Magnetism in NdMn0.1Fe0.9O3 compound

Journal Pre-proofs Magnetism in NdMn0.1Fe0.9O3 compound Matú š Mihalik, Pavla Roupcová, Róbert Tarasenko, Michał Rams, Andreas Hoser, Marián Mihalik PII: DOI: Reference:

S0304-8853(19)33890-9 https://doi.org/10.1016/j.jmmm.2020.166539 MAGMA 166539

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

13 November 2019 24 January 2020 30 January 2020

Please cite this article as: M. Mihalik, P. Roupcová, R. Tarasenko, M. Rams, A. Hoser, M. Mihalik, Magnetism in NdMn0.1Fe0.9O3 compound, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/ j.jmmm.2020.166539

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Magnetism in NdMn0.1Fe0.9O3 compound Matúš Mihalika, Pavla Roupcováb,c, Róbert Tarasenkod, Michał Ramse, Andreas Hoserf, Marián Mihalika aInstitute

of Experimental Physics SAS, Watsonova 47, 040 01 Košice, Slovak Republic of Physics of Materials, Academy of Sciences of the Czech Republic v. v. i., Žižkova 22, 616 62 Brno, Czech Republic cBrno University of Technology, Central European Institute of Technology, 616 62 Brno, Czech Republic dInstitute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovak Republic eInstitute of Physics, Jagiellonian University, Łojasiewicza 11, 30348 Kraków, Poland fHelmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany bInstitute

Abstract The low temperature crystal and magnetic structures of NdMn0.1Fe0.9O3 were determined on the basis of X-ray and neutron powder diffraction experiments as well as from specific heat and magnetization measurements. The compound crystallizes in the orthorhombic crystal structure, space group Pnma, in the entire temperature interval 20 mK < T < 300 K. The lattice parameters exhibit standard thermal expansion effects for T > 20 K and at lower temperatures the anomalies due to magnetostriction effect were observed. The iron sublattice orders magnetically into 3 different magnetic structures, namely into 5 = (Ax, Fy, Gz) for 130 K < T < TN (Néel temperature); 1 = (Gx, Cy, Az) for 15 K < T < 130 K and 3 = (Cx, Gy, Fz) for 20 mK < T < 15 K. The Nd ions order atm temperatures below 1.6 – 1.75 K into the same 3 phase as the iron sublattice at these temperatures. The obtained magnetic structures fit perfectly in between the magnetic phases of closely related NdFeO3 and NdMn0.5Fe0.5O3 compounds. Our study, together with all previously published data, completes the entire magnetic phase diagram of NdMn1-xFexO3 (0  x  1) solid solution substitutional system.

Introduction Distorted perovskite structure oxides, of which manganites (general formula: REMnO3; RE = Rare earth) and orthoferrites (general formula REFeO3) are a subset, host multiferroicity, magnetoelectricity, complex magnetic structures and other interesting physical phenomena. For example, La1−xCaxMnO3 and La1−xSrxMnO3 exhibit colossal magnetoresistance [1] and TbMnO3 compound exhibits multiferroic behavior [2]. The magnetic structure of these compounds is driven by the competition between the double exchange, superexchange, and Dzyaloshinskii-Moriya interactions [3]. These interactions strongly depend on the structural changes induced by doping. For that reason the magnetism in these systems is affected by doping, too. Various substitutions are frequently used to probe the magnetic interaction in these materials either in the RE site [1, 4, 5], or in the transition metal site [6, 7, 8, 9, 10, 11]. The transition metal site substitution, especially Mn-Fe substitution looks interesting, since Mn3+ is Jahn-Teller (JT) active ion, while Fe3+ is not. Both ions have in the high spin state and 1

coordination number 6 (our case) the same effective Shanon radii [12], so the structural change induced by the Mn-Fe substitution is directly connected with the lifting of the JT distortion in the system. NdMn1−xFexO3 system is a magnetic insulator that crystallizes in the orthorhombic crystal structure (space group Pnma1) and contains three magnetic ions with well-documented magnetochemistry [13]. The Nd3+ has a 4f3, 10-fold degenerate magnetic 4I ground state that is split and mixed in the perovskite host lattice to have both orbital and spin components. The Mn3+ ion is S = 2, 3d4 with a Jahn-Teller active 5Eg ground state and the Fe3+ ion has a half-filled d-shell S = 5/2, 6A1 ground state. The first neutron diffraction study of NdFeO3 compound reported that the compound orders antiferromagnetically with TN = 760 K [14]. Several, more detailed later neutron diffraction studies [15, 16] settled up that in NdFeO3 the Fe sublattice orders at TN into (0, Fy, Gz) structure with weak ferromagnetic component and undergoes spin reorientation phase transition at temperatures 100 K < T < 200 K into the low temperature (0, Gy, Fz) structure [15]. Bartolome et al. [16] reported that Nd3+ ions polarize already at 25 K due to Nd-Fe interaction, but the true ordering due to Nd-Nd magnetic interaction takes place only below 1.05(1) K [17]. The different situation is in the NdMnO3 compound. In this compound the Mn3+ ions order antiferromagnetically at TN = 82 K into (Ax, Fy, 0) [18] or (Ax, 0, 0) magnetic structure with subsequent transition into (Ax, Fy, 0) state at lower temperatures [19]. The Nd ions order below T1 = 20 K into (0, fy ,0) magnetic structure [18, 19]. It is noteworthy that Nd ions are polarized already at 55 K > T > T1 [20]. The iron substitution of manganese in the NdMnO3 compound generates Gz component for Mn sublattice for NdMn0.8Fe0.2O3 compound [21] and the extension of the temperature interval in which the Nd ions are ordered [21]. Further doping leads to suppression of the magnetism in NdMn0.7Fe0.3O3 compound [22]. For 50 % of iron doping (compound NdMn0.5Fe0.5O3), the situation changes, and the magnetism is most probably already driven by iron ions. For this composition, the Gx magnetic configuration of manganese and iron ions was reported in temperature range 75 K < T < TN (= 250 K) [23]. In temperature range 25 < T < 75 K this system undergoes spin reorientation phase transition into Gy low temperature magnetic structure, where the noticeable Fz component is observed at 1.5 K due to Nd ions [23]. The reported magnetic structures for NdMn0.5Fe0.5O3 are different from the presented magnetic scenario of NdFeO3, so the magnetism in this system should somehow evolve even in this concentration range. Since there is only scarce information about the Fe-rich part of this substitutional system, we decided to study the magnetism of NdMn0.1Fe0.9O3 compound in detail. Herein, we present our results and we propose the magnetic phase diagram of NdMn0.1Fe0.9O3 compound for temperatures 20 mK < T < TN ( 650 K).

Sample preparation experimental setup and analysis protocols Samples were prepared by a vertical floating zone (FZ) method in an optical mirror furnace. The starting materials consisted of high-purity oxides of MnO2 (purity: 99.9 %, producer: Alpha Aesar), Nd2O3 (purity 99.9 %, producer: Sigma Aldrich), and Fe2O3 (purity 99 %, producer: Sigma 1Unless

otherwise stated, the data and analysis reported herein use the orthorhombic space group . Some accessible literature use the Pbnm formalism. In such a case, we applied the Pbnm  Pnma transformation to the previously published data.

