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Magnetic Interactions in the Double Perovskites R2NiMnO6 (R = Tb, Ho, Er, Tm) Investigated by Neutron Diffraction María Retuerto,† Á ngel Muñoz,‡ María Jesús Martínez-Lope,§ José Antonio Alonso,§ Federico J. Mompeán,§ María Teresa Fernández-Díaz,∥ and Javier Sánchez-Benítez*,⊥ †

Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark Universidad Carlos III, Avenida Universidad 30, E-28911 Leganés-Madrid, Spain § Instituto de Ciencia de Materiales de Madrid, C.S.I.C., Cantoblanco, E-28049 Madrid, Spain ∥ Institut Laue Langevin, BP 156X, Grenoble F-38042, France ⊥ Departamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain ‡

S Supporting Information *

ABSTRACT: R2NiMnO6 (R = Tb, Ho, Er, Tm) perovskites have been prepared by soft-chemistry techniques followed by high oxygen-pressure treatments; they have been investigated by X-ray diffraction, neutron powder diffraction (NPD), and magnetic measurements. In all cases the crystal structure is defined in the monoclinic P21/n space group, with an almost complete order between Ni2+ and Mn4+ cations in the octahedral perovskite sublattice. The low temperature NPD data and the macroscopic magnetic measurements indicate that all the compounds are ferrimagnetic, with a net magnetic moment different from zero and a distinct alignment of Ni and Mn spins depending on the nