Magnetic Structure of the Mixed Antiferromagnet NdMnFeO
The magnetic structure of the mixed antiferromagnet NdMnFeO was resolved. Neutron powder diffraction data definitively resolve the Mn-sublattice with a magnetic propagation vector and with the magnetic structure (A, F, G) for 1.6 K K). The Nd-sublattice has a (0, f, 0) contribution in the same temperature interval. The Mn sublattice undergoes spin-reorientation transition at K while the Nd magnetic moment keep ordered abruptly increases at this temperature. Powder X-ray diffraction shows a strong magnetoelastic effect at but no additional structural phase transitions from 2 K to 300 K. Density functional theory calculations confirm the magnetic structure of the undoped NdMnO as part of our analysis. Taken together, these results show the magnetic structure of Mn-sublattice in NdMnFeO is a combination of the Mn and Fe parent compounds, but the magnetic ordering of Nd sublattice spans over broader temperature interval than in case of NdMnO and NdFeO. This result is a consequence of the fact that the Nd ions do not order independently, but via polarization from Mn/Fe sublattice.
Complex oxides, of which manganites are a subset, host multiferroicity and magnetoelectricity.Martin and Ramesh (2012) One motivation for investigating MnO hole-doped manganites, where is a rare earth and is an alkali element, is colossal magnetoresistance (CMR).Coey (1998); Salamon and Jaime (2001) The most studied CMR material is LaCaMnO that shows a complex interplay between magnetic, charge, and structural order, all of which may affect CMR,Ramirez (1997) and the NdCaMnO material shows similar CMR features.Millange et al. (2000) Recently, neutron scattering experiments and density functional theory analysis of SrMnO and NdMnO heterostructures displayed an interfacial ferromagnetism that is a step towards manganite-based multiferroic devices.Glavic et al. (2016)
NdMnFeO is a magnetic insulator that contains three ions with well documented magnetochemistry.Carlin (1986) The Nd has a 4, 10-fold degenerate magnetic I ground state, which is split and mixed in the perovskite host lattice to have both orbital and spin components. The Mn ion is , 3 with a Jahn-Teller active E ground state. The Fe ion has a half-full -shell , A ground state. An understanding of the alloyed, solid-solution materials begins with a description of the well-studied end members NdMnO and NdFeO. In the following, the discussion will be restricted to K), where the Nd-Nd interaction becomes important and an additional order parameter must be introduced.Bartolomé et al. (1997)
Neutron diffraction studies have shown that NdMnO is an A-type antiferromagnet, where Mn sublattice orders to make it orders into a (A, F, 0)Muñoz et al. (2000) or (A,0, 0) Chatterji et al. (2009a) magnetic structure below K.Muñoz et al. (2000); Chatterji et al. (2009a) The moment axes are dictated by the strong anisotropy ( K) of the Jahn-Teller distorted manganese.Jahn and Teller (1937) In NdMnO, below K, there is a second transition that is associated with a ferromagnetic Mn-Nd interaction causing ordering of Nd sublattice to the (0, f, 0) magnetic structure,Muñoz et al. (2000); Chatterji et al. (2009a) while no effect on the Mn sublattice was observedMuñoz et al. (2000) or additional canting of the Mn-moments to the (A, F, 0) is reported. Chatterji et al. (2009a) It is noteworthy that, due to antisymmetric exchange, weak ferromagnetism in MnO compounds gives (A, F, 0) ordering with F and/or A being rather small for the majority of light rare earth ions.Muñoz et al. (2000); Chatterji et al. (2009a); Skumryev et al. (1999); Jirák et al. (1997); O’Flynn et al. (2011) The magnetic excitation of the Nd ions below has been confirmed by a neutron backscattering experimentChatterji et al. (2009b) with no applied magnetic field, but the same experiment revealed non-zero polarization of the Nd ions below 40 K while X-ray magnetic circular dichroism data acquired in an applied magnetic field showed ordering of Nd sublattice already below .Bartolomé et al. (2005)
NdFeO is a G-type antiferromagnet with weak ferromagnetism with = (0, F, G)
So in the context of the two pure end-point compounds, NdMnFeO is a mixed-anisotropy, mixed-type antiferromagnet with a phase diagram reported for that shows a similar suppression of in the given interval as other members of the MnFeO family.Troyanchuk et al. (2007); Chiang et al. (2011); Mihalik et al. (2016); Mihalik jr. et al. (2017) Recently, additional investigations have been performed for .Mihalik et al. (2013, 2014); Lazurova et al. (2015) The substitution of Fe for Mn ions modifies the superexchange interactions, alters the polarization of the Nd ions through the Nd-Mn and Nd-Fe interactions, and changes the electron-phonon coupling due to reduction of the Jahn-Teller effect.Troyanchuk (2001) Although NdFeO has a significantly higher