2

Aldrich). The starting materials were mixed in a stoichiometric ratio, isostatically cold-pressed into rods, and subsequently sintered at 1373 K for 12 h in air. The floating zone experiment was performed using a four-mirror optical furnace equipped with 1 kW halogen lamps, a pulling speed of 7 mm/h, a counter-rotation of both seed and feed rods 15 rpm and a flowing (2 l/min) air atmosphere. The samples were checked by room temperature X-ray powder diffraction (XRPD) experiment performed on Ultima IV (Rigaku) powder diffractometer and were found to be singlephased. The room temperature XRPD experiment confirmed the same crystal structure as published before [24, 25]. Low temperature XRPD measurements were performed on Empyrean diffractometer from PANAnalytical equipped by low temperature chamber PheniX from Oxford Cryogenics (accessible temperature range 13K – room temperature). The experimental setup was: Bragg-Brentano geometry; cobalt K doublet line (K1 = 1.789 Å; K2 = 1.793 Å); iron beta filter; flat, powdered sample mounted on Si single crystal plate cut in non-diffracting orientation and PIXcel3D detector in 1D mode. Two neutron powder diffraction (NPD) experiments were performed on E9 Fine Resolution Powder Diffractometer located in Helmholtz-Zentrum Berlin für Materialien und Energie. The first experiment covered temperature range 3.5 K  T  300 K. For this experiment we have used the sample enclosed, along with the helium exchange gas, in vanadium container with diameter of 5 mm and the cooling was provided by the closed-cycle refrigerator. The second experiment was performed in 3He-4He dilution refrigerator and covered the temperature range 20 mK  T  4 K. In this case the powder was mounted inside Cu tube and the thermal equilibration was provided by the mixture of deuterated Ethanol (99% deuteration; supplied by Merck) and Methanol (99.8% deuteration; supplied by Merck). In both experiments, freshly ground powder was used and the neutron wavelength was determined prior the experiment by measuring the Y2O3 standard. The diffraction patterns were collected for Bragg angles 10  2  140. Since the compound orders well above the room temperature [25, 26], it was impossible to collect the paramagnetic neutron diffraction pattern. For that reason, all NPD data were fitted using both, crystallographic and magnetic contribution. All diffraction data were fitted using Le Baill and Rietveld methods implemented in the FullProf program [27]. The background was in all cases estimated manually due to its nontrivial shape. Since the instrumental functions of the apparatuses were not established, the peak shape was modeled by a Thompson-Cox-Hastings pseudo-Voigt function for the XRPD and by a Gaussian function for the NPD data. The standard magnetic form factors for Fe3+, and Nd3+ ions that are incorporated in the FullProf program [27] were used to describe the magnetic contributions. All parameters allowed by the crystal symmetry of the crystallographic unit cell were refined. The symmetry analysis was performed using the program BASIREPS, which is part of the FullProf Suite package of programs [28]. To find the global minima of the magnetic models, we have generated a large set of starting values of magnetic moments by a home-written java program. In these set, μFex , μFey, and μFez starting values were tabulated in the range from −6 μB to 6 μB with 3 μB step; and the μNdx , μNdy, and μNdz starting values were in the range 0−4 μB with the step of 2 μB. Each point from this starting set was then used separately in the FullProf program and refined for 10 cycles to get the 3

Fig. 1: Temperature variation of the X-ray diffraction intensities as a function of 2 for NdMn0.1Fe0.9O3. The color scale for the observed intensity is given to the right of the main plot of data. To keep the figure clear, only the strongest reflections are indexed.

representative values of the Bragg R factors. This test was applied for long statistics scans collected at 3.5, 15, 80, 180, and 300 K and for all magnetic structures allowed by the symmetry analysis of the problem. The low temperature specific heat experiment was performed on PPMS (Quantum Design) apparatus equipped with the 3He insert. The non-oriented single crystalline sample was used for this experiment. The sample was attached by Apiezon N grease to the standard 3He microcalorimeter produced by Quantum Design. The low temperature magnetic experiments were performed in a commercial MPMS magnetometer (Quantum Design) with a 3He insert. The oriented single crystalline samples glued by GE varnish glue into the capsule were used for this experiment.

