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[Ceramics International-V50-43414-ErMnO3-Mn_Accepted_Version.pdf](https://mdr.nims.go.jp/filesets/0c2d2ff7-c84a-4011-be43-7917661f2196/download)

## Creator

[Andreas Dönni](https://orcid.org/0000-0002-7300-9175), Vladimir Y. Pomjakushin, Martin Rotter, [Lei Zhang](https://orcid.org/0000-0003-1173-4328), [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244), [Alexei A. Belik](https://orcid.org/0000-0001-9031-2355)

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[Ferrimagnetic structures with rare-earth induced spin-reorientation in the Mn self-doped perovskite (Er0.7Mn0.3)MnO3](https://mdr.nims.go.jp/datasets/2a2613da-8d30-4385-8c8a-c71bb26b7695)

## Fulltext

Synthesis and study of vanadates Me3+1 1 Ferrimagnetic structures with rare-earth induced spin-reorientation in the Mn self-doped perovskite (Er0.7Mn0.3)MnO3  Andreas Dönni,1 Vladimir Y. Pomjakushin,2 Martin Rotter,3 Lei Zhang,1,4  Kazunari Yamaura,1,4 Alexei A. Belik1,*  1 Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan 2 Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland 3 McPhase Project, 30121 Venice, Italy 4 Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan  * Corresponding Author: Alexei.Belik@nims.go.jp   Ceramics International 50(21), 43414-43423 (2024) https://doi.org/10.1016/j.ceramint.2024.08.191  Accepted manuscript 11 August 2024  Keywords: Perovskites; Crystal structure; magnetic structure; spin-reorientation; ferrimagnets   2 Abstract The search for spin-reorientation (SR) phase transitions, a spontaneous rotation of ordered magnetic moments, in ferrimagnetic (FiM) materials, which carry a net magnetization, is of fundamental and practical interest for applications in the field of spintronics. In this work, we have investigated Mn self-doped (Er0.7Mn0.3)MnO3 solid solution with GdFeO3-type Pnma perovskite structure by combining specific heat, magnetic susceptibility and neutron powder diffraction measurements. We provide experimental evidence for FiM order below TC = 104 K, and a spontaneous SR transition at TSR = 11 K. A FiM structure appears in all (R1-xMnx)MnO3 compounds with R = Dy-Lu for x ≥ 0.2. But in this structural family, R = Er is the only material with a SR transition. Below TC = 104 K, FiM order in (Er0.7Mn0.3)MnO3 appears with ferromagnetic (FM) ordering of Mn3+ and Mn4+ cations at the B site pointing along the a-direction, which are antiferromagnetically (AFM) coupled with Er3+ and Mn2+ cations at the A site. At TSR = 11 K, ordered Er3+ cations change direction from the magnetically harder a-axis to the magnetically easy b-axis and induce a change of the whole FiM structure, including the direction of all Mn spins from the irreducible representation mGM3+ to mGM4+. We calculated the crystal-field (CF) anisotropy for Ho3+ in (Ho0.8Mn0.2)MnO3 and Er3+ in (Er0.7Mn0.3)MnO3, based on the point charge model. The results show large magnetic anisotropies. For the FiM structure of (Ho0.8Mn0.2)MnO3, the magnetically easy a-axis of Ho3+ keeps the high-temperature magnetic directions along the a-axis and gives rise to a pronounced magnetization reversal effect at low temperature because of a significant rise of the Ho3+ ordered moments. On the other hand, for the FiM structure of (Er0.7Mn0.3)MnO3, the magnetically easy b-axis of Er3+ gives rise to a SR phase transition at TSR, which does not lead to magnetization reversal even though the Er3+ ordered moments rise significantly at low temperatures.    3 1. Introduction Spin-reorientation (SR) phase transitions involve a spontaneous rotation of ordered magnetic moments [1, 2]. They are an important phenomenon of rare-earth perovskites containing unpaired 3d and 4f electrons and arise from competing rare-earth and transition metal anisotropies that are coupled by magnetic exchange interactions. The structural families of the orthoferrites RFeO3 [3] and orthochromites RCrO3 [4] have been extensively studied. In both cases, rare-earth and transition metal cations are located on different sublattices and the temperature of the SR transition depends on the rare-earth (R) cation.  Compounds with SR transitions have the potential to be utilized for ultrafast repeatable magnetization switching in spintronic components [5, 6]. Ferrimagnetic (FiM) materials are particularly attractive because they carry a net magnetization [7, 8]. Using a FiM GdFeCo thin film, a magnetization reversal in the time scale of ~10 picoseconds has been reported [6]. In this sense, the search for new FiM materials with SR phase transitions is both, of fundamental and practical interest. In this work, we provide experimental evidence that (Er0.7Mn0.3)MnO3 is a new FiM material (TC = 104 K) with a SR phase transition (TSR = 11 K). Perovskite-structure rare-earth manganites, R3+Mn3+O3, have received a lot of attention in literature [9-15]. They possess different degrees of freedom, such as, spin and orbital, and a variety of electric and magnetic phases appear as a function of temperature, magnetic field and size of the R3+ cation, including structural orbital-order transitions and spin-order transitions involving 3d Mn3+ cations. Of particular interest are compounds with smaller R3+ cations (R = Tb-Lu) as Mn spin order produces spin-induced ferroelectric properties [9-13]. Doping of RMnO3 by aliovalent A cations, (R1−xAx)MnO3, introduces a charge degree of freedom and mixed valent Mn3+/Mn4+ cations. Interactions between Mn3+ and Mn4+ cations give rise to high-temperature (above room temperature) ferromagnetic properties [16, 17]. Aliovalent doping is usually realized with Ca2+ and Sr2+ cations, which have comparable sizes with R3+ cations. However, aliovalent doping can also be realized with small Mn2+ cations. In such a case, (R1−xMnx)MnO3 compounds can be called as self-doped by Mn. The coexistence of three different valence states (Mn2+, Mn3+ and Mn4+) in (R1−xMnx)MnO3 compounds has been experimentally confirmed by Hard X-ray Photoelectron Spectroscopy (HAXPES) spectra measured for two members (Lu0.6Mn0.4)MnO3 and (Er0.667Mn0.333)MnO3 [18].  4 A conventional solid-state synthesis at ambient pressure results in very limited ranges (x) of solid solutions (R1−xMnx)MnO3 [19-22]. In addition, it is difficult to control the oxygen content in (R1−xMnx)MnO3 during conventional solid-state reactions. We, however, found that a high-pressure high-temperature synthesis method can significantly expand solid solution limits in (R1−xMnx)MnO3 and allows controlling the oxygen content more precisely [18, 23-26]. The solubility limit of (R1−xMnx)MnO3 solid solutions decreases with increasing size of the rare-earth cation (from x slightly above 0.4 for R = Lu [18], to x close to 0.33 for R = Tm [24], to x slightly above 0.3 for R = Er [18] and to x slightly below 0.3 for R = Ho [26]).  Magnetic property measurements (magnetic susceptibility, magnetization and specific heat) of Mn self-doped orthorhombic perovskite (Er1−xMnx)MnO3 compounds with x = 0.333, 0.3 and 0.2 have been reported in [18]. The parent compound ErMnO3 (x = 0) shows two antiferromagnetic phase transitions at 42 and 28 K originating from Mn ordering [27, 28], and spin-induced ferroelectricity appears below 28 K. When self-doping Mn onto the A site, it appears as Mn2+ and produces a charge transfer from the A site (Er3+, Mn2+) to the B site (Mn3+, Mn4+). For x = 0.2 and larger, ferroelectricity disappeared and a ferrimagnetic (FiM) structure appears with a macroscopic ferromagnetic (FM) moment. The fact that (Er0.667Mn0.333)MnO3 contained an impurity phase (about 4 wt % Er0.88Mn3O5.82 [29]) indicated that the substitution limit at the A site is a little bit smaller than 33% at the synthesis conditions used. (Er1−xMnx)MnO3 compounds with x = 0.2 and x = 0.3 were both single phase. The FiM ordering temperature TC increased with increasing Mn4+ content from 75 K (x = 0.2) to 104 K (x = 0.3) and 109 K (x = 0.333). (Er1−xMnx)MnO3 compounds show an additional first-order phase transition with the ordering temperature TSR decreasing with decreasing Er3+ content from 16 K (x = 0.2) to 10 K (x = 0.3) and 9.5 K (x = 0.333). (R1−xMnx)MnO3 compounds with x ≥ 0.2 and R = Ho, Tm, Yb, Lu generally show FiM ordering [23-26]. But an additional phase transition at TSR has not been observed in any of these materials. In this work we have selected Er0.7Mn0.3MnO3 (x = 0.3) and used neutron diffraction to measure the crystal structure (structural parameters, strain broadening) and magnetic structures (to clarify the nature of the phase transition at TSR). We performed additional magnetic property measurements (magnetic susceptibility and specific heat) and present a calculation of the crystal field (CF) anisotropy based on the point charge model to compare magnetic  5 properties of the two compounds Ho0.8Mn0.2MnO3 and Er0.7Mn0.3MnO3 with large rare-earth moments.  2. Experimental For magnetic properties measurements and neutron diffraction experiments, several batches of (Er0.7Mn0.3)MnO3 solid solution (with the total weight of 3 g) were synthesized from a stoichiometric mixture of Er2O3 (99.9%) and Mn2O3. Single-phase Mn2O3 was prepared from commercial MnO2 (99.99%) by heating in air at 923 K for 24 h. The mixture was placed in a Pt capsule and treated at 1670 K and 6 GPa for 2 h in a belt-type HP apparatus. The heating time to the synthesis temperature was about 10 min. After the heat treatment, the (Er0.7Mn0.3)MnO3 sample was quenched to room temperature (RT), and the pressure was slowly released. All measurements reported in this work were performed on this (Er0.7Mn0.3)MnO3 sample. The magnetic susceptibility was measured on a SQUID magnetometer (Quantum Design MPMS-XL-7T) between 2 and 300 K in a very small applied magnetic field of H = 1 Oe under field-cooled upon cooling (FCC) condition. The specific heat (Cp) values were recorded in magnetic fields of 0 and 70 kOe between 2 and 300 K upon cooling and heating by a pulse relaxation method using a commercial calorimeter (Quantum Design PPMS). To determine the magnetic structures of (Er0.7Mn0.3)MnO3, powder neutron diffraction experiments were performed at the Paul Scherrer Institute, Switzerland, on the high-resolution powder diffractometer for thermal neutrons (HRPT) [30] using an incident neutron wavelength of λ = 1.886 Å. Data were collected in the magnetically ordered and paramagnetic states at temperatures between 1.8 and 130 K for a 2θ range of 3.55° – 164.50° and a step width of 0.05°. The diffraction patterns were analyzed by the Rietveld method using the FullProf Suite [31]. Possible models for the magnetic structures were deducted based on a group theory analysis using the programs ISODISTORT [32] and BASIREPS in the FullProf Suite program package [31]. The shapes of the Bragg peaks were refined using a Thompson-Cox-Hastings pseudo-Voigt function that consists of a Gaussian and a Lorentzian component. The correlation length (L) of the magnetic structure has been estimated from the Lorentzian peak broadening of the  6 resolution parameter Y (Ym of the magnetic structure compared to Yn of the crystal structure), by using the well-known Debye-Scherrer formula σ1 = Ym −Yn = λ/L [33]. Here, λ = 1.886 Å is the neutron wavelength. Strain broadening was modeled for (100) anisotropic broadening in an orthorhombic lattice using quartic form in reciprocal space [34, 35]. Orthorhombic symmetry allows six independent strain parameters SHKL [35]. Four of them (e.g., S040, S004, S220, and S022) turned out to be zero within experimental error, whereas the other two parameters, S400 and S202, significantly deviated from zero and were refined. Calculations of the CF anisotropy were performed for the compounds (Er0.7Mn0.3)MnO3, (Er0.8Mn0.3)MnO3 and (Ho0.8Mn0.2)MnO3, using the McPhase program [36-38].  