ordering temperature than NdMnO, is found to monotonically decrease with iron doping in the range of that was studied.Mihalik et al. (2013) On the other hand, below , a low-temperature magnetic transition, , defined by an anomaly in AC susceptibility decreases with increasing doping.Mihalik et al. (2013) Extrapolating from the NdMnO compound, this anomaly was tentatively assigned to the ordering of Nd ions,Mihalik et al. (2013) although no microscopic study of this transition has been published until now. The AC susceptibility peak width of broadens with increasing , for both in phase and out-of-phase components. The AC peak associated with varies non-monotonically in position between 11 K to 16 K and also in intensity, with the maximum intensity of and when . Furthermore, hysteretic behavior between magnetization measurements with zero-field-cooled (ZFC) and field-cooled (FC) protocols was observed, while magnetic pole inversion, with a compensation temperature near 27 K was observed for samples with and 0.25.Mihalik et al. (2013)
The alloying of different type antiferromagnets has previously been studied in detail to understand the oblique antiferromagnetic (OAF) phase where spins point at an angle between those of the parent compounds, and three classic examples are the highly two-dimensional FeCoClTawaraya et al. (1980) and the three-dimensional, hexagonal KMnFeFBevaart et al. (1978) and FeCoTiOTorikai et al. (1986) compounds. Such compounds show the characteristic dip in ordering temperatures between the two parent compounds with a minimum at a tricritical point in the plane, similar to MnFeO family of compounds.Troyanchuk et al. (2007); Chiang et al. (2011); Mihalik et al. (2016); Mihalik jr. et al. (2017) In addition, the CMR material CaSmMnO is a pseudo-perovskite manganite that showed phase separation into C-type and G-type antiferromagnetism.Mahendiran et al. (2000) Given the different magnetic behavior above and below for NdMnFeO, the present neutron powder diffraction (NPD) work was undertaken to determine the magnetic structure of the mixed A-type and G-type magnetism on a three-dimensional cubic lattice NdMnFeO, which is near the OAF phase approaching the tricritical doping.
Herein, our NPD data establish NdMnFeO orders magnetically with a magnetic propagation vector . The 3 ions order into (A, F, G) magnetic structure and Nd ions order into (0, f, 0) magnetic structure in the interval 1.6 K K), Fig. 1. At K, a spin reorientation transition was observed, and this change is likely the origin of the anomalies reported from bulk measurements. Mihalik et al. (2013) The details of moment assignment will be discussed in the context of experimental and theoretical work and the presentation will be as follows, with the synthesis and experimental details presented in the next section, Section II. In Section III, results from temperature-dependent X-ray powder diffraction (XRPD) data are presented and have been used to study the structural transitions in the sample, while NPD has been used to extract the magnetic structure. Section IV describes the energies from density functional theory (DFT) of four most-probable magnetic structures in the numerically tractable undoped NdMnO. Finally, a coherent picture of these results is discussed in Section V and summarized in Section VI.
Ii Experimental Methods, Analysis Protocols, and Computational Details
ii.1 Sample preparation and characterization
Samples were prepared by a vertical floating zone (FZ) method in an optical mirror furnace. Starting materials consisted of high purity oxides of MnO (purity 3N, Alpha Aesar), NdO (purity 3N, Sigma Aldrich), and FeO (purity 2N, Sigma Aldrich). These starting materials were mixed in a stoichiometric ratio, isostatically cold-pressed into rods, and subsequently sintered at C for 12 to 24 hours in air. The sintering procedure followed the solid state reaction preparation route,Pena et al. (2002) and the starting rods were already partially recrystallized after heat treatment. The floating zone experiment was performed using a 4-mirror optical furnace equipped with 1 kW halogen lamps and a pulling speed of 6 mm/h, a feeding speed of 4 mm/h, and a flowing (2 /min) air atmosphere. The oxygen content was checked by iodometric titration, where a known amount of sample was dissolved in HCl solution (1:1, v/v) in the presence of KI. Immediately, the color of the solution turned to the yellow from I arising from the oxidation of iodine anions. Simultaneously with iodine oxidation, the manganese reduction proceeds to the 2+ oxidation state. Finally after completely dissolving the sample, the amount of iodine was determined by iodometric titration with NaSO solution. Ultimately, a small excess of oxygen was detected, amounting to for NdMnFeO, and this excess oxygen indicates trace amounts of Mn ions are incorporated in our sample, which we will refer to as NdMnFeO.