Results Crystal structure refinement Since all reported members from the NdMn1−xFexO3 family [15, 18, 22, 23, 25, 29] crystallize in the orthorhombic crystal structure, space group Pnma (#62 according to the International Tables for Crystallography [30]), we have used the same crystallographic model also for NdMn0.1Fe0.9O3 compound. In this model, the Nd ions occupy 4c (xNd  0.05; zNd  0.98) crystallographic position, Fe and Mn ions are randomly distributed on 4b crystallographic site and oxygen ions occupy two different crystallographic positions: 4c (xO1  0.43; zO1  0.06) and 8d (xO2  0.29; yO2  0.02; zO2  0.72). We have found perfect match between this model and the XRPD data collected at room temperature.

4

5.600

b)

7.740

7.735

b (Å)

a (Å)

5.599

5.598

7.730

a)

5.597 5.446

7.725 236.0

d)

c)

5.444

235.8

5.440 235.4

3

235.6

V (Å )

c (Å)

5.442

5.438 235.2

5.436 0

50

100

150

200

250

300

T (K)

50

100

150

200

250

300

T (K)

Fig. 2: Temperature variation of the calculated crystallographic parameters from the Rietveld fit. a) lattice constant a; b) lattice constant b; c) lattice constant c and d) calculated volume of the unit cell.

The low temperature XRPD experiment (Fig. 1) revealed that the diffraction peaks do not change the intensity in the entire temperature range and that their position shifts only moderately. The natural first assumption is that the shift of the peaks is the effect of thermal expansion and for that reason the room temperature crystal structure was the initial starting point also for the low temperature XRPD data analysis. The Rietveld fits from this starting point converged to good match between the model and experimental data with low R-factors (see supplementary online material, Table SM1). The temperature evolution of b and c lattice constants as well as calculated volume (Fig. 2) shows decrease with decreasing temperature for temperatures higher than 30 K. This effect can be attributed to the thermal expansion effect. For temperatures lower than 20 K, there was observed the upturn for b and c lattice constant, while a lattice constant remains within the experimental error constant with temperature. This effect takes place at the same temperatures as the upturn of the magnetization data [26]. Since the upturn of the magnetization was ascribed to the appearing of the ferromagnetic component due to magnetic order-order phase transition (see ref. [26] and the next section), this anomaly in temperature evolution of lattice parameters can be attributed to the magnetostriction effect. The similar upturn for c lattice constant was observed also for NdFeO3 in spin reorientation region [29] and in NdMn0.8Fe0.2O3 compound at TN [21], while for pure NdMnO3 the decrease of all three lattice constants was observed at TN [19]. No extra peaks were observed at temperatures below 300 K (see Fig. 1), and there were no essential shifts of fractional coordinates (see supplementary online material, Fig. SM1). These results imply that no structural phase transitions occur in the temperature range 13 K  T  300 K. Consequently, when determining the magnetic structure of NdMn0.1Fe0.9O3 (see the next section), the crystal structure was fixed to be the orthorhombic structure, space group Pnma. 5

Fig. 3: Temperature variation of the neutron diffraction intensities as a function of 2. The color scale for the observed intensity is given to the right of the main plot of data. To keep the figure clear, only the strongest reflections are indexed and 2 is cut at 75 degrees. The entire 2 range is presented in supplementary online material, Fig. SM2.