3. Results and discussion 3.1. Structural Properties of (Ho1-xMnx)MnO3 The orthorhombic perovskite crystal structure of (Er0.7Mn0.3)MnO3 (space group Pnma, No. 62) is shown in Fig. 1. Magnetic ions are located on alternating layers of A site (70% Er3+, 30% Mn2+) and B site (70% Mn3+, 30% Mn4+). Room temperature lattice constants (based on laboratory powder X-ray diffraction) have been reported in Ref. [18], but no structural parameters. We have determined the structural parameters of paramagnetic (Er0.7Mn0.3)MnO3 at T = 130 K by neutron diffraction. The results are summarized in Table 1. Calculated values for selected bond lengths, Mn-O-Mn bond angles, and bond-valence sums (BVS) [39] are given in Table 2. Doping on the A site of 70% Er3+ and 30% Mn2+ ions with different sizes and mass causes micro strain effects and anisotropic broadening of some Bragg reflections. The refinement of the crystal structure of paramagnetic (Er0.7Mn0.3)MnO3 at T = 130 K shown in Supplementary Fig. S1 gives a rather poor agreement (χ2 = 4.03). A refinement that includes corrections for strain broadening (details as described in section 2) shown in Fig. 2a gives a much better agreement (χ2 improved from 4.03 to 2.28). Such strain effects are a common feature in orthorhombic Mn self-doped (R1−xMnx)MnO3 materials (R = Ho-Lu) [23-26]. Fig. 3 shows the temperature dependence of the lattice constants a, b, c and the volume V of (Er0.7Mn0.3)MnO3 below T= 130 K based on neutron diffraction data. A pronounced anomaly (maximum) is observed at TSR for all four parameters due to spin lattice coupling. Below TC = 104 K, the inter-layer distance (lattice constant b) increases with decreasing temperature,  7 whereas the intra-layer distances (lattice constants a, c) as well as the volume V decrease. Such a behavior has already been observed at the FiM phase transition TC of other Mn self-doped (R1−xMnx)MnO3 materials (R = Ho-Lu) [23-26]. Fig. 4a shows the temperature dependence of the specific heat Cp/T (measured at zero field) and the magnetic susceptibility χ (measured in a very small applied magnetic field of H = 1 Oe) for our (Er0.7Mn0.3)MnO3 sample. These data provide evidence for magnetic phase transitions at TC = 104 K (second order) and TSR = 11 K (first order). As shown in Fig. S3b of [18], for our (Er0.7Mn0.3)MnO3 sample, TSR = 11 K is found to be slightly larger than TSR = 10 K measured for (Er0.7Mn0.3)MnO3 sample No. 2. In the Cp/T curves a very sharp anomaly appears at TSR = 11 K for heating but not for cooling which is an artifact of the pulse relaxation method used in the measurement. The maximum of Cp/T at T = 5 K indicates magnetic saturation. The magnetic field dependence of the Cp/T anomaly at TSR is displayed in Fig. 4b. The peak position decreased from 11 K (H = 0 T) to 7 K (H = 30 kOe) and the peak broadens with increasing field. Specific heat curves Cp/T measured in an external magnetic field of H = 70 kOe are shown in Supplementary Fig. S2. The magnetic phase transition at TSR has disappeared and the maximum at magnetic saturation has slightly increased to T = 8 K. Magnetic susceptibility data measured in larger magnetic fields of H = 100 Oe and H = 10 kOe have been published in Fig. 4b of [18].   3.2. Magnetic structures of (Er0.7Mn0.3)MnO3 Fig. 2 shows the refinement of neutron diffraction patterns of (Er0.7Mn0.3)MnO3 measured in the paramagnetic state at (a) T =130 K, and in the magnetically ordered states at (b) T = 20 K (between TSR and TC) and (c) T = 1.8 K (below TSR). Simultaneous refinements of crystal and magnetic structures were performed in the full range of scattering angles 2θ up to 162°. The inset of Fig. 2a shows a very weak Bragg peak near 2θ = 20.9° from an impurity phase. This peak has been excluded from the refinements in the magnetically ordered state. Below TC = 104 K, all observed magnetic Bragg peaks can be indexed with a propagation vector k1 = (0, 0, 0). At TSR = 11 K, a drastic change of intensities of magnetic Bragg peaks is observed (Figs. 2b, 2c), but no change of the propagation vector k1. For the space group Pnma, the propagation vector k1 and sites 4c (A site) and 4b (B site), representation analysis for the possible magnetic  8 structures gives the result summarized in Table 3. There are eight irreducible representations (irreps) with different symmetry. Three of them, mGM3+, mGM4+ and mGM2+, allow a FM moment (F, f) at both, A- and B sites, along the a-, b- and c-directions, respectively. The 2θ values of the Bragg peak positions of magnetic and crystal structures are the same for the FM components (F, f) and are different for the AFM components (C, c, G, g, A, a). As shown in the inset of Fig. 2c, observed intensities of the AFM Bragg peaks are extremely weak. No intensity was detected for the (0, 0, 1) peak. The (1, 0, 0) peak has intensity at T = 20 K, but not at 1.8 K. On the other hand, for the (0, 1, 0) peak, intensity was detected at T = 1.8 K, but not at 20 K.  