It is generally accepted that solid solutions with a uniform chemical composition can be prepared by FZ techniques. In order to verify this assumption, the crystal structure of NdMnFeO was investigated by X-ray powder diffraction (XRPD), and all of the samples were established to be single-phase. Next, two parts of the sample, one from the start and one from the end of the resulting ingot, were investigated by a scanning electron microscope (SEM), Mira III FE (produced by Tescan), which was equipped with an energy dispersive X-ray (EDX) analyzer, PentaFET Precision (produced by Oxford Instruments). The SEM and EDX investigations revealed that both parts of the ingot were free of any inclusions, and no concentration gradient between the two ends of the crystal was detected. Finally, the Nd:Mn:Fe ratio of 1:0.8:0.2, as determined by EDX analysis, was consistent with the other determinations within experimental uncertainties.
ii.2 Neutron diffraction studies
The initial neutron powder diffraction (NPD) experiment was performed on the E6 neutron powder diffractometer at the Helmholtz-Zentrum Berlin (HZB). A freshly-ground powder sample with mass of about 5 g was enclosed, along with He exchange gas, in a vanadium container with a diameter of 5 mm. The settings of the diffractometer were as follows (downstream from the nuclear reactor): 30 Soller slit, pyrolytic graphite (PG) monochromator ( nm), PG filter, 30 Soller slit, sample enclosed in standard Orange cryostat, moving fan collimator, two position-sensitive detectors. Long scans were collected for at temperatures of 1.6 K, 20 K, 35 K, and 65 K. In addition, several short scans were acquired in the temperature range 1.6 K 65 K.
An additional NPD experiment was performed on HB-3 triple-axis neutron spectrometer at the High Flux Isotope Reactor (HFIR) located at Oak Ridge National Laboratory (ORNL). During the experiment, the spectrometer was configured for elastic scattering with incident neutron energy 14.7 meV and nm. Soller collimations of reactor 48 mono 40 sample 40 analyzer 240 dectector were used, with slits optimized at a Bragg peak. For this experiment, approximately 20 g of freshly-ground powder along with He exchange gas was confined to an aluminum sample can, which was attached to a standard insert used with a standard Orange cryostat. The one-day experiment focused on collecting data for at temperatures of 1.7 K, 20 K, and 65 K.
ii.3 Low temperature XRPD studies
Low-temperature XRPD was performed using a refurbished Siemens D500 diffractometer equipped with a closed-cycle cryocooler (Sumitomo Heavy Industries) enabling measurements over a range of temperatures (3 K 300 K). Data were acquired with Cu-K radiation and a Bragg-Brentano geometry with a source-sample and sample-detector distance of 330 mm. The sample environment consisted of a single crystalline sapphire sample holder, providing good thermal equilibration and low diffraction background, and He exchange gas to ensure homogeneous sample temperature. The measurements were performed in reflection geometry with a fixed divergence slit size, resulting in a primary beam with 0.44 divergence. A linear detector (MYTHEN 1K) along with an optimized integration procedure Kriegner et al. (2015) were used to avoid geometrical defocusing, while a Ni-foil was used to remove the K radiation.