Magnetic structure for T  3.5 K The magnetization data suggest that NdMn0.1Fe0.9O3 compound orders at temperatures above 648 K [26]. As a consequence, with the given experimental setup, all NPD data were collected only in magnetically ordered state. Le Baill fit of NPD data revealed that all peaks can be indexed by integer hkl indices. This implies that the magnetic propagation vector is k = (0 0 0) in the entire temperature interval 3.5 K  T  300 K. The closer inspection revealed that intensities of some reflections change with decreasing temperature (Fig. 3) which indicates three intervals, where presumably different magnetic structure is present: i. Temperature interval for T > 130 K, where for example (110) and (211) reflections are present, while (011) reflection is missing. Since the magnetization data show no anomaly in the temperature range 300 K < T < TN [26], this interval spans up to paramagnetic-to-magnetic ordering phase transition. ii. Temperature interval 15 K  T < 130 K which is characteristic by presence of (011) reflection, while (110) reflection is missing. iii. Temperature interval 3.5 K < T < 15 K, where both, (110) and (011) reflections are present. Assuming no spin-lattice-induced change in the space group, the possible magnetic modes compatible with the crystal symmetry and with the magnetic propagation vector k = (0 0 0) have been obtained using the program BASIREPS [28]. Following the notation incorporated in BASIREPS one obtains Mn/Fe = 3(1+3+5+7) for Mn and Fe atoms on 4b site. For Nd atoms on the 4c site, the decomposition into magnetic modes is Nd = 1+4+5+8 +2(2+3+6+7)

6

3.0

2.0

-1

-1

C (Jmol K )

2.5

1.5 1.0 0.5 0.0

0

2

4

6

8

10

T(K) Fig. 4: Low temperature specific heat data (points) together with the fit (line) as described in text. The difference between experimental data and fit is visualized in supplementary online material, Fig. SM3.

The basis vectors obtained for each irreducible representation i are summarized in the Supplementary online material; see Table SM2. The occupation on the 4c site is 90 % of iron atoms and 10 % of Mn atoms and that is why we have considered Mn ions to be disordered for the initial state of refinement. Also, it is widely accepted that RE ions in REMnO3 and REFeO3 order only at low temperatures. For example, in NdFeO3 the Nd ions polarize due to Nd-Fe interaction below 25 K [16], but the true ordering due to Nd-Nd magnetic interaction takes place only below 1.05(1) K [17]. For that reason we have assumed no ordered Nd moment for the early stages of refinement. The results from these refinements are summarized in supplementary online material, Table SM3. The analysis of scans with good statistics was unambiguous for each temperature and it resulted to following magnetic structures: the 3 = (Cx, Gy, Fz) magnetic structure of Fe ions resulted to lowest Bragg R-factors for temperatures lower than 15 K; 1 = (Gx, Cy, Az) magnetic structure for temperature interval 15 K  T < 130 K and 5 = (Ax, Fy, Gz) structure for temperatures higher than 130 K (see supplementary online material, Table SM3). The additional question is, if Nd ions order in this material. The XRPD studies (see previous section) suggest that there is no structural phase transition in the studied temperature range. This inference implies that if Nd ions order, then they should order within the same magnetic space group as the Fe sublattice. The corresponding fits following this assumption led to additional decrease of R-factors by roughly 5 % for 3.5 K NPD data (see supplementary online material, Table SM4). However, if one adds more free parameters into the model, one should get better match between model and the data. For that reason we have performed the same analysis also for other long statistic scans and we have found the similar decrease of R-factors in the range 0.1 – 7 % (supplementary online material, Table SM4). Since it is not physical that Nd ions will orient already at 300 K, we have concluded that this effect is not intrinsic, but numerical. For this reason we conclude that there is no magnetic ordering of Nd sublattice at temperatures higher than 3.5 K.

7

0.0118

2

-1

M (Am mol )

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a)

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b-axis

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M (Am mol )

0.0091

0.0090

0.0089 1.02

-1

0.96

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M (Am mol )

0.99

0.93 0.90 0.87

c)

0.6

c-axis 0.8

1.0

1.2

1.4

1.6

1.8

T (K)

Fig. 5: Magnetization measured on single crystalline samples in applied magnetic field of 0H = 100 Oe a) a-axis; b) b-axis; c) c-axis. The dashed line represents temperatures T = 1.61 K and 1.74 K as determined from the d(T)/dT curves (see supplementary online material, Fig. SM4).