At T = 20 K, the observed magnetic structure of (Er0.7Mn0.3)MnO3 belongs to the irrep mGM3+ (Γ7). Mn2 at the B site can have ordered moments (Fx, Ay, Cz) along all 3 directions. For Er and Mn1 at the A site, ordered moments (fx, 0, cz) lie within the ac-plane. The result of the refinement of the average ordered moments at A- and B sites at T = 20 K is given in Table 4. The magnetic structure is FiM and dominated by large values for Fx,ave = 2.95(5) μB and fx,ave = -2.00(4) μB with AFM coupling between A- and B sites. There is a macroscopic FM moment of Fa = Fx,ave + fx,ave = 0.96(9) μB along the a-direction. At T = 20 K, the purely magnetic weak Bragg peak (1,0,0) at 2θ = 19.6°, shown in the inset of Fig. 2c, gives rise to an AFM component cz, ave = 1.01(6) μB at the A site and a small canting of the FiM structure. The magnetic structure of (Er0.7Mn0.3)MnO3 at T = 20 K is shown in Fig. 5a. At T = 1.8 K, the observed magnetic structure of (Er0.7Mn0.3)MnO3 belongs to the irrep mGM4+ (Γ5). Mn2 at the B site can have ordered moments (Cx, Fy, Az) along all 3 directions, whereas the ordered moments of Er and Mn1 at the A site point along the b-direction (0, fy, 0). The result of the refinement of the average ordered moments at A- and B sites is given in Table 4. The magnetic structure is FiM and dominated by large values for Fy,ave = -3.05(3) μB and fy,ave = 4.60(3) μB with AFM coupling between A- and B sites. There is a macroscopic FM moment of Fb = Fy,ave + fy,ave = 1.55(6) μB along the b-direction. At T = 1.8 K, the purely magnetic weak Bragg peak (0,1,0) at 2θ = 14.6° shown in the inset of Fig. 2c gives rise to an AFM component Ax, ave = -0.44(3) μB at the B site and a small canting of the FiM structure. The magnetic structure of (Er0.7Mn0.3)MnO3 at T = 1.8 K is shown in Fig. 5b.  9 Fig. 6a shows the temperature dependence of the average ordered moments. TSR = 11 K is a spin-reorientation (SR) temperature, where all FM components change direction from the a-direction (above TSR) to the b-direction (below TSR). At TSR, the magnitude of the ordered Mn moments at the B site (Fx,ave, Fy,ave) doesn’t change, whereas the average ordered FM moment at the A site (fx,ave, fy,ave) jumps to a larger value at lower temperature. A coexistence of both phases (28% GM3+, 72% GM4+) is observed in the measurement at T = 10 K, which indicates that TSR is a first-order magnetic phase transition. Above TSR, the temperature dependence of the macroscopic average FM moment, Fa, agrees with that of the FCC magnetic susceptibility χ measured in a very small magnetic field of H = 1 Oe (Fig. 6b). The temperature dependence of the correlation length of the magnetic structure is shown in Fig. 6c. The correlation length (determined as described in section 2) strongly increases towards low temperature from 242(26) nm at T = 20 K to 593(15) nm at T = 1.8 K (Table 4). In the refinement, we have determined the average values for the ordered moments at the A site, (fx,ave, cz,ave) above TSR and (fy,ave) below TSR. Since, apart from the difference of the magnetic form factors for Er3+ and Mn2+ (not accurate), our neutron diffraction data cannot distinguish between the contributions from 70% of Er3+ and 30% of Mn2+ to the average value at the A site, it is necessary to use an approximation. It is reasonable to assign the AFM component cz to Er3+, since magnetic intensity appears close to TSR = 11 K and not close to TC = 104 K.  Then, for mGM3+ (above TSR), we have  A site: Mn (fx,Mn, 0, 0), Er (fx,Er, 0, cz,Er); B site: Mn (Fx,Mn, 0, 0). For mGM4+ (below TSR), we have A site: Mn (0, fy,Mn, 0), Er (0, Fy,Er, 0); B site: Mn (Ax,Mn, Fy.Mn, 0). Following the data analysis of the magnetic structure of (Ho0.8Mn0.2)MnO3 in the previous work [26], we correlate the ordered Mn moments at B and A sites as follows: (Model #1): -fx,Mn = 1.53 ⸱ Fx,Mn and -fy,Mn = 1.53 ⸱ Fy,Mn. (Model #2): -fx,Mn = 1.23 ⸱ Fx,Mn and -fy,Mn = 1.23 ⸱ Fy,Mn.  10 The factor 1.53 of Model #1 is based on the experimentally observed ratio of the ordered Mn moments at B and A sites in (Lu0.6Mn0.4)MnO3 [23]. The factor 1.23 of Model #2 has been used to refine the magnetic structure of (Tm0.7Mn0.3)MnO3 [24]. The temperature dependence of the magnetic structure of (Er0.7Mn0.3)MnO3 calculated for Models #1 and #2 is shown in Fig. 7 and Supplementary Fig. S3, respectively. Near TSR, the magnitude of the ordered Mn moments at A site (fx,Mn and fy.Mn) and B site (Fx,Mn and Fy,Mn) both show a continuous behavior, whereas ordered Er moments jump from a smaller (fx,Er) to a larger value (fy,Er). At the lowest measured temperature T = 1.8 K, fy,Er reaches a similar value as fy,Mn for Model #1 and a larger value for Model #2. Our powder neutron diffraction data can’t distinguish between Model #1 and Model #2.  3.3. Calculations of the crystal-field anisotropy FiM order appears in both Mn-self doped compounds (Er0.7Mn0.3)MnO3 [this work] and (Ho0.8Mn0.2)MnO3 [26]. To compare magnetic properties of the two compounds, the CF anisotropy of Er3+ in (Er0.7Mn0.3)MnO3 and Ho3+ in (Ho0.8Mn0.2)MnO3 was calculated based on the point charge model using the McPhase program [36-38]. With the structural parameters of (Er0.7Mn0.3)MnO3 at T = 130 K (Table 1) as input, the CF energy splitting for Er3+ at the A site (4c), was calculated by considering all neighboring ions up to a distance of 20 Å with average charges of +2.71 on the A site (for 0.71⸱Er3+ + 0.29⸱Mn2+), +3.29 on the B site (for 0.71⸱Mn3+ + 0.29⸱Mn4+), and -2 for O2- on sites (4c and 8d). The number of neighboring ions was 3125. For Er3+ (4I15/2) with a total angular moment J = 15/2, a Landé factor gJ = 6/5 and a magnitude of moment gJJ = 9 μB, we obtained a splitting into sixteen (2J + 1 = 16) CF levels (eight doublets) due to the charges of the surrounding ions. The calculated CF energy levels are given in Table 5. For applying an external magnetic field of H = 10 