ii.4 Diffraction analysis protocols and programs
All diffraction data were fitted using Le Bail and Rietveld methods implemented in the FullProf program.Rodríguez-Carvajal (1993) The background was modeled by a polynomial function of maximum 5th order for room temperature (RT) XRPD data and NPD data. The background for the low temperature (LT) XRPD data was estimated manually due to a non-trivial shape caused by scattering by the windows of the sample chamber. Since the instrumental functions of the apparatuses were not established, the peak shape was modeled by a Thompson-Cox-Hastings pseudo-Voight function for the XRPD and by a Gaussian function for the NPD data. The initial conjectures of the profile functions for the NPD and LT XRPD data sets were obtained by Le Bail fits of a YIG standard and a LaB NIST standard (standard number 660b), respectively. For describing the magnetic contributions to the NPD data, the standard magnetic form factors for Mn, Fe, and Nd ions that are incorporated in the FullProf program Rodríguez-Carvajal (1993) were used. 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.FullProf-Team (2016) To find the global minimum of the best magnetic model we have generated large seeds of starting magnetic moments by home written java program. In these seeds, , and starting values were tabulated within interval -4 to 4 ; , and starting values within interval -5 to 5 and starting value within interval 0 – 3.2 with steps between 0.5 and 1.5 , depending on the complexity of the calculations. Each point from this starting seed was then separately loaded into the FullProf program and refined for 10 cycles to get the representative values of R-factors.
ii.5 Computational details
The first-principles (ab initio) calculations are based on the density functional theoryHohenberg and Kohn (1964) within the single-electron framework and are used herein to treat the pure stochiometric NdMnO compound. The VASP (Vienna Ab-initio Simulation Package) package,Kresse and Furthmüller (1996a, b) a plane-wave pseudopotential code, was used to perform spin-polarized calculations including the spin-orbit interaction. Projector-augmented-wave pseudopotentials were used for Nd, Mn, and O atoms with the electronic valence configurations of [Xe] (oxidation state 3+), [Ar] , and [He] , respectively. General gradient-corrected exchange-correlation functionals parametrized by Perdew-Burke-Ernzerhof (PBE)Perdew et al. (1996) and a plane-wave cut-off of 600 eV were employed. The unit cell was sampled with a -point mesh of generated according to the scheme proposed by Monkhorst and Pack.Monkhorst and Pack (1976) The convergence criteria for the total energies and forces were set to 10 eV and 10 eV/Å, respectively. Electron correlation beyond the PBE was taken into account within the framework of so-called GGA +U method and the approach proposed by Dudarev et al.Dudarev et al. (1998) Calculations were carried out with the Coulomb repulsion and the exchange parameter in the range of eV for the d- and f-electrons of Mn and Nd atoms. The spin-orbit interaction of the valence states was taken into account.
iii.1 Crystal structure refinement
The crystal structure of NdMnFeO was refined from the XRPD and NPD data at room temperature. The process was done by first treating the XRPD and the NPD data sets separately, and subsequently, these two diffractograms were co-refined. Since NdMnO and NdFeO adopt the same crystal structureMuñoz et al. (2000); Sławiński et al. (2005) (orthorhombic structure, space group , with atomic positions: Mn/Fe: 4; Nd: 4; O: 4; O: 8), the crystal structure of NdMnO reported by Muñoz et al. Muñoz et al. (2000) was used as a starting model. The Rietveld fit using this model resulted in low -factors and to the crystallographic parameters presented in Table 1, and these results indicate that NdMnFeO maintains the structure of the parent compound NdMnO. To determine the rare-earth deficiency,Cherepanov et al. (1995) the occupancy factor of the Nd atoms was allowed to vary during the first stages of the refinement of the NPD data, and the value converged to 1.04(1), thereby indicating no appreciable evidence of Nd non-stoichiometry. Consequently, the Nd site was considered to be fully occupied in the next stages of refinement and for the processing of all experimental data collected below room temperature.
The calculated lattice parameters decrease monotonically in the temperature range 80 K 300 K (Fig. 2), and the observed changes are consistent with thermal contraction. Below 65(10) K, there is a clear increase of the -axis length, while the -axis, -axis, and volume changes are more subtle. In comparison, bulk probes found K.Mihalik et al. (2013) The similar temperature evolution of the crystallographic parameters was observed in the case of NdFeO compound in the spin reorientation region,Sławiński et al. (2005) but in the case of NdMnO, the sudden drop of all three crystallographic parameters was observed at T.Chatterji et al. (2009a) Therefore, the magnetoelastic coupling in NdMnFeO is different from NdMnO, but can be similar to NdFeO. No extra peaks were observed at temperatures below 300 K [see Fig. SM2], and no essential shifts of fractional coordinates (see Fig. SM3), which would imply the presence of spin-rotation/octahedral-rocking that was detected in NdFeO,Belov et al. (1972); Koshizuka and Hayashi (1988) were observed. These results imply that no structural phase transitions exist in the temperature range 3 K K. Consequently, when determining the magnetic structure of NdMnFeO (see next section), the crystal structure was fixed to be the orthorhombic structure, space group .