Magnetic structure below 3.5 K Since the Nd ions in NdFeO3 order only below 1.05(1) K [17], there might be the ordering of Nd sublattice also in NdMn0.1Fe0.9O3 compound. For these reasons we have extended the measurements of physical properties to low temperatures. The specific heat measured at temperatures above 2 K [24] indicated the onset of some anomaly at the lowest-reachable temperature. The measurements extended to lower temperatures (Fig. 4) reveal a broad feature with maximum around 2.6 K. Since the onset of maximum shifts with the magnetic field [24], we assumed that this feature is of the magnetic origin. The situation is similar to the NdFeO3 case, where such a broad bump with maximum between 2 and 3 K was observed and it was ascribed to 5.3 K Zeeman splitting of the lowest-lying Krammers doublet of the Nd ion [31]. This scenario was further confirmed by the inelastic neutron scattering experiment [32]. Extrapolating from NdFeO3, one can try to assign the low temperature bump in NdMn0.1Fe0.9O3 case also to the Zeeman splitting of the lowest-lying Krammers doublet of the Nd ion. However, the situation is slightly more complicated, since the surrounding of Nd3+ ions can contain Fe3+ ions as well as the Mn3+ ions. Then the specific heat can be modelled by the equation 𝐶 = 𝑇3 +

∑𝑃𝐶 𝑖

𝑖 𝑚𝑖

where the T3 is the low temperature approximation of the phonon contribution within Debye model, Pi is the probability to have Nd ion inside the i-th given magnetic surrounding formed by Fe3+ and/or Mn3+ ions and Cmi is the two-level Schottky anomaly given by: 8

4.8

(001)

20 mK 4K

4.6

14

Intensity (arb. units)

Intensity (arb. units)

a)

4.4

4.2

4.0 18

19

b)

12

20 mK 4K (110)

8 6 4 21

20

(011)

10

22

23

24

25

2 (deg) 2 (deg) Fig. 6: The comparison of the 20 mK and 4 K scans at the position of a) (001) and b) (110) and (011) reflections. The lines represent the best fit using the Gaussian functions and linear background.

𝐶𝑚𝑖 = 𝑅

∆𝑖 2

() 𝑇

exp(∆𝑖/𝑇)

[1 + exp(∆𝑖/𝑇)]2

where R is the gas constant and i is the corresponding gap. The random distribution of Fe3+ and Mn3+ ions on 4b crystallographic site leads to binomial distribution of the probabilities Pi. If one takes into account only the 8 nearest neighbors ions, the most probable situations are: pure iron surrounding of Nd3+ ion with probability P0 = 0.430 and surroundings with 1; 2 and 3 Mn3+ ions with probabilities P1 = 0.383, P2 = 0.149, and P3 = 0.033, respectively. The fit of the data in the temperature range 0.37 K < T < 10 K yield  = 1.38(1)10-4 J mol-1K-4 (thence Debye temperature D = 413(1) K) and 0 = 4.82(2) K; 1 = 6.99(1) K; 2 = 11.21(7) K and 3 = 2.36(5) K and it is visualized in Fig. 4. The perfect match between the data and the fit suggests that this feature is indeed the Zeeman splitting of the lowest-lying Krammers doublet of the Nd ion. The M(T) curves (Fig. 5) show two anomalies for the measurements performed along the aand c-axis. The position of the anomalies was determined from the extremes in d(T)/dT curves (see supplementary online material, Fig. SM4) to be T = 1.61 K and 1.74 K. These anomalies may point out that there is some reordering of magnetic spins in a-c plane and/or the Nd sublattice orders. The neutron powder diffraction experiment performed in 3He-4He dilution refrigerator revealed the new magnetic intensity on (001) reflection and the intensity increase on some other magnetic reflections (Fig. 6) for T < 1.6 K. Since all reflections observed on the data collected at 20 mK were successfully indexed by integer hkl indices, the magnetic propagation vector remains k = (0 0 0). The new magnetic signal can be better described by the ordering of Nd sublattice than by the spin reorientation of the iron sublattice. Nd ordering at similar temperatures was also observed in the NdFeO3 compound [17], which gives another hint that the phase transition at 1.6 K is the ordering of Nd sublattice. The very low intensity of the new magnetic peaks did not allow us to make the whole symmetry analysis, but since the magnetic propagation vector does not change, one can expect that Nd sublattice orders also within the 3 representation as the Fe sublattice. The anomalies in M(T) curves and new magnetic intensities in NPD below 1.6 K are very small effects which point to only small differences between these two magnetic phases. This is one of the possible reasons why there was spotted no anomaly connected with this transition in the specific heat data. The second possibility is that the transition is of higher order, so no peak can be expected 9

x

5

y

4

 (B)

3

T2 = 15 K

T1 = 130 K

z

2 1 0 -1 10

100

T (K) Fig. 7: The temperature evolution of the components of the magnetic moment in iron sublattice. The dashed lines represent the magnetic phase transition temperatures.

in C(T) data and the features connected with this transition are hidden within the strong signal originating from the Zeeman splitting of the Nd ion.

Discussion Our study revealed four magnetic phase transitions at different temperatures: TN  748 K [26] (paramagnetic to magnetic ordering phase transition); T1 = 130 K; T2 = 15 K and T3  1.6 K (Fig. 7). The magnetic structure in the range TN > T > T1 is of the 5 type. In this interval the strongest magnetic component is along the c-axis and is antiferromagnetically coupled (Fig. 7). The ferromagnetic component aligns along the b-axis and is much weaker than the c-axis component. The component along the a-axis is close to zero. The 5 structure is consistent with the bulk magnetization curves presented in [26]. In this reference magnetization curves measured at T = 250 K exhibit pure antiferromagnetic signal for a- and c-axis and hysteresis behavior for b-axis. The switching from 5 type to 1 type at T1 is accompanied with the abrupt change of the magnetic moment from b-c plane close to the a-axis direction. 1 structure is purely antiferromagnetic, no ferromagnetic component is present, which explains the decrease of the bulk magnetization when cooling below T1 and purely antiferromagnetic behavior of magnetization curves at these temperatures [26]. The recovery of the ferromagnetic component is accompanied with the change of magnetic structure from 1 to 3 below T2 (Fig. 7). This ferromagnetic component reaches approximately the same value as bcomponent of 5 phase, however, in 3 phase and for temperatures T < T2 is aligned along the c-axis. Reappearing of this ferromagnetic component is the reason for the increase of magnetization measured for cooling below T2 and appearing the hysteresis on the c-axis magnetization curve [26]. This means that the magnetic structures proposed in this manuscript are consistent with the previously published bulk magnetization measurements [26]. The high temperature phase of NdFeO3 is 5 = (0, Fy, Gz) [15]. For NdMn0.1Fe0.9O3 we propose 5 = (Ax, Fy, Gz) with Ax component very close to zero (Fig. 7). NdFeO3 undergoes spin reorientation transition at temperatures 100 K < T < 200 K into the low temperature 3 = (0, Gy, Fz) structure [15]. In our case we have obtained 1 magnetic structure between T1 and T2 phase which was not observed in NdFeO3 and 3 = (Cx, Gy, Fz) structure with all nonzero components below T2 (Fig. 7). The 1 = (Gx, 0, 0) phase was observed in NdMn0.5Fe0.5O3 compound below TN  250 K [23]. The 1 phase 10

is unstable in this compound and it transforms to 3 = (0, Gy, Fz) phase by spin reorientation transition in the temperature interval 75 K > T > 25 K [23]. At lowest temperatures the Nd ordering was observed in several NdMn1-xFexO3 compounds. For example, in NdFeO3 the Nd ordering takes place below 1.05(1) K [17] and in NdMn0.5Fe0.5O3 the small Nd moment amounting 0.13 B was observed at 1.5 K [23]. Our study indicates the ordering of Nd lattice at temperatures below 1.6 – 1.75 K, and with small Nd moment. Presented magnetic structure of NdMn0.1Fe0.9O3 is compatible with other similar systems and it fits very well in between the magnetic structure of closely related NdFeO3 and NdMn0.5Fe0.5O3 compounds. The magnetic structure in perovskite compounds is driven by the competition between the double exchange, superexchange, and Dzyaloshinskii-Moriya interactions [3]. These interactions strongly depend on doping. Basing on Néel temperatures we expect that Fe-O-Fe magnetic interaction is much stronger than Mn-O-Mn and both of them are stronger than Mn-O-Fe magnetic interactions [6, 10]. The spin reorientation region in NdFeO3 suggests that 3 and 5 phase is energetically very close to each other. Random Mn doping results in the situation that some Fe ions have Mn neighbors. That is why some Fe-O-Fe interactions are replaced by weak Mn-O-Fe interactions and manganese dopant increases the energy of both, 3 and 5 phases. Since in NdMn0.1Fe0.9O3 the TN shifts by doping only slightly, but T2 shifts from the spin reorientation region of NdFeO3 significantly, the Mn doping affects the 3 phase more than 5 phase. This opens a temperature window for additional intermediate phase, which is 1 phase. This phase is stable for Mn concentrations 0.5  x  0.9. Further increase of Mn doping (hence lowering of x) switches from Fe-driven magnetism to Mn-driven magnetism. This switching takes place around x = 0.3, where the minimum of TN in the whole NdMn1-xFexOe system was observed [22]. Further lowering of x results in stabilization the 5 phase for x = 0.2 and x = 0 [18, 19, 21], which is the appropriate magnetic phase for the Mn-O-Mn magnetic interaction. In summary the microscopic magnetic study of NdMn0.1Fe0.9O3 compound presented in this manuscript filled the gap of the knowledge in order to complete the magnetic phase diagram of the NdMn1-xFexO3 solid solution substitutional system.

Conclusions Our low temperature X-ray and neutron powder diffraction study confirmed that NdMn0.1Fe0.9O3 adopts orthorhombic crystal structure Pnma and did not reveal any transition of crystal structure in the entire temperature range 20 mK < T < 300 K. The lattice parameters exhibit standard thermal expansion effects for T > 20 K but below this temperature the anomalies due to magnetostriction effects were observed. Results of NPD measurements are in agreement with magnetic structure proposed from magnetization measurements on single crystal [26] and heat capacity study. Iron sublattice orders into magnetic structure 5 = (Ax, Fy, Gz), which is very similar to magnetic structure of NdFeO3, in the high temperature range from TN  648 K to T1 = 130 K. Our study indicates different magnetic structure of NdFe0.9Mn0.1O3 below 130 K in comparison with NdFeO3. Completely new magnetic phase 1 = (Gx, Cy, Az), which does not have any ferromagnetic component, exists in the range from T1 = 130 K to T2 = 14 K. Magnetic structure 3 = (Cx, Gy, Fz) is present below T2 down to 20 mK and Nd ions order below T3  1.6 K into the same 3 magnetic structure.

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Our study fills the gap of magnetic structure which was present in magnetic phase diagram of NdMn1-xFexO3 and completes the entire magnetic phase diagram.

Acknowledgment We thankfully acknowledge the financial support by HZB. The research was also supported by VEGA project No. 2/0137/19, ERDF EU under Contract No. ITMS-26220220061 and Grant Agency of the Czech Republic, project 19-00408S.

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Highlights   

Neutron powder diffraction experiments in temperature range 20 mK – 300 K. Completing the magnetic phase diagram of NdMn1-xFexO3 substitutional system. X-rays and neutrons used as complementary probe.

Author statement Hereby we declare that the work is original and it is not considered for publication by other journal. Declaration of interests

☒ 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.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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