T along the three axes a, b, c, we calculated the induced ordered magnetic Er moments at T = 1 K. The results shown in Table 6, contain a FM component parallel to the field direction and components perpendicular to the field direction due to the CF anisotropy. The obtained induced Er3+ moments for H || a, H || b and H || c, belong to the irreps mGM3+, mGM4+ and mGM2+, respectively (Table 3). For (Er0.7Mn0.3)MnO3, the lowest 8 CF levels have an energy separation of only 6.7 meV (Table 5). The CF levels are found to be very sensitive to small changes of  11 the structural parameters inside the ac-plane, but not along the b-direction. As a result, in Table 6, the errors turn out to be larger for <Ma> and <Mc>, compared to <Mb>. The field dependence of the single-ion magnetization (induced FM component parallel to the field) of Er3+ at T = 1 K is plotted in Fig. 8a for magnetic fields up to 10 T applied along the a-, b- and c-axes. (Er0.7Mn0.3)MnO3 shows a large CF anisotropy that favors the b-direction over the a- and c-directions.  We performed a similar calculation for Ho3+ in (Ho0.8Mn0.2)MnO3, based on the structural parameters at T = 130 K published in Table 1 of [26]. The CF energy splitting for Ho3+ at the A site (4c), was calculated by considering all neighboring ions up to a distance of 20 Å with average charges of +2.83 on the A site (for 0.83⸱Ho3+ + 0.17⸱Mn2+), +3.17 on the B site (for 0.83⸱Mn3+ + 0.17⸱Mn4+), and -2 for O2- on sites (4c and 8d). The number of neighboring ions was 3059. For Ho3+ (5I8) with a total angular moment J = 8, a Landé factor gJ = 5/4 and a magnitude of moment gJJ = 10 μB, we obtained a splitting into seventeen (2J + 1 = 17) CF levels (all singlets) due to the charges of the surrounding ions. The calculated CF energy levels are given in Table 5. The two lowest CF singlets form a quasi doublet that is well separated (by at least 11.39 meV) from the higher energy CF levels. The ordered magnetic Ho3+ moments at T = 1 K induced by an external magnetic field of H = 10 T applied along the three axes a, b, c, are summarized in Table 7. Fig. 8b displays the calculated field dependence of the single-ion magnetization of Ho3+ at T = 1 K for magnetic fields up to 10 T applied along the a-, b- and c-axes. For (Ho0.8Mn0.2)MnO3, the CF anisotropy has a magnetically easy a-direction and a magnetically hard b-direction. The calculated CF anisotropies for Er3+ in (Er0.7Mn0.3)MnO3 and Ho3+ in (Ho0.8Mn0.2)MnO3 correspond to different rare-earth elements with different compositions (70% Er3+ versus 80% Ho3+). The FiM structure is observed for (Er0.7Mn0.3)MnO3, (Er0.8Mn0.2)MnO3 and (Ho0.8Mn0.2)MnO3, whereas the composition (Ho0.7Mn0.3)MnO3 lies outside the solubility limit. To investigate the composition dependence, we performed an additional calculation of the CF anisotropy for (Er0.8Mn0.2)MnO3, a material for which no structural parameters have been published. As an approximation, we used the structural parameters determined for (Er0.7Mn0.3)MnO3 (Table 1 of this work) together with the room temperature lattice constants of (Er0.8Mn0.2)MnO3 measured by x-ray diffraction (Table 1 in  12 [18]). The results of the CF anisotropy calculated for (Er0.8Mn0.2)MnO3 are shown in the Supplementary in Table S1 (CF levels), Table S2 (Induced magnetic Er3+ moments) and Fig. S4 (Field dependence of single-ion magnetization). Comparing the results obtained for (Er0.7Mn0.3)MnO3 and (Er0.8Mn0.2)MnO3 (Fig. S4), suggests that the large CF anisotropy with a magnetically easy b-direction is independent of the composition for (Er1-xMnx)MnO3 compounds within the stability range of the FiM structure x ≥ 0.2. In both compounds the overall energy splitting of the CF levels is similar (Table S1). But small differences in the energies of the CF levels give rise to a composition dependence of <Ma> and <Mc> along the magnetically harder directions inside the ac-plane (Fig. S4, Table S2 and Table 6).  3.4. Comparison of the ferrimagnetic structures of (Ho0.8Mn0.2)MnO3 and (Er0.7Mn0.3)MnO3 The determination of the FiM structure of (Ho0.8Mn0.2)MnO3 has been reported in [26]. Below TC = 76 K, FM order along the a-direction appears for the Mn3+ and Mn4+ cations at the B site, and for the Ho3+ and Mn2+ cations at the A site. AFM coupling between the B and A sites gives rise to a FiM structure. With decreasing temperature, the ordered magnetic moment of the Ho3+ cations increases significantly and overcomes the saturated magnetic moment of Mn3+ and Mn4+ cations at the B site, resulting in a magnetization reversal behaviour below a compensation temperature of about 35 K (Fig. 5a of 26). The calculated large CF anisotropy for Ho3+ in (Ho0.8Mn0.2)MnO3 shown in Fig. 8b has a magnetically easy a-axis, similar to the high-temperature magnetic directions. Therefore, a spin-reorientation temperature TSR is not observed. The FiM structure of (Ho0.8Mn0.2)MnO3 is collinear below TC = 76 K and develops of a spin canting of Ho3+ at the A site below 40 K (non-zero cz,Ho component).  