iii.2 Magnetic structure refinement
Although the XRPD study below 65 K suggests the orthorhombic symmetry of the crystal structure remains unchanged, the NPD experiment revealed that intensities of some reflections increase with decreasing temperature, for example the (111) reflection, and a gradual increase of intensity appears, for example on the (010) reflection, which is forbidden by the space group Hahn (2011) (Fig. 3). These changes are associated with magnetic ordering setting in below K, which is in agreement with our AC susceptibility and magnetization measurements.Mihalik et al. (2013) Since all magnetic reflections can be indexed by integer indices, the magnetic ordering wavevector is . Furthermore, below K, remarkable changes in the intensity of some magnetic peaks, namely the overlapping (121), (002), and (210) reflections and the (200) reflection are observed, see Fig. 4. These increases of intensities indicate the magnetic structure is evolving and/or the other magnetic ion is ordering. These low temperature changes of the diffraction pattern onset with an anomaly detected in the AC susceptibility at K.Mihalik et al. (2013) For , no additional magnetic peaks appear, and the magnetic structure is described by the same propagation vector .
Assuming no spin-lattice induced change in the space group, the possible magnetic modes compatible with the crystal symmetry have been obtained using the program BasIreps.FullProf-Team (2016) For , the little group, , coincides with the space group . Of the eight ’s for the 4 position of the Mn and Fe, four allow magnetic order such that
For Nd atoms on the site, the decomposition is
The basis vectors obtained for each irreducible representation are reported in the Appendix, see Table A1.
Based on the results for LaMnOMoussa et al. (1996) and extapolated generically to MnO, it is widely accepted that the Mn-sublattice orders at much higher temperatures than those where the ions become polarized due to the –Mn interaction. However, several different magnetic structures for NdMnO have been reported by various groups, including the possibility that Nd ions order already at T.Muñoz et al. (2000); Chatterji et al. (2009a); Jandl et al. (2003); Bartolomé et al. (2005) For this reason, all possible magnetic structures allowed by the basic symmetry constraints were considered, including the independent ordering of Mn/Fe- and Nd-sublattices and the plausible case that the Nd moments remain disordered (denoted as state). In total, 36 model structures were compared with the NPD data sets collected at = 1.6 K at HZB. When all experimentally detected peaks were described by a model structure and no extra peaks with intensities higher than the experimental noise were generated, then plausible matches were considered to be established between a model structure and the data. The next step involved Rietveld analysis starting with each plausible model structure. The results of this comprehensive analysis are summarized and tabulated in Table SM1, where the magnetically ordered state notation, is defined and cross-referenced. This analysis resulted in four magnetic structures whose refined R-factors did not distinguish any single structure as the unambiguous solution. These four magnetic structures are: , , and .
In all cases, the best fit for K is found to be for Mn/Fe sublattice, but the goodness of fit parameters cannot unambiguously distinguish between , , , and . The absence of any additional structural phase transitions in the XRPD is suggestive that the magnetic space group does not change at . Also extrapolating from LaMnO,Moussa et al. (1996) it is generally accepted the Mn sublattice orders at . This inference implies that if the Nd sublattice order, then it should order within the same magnetic space group as Mn sublattice. Consequently, the and are not physically allowed, but , and remain as plausible configurations. Note that the notation means the Nd ions do not order into long range magnetic structure, which is consistent with the statement that at the magnetic structure evolves, but no additional ion orders at that temperature. Therefore, the magnetic space group of NdMnFeO is assigned to be .
Considering the 4 transition metal site, the representation can host A-type (as for NdMnO) and G-type (as for NdFeO) antiferromagnetism. Since 4 site hosts Mn and Fe ions, we have tried to fit independently Mn and Fe magnetic moments. Second analysis was done with Mn magnetic moments constrained to the (A, F, 0) magnetic structure (as for NdMnO) and the Fe magnetic moments to (0, F, G) magnetic structure (as for NdFeO). Despite the fact that large seeds of initial fitting parameters were used (see section II.4), all fits in both cases converged to unphysical results. Consequently, these two options were rejected, leaving the only two possibilities that either the Mn or the Fe ions exclusively order. Since for = 0.2 is smaller than for = 0 and a minimum of is expected at concentrations 0.25,Mihalik et al. (2013) one can expect that the Fe ions act only as a perturbation and the magnetism is mainly driven by the Mn ions. As a result on the site, only the Mn ions order and the possible magnetic ordering can be , or . Finally, the large seed initial fitting parameters test (see Section II.4) for structures and revealed 6 local minima in the entire parameter space, where the fitting parameters resulted in physically meaningful values (see Table SM2, where the numbering of the minima is also defined). From these 6 candidates, only two plausible descriptions emerge, see Table SM2 for details.
iii.3 Temperature dependences of the magnetic moments
The temperature dependences of the two remaining candidates for the magnetic structure are shown in Fig. 5. In the case of , the Nd ions order at T, but exhibits an abrupt increase at and flips to the opposite direction at the same temperature. In case of , can be attributed to the evolution of the component.
In both cases, is also connected with the continuous decrease of the component, which is typical for a spin-reorientation phase transition. Since this effect is rather weak, additional tests are needed to distinguish if the effect is real. The permitted reflections for G mode have constraints is odd and . Consequently, the strongest contribution to the magnetic signal from the G mode should be observed for the (110) reflection. Since the intensity of the (110) reflection is close to the background of NPD patterns collected at HZB, an additional NPD experiment focused on resolving this issue was performed at ORNL. The data from this experiment unambiguously show that the magnetic signal on the (110) reflection, Fig. 6, is stronger at 23(2) K than at 1.6(1) K, thereby confirming that the spin reorientation phase transition is real effect.
According to a molecular field model,Kozlenko et al. (2004) the temperature evolution of the total magnetic moment follows a self-consistent expression written as
where is the magnetic moment at , is the Brillouin function, is the ordering temperature. Fits according to Eq. 3 yeld = 58.7 K and = 57.6 K for the and magnetic structures, respectively. The value of for the magnetic structure is closer to K, obtained from bulk magnetization measurements.Mihalik et al. (2013) The magnetic moment of the Mn sublattice extrapolated to K is 2.69 for , and this result is lower than = 3.87(3) reported for LaMnO.Moussa et al. (1996) On the other hand for the structure, the magnetic moment in the limit is = 3.27 , which is much closer to reported for LaMnO.Moussa et al. (1996) However, the data for the structure are not well-modeled by a single Brillouin function, and this result may suggest the presence of a phase transition at . Since specific heat data of the NdMnFeO compound show no anomaly at ,Mihalik et al. (2013) it is plausible that is not connected with a phase transition. Additionally, the R-factors determined at 20 K are much lower for the magnetic structure than for the (see Table SM3). Finally, a recent backscattering experimentPajerowski () resolved a non-zero polarization of the Nd ions for , so the magnetic configuration can be eliminated as a physical option, thereby leaving as the only possible description. Specifically, the magnetic configuration is (A, F, G) for Mn ions and (0, f, 0) for Nd sublattice in the whole temperature range 1.6 K .
Iv NdMnO Magnetic structure by density funtional theory calculations
In the previous section, the magnetic structure of NdMnFeO was experimentally established to be (A,F,G) + (0, f, 0). Since our analysis of NdMnFeO resulted in a magnetic structure different than the most-accepted magnetic structure of NdMnO phase, but there have been some inconsistencies in the literature about the NdMnO magnetic structure,Muñoz et al. (2000); Chatterji et al. (2009a); Jandl et al. (2003); Bartolomé et al. (2005) this section describes a theoretical approach to understand the magnetic structure of the pure NdMnO.
