Strong magnetoelectric coupling in mixed ferrimagnetic-multiferroic phases of a double perovskite

Exploring new magnetic materials is essential for finding advantageous functional properties such as magnetoresistance, magnetocaloric effect, spintronic functionality, and multiferroicity. Versatile classes of double perovskite compounds have been recently investigated because of intriguing physical properties arising from the proper combination of several magnetic ions. In this study, it is observed that the dominant ferrimagnetic phase is coexisted with a minor multiferroic phase in single-crystalline double-perovskite Er2CoMnO6. The majority portion of the ferrimagnetic order is activated by the long-range order of Er3+ moments below TEr = 10 K in addition to the ferromagnetic order of Co2+ and Mn4+ moments arising at TC = 67 K, characterized by compensated magnetization at TComp = 3.15 K. The inverted magnetic hysteresis loop observed below TComp can be described by an extended Stoner–Wohlfarth model. The additional multiferroic phase is identified by the ferroelectric polarization of ~0.9 μC/m2 at 2 K. The coexisting ferrimagnetic and multiferroic phases appear to be strongly correlated in that metamagnetic and ferroelectric transitions occur simultaneously. The results based on intricate magnetic correlations and phases in Er2CoMnO6 enrich fundamental and applied research on magnetic materials through the scope of distinct magnetic characteristics in double perovskites.

www.nature.com/scientificreports www.nature.com/scientificreports/ dominant FM order 27,29,30 of Co 2+ and Mn 4+ moments is known as the mechanism for the observed magnetic exchange bias in polycrystalline Y 2 CoMnO 6 19 . In Tm 2 CoMnO 6 and Er 2 CoMnO 6 (ECMO), the neutron diffraction studies confirm that the order of Co 2+ and Mn 4+ moments is FM and the order of Er 3+ /Tm 3+ moments at lower temperature activates the additional ferrimagnetic (FIM) order between Er 3+ /Tm 3+ and ferromagnetic Co 2+ /Mn 4+ sublattices [31][32][33] . The FIM order exhibits an inversion of the magnetic hysteresis loop in polycrystalline ECMO 34 . In Yb 2 CoMnO 6 and Lu 2 CoMnO 6 , the Co 2+ and Mn 4+ ions display the up-up-down-down (↑↑↓↓) spin configuration in which the ferroelectricity emerges perpendicular to the c-axis from the cooperative O 2− displacements through the symmetric exchange striction [23][24][25] . Evidently, a scientific understanding of diverse magnetic phases and interactions is crucial for finding novel functional properties in double perovskites.
In this work, the magnetic and magnetoelectric properties of single crystals of double-perovskite ECMO were studied to reveal the characteristics corresponding to the mixed FIM and MF phases. The dominant FIM order between Er 3+ and FM Co 2+ /Mn 4+ sublattices was identified by compensated magnetization (M) occurring at T Comp = 3.15 K. From our precise measurement of isothermal M in the low T regime, the inversion of the magnetic hysteresis loop was observed below T Comp , which can be explained by the delicate balance between different magnetic moments, and qualitatively by an extended Stoner-Wohlfarth model [35][36][37][38] . The ferroelectric polarization (P) and dielectric constant (ε′) measurements demonstrated an additional inclusion of the MF phase as found in Yb 2 CoMnO 6 and Lu 2 CoMnO 6 23,24 . Associated with the coexistence of FIM and MF phases, the disappearance of MF phase by an external H occurs simultaneously with the metamagnetic transition, revealing exclusive characteristics of the double perovskite.

Results and Discussion
Figure 1(a) shows the X-ray powder diffraction pattern for the ground single crystals of double perovskite ECMO at room T. The crystallographic structure was refined as a monoclinic structure with the P2 1 /n space group. The lattice constants were found to be a = 5.228 Å, b = 5.594 Å, and c = 7.477 Å with β = 90.244° with good agreement factors, χ 2 = 1.74, R p = 7.97, R wp = 6.23, and R exp = 4.72. The crystal structures viewed from the a-and c-axes are depicted in Fig. 1(b,c), respectively. Co 2+ and Mn 4+ ions are alternatingly located in corner-shared octahedral environments. The oxygen octahedral cages are strongly distorted due to the small radius of the Er 3+ ion 28 .
