and BFO/BMO prepared by PLD on (001) STO substrates. The ferroelectricity at room temperature for both samples has been inferred from the observation of PFM hysteresis loops and electrical writing of ferroelectric domains. Irreversibility in FC and ZFC M-T curves has been observed in both samples, with a cusp at around 243 K for BFMO and 190 K for BFO/ BMO in ZFC curves. The decay of thermo-remnant magnetization with time confirms the spin glass behavior. XMCD measurements confirm the AF interaction of Fe-O-Mn. Spin glass behavior in BFMO has been classified to cluster spin glass due to Mn-rich FM clusters embedded in AF matrix. Spin glass behavior in BFO/BMO is due to competition among AF Fe-O-Fe interaction in BFO, AF Fe-O-Mn interaction at interface, and FM Mn-O-Mn interaction in BMO in the well ordered square lattices at interfaces of BFO and BMO.

Methods
BFMO, BFO and BMO ceramic targets were prepared by tartaric acid modified sol-gel method 43 . BFMO and BFO/BMO films were deposited on (001) STO substrates by pulsed laser deposition (PLD) system with a KrF eximer laser of 248 nm and a repetition rate of 5 Hz. Laser energy was 300 mJ and target-to-substrate distance was kept at 5 cm. Substrate temperature T s was kept at 750uC with oxygen pressure P O2 of 2 Pa. BFO/BMO was prepared by alternatively ablating BFO and BMO targets with 5 pulses for each layer and the stacking sequence was repeated 50 times. The thickness of about one pseudo-cubic unit cell was deposited by 5 laser pulses, estimated from the average growth speed of BFO film. For BFMO, 500 pulses were selected. After deposition, both BFMO and BFO-BMO were annealed for 0.5 h at 550uC and cooled down to room temperature in an oxygen pressure of 1 3 10 5 Pa. The film thickness was determined by the cross-sectional scanning electron microscopy (SEM, FEI) images to be 34 nm for BFO/BMO and 25 nm for BFMO. For magnetization measurements, the films were directly deposited on STO surface, while a LNO buffer layer with thickness of about 30 nm was deposited first at T s 5880uC and P O2 540 Pa for the other measurements.
The crystal structure of films was examined by XRD with Cu Ka radiation (Rigaku Smartlab3). The valence states of Fe and Mn were characterized by XPS (ThermoFisher SCIENTIFIC) with Al Ka X-ray source (hn51486.6 eV). The crosssectional specimen for HRTEM was prepared by mechanical polishing followed by argon ion milling. The thinned sample was examined using a JEM-200CX. The surface morphology and ferroelectric domains were characterized by scanning probe microscopy (SPM, Asylum Research Cypher). Temperature dependent magnetic properties were carefully measured by a commercial SQUID-VSM (Quantum Design) from 5 K to 300 K. XAS measurements were performed at the beam line UE46/PGM-1 at BESSY II (Helmholtz-Zentrum Berlin) with a circular degree of polarization of around 90%. The spectra were acquired and normalized to the incident beam in total electron yield (TEY) mode by recording the sample drain current as a function of photon energy. Right-handed (m 1 ) and left-handed (m 2 ) circularly polarized XAS spectra were obtained by reversing photon helicity under H 5 10 kOe. The field is parallel to the beam, and the beam is perpendicular to the surface plane of our samples. XMCD spectrum was obtained as (m 1 2m 2 ) and normalized to the maximum peak intensity of XAS [(m 1 1 m 2 )/2].