To start, varying and values as initial parameters yielded eV, eV for the -shell of Nd, and with eV and eV for the -shell of Mn atoms to preserve insulating behavior and the magnetic moment length. These calculations ultimately led to values for the magnetic moments and and to the band gap of 1.75 eV, and these results are comparable to the experimental observations.Mihalik et al. (2013); Muñoz et al. (2000); Chatterji et al. (2009a); Shetkar and Salker (2010) These first-principle calculations revealed that the total magnetic moment of the Nd atom is reduced by the large orbital moment ca. 1.5 atom that is antiparallel with respect to its spin moment of 2.9 atom.
Next, the crystallographic structure was optimized by performing a complete relaxation of the lattice vectors as well as the atomic positions and internal degrees of freedom. During this initial optimization, two different types of exchange interactions, either antiferromagnetic or ferromagnetic between Mn spins, were considered. This crystallographic optimization led, in both cases, to a decrease of the space group symmetry from to . However, a closer look to the optimized structure revealed, in both cases, only the minor shifts of the -position of the Nd ion, from 1/4 to , where stands for non-zero digit lower than 5, but such small shifts are below the precision of the experimental methods. Consequently, the orthorhombic symmetry (space group ) was employed in all of the following steps of the calculations.
Ultimately, two different crystallographic structures were obtained, and for the purposes of these numerical studies, these structures are denoted as p and p. When assuming antiferromagnetic interactions between the Mn ions, the p state is identified with lattice parameters nm, nm, and nm. Conversely, when assuming ferromagnetic interactions between the Mn ions, the p configuration is found with lattice parameters nm, nm, and nm. Both structures were obtained by relaxing all degrees of freedom, while only the initial magnetic pattern was different. The optimized lattice parameters are roughly 1.5% to 2.5% higher than the experimentally determined lattice parameters as presented in Section III.1 and Table 1, and p will designate the observed lattice. These results are consistent with the well-known over-binding effects of the GGA (PBE) exchange-correlation approximation employed for this work, see Section II.5 for details. Furthermore, such small differences in lattice parameters indicate a very good match between theory and experiment.
Finally, four magnetically ordered states, namely [Mn (A, F, G) and Nd (f, 0, 0)], [Mn (A, F, G) and Nd (0, 0, f)], [Mn (A, F, 0) and Nd (0, f, 0)], and [Mn (A, F, G) and with Nd disordered], were introduced for p, p, and p structures and only the electronic degrees of freedom were converged, i.e. the atomic positions were kept fixed.
These magnetic structures probe the direction of the Nd polarization, and antiferromagnetic modes that are allowed within the specific irreducible representations are suppressed for this analysis.
The calculated total energies for each crystallographic structure, p, p, and p, and the plausible magnetically ordered states are summarized in Table 2. From this tabulation, one immediately notices the total energies of all three structures p, p, and p with magnetic ordering of and are higher in energy than other two structures ( and ), with exception p and . Consequently, these higher energy results are excluded from further consideration. It is important to note that the p and structure may have a higher energy because of the lack of suitable charge convergence with respect to the other entries in the table.
|(A, F, G)||(f, 0, 0)||10.2||12.5||9.5|
|(A, F, G)||(0, 0, f)||25.5||41.2||10.7|
|(A, F, 0)||(0, f, 0)||23.5||0.0||0.0|
|(A, F, G)||disordered||0.0||1.0||2.4|
At this point, magnetically ordered options remain, and , which have very similar total energies for a fixed geometry as in experimental studies (p structure) and for the ferromagnetically antiferromagnetically ordered MnMn options, p and p structures, respectively. However, the last row in Table 2, with magnetic ordered state , requires special attention since a “randomly” oriented atom was used. To improve the “randomness”, the simulation window was increased by a factor of two in every dimension to give a supercell containing 160 atoms, of which 16 are Nd atoms. (Periodic boundary conditions means that only magnetic moments inside the supercell are really random). This supercell approach did not change any of the details of the calculation (e.g. stability and magnetic ordering of the Mn atoms), and now the average Nd magnetic moment was closer to zero, as the statistics were significantly improved. Therefore, these calculations cannot unambiguously determine if Nd ions order, or not, leaving both of these possibilities acceptable from the theoretical point of view.
The NdMnFeO compound mixes an orthomanganite and orthoferrite with similar structures, excepting the Jahn-Teller long bond of the Mn. Magnetically, NdMnO is highly anisotropic with A-type antiferromagnetismMuñoz et al. (2000); Chatterji et al. (2009a) and NdFeO is weakly anisotropic with G-type antiferromagnetism.Belov et al. (1972); Koshizuka and Hayashi (1988) Our study is an investigation of single-ion doping in the anisotropic-A-type, pseudo-isotropic-G-type phase diagram to better understand the experimental magnetic structure.