To investigate intricate magnetic properties as anticipated in the double perovskite incorporating three different magnetic ions, the T-dependence of magnetic susceptibility (χ = M/H) was obtained. The anisotropic χ in H = 0.05 kOe along (H//c) and perpendicular (H⊥c) to the c-axis was measured upon warming in H after zero-field cooling (ZFC) and upon cooling at the same H (FC), as shown in Fig. 2(a). The overall T-dependence of χ's for two different orientations exhibits strong magnetic anisotropy, which indicates that the spins are mainly aligned along the c-axis. The FM order relevant to the dominant Co 2+ and Mn 4+ superexchange interactions sets in at T C = 67 K, which can be determined by the sharp anomaly in the T derivative of χ in H//c. The T-dependence of heat capacity divided by the temperature (C/T) measured upon warming in zero H also exhibits the anomaly powder X-ray diffraction patterns for ground Er 2 CoMnO 6 (ECMO) single crystals. Y obs , Y cal , and Y obs −Y cal represent the intensities of the observed patterns, calculated patterns, and their difference, respectively. The green short lines denote the Bragg positions. (b,c) Views of the crystal structure of double perovskite ECMO from the a-and c-axes, respectively. The purple, pink, blue, and yellow spheres represent Er 3+ , Co 2+ , Mn 4+ , and O 2− ions, respectively. starting from T C , shown in Fig. 2(b). Upon further cooling, C/T shows an abrupt increase below T Er ≈ 10 K, which corresponds to the ordering of Er 3+ moments. Below T Er , the reversal of χ was observed in both ZFC and FC measurements ( Fig. 2(a)) as a characteristic signature of a ferrimagnet [39][40][41][42][43][44][45][46] .
A ferrimagnet is a substance that involves a portion of opposing magnetic moments as in antiferromagnetism, but generates a net M from unequal magnetic moments in the opposite directions, thus exhibiting distinct characteristics of magnetism. The FIM interaction between Er 3+ and FM Co 2+ /Mn 4+ sublattices generates the intriguing T-dependence of χ following the different sequence of measurement. In the FC measurement in H//c, χ increases smoothly below T C with the parallel alignment of Co 2+ and Mn 4+ moments. Upon cooling further below T Er , the Er 3+ moments begin to align oppositely to the Co 2+ /Mn 4+ moments, which leads to a gradual decrease in χ. At lower T, χ intersects the zero point owing to the large moment of Er 3+ spin. On the other hand, ZFC χ shows a positive value at 2 K since the Er 3+ moments tend to orient along the H direction. The decrease in the effective Er 3+ moments upon increasing T results in the sign change of χ. Above T Er , the negatively magnetized Co 2+ / Mn 4+ spins begin to flip along the applied H due to thermal fluctuation, which causes another sign change of χ at 48 K. To find the compensation T precisely, the thermoremanent magnetization (M rem ) 47 was measured in H//c (Fig. 2(c)). At 2 K, H = 50 kOe was applied in H//c and then turned off, and M rem was recorded in the absence of H upon warming from 2 K. The sign reversal of M rem occurs at T Comp = 3.15 K, which manifests the FIM feature of this double perovskite compound.  [35][36][37][38] (see Experimental section for detail). The experimental observation of inversed magnetic hysteresis loop in ECMO suggests the considerable difference of magnetic anisotropy energies between Er 3+ and Co 2+ /Mn 4+ moments. In our calculation, we assumed that the magnetocrystalline anisotropy energy of Co 2+ /Mn 4+ moments is three times larger than that of Er 3+ moments. With qualitative similarity, the magnetic hysteresis loop was attained from the model, as illustrated in Fig. 3(b). Based on the result, the evolution of the spin configuration for Er 3+ and Co 2+ /Mn 4+ ions during the sweeping of H from +90 to −90 kOe in H//c is schematically depicted in Fig. 3(b). The red and blue arrows indicate the effective moments of Er 3+ and Co 2+ / Mn 4+ ions, respectively. At high H, the Er 3+ and Co 2+ /Mn 4+ moments tend to be aligned in the same direction due to the dominant Zeeman energy. Upon decreasing H, the negative exchange coupling between Er 3+ and Co 2+ /Mn 4+ spins