Introduction

Multiferroic materials which possess simultaneous magnetic and electric orderings have attracted vast amount of interests, due to their importance in both fundamental physics and practical applications1,2,3. In the past decades, most research attentions on multiferroics have been paid on various transition oxides. Despite the great progress of multiferroic oxides, there are still many drawbacks of these materials, such as low working temperatures and weak polarization/magnetization, which prevents their immediate applications. In fact, there are many multiferroics beyond oxides, e.g. some fluorides4, which may own better performance and novel physics but have not been well studied.

The fluoride BaMnF4 belongs to a group of isostructural compounds BaMF4 (M = Mn, Fe, Co, Ni, etc.) which have unusual magnetic and electrical properties. Interest in these materials was stimulated by the discovery of both antiferromagnetism and piezoelectricity in 19685. As a typical multiferroic material, BaMnF4 was sporadically studied in the past decades6,7,8,9,10,11, because high quality samples were not easy to be synthesized. The room-temperature structure of BaMnF4 is orthorhombic with space group of A21am (a = 5.9845 Å, b = 15.098 Å, c = 4.2216 Å)9. MnF6 octahedra linked at the corners form puckered sheets perpendicular to the b axis, which are separated by the intercalation layers of Ba ions, as sketched in Fig. 1(a,b). A structural phase transition occurring at TC = 247 K has been reported, with incommensurate superlattice peaks below TC at and its multiples: and 6. These wave vectors do not change with decreasing temperature and such a modulation of structure leads to the distortion of F octahedra6. BaMnF4 has a spontaneous polarization PS = 11.5 μC/cm2 along a axis at room temperature7. However, the reversal of polarization by electric field has not been observed because of its high conductivity and large potential barrier for the ferroelectric reversal. Thus BaMnF4 is a pyroelectric material and the temperature dependent dielectric constant measurements indicate that the ferroelectric Curie temperature TCFE should be higher than its melting point6. With decreasing temperature to around 50 K, a broad peak of magnetization was observed, which was attributed to the two-dimensional antiferromagnetic (2D AFM) transition6,12. The Néel temperature (TN) of BaMnF4 is about 26 K, below which three-dimensional (3D) AFM correlation is established6. The ordered magnetic moment was reported to be 4.8 μB/Mn2+ and lies in the bc plane, 9° from b axis (Fig. 1(c)), with AFM ordering along both b and c directions6. Weak ferromagnetism with net magnetization along c axis induced by magnetoelectric coupling (ME) effect was theoretically predicted13 and has been experimentally found (0.01 μB/Mn) by AFM resonance14. However, some other experimental studies, e.g. susceptibility measurement and neutron diffraction, cannot confirm such ferromagnetism4,15. Therefore, the ME effect induced ferromagnetism, or its net magnetization, needs further experimental verification.

Figure 1
figure 1

The schematic crystal structure of BaMnF4 in (a) bc plane and (b) ab plane.(c) the AFM structure, where the AFM axis lies in bc plane and is directed about 9° from b axis.

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Among various magnetic properties, exchange bias (EB) is a very interesting one which has important applications in spintronics16,17. EB was reported mostly in heterostructure systems, such as ferromagnetic (FM)/AFM bilayers, AFM nano-materials with AFM core and spin glass like shell, etc. and the mechanism was generally attributed to interfacial exchange coupling18,19,20. Based on the basic idea of EB in FM/AFM bilayers, such a phenomenon might also be observed in other systems if the FM moment could be pinned through coupling with other physical quantities. Recently, Dong et al. reported that EB might be induced by polarization through the ME effect21. BaMnF4 has a spontaneous polarization with ME induced AFM spin canting, thus the weak FM moment, if indeed exist, should be coupled to the polarization22. Thus, it is reasonable to suspect the EB in BaMnF4 as a fingerprint of ME induced weak ferromagnetism, which has not been reported till now. In this letter, BaMnF4 powder were prepared by hydrothermal method, magnetic transitions to 2D AFM structure at 65 K and 3D AFM structure at 26 K were observed. EB has been observed below 65 K, which has been ascribed to the polarization pinned magnetization through ME effect.

Results

Figure 2(a) presents the XRD pattern of BaMnF4 powder. It is clear that the diffraction pattern can be well indexed to the orthorhombic structure of standard JPCDS: 21-0077, confirming the space group of A21am. No impurity phase can be observed from the diffraction pattern. The size of crystalline grains evaluated by Scherrer formula is greater than 1000 nm, beyond its validity limit, suggesting the much large particle size of our BaMnF4 powder. From the SEM image in Fig. 2(b), BaMnF4 powder show the sheet structure, generally with lateral size in the order of 10 μm, although there are also some smaller fragments. This micro-sheet morphology suggests the anisotropic growth under hydrothermal condition, which is related to the anisotropic crystal structure, as sketched in Fig. 1(a,b). As aforementioned, these bilayers of corner-connected octahedra are separated by layers of Ba cations, making a quasi-2D structure. Figure 2(c) shows the electron diffraction pattern from one BaMnF4 sheet with electron beam perpendicular to the sheet plane (inset of Fig. 2(c)). The regular rectangle spotty structure of diffraction pattern suggests the single crystalline structure of each sheet. The ratio of lattice plane distance along the two orthogonal directions (1 and 2 shown in Fig. 2(c)) can be calculated from the diffraction pattern to be 1.42, which coincides well with the ratio of lattice constant a and c (a:c = 1.42). This suggests that direction 1 is along a axis and 2 along c axis, while the normal of sheet is along b axis. It is naturally supposed that different facet has different growth speed due to the anisotropic cation and anion arrangements, leading to the different adsorption of growth units23.

Figure 2
figure 2

(a) The XRD pattern and (b) SEM image of BaMnF4 powder. (c) The electron diffraction pattern from one BaMnF4 sheet with electron beam perpendicular to the sheet, as shown in the inset.

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The temperature dependent magnetization (M-T) under a magnetic field of 200 Oe was measured after zero field cooling (ZFC) and field cooling (FC) processes with a cooling field (Hcool) of 200 Oe. As shown in Fig. 3(a), the ZFC M-T curve shows a clear maximum at around 50 K, while continuous increase of magnetization with decreasing temperature was observed in the FC M-T curve. This peak temperature agrees well with the previous report of a broad peak at around 50 K in the M-T curve, which was ascribed to the 2D AFM transition12. The previous magnetic investigations were mainly performed on single crystalline samples15,24. Isotropic magnetic properties were observed at T > 30 K, below which a continuous decrease of magnetization was observed with a field along b axis, while a minimum was observed at around 25 K and then increased with further decreasing temperature with a field perpendicular to b axis. Due to the powder nature of our samples, the ZFC M-T curve is the average result with a field along random crystalline orientations. Thus, although the minimum of ZFC magnetization can still be observed, its temperature is much lower than 25 K and the increase of magnetization with further decreasing temperature is much weaker. A clear kink can be observed at around 26 K in the FC M-T curve, which coincides with the reported TN of 3D AFM transition6.

Figure 3
figure 3

(a) ZFC and FC M-T curves measured under H = 200 Oe (main plot). ZFC M-T curve measured under H = 50 Oe (inset). (b) ZFC and FC M-T curves measured under H = 50 kOe.

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A splitting of ZFC and FC M-T curves is observed below 65 K, which is assigned to Tirr (irreversible temperature) here and has not been reported in BaMnF4 previously. Such a splitting is generally observed in those systems with unstable magnetic structures, such as spin glass, superparamagnetism, etc.25,26,27. The typical character of spin glass is the memory effect25,26. Memory effect experiment was performed following the reported protocol28. A ZFC M-T curve was measured with a stop at 32 K for 6 hours during the cooling process first and then another ZFC M-T curve was measured with continuous decrease of temperature. No signature of spin glass was observed29. We further performed the AC magnetic susceptibility measurements on BaMnF4 powder with various frequencies and the results are shown in Fig. 4. A broad peak can be observed for all susceptibility (real and imaginary) curves and there’s no frequency-dependent peak shift, which can also exclude the possible spin glass contribution. The weak ferromagnetism has been reported to be induced by the ME effect in 3D antiferromagnetism below TN13. The onset magnetization in FC M-T curve below 65 K suggests that weak ferromagnetism might be induced by polarization through the ME effect even in the 2D AFM phase. We attributed 65 K to the onset temperature of the 2D AFM structure. The observed irreversibility can be understood by the magnetic anisotropy of the ME induced spin-canted magnetic domains27. There might be metastable states below 65 K, due to the competition between magnetic crystalline anisotropy and domain wall pinning. The energy configuration is determined by applied field and temperature, influencing the spin flipping from metastable states to stable states. Similar to increasing temperature, increasing the applied field can also decrease the energy barrier and suppress the irreversibility27. The ZFC and FC M-T curves under magnetic field of 50 kOe were further measured, as shown in Fig. 3(b). The nearly overlapping of ZFC and FC M-T curves indicates that the Zeeman energy of weak ferromagnetic moment under field of 50 kOe is enough to overwhelm the energy barrier. The broad peak at around 50 K can still be observed for both curves. Furthermore, clear minima at around 28 K corresponding to the 3D AFM transition, can be clearly observed for both ZFC and FC M-T curves. It has been reported that the spins of Mn ions are easily aligned to the field direction in two-dimensional AFM phases15, suggesting that the magnetic field should be smaller to observe the low-temperature anomaly. With decreasing field to 50 Oe during the ZFC M-T measurement (inset of Fig. 3(a)), a small peak at 65 K can be clearly observed, confirming an AFM transition at Tirr.

Figure 4
figure 4

AC magnetic susceptibility M’ (real part) of BaMnF4 measured under various frequencies.

Inset: the imaginary part M”. It should be noted that the value of M” is too small to be measured under low frequencies.

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Figure 5(a) shows the M-H loops of BaMnF4 measured at 300 K and 5 K after cooling from 300 K with Hcool of 200 Oe. The loop of 300 K is a straight line, revealing that BaMnF4 is paramagnetic at room temperature. At 5 K, a clear hysteretic M-H loop has been observed, with remanent magnetization of 0.015 emu/g (7.2 × 10−4 μB/Mn2+), suggesting the weak ferromagnetism. Theoretically, it has been predicted that there is a tiny FM component along c axis: Mc ~ 4παacPa, where Pa is the ferroelectric polarization and αac the magnetoelectric tensor element related to the ordering of antiferromagnetism22. However, such ME induced weak ferromagnetism was doubted recently, since no FM component was observed using neutron diffraction and susceptibility measurements10,15. The exact origin for this discrepancy is not clear at this moment. The observed hysteretic M-H loop in our samples at 5 K confirms the ME induced weak ferromagnetism. However, its remanant magnetization is much weaker than the reported value of 0.01 μB/Mn, which may be the reason for the discrepancy between different experimental methods. In contrast to ordinary M-H loops, an upward deviation from straight line can be observed with increasing magnetic field in the 5 K M-H loop, which has been ascribed to the spin-flop transition at low temperatures12. For the M-H loop at 5 K with Hcool of 200 Oe, a clear shift to left has been observed (left inset of Fig. 5(a)), indicating the EB, which has not been observed in the loop at 300 K. To exclude the possible measuring errors, M-H loop at 5 K with Hcool of −200 Oe was measured and is shown in the right inset of Fig. 5(a). The clear right shift confirms the observed EB.

Figure 5
figure 5

(a) M-H loops of BaMnF4 at T = 300 K and T = 5 K after cooling with a field of 200 Oe with the enlarged view in left inset. Right inset: the enlarged view of M-H loop measured with cooling field of −200 Oe. (b) Temperature dependence of HE and HC. The inset shows the enlarge view of M-H loop measured at 5 K with maximum field (Hmax) of 10 kOe after cooling under field of 200 Oe. The arrow indicates the closure of hysteresis loop at Hirr. (c) Enlarged view of M-H loops measured under different Hmax at 5 K after cooling under field of 200 Oe. The inset shows the dependence of HE and HC on Hmax.

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It has been reported that if the applied maximum field is not enough to reverse the magnetization of FM phase, the minor loop might also lead to the similar phenomenon of EB30,31,32,33. As the coercivity of our sample is only about 100 Oe, the applied field of 10 kOe is much larger than the coercivity, the M-H loops measured under maximum field of 10 kOe are not likely to be minor loop. The system can be considered effectively saturated if the ascending and descending branches of its hysteresis loop coincide for fields higher than the anisotropy field34. The inset of Fig. 5(b) shows that the magnetization is reversible in high fields, the arrow marking the field of loop closure (Hirr ~ 7.6 kOe). The applied field of 10 kOe is much larger than Hirr, which excludes the minor loop effect. Furthermore, if the observed EB is due to minor loop, the M-H loop measured with maximum field of 10 kOe at 5 K should shift to left in the case of Hcool of −200 Oe, in contrast to the experimental observed positive shift. We applied different maximum field up to 70 kOe to measure the M-H loops and the results are shown in Fig. 5(c). As can be seen, with increasing maximum field to above 10 kOe, the descending parts of M-H loops are nearly overlapping, while significant shift to right can be observed in the ascending parts. The inset shows the HE and HC in dependence on the maximum field. HE and HC are defined as HE = −(HL+HR)/2 and HC = (HR−HL)/2, where HL and HR are the left and right coercivities, respectively. HE decreases with increasing the maximum field and starts to saturate with higher field. HE of 24 Oe can still be observed with maximum field of 70 kOe, which confirms the intrinsic nature of EB. The continuous decrease of HE is mainly due to continuous right shift of the ascending parts of M-H loops. This might be understood by that the reversed magnetization might be pinned in metastable states with increasing the reversed maximum field, which will become harder to be reversed with positive field35.