Below TC = 104 K, the FiM structure of (Er0.7Mn0.3)MnO3 (Fig. 6b) is similar to that of (Ho0.8Mn0.2)MnO3 with the FM moments pointing along the a-direction. However, the calculated large CF anisotropy of Er3+ favours the b-direction (Fig. 8a) and limits the development of a large FM Er3+ moment along the magnetically harder a-direction. A magnetization reversal behaviour as in (Ho0.8Mn0.2)MnO3 is not observed in (Er0.7Mn0.3)MnO3. In order to grow to a large value, the FM component of the Er3+ ions changes direction at TSR = 11 K from the magnetically harder a-axis to the magnetically easy b-axis. Mn cations are magnetically coupled to Er3+ cations and follow the first-order phase transition at TSR from  13 mGM3+ to mGM4+, which is induced by the CF anisotropy of Er3+ ions. Similar to (Ho0.8Mn0.2)MnO3, the FiM structure of (Er0.7Mn0.3)MnO3 is collinear below TC = 104 K and develops a spin-canting (non-zero cz,Er component) below about 30 K (Fig. 6a). For rare-earth perovskites, orthoferrites RFeO3 and orthochromites RCrO3, a simple but realistic microscopic theory of spontaneous spin reorientation [42] suggested that both the temperature and the nature of the spin-reorientation transition are the result of competition between the second- and fourth-order spin anisotropy of the 3d sublattice, the crystal field of 4f cations, and 4f-3d magnetic exchange interactions. For all FiM members of (R1-xMnx)MnO3 compounds (x ≥ 0.2, R = Ho-Lu [23-26]), the Mn cations select the a-axis for the FM components below TC. The occurrence of a spontaneous spin reorientation in these compounds may have some requirements like a R3+ cation with a large enough ordered moment. But when comparing (Ho0.8Mn0.2)MnO3 and (Er0.7Mn0.3)MnO3, the results presented in this work suggest that the large CF anisotropy is the decisive factor for the absence and appearance, respectively, of the spontaneous spin reorientation.  3.5. Mn self-doping and magnetic exchange interactions In intermetallic compounds, competing magnetic exchange interactions among and between unpaired 3d and 4f electron spins may account for complex magnetic properties with multiple phase transitions. 3d-3d, 3d-4f and 4f-4f exchange interactions have different strengths and shape the magnetic structures at different temperatures, as illustrated by recent neutron diffraction measurements on the isostructural spin-chain compounds BaRFeO4 (R = Yb, Tm, Er) [43, 44]. These orthorhombic compounds (space group Pnma) undergo three successive magnetic phase transitions (at TN1, TN2 and TN3), and magnetic Fe3+ and R3+ cations are located on different sublattices. At the highest Néel temperature (TN1), only Fe3+ ions order due to the strongest 3d-3d interactions. At the lowest Néel temperature (TN3), 4f-4f interactions dominate in BaYbFeO4 (long-range magnetic Yb3+ order), whereas 3d-4f interactions dominate in BaTmFeO4 (ordered Tm3+ moments on one sublattice coexist with disordered Tm3+ moments on the other sublattice). In BaErFeO4, 3d-4f interactions dominate at TN2 (change of magnetic propagation vector and induced Er3+ order) and 4f-4f interactions at TN3 (modified magnetic structure with constant magnetic phase inside each chain of Er3+ cations).  14 For orthoferrites RFeO3, orthochromites RCrO3 as well as undoped RMnO3 perovskites, transition metal 3d ions and rare-earth 4f ions are located on different sublattices with only 3d-4f exchange interactions between them and only 3d-3d or 4f-4f interactions inside one sublattice. Mn self-doping in (R1-xMnx)MnO3 compounds creates a different group of materials with a coexistence of unpaired 3d and 4f electrons on the same sublattice (A site). Here three kinds of exchange interactions (3d-3d, 3d-4f and 4f-4f) are present at the A site and two kinds (3d-3d, 3d-4f) between A- und B sites. When the self-doping reaches a certain threshold (x ≥ 0.2), the FiM structure appears at TC, fully stabilized by 3d-3d interactions, with FM components along the a-direction, independent of the kind of the R3+ cation (even for nonmagnetic R = Lu3+). Below TC, the FM structure at the A site is collinear and contains only FM components for Mn1 (due to 3d-3d interactions) and R (small moment induced by 3d-4f interactions). With decreasing temperature, 4f-4f interactions become stronger and at some temperature create magnetic R3+ order with a larger FM component and a nonzero AFM component. Magnetization reversal has been observed in (Ho0.8Mn0.2)MnO3 [26] and in (Tm0.7Mn0.2)MnO3 [24], but not in (Yb0.667Mn0.333)MnO3 [25] (because of too small ordered Yb3+ moments), and not in (Er0.7Mn0.3)MnO3 (this work, because of the CF anisotropy). Compared to the parent compound ErMnO3, Mn self-doping in (Er0.7Mn0.3)MnO3 increases the number of magnetic Mn ions by 30%. They are coupled by the strongest 3d-3d exchange interactions and give rise to a large increase of the highest ordering temperature of Mn from TN1 = 42 K in ErMnO3 to TC = 104 K in in (Er0.7Mn0.3)MnO3. This argument is also valid for (R1-xMnx)MnO3 compounds with other rare-earth cations. Furthermore, Mn self-doping and magnetic exchange interactions can rationalize why magnetic order of Er3+ appears at TC = 104 K in (Er0.7Mn0.3)MnO3, but is absent at the highest two phase transitions (42 K, 28 K) in the parent compound ErMnO3.   4. Conclusions (Er0.7Mn0.3)MnO3 solid solution with GdFeO3-type perovskite structure was successfully prepared by a high-pressure high-temperature method at 6 GPa and 1670 K. By combining specific heat, magnetic susceptibility and neutron diffraction, we have investigated the magnetic phase transitions (TC = 104 K, TSR = 11 K) and determined crystal and magnetic  15 structures. When self-doping Mn onto the A site, it appears as Mn2+ and produces a charge transfer from the A site (Er3+, Mn2+) to the B site (Mn3+, Mn4+). Mn self-doping creates a different group of materials with a coexistence of unpaired 3d and 4f electrons on the same sublattice (A site). In contrast, in the undoped parent compound ErMnO3, rare-earth cations (A site) and transition metals (B site) are located on different sublattices. Compared to ErMnO3 with the highest ordering temperature of Mn at TN1 = 42 K, an increase of the number of magnetic Mn ions by 30% in (Er0.7Mn0.3)MnO3 gives rise to FiM order at much higher temperature TC = 104 K. This work reports the discovery of a spontaneous SR transition in (Er0.7Mn0.3)MnO3 at TSR = 11 K, where all FM components of Mn and Er ions change direction from the a-axis (above) to the b-axis (below). In the family of (R1-xMnx)MnO3 compounds (R = Dy-Lu), FiM order appears at x ≥ 0.2 for all members. But R = Er is the only material with a spontaneous SR transition. Our calculation of the CF anisotropy of Er3+ in (Er0.7Mn0.3)MnO3, and Ho3+ in (Ho0.8Mn0.2)MnO3 revealed large magnetic anisotropies that can explain the appearance and absence of the SR transition for R = Er and Ho, respectively.  FiM materials with spontaneous SR transitions are of practical interest because deterministic magnetization switching may be used in nanoscale functional spintronic components [6]. Fundamental understanding of the origin and mechanisms of the spontaneous SR transition in (Er0.7Mn0.3)MnO3, a member of a new group of materials, is important for the design of future materials that can be used in spintronics.    16 CRediT authorship contribution statement Andreas Dönni: Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Data curation. Vladimir Y. Pomjakushin: Investigation. Martin Rotter: Investigation. Lei Zhang: Investigation. Kazunari Yamaura: Investigation, Funding acquisition. Alexei A. Belik: Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Data curation, Conceptualization.  Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.  Acknowledgements This study is partially based on experiments performed on HRPT diffractometer (Proposal No. 20180113) at the Swiss Spallation Neutron Source SINQ, Paul Scherrer Institute, Switzerland. This study was supported in part by the World Premier International Research Center Initiative (WPI), the Japan Society for the Promotion of Science KAKENHI (Grant No. JP22H04601), and a grant from the Kazuchika Okura Memorial Foundation (No. 2022-11).  Appendix A. 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Atom Site g x y z B (Å2) Er 4c 0.709(3) 0.0740(4) 0.25 0.9823(4) 0.17(7) Mn1 4c 0.291(3) = x(Er) 0.25 = z(Er) = B(Er) Mn2 4b 1 0 0 0.5 0.38(6) O1 4c 1 0.4600(4) 0.25 0.1063(3) 1.04(5) O2 8d 1 0.3152(3) 0.0533(2) 0.6950(3) 1.20(4)     23 Table 2 Calculated values for selected bond lengths (Å), bond angles (deg), Bond Valence Sums, BVS, and distortion parameter ∆(Mn2) of MnO6 for (Er0.7Mn0.3)MnO3 at T = 130 K based on powder neutron diffraction data.   (Er0.7Mn0.3)MnO3 T = 130 K Er/Mn1 – O1 Er/Mn1 – O1 Er/Mn1 – O2 (×2) Er/Mn1 – O2 (×2) Er/Mn1 – O2 (×2) BVS(Er3+) BVS(Mn12+) 2.235(3) 2.240(3) 2.242(2) 2.481(2) 2.5765(17) +3.14 +1.73 Mn2 – O1 (×2) Mn2 – O2 (×2) Mn2 – O2 (×2) BVS(Mn23+) ∆(Mn2) Mn2 – O1 – Mn2 (×2) Mn2 – O2 – Mn2 (×4) 1.9349(16) 1.9422(5) 2.0602(16) +3.36 8.4 ×10−4 144.13(2) 144.80(7)  Note: BVS = ∑=Nii1ν , νi = exp[(R0 − li)/B], N is the coordination number, B = 0.37, R0(Er3+) = 2.01, R0(Mn2+) = 1.79, and R0(Mn3+) = 1.76 [39]. ∆ = (1/N)∑=Ni 1[(li − lav)/lav]2, where lav = (1/N)∑=Niil1 is the average Mn-O distance and N is the coordination number.    24 Table 3 Group theory analysis for the magnetic structure of (Er0.7Mn0.3)MnO3 calculated using the programs ISODISTORT [32], BasIreps [31] and Magnetic Space groups [41]. The character set corresponds to the following symmetry elements [31]: Symm(1): 1; Symm(2): 2 (0,0,1/2) 1/4,0,z; Symm(3): 2 (0,1/2,0) 0,y,0; Symm(4): 2 (1/2,0,0) x,1/4,1/4; Symm(5): –1 0,0,0; Symm(6): a x,y,1/4; Symm(7): m x,1/4,z; Symm(8): n (0,1/2,1/2) 1/4,y,z. irrep denotes irreducible representation. The crystallographic space group is Pnma (No. 62). The magnetic propagation vector is k1 = (0, 0, 0). Magnetic ions Mn3+ and Mn4+ are located on a 4b site (B site). Er3+ and Mn2+ are on a 4c site (A site).  irrep (Isodistort) irrep (BasIreps) Character set Magnetic space group 4b site (B site) 4c site (A site) mGM1+ Γ1 (1, 1, 1, 1, 1, 1, 1, 1) 62.1.502 (Gx, Cy, Az) (–, cy, –) mGM1– Γ2 (1, 1, 1, 1, –1, –1, –1, –1) 62.9.510 – (gx, –, az) mGM2+ Γ3 (1, 1, –1, –1, 1, 1, –1, –1) 62.6.507 (Cx, Gy, Fz) (cx, –, fz) mGM2– Γ4 (1, 1, –1, –1, –1, –1, 1, 1) 62.5.506 – (–, gy, –) mGM3+ Γ7 (1, –1, –1, 1, 1, –1, –1, 1) 62.5.508 (Fx, Ay, Cz) (fx, –, cz) mGM3– Γ8 (1, –1, –1, 1, –1, 1, 1, –1) 62.5.504 – (–, ay, –) mGM4+ Γ5 (1, –1, 1, –1, 1, –1, 1, –1) 62.5.509 (Ax, Fy, Gz) (–, fy, –) mGM4– Γ6 (1, –1, 1, –1, –1, 1, –1, 1) 62.5.505 – (ax, –, gz) F = f = m1 + m2 + m3 + m4 C = c = m1 – m2 + m3 – m4 G = g = m1 – m2 – m3 + m4 A = a = m1 + m2 – m3 – m4 Site 4b (B site): Mn21 (0, 0, 1/2); Mn22 (1/2, 0, 0); Mn23 (0, 1/2, 1/2); Mn24 (1/2, 1/2, 0) Site 4c (A site): Er11 / Mn11 (x, 1/4, z); Er12 / Mn12 (–x+1/2, 3/4, z+1/2)  Er13 / Mn13 (–x, 3/4, –z); Er14 / Mn14 (x+1/2, 1/4, –z+1/2)     25 Table 4 Result of the refinement of the average ordered moments of (Er0.7Mn0.3)MnO3 at T = 20 and 1.8 K based on powder neutron diffraction data. The refinement is based on the occupation factor given in Table 1 (g = 0.709 for Er3+ and Mn23+, and g = 0.291 for Mn12+ and Mn24+) using magnetic form factors for Er3+, Mn2+, Mn3+ and Mn4+. As an approximation, in the refinement, the ordered moments of Er3+ and Mn12+, as well as of Mn23+ and Mn24+, were fixed to equal values, respectively.   T = 20 K:  k1 = (0, 0, 0); irrep: mGM3+ (Γ7) A site (Er, Mn1) (fx, 0, cz) B site (Mn2)  (Fx, Ay, Cz); Ay = 0, Cz = 0 Average moments: fx,ave = -2.00(4) μB; cz,ave = 1.01(6) μB; Fx,ave = 2.95(5) μB Ferromagnetic moment: Fa = Fx,ave + fx,ave = 0.96(9) μB; along a direction Correlation length: 242(26) nm T = 1.8 K:  k1 = (0, 0, 0); irrep: mGM4+ (Γ5) A site (Er, Mn1) (0, fy, 0) B site (Mn2)  (Ax, Fy, Gz); Gz  = 0 Average moments: fy,ave = 4.60(3) μB; Ax,ave = -0.44(3) μB; Fy,ave = -3.05(3) μB Ferromagnetic moment: Fb = Fy,ave + fy,ave = 1.55(6) μB; along b direction Correlation length: 593(15) nm χ2 = 2.00; Rwp = 4.11 %; Rexp = 2.91 %; RBragg = 4.22 %; Rmag = 6.69 % (at 20 K). χ2 = 2.67; Rwp = 4.28 %; Rexp = 2.62 %; RBragg = 4.70 %; Rmag = 3.06 % (at 1.8 K).    26 Table 5 Energy levels of the crystal field (CF) splitting of Er3+ in (Er0.7Mn0.3)MnO3 and Ho3+ in (Ho0.8Mn0.2)MnO3 based on the point charge model, calculated by McPhase. Energies are given in absolute values (second and fourth columns) and relative to the CF ground-state (third and fifth columns). Uncertainties due to the experimental errors in the crystal-structural parameters were evaluated using gauss law of error propagation and are shown in parentheses.  Number of  CF level (Er0.7Mn0.3)MnO3 Er3+ energy (meV) (Ho0.8Mn0.2)MnO3 Ho3+ energy (meV) 17   14.23  38.66(41) 16 23.72  36.96(39) 13.99  38.42(42) 15 23.72  36.96(39) 10.67  35.10(41) 14 12.63  25.87(25) 10.33  34.76(38) 13 12.63  25.87(25) 8.89  33.32(32) 12 4.12  17.36(20) 8.47  32.90(35) 11 4.12  17.36(20) 8.05  32.48(40) 10 -0.70  12.54(25) 5.46  29.90(32) 9 -0.70  12.54(25) 4.78  29.22(30) 8 -6.54  6.70(16) -0.24  24.19(45) 7 -6.54  6.70(16) -0.65  23.79(44) 6 -9.69  3.55(25) -4.52  19.91(30) 5 -9.69  3.55(25) -4.55  19.88(30) 4 -10.32  2.92(27) -13.00  11.43(20) 3 -10.32  2.92(27) -13.04  11.39(20) 2 -13.24  0.00(0) -24.43  0.01(0) 1 -13.24  0.00 -24.43  0.00    27 Table 6 Induced magnetic Er3+ moments in (Er0.7Mn0.3)MnO3 at T = 1 K in an external magnetic field of H = 10 T applied along the three axes a, b, c calculated by McPhase. Uncertainties due to the experimental errors in the crystal-structural parameters were evaluated using gauss law of error propagation and are shown in parentheses only for Er11 for simplicity.  H || a <Ma> <Mb> <Mc> <M> Er11 6.177(435) 0(0) -3.041(280) 6.885(514) Er12 6.177 0 3.041 6.885 Er13 6.177 0 -3.041 6.885 Er14 6.177 0 3.041 6.885 H || b <Ma> <Mb> <Mc> <M> Er11 0(0) 8.329(26) 0(0) 8.329(26) Er12 0 8.329 0 8.329 Er13 0 8.329 0 8.329 Er14 0 8.329 0 8.329 H || c <Ma> <Mb> <Mc> <M> Er11 -1.074(101) 0(0) 5.030(258) 5.143(274) Er12 1.074 0 5.030 5.143 Er13 -1.074 0 5.030 5.143 Er14 1.074 0 5.030 5.143     28 Table 7 Induced magnetic Ho3+ moments in (Ho0.8Mn0.2)MnO3 at T = 1 K in an external magnetic field of H = 10 T applied along the three axes a, b, c calculated by McPhase. Uncertainties due to the experimental errors in the crystal-structural parameters were evaluated using gauss law of error propagation and are shown in parentheses only for Ho11 for simplicity.  H || a <Ma> <Mb> <Mc> <M> Ho11 8.932(9) 0(0) 4.112(17) 9.833(15) Ho12 8.932 0 -4.112 9.833 Ho13 8.932 0 4.112 9.833 Ho14 8.932 0 -4.112 9.833 H || b <Ma> <Mb> <Mc> <M> Ho11 0(0) 1.218(80) 0(0) 1.218(80) Ho12 0 1.218 0 1.218 Ho13 0 1.218 0 1.218 Ho14 0 1.218 0 1.218 H || c <Ma> <Mb> <Mc> <M> Ho11 8.692(23) 0(0) 4.505(28) 9.790(33) Ho12 -8.692 0 4.505 9.790 Ho13 8.692 0 4.505 9.790 Ho14 -8.692 0 4.505 9.790     29  Fig. 1. Orthorhombic perovskite crystal structure of Mn self-doped (Er0.7Mn0.3)MnO3. The drawing was made using the program VESTA [40].    30   Fig. 2. Experimental (black dots), calculated (red line), and difference (blue line) neutron diffraction patterns of (Er0.7Mn0.3)MnO3 in the paramagnetic state at T = 130 K (a) and in the magnetically ordered states at T = 20 (b) and 1.8 K (c). The tick marks indicate Bragg peak positions: the first row is for the nuclear peaks, and the second row is for the magnetic peaks. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)    31  Fig. 3. Temperature dependence of the orthorhombic lattice parameters (a, b, and c) and the unit cell volume (V) of (Er0.7Mn0.3)MnO3 refined from neutron diffraction data. The vertical dashed lines indicate the FiM phase transition at TC = 104 K and the SR temperature at TSR = 11 K.    32    Fig. 4. (a) Temperature dependence of the specific heat Cp/T and magnetic susceptibility χ of (Er0.7Mn0.3)MnO3 providing evidence for two successive magnetic phase transitions. The vertical dashed lines indicate the FiM phase transition at TC = 104 K and the SR temperature at TSR = 11 K. (b) Cp/T versus T curves of (Er0.7Mn0.3)MnO3 measured on cooling (filled symbols) and heating (empty symbols) at different magnetic fields between 0 and 70 kOe. The curves are shifted by 0.1 J K-2 mol-1 from each other for clarity.     33  Fig. 5. Magnetic structures of (Er0.7Mn0.3)MnO3 at T = 20 K (a) and 1.8 K (b) refined from neutron diffraction data. Ordered magnetic moments (based on Model #1) are shown by arrows in blue (Mn) and red (Er). The drawings were made using the program VESTA [40]. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)    34    Fig. 6. Temperature dependence of the FiM structure of (Er0.7Mn0.3)MnO3 refined from neutron diffraction data. Left hand axes show (a) the average ordered Mn and Er moments Mave, (b) the macroscopic FM moment per formula unit, and (c) the correlation length of the magnetic structure. Right hand axes display the magnetic susceptibility χ. The vertical dashed lines indicate the FiM phase transition at TC = 104 K and the Spin-reorientation temperature at TSR = 11 K.   35  Fig. 7. Temperature dependence of the ordered Mn and Er moments of (Er0.7Mn0.3)MnO3 based on Model #1. The vertical dashed lines indicate the FiM phase transition at TC = 104 K and the Spin-reorientation temperature at TSR = 11 K.    36  Fig. 8. Field dependence of the single-ion magnetization in an external magnetic field applied along the a-, b- and c-axes for Er3+ in (Er0.7Mn0.3)MnO3 (a) and Ho3+ in (Ho0.8Mn0.2)MnO3 (b) at T= 1 K calculated by McPhase.   3. Results and discussion 4. Conclusions BVS(Mn23+)