accompanied by a smaller magnetocrystalline anisotropy energy and larger moment of Er 3+ ions leads to the progressive decrease in the net Er 3+ moments, followed by zero net M even at a positive H and negative M r . Decreasing H further in the negative direction induces an abrupt drop in M, where the Co 2+ /Mn 4+ spins are fully reversed because the Zeeman energy of Co 2+ /Mn 4+ sublattices overcomes the anisotropy energy. Since the change in magnitude of M caused by the reversal of Co 2+ /Mn 4+ moment at the metamagnetic transition is found to be ~9 μ B /f.u. (Fig. 3(a)), the net magnetic moment of Co 2+ /Mn 4+ spins should be ~4.5 μ B /f.u., which is smaller than the summation of Co 2+ and Mn 4+ moments (6 μ B /f.u.). The smaller net magnetic moment of Co 2+ / Mn 4+ spins is acceptable because a small portion of Co 2+ /Mn 4+ spins is naturally reversed during the magnetization process from +90 kOe to −26.5 kOe and antiferromagnetic exchange couplings of Co 2+ -Co 2+ or Mn 4+ -Mn 4+ pairs are originally included from the presence of anti-sites of ionic disorders and/or antiphase boundaries. www.nature.com/scientificreports www.nature.com/scientificreports/ The close relevance of M r to T Comp was cautiously examined by the T dependent evolution of M r . The full hysteresis curves up to ±90 kOe were recorded in H//c at various T's. The hysteresis loops below and above T Comp are shown within the range of ±5 kOe in Fig. 3(c,d), respectively. Below T Comp , all the curves present the inverted magnetic hysteresis. Upon increasing T, the inverted loop becomes narrow and the magnitude of negative M r decreases linearly, resulting from the reduced net Er 3+ moments by thermal fluctuation. By crossing T Comp , the sign of M r changes and it increases gradually with an increasing T.
Recently, new magnetism-driven ferroelectrics, i.e. type-II multiferroics, were found in double-perovskite Yb 2 CoMnO 6 and Lu 2 CoMnO 6 23,24 . The initial polycrystalline analysis of neutron diffraction and bulk electric properties for Lu 2 CoMnO 6 suggested that the ferroelectricity arises from the symmetric exchange striction of the ↑↑↓↓ spin chains with alternating Co 2+ and Mn 4+ charge valences 48 , consistent with the Ising spin chain magnet of Ca 3 CoMnO 6 49 . However, studies on the single crystals of Yb 2 CoMnO 6 and Lu 2 CoMnO 6 revealed that the ferroelectricity emerges perpendicular to the c-axis below T C = 52 and 48 K, respectively. Several theoretical works provided a plausible explanation for the ferroelecticity, in which the symmetric exchange strictions along the ↑↑↓↓ spin chain with alternatingly shifted O 2− ions generate cooperative O 2− displacements perpendicular to the c-axis [50][51][52] .
The possible formation of an additional MF phase in ECMO was examined by the H-dependence of P obtained by integrating magnetoelectric current density (J), measured perpendicular to the c-axis (E⊥c) at 2 K, shown in Fig. 4(a,b). After poling from 100 K to 2 K in H = 0 kOe and E = 5.7 kV/cm, the J in H//c exhibits a very sharp peak with peak height of ~0.76 μA/m 2 at the metamagnetic transition, H C = 26.5 kOe. The corresponding P value at H = 0 kOe and 2 K was estimated as ~0.9 μC/m 2 , which is only two orders of magnitude smaller than the P observed in Lu 2 CoMnO 6 and signifies the presence of a small amount of the MF phase. The tiny magnitude of P at 2 K implies that the exact magnetic configuration of MF phase could hardly be identified by the neutron diffraction experiment. Upon increasing H, the P shows the sharp step at H C and disappears above H C . The simultaneous transitions at H C for the suppression of the ferroelectricity and the reversal of Co 2+ /Mn 4+ spins in the FIM state suggest that the small amount of the additional MF phase is strongly influenced by the dominant FIM phase. In analogy with the ferroelectricity in Lu 2 CoMnO 6 , the P emerged perpendicular to the c axis at H = 0 kOe in ECMO suggests that the most plausible spin configuration of the minor MF phase would be ↑↑↓↓. The disappearance of the P by applying H along the c axis can be explained by the change of spin configuration from the ↑↑↓↓ to ↑↑↑↑.