The magnetic structure of NdMnFeO was unambiguously identified to be , (A, F, G) for the Mn ions over the whole temperature range 1.6 K . This structure is within the magnetic space group of NdMnO and the high temperature magnetic structure of NdFeO. On the other hand in low temperature magnetic structure of NdFeO, G-type antiferromagnetism is accommodated by the -direction, which means the representation. The most surprising finding of this work is that the magnetic structure of Nd sublattice is also within the , (0, f, 0) representation and the Nd ions exhibit long range magnetic order at temperatures below . This finding is different from NdMnO, where the ordering of Nd ions was reported only below KChatterji et al. (2009a) and different also from NdFeO, where the ordering of Nd sublattice is suppressed below 4.5 K.Przeniosło et al. (2006) On the other hand, Chatterji et al. Chatterji et al. (2009b) conclude from their neutron backscattering data that the “finite energy of the inelastic peak and its much smaller temperature dependence at K (are) due to the polarization of the Nd magnetic moment by the field of Mn moments”. In fact, the finite energy of the inellastic peak in NdMnO was observed below 40 K. A similar effect was also observed by our neutron backscattering experiment performed on NdMnFeO below .Pajerowski () The backscattering results prove the Nd ions become polarized at . Since the backscattering experiment probes events with characteristic timescale s, this experiment can not distinguish polarized Nd ions in short range magnetic correlations from those in static long range magnetic structure. Consequently, the Nd ions order at K in case of NdMnO,Chatterji et al. (2009a, b) whereas the Nd ions order at in NdMnFeO, even though both compounds exhibit essentially the same neutron backscattering spectra.
Our analysis shows that the effect observed at K by AC susceptibility is the spin reorientation effect. Such an effect was not observed in NdMnO, but spin reorientation is well reported for NdFeO compound.Sławiński et al. (2005) Presumably the Fe ions start to destabilize the magnetic structure of the Mn sublattice at the concentration studied in this work (), and the spin reorientation is the consequence of Fe doping. Another consequence is the stabilization of the long range magnetic structure of Nd ions.
Finally, in all of the diffraction data sets, there is one sharp reflection for a given family of planes. However, as the crystal and magnetic structures of the parent compounds are so similar, it is possible that minor chemical inhomogeneities exist over nanometer-sized length scales.Shulyatev et al. (2009) Along with subtleties of stoichiometry, such effects may be important when comparing samples from different laboratories.
The magnetic structure of NdMnFeO has been investigated using NPD. The resulting model for has wavevector and the magnetic structure with the (A, F, G) configuration for the Mn ions and the (0, f, 0) arrangement for the Nd ions. The magnetic structure follows the dominant Mn ion, but finds a way to accommodate the interactions of the less populous Fe ion which affects fine details of the magnetic structure. Quantitative analysis to substantiate this model are underway with additional probes.
Acknowledgements.This research project has been supported, in part, by the European Commission under the 7th Framework Programme through the ‘Research Infrastructure’ action of the ‘Capacities’ Programme, NMI3-II Grant number 283883, VEGA project number 2/0132/16, and ERDF EU under the contract No. ITMS-26220120047, by the US National Science Foundation through Grants DMR-1202033 (MWM) and DMR-1157490 (NHMFL), and by the Czech Science Foundation project 14-08124S (DK). A portion of this research used resources at the High Flux Isotope Reactor (HFIR), a Department of Energy Office of Science User Facility operated by the Oak Ridge National Laboratory. The intensive numerical calculations (by DL and KLM) were supported by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations project âIT4Innovations National Supercomputing Center â LM2015070 and National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science” - LQ1602 and D.L. also by the Grant Agency of the Czech Republic, project No. 17-27790S.
|(G, C, A)||( – , c, – )|
|–||(g, – , a)|
|(C, G, F)||(c, – , f)|
|–||( – , g, – )|
|(A, F, G)||( – , f, – )|
|–||(a, – , g)|
|(F, A, C)||(f, – , c)|
|–||( – , a, – )|
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