In order to explore the relationship between temperature and EB, we measured the M-H loops at various temperatures after cooling under field of 200 Oe. Figure 5(b) shows HE and HC as a function of temperature. HC was also measured at 5 K under ZFC process, which is about 138 Oe and slightly larger than the value measured under FC process (star in Fig. 5(b)). With temperature above Tirr = 65 K, both HE and HC are nearly zero. As HC is closely related to the remanent magnetization due to weak ferromagnetism, the near zero HC suggests the near zero remanent magnetization. Thus, above Tirr = 65 K, there is no ME induced weak ferromagnetism. Generally, the temperature where EB disappears is called blocking temperature TB. The coincidence of TB and disappearing temperature of remanent magnetization suggests the coupling between weak ferromagnetism and EB. With decreasing temperature, both HE and HC show the tendency of saturation. With further decreasing temperature below 40 K, an upturn of both HE and HC can be observed, which again start to saturate below 20 K. This upturn of HE and HC can be understood by the emergence of 3D AFM structure.

Discussion

EB in complex bulk oxides generally results from interfaces between ferromagnetic, antiferromagnetic, or spin glass regions29. For those antiferromagnetic oxides showing ferromagnetic-like or spin glass surface, previous experiments were mostly focused the nanosized systems, in which the similar behavior (remnant M and EB) were indeed observed36,37,38,39. However, the grain size of our power sample is in the micrometer scale, thus the surface ratio is much reduced comparing with those nanosized materials. As has been discussed, the magnetic contribution of spin glass has been excluded in our BaMnF4 powder from the memory effect and AC magnetic susceptibility measurements. The magnetic contribution from surface disorders can be safely excluded. Thus the possible mechanism of exchange coupling between AFM core and spin glass like surface can be excluded10,18,40,41,42,43. Furthermore, the ME induced weak ferromagnetic moment in the particle core might also be pinned by the disordered surface spins44,45. However, since this is an interface effect, the EB will decrease drastically with increasing the thickness of FM layer, similar to the conventional FM/AFM bilayers46. The influence of Hcool on HE and HC was further studied, as shown in Fig. 6. The sample was cooled down from 300 K to 5 K under different field up to 50 kOe. We notice that there are two regions for the variation of HE and HC. At low cooling field up to around 5 kOe, HE increases abruptly while HC decreases abruptly with increasing Hcool. At high cooling field, both HE and HC show saturated behavior. In conventional AFM/FM bilayer system, both HE and HC increase with increasing Hcool in the low field range47,48,49, while in the exchange bias system with frustrated AFM spins at interface, HE tends to decrease50, even changes the sign with increasing Hcool in the low field range51,52,53. The increase of HE with increasing Hcool in the low field region further excludes the possible coupling with the surface disorder spins. When the cooling field is low, it is not enough to make all the weak ferromagnetic magnetization aligned. With the increase of cooling field, the degree of the weak ferromagnetic moment alignment is enhanced, which reduce the effect of the averaging of anisotropy due to randomness54. Interestingly, HC shows a decrease with increasing Hcool in the low field range, which is rather unusual and cannot be explained at this moment.

Figure 6
figure 6

The dependence of HE and HC on Hcool, measured at 5 K with maximum field of 10 kOe.

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Instead, we’d like to attribute the origin of EB to its magnetoelectricity, which can give a self-consistent scenario to understand above experimental observations. First, the critical temperature for the 2D AFM transition is Tirr = TB = 65 K, instead of previous supposed 50 K. In addition, Scott also mentioned that in BaMnF4 the spins order in planes up to until approximately T = 3TN4, which is closer to our observed blocking temperature of 65 K rather than the reported 50 K. Below this temperature, weak FM moments can be induced by the polarization and AFM ordering through ME effect in BaMnF422, as sketched in Fig. 7. Since the ferroelectric Curie temperature TCFE of BaMnF4 is very high (higher than its melting point), Pa should be robust during our magnetic measurements with temperature decreasing from 300 K to 5 K. Due to the ME effect, the easy axes of neighboring Mn ions are not exactly in line, but with a small angle. The spin structures after FC process are shown in Fig. 7(a,b) with Hcool of opposite direction. The induced Mc due to spin canting will be aligned along the direction of Hcool, even when there’s only 2D AFM correlation below 65 K. Of course, such an ME effect also works after the 3D AFM transition at 26 K. After the establishment of such spin structures at low temperatures, the magnetization has preferred orientation along the direction of Hcool. With applied field (Happl) opposite to the direction of Hcool during the M-H loop measurements, the spins S1 and S2 slightly rotate away from the easy axes with net magnetization along the direction of Happl, as shown in Fig. 7(c,d) ((a) to (c) and (b) to (d)). However, the spins S1 and S2 will rotate back to their easy axes after switching off the field. The spin structures tend to switch back to their initial states ((c) to (a) and (d) to (b)), respectively. Thus, HL is larger than HR in the case of positive Hcool and HL is smaller than HR in the case of negative Hcool, leading to the observe EB. In contrast to the general mechanism of interfacial exchange coupling in heterostructures, here the EB in BaMnF4 is a bulk effect, due to the magnetization pinned by polarization through ME effect. EB is a special method to verify the ME induced weak ferromagnetism in multiferroics. Following this mechanism, the electrical-controllable EB is expected by flipping the polarization. Although there are some experimental difficulties for BaMnF4 studied here, the ferroelectric polarization flip may be possible in near future, e.g. using ion substitution to reduce its ferroelectric energy barrier and suppress its leakage.

Figure 7
figure 7

The illustration of magnetoelectricity induced EB.

With given polarization Pa, the canting of neighboring AFM spins S1 and S2 can be affected by the cooling field direction due to Zeeman energy of net moment Mc. The dashed lines are the easy axes of neighboring Mn ions.

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In summary, we have successfully synthesized pure BaMnF4 powder by hydrothermal method. The powder is consist of single crystals in sheet structure, with b axis as the normal of sheet plane. Weak ferromagnetism induced by the ME effect has been confirmed in both 2D and 3D AFM phases by the observation of hysteretic M-H loops. A significant EB after FC treatments was observed, which is strongly dependent on the temperature. The EB is visible only below 65 K, which has been assigned to the temperature of 2D AFM transition. An upturn was observed in the temperature dependent HE and HC from 40 K to 20 K, coinciding with TN of 26 K, where the 3D AFM transition happens. The mechanism of EB has been explained by the magnetization pinned by polarization through ME effect. In a word, the magnetic poling can fix the sign of α without the help of electric field. This would be a very unique property of ME antiferromagnets. More direct measurements, e.g. magnetoelectric measurements after magnetic field cooling processes, can further check the sign of ME tensor component. Following this mechanism, the electrical-controllable EB might be realized and applied in spintronics.

Methods

BaMnF4 powder was synthesized by hydrothermal method55. Appropriate amounts of BaF2 and Mn(CH3COO)2·4H2O were dissolved in trifluoroacetic acid solution (5 ml CF3COOH and 10 ml distilled water) and the diluted solution was formed by magnetic stirring, which was then put into an autoclave. The autoclave was gradually heated to 220 °C, held for 20 hours, then slowly cooled down to room temperature. The upper remaining liquid was discarded and the precipitates were kept and washed with ethanol for several times. The washed products were placed in a vacuum drying oven and dried at 95 °C, resulting in the final pale pink powder.

The structure of samples was studied by X-ray diffraction (XRD, Rigaku Smartlab3) using a Cu Kα radiation and transmission electron microscope (TEM, Tecnai F20). The morphology was studied by a scanning electron microscope (SEM, FEI Inspection F50). The DC magnetization was measured by a superconducting quantum interference device (SQUID, Quantum Design) from 5 K to 300 K. AC magnetic measurements were carried out using a physical property measurement system (PPMS, Quantum Design).

Additional Information

How to cite this article: Zhou, S. et al. Magnetoelectricity coupled exchange bias in BaMnF4. Sci. Rep. 5, 18392; doi: 10.1038/srep18392 (2015).