In Fig. 4(c), the H-dependence of ε′ in E⊥c is plotted, measured in H//c up to ±90 kOe at f = 100 kHz and T = 2 K. By sweeping H between +90 to −90 kOe, the whole variation of ε′ is only about 1% with strong hysteretic behaviour. The maximum values occur at H = ±6 kOe, followed by the sharp transitions at H C . The ε′ shows the rather complicated H dependence in comparison with the H dependence of P. In addition to the small portion of www.nature.com/scientificreports www.nature.com/scientificreports/ MF phase, the additional AFM clusters formed by anti-site disorders and antiphase boundaries in the ferromagnetic Co 2+ /Mn 4+ sublattices would also affect the isothermal ε′. The complicated but tiny magnitude variation of isothermal ε′ may result from the intricate contributions from the small portions of MF phase and AFM clusters. For a comparison with ε′(H), the H derivative of isothermal M, dM/dH at 2 K is also plotted in Fig. 4(d). The dM/dH reveals the similar hysteretic variation of ε′. The isothermal M mainly reflects the response of the FIM order between the Er 3+ and Co 2+ /Mn 4+ moments to the external H, as illustrated in Fig. 3(b), but also affects strongly on the hysteretic behaviour of ε′(H).
The T-dependence of the dielectric constant (ε′) and tangential loss (tanδ) is displayed in Fig. 5(a,b), respectively, measured perpendicular to the c-axis (E⊥c) at f = 100 kHz in H//c with H = 0, 10, 20, and 30 kOe. At zero H, a small and broad peak of ε′ at T C = 67 K was observed in Fig. 5(a), which signifies the emergence of a small amount of MF phase. Compared to the peak height of ~15%, normalized by the value at T C = 48 K in Lu 2 CoMnO 6 23 , it can be estimated as only about 1% in ECMO. Despite a small portion of the MF phase in ECMO, T C is fairly enhanced. The broad peak of ε′ is gradually suppressed by applying H along the c-axis, ascribed to the change in the spin configuration from ↑↑↓↓ to ↑↑↑↑, similar to that in Lu 2 CoMnO 6 23 . Upon decreasing T, ε′ decreases linearly until it declines faster below 20 K. The overall T-dependence of ε′ and tanδ (Fig. 5(b)) below T C appears similar to those of Lu 2 CoMnO 6 .
While the intrinsic coupling phenomena between magnetic and ferroelectric states in single-phase type-II multiferroics were extensively explored, detailed properties of an MF phase mixed with another magnetic phase have scarcely been revealed. The T evolution of magnetoelectric effect in the mixed FIM and MF phases was examined by comparison between isothermal P and M at T's below T comp . Figure 6(a,b) show the H-dependence of P's and M's, respectively, in E⊥c and H//c at T = 2, 2.25, 2.5, 2.75, and 3 K, indicating that both of P and M vary delicately to the change of T. The estimated P's at 2.25 and 2.5 K were 0.79 and 0.47 μC/m 2 , respectively. As H is increased, the P's are suppressed with steep steps at H = 28.0 and 28.7 kOe. The initial curve of M at 2, 2.25, and 2.5 K also shows the step at the same H as P, suggesting the strong intercorrelation between FIM and MF phases. At 2.75 and 3 K, P magnitudes at 0 kOe are reduced as 0.43 and 0.32 μC/m 2 , respectively. Upon increasing H, the P's are gradually reduced and vanish above ~37 kOe, corresponding to the overall broad feature of M's. Note that P above T comp could not hardly be obtained because of the almost suppressed magnitude of J with a broadened feature. Figure 6(c,d) display isothermal ε′ in E⊥c at f = 100 kHz and J in H//c, respectively, at T = 2, 2.25, 2.5, 2.75, and 3 K. The initial curve of ε′ at 2 and 2.25 K indicates both a sharp peak and step-like feature at the metamagnetic transition but the ε′ at 2.5 K shows only a step. The sharp peak of the J at 2 K shifts to higher H and the www.nature.com/scientificreports www.nature.com/scientificreports/ peak height is reduced upon slightly increasing the T. The weak anomaly was observed in the ε′ at 2.75 and 3 K, corresponding to the disappearance of P. As shown in the inset of Fig. 6(d), J's at 2.75 and 3 K exhibit wide and small peaks around 35 kOe.
The T evolution of the magnetodielectric effect in a wide range of T's in the mixed FIM and MF phases was also investigated by comparison between isothermal ε′ and M. Figure 7 displays the isothermal ε′ in E⊥c at f = 100 kHz and M in H//c and H⊥c, at T = 5, 10, 20, 35, 50, and 65 K. At 5 K, a butterfly-like shape of ε′ was observed with a strong magnetic hysteresis, with the absence of the step-like metamagnetic transition ( Fig. 7(a)). The broadened feature of ε′ is compatible with the modulation of M in H//c with the narrow magnetic hysteresis described as small values of M r = 1.22 μ B /f.u. and the coercive field of H c = 2.10 kOe (Fig. 7(g)). At 10 K, the butterfly-like shape of ε′ is maintained ( Fig. 7(b)), but the magnetic hysteresis is considerably reduced. The central part of the hysteresis loop in H//c is extended as M r = 2.73 μ B /f.u. and H c = 7.24 kOe (Fig. 7(h)), indicative of the reduced strength of the Er 3+ spin order. In addition, the slight and elongated hysteretic behaviour of M in H⊥c emerges. As T increases further, the magnetic hysteresis in both ε′ and M is progressively reduced. At 65 K, just below T C , the sharp cusp of ε′ occurs at zero H with the hysteresis loop in M vanishing.
In summary, we explored the magnetic and magnetoelectric properties of mixed ferrimagnetic and multiferroic phases of single-crystalline double-perovskite Er 2 CoMnO 6 . The dominant Co 2+ and Mn 4+ superexchange interactions lead to the ferromagnetic order below T C = 67 K, aligned mainly along the c-axis. The long-range order of Er 3+ moments below T Er = 10 K induces the ferrimagnetic order and magnetization compensation at T Comp = 3.15 K, delicately balanced with the ferromagnetic Co 2+ /Mn 4+ sublattice. The extended Stoner-Wohlfarth model depicts qualitatively the inverted magnetic hysteresis loop observed below T Comp . The observation of electric polarization at low temperature is indicative of the presence of a small portion of a multiferroic phase simultaneously with the ferrimagnetic phase. The strong magnetoelectric correlation at the metamagnetic transition in the phase coexistence reveals the unique characteristic of the double perovskite compound, which offers crucial clues for exploring suitable materials for magnetoelectric functional applications.

Methods
Rod-shaped single crystals of ECMO with a typical size of 2 × 2 × 5 mm 3 were grown by the conventional flux method with Bi 2 O 3 flux in air. Er 2 O 3 , Co 3 O 4 , and MnO 2 powders were mixed in the stoichiometric ratio for ECMO and ground in a mortar, followed by pelletizing and calcining at 1000 °C for 12 h in a box furnace. The calcined pellet was delicately reground and sintered at 1100 °C for 24 h. The same sintering procedure after regrinding was carried out at 1200 °C for 48 h. A mixture of pre-sintered polycrystalline powder and Bi 2 O 3 flux with a ratio of 1:12 ratio was heated to 1300 °C in a Pt crucible. It was melted at the soaking T for 5 h, slowly cooled to www.nature.com/scientificreports www.nature.com/scientificreports/ 985 °C at a rate of 2 °C/h, and cooled to room T at a rate of 250 °C/h. The crystallographic structure and absence of a second phase were checked by the Rietveld refinement 53 using the FullProf program 54 for the power X-ray diffraction data. The data were obtained with a Rigaku D/Max 2500 powder X-ray diffractometer using Cu-K α radiation.
The T and H dependences of DC M were examined by using a VSM magnetometer in a Quantum Design PPMS (Physical Properties Measurement System). The specific heat (C) was measured with the standard relaxation method in PPMS. The T and H dependences of ε′ were observed at f = 100 kHz using an LCR meter (E4980, Agilent). The H dependence of electric polarization (P) was obtained by the integration of magnetoelectric current measured with the H variation of 0.1 kOe/s after poling in a static electric field of E = 5.7 kV/cm.
In our extended Stoner-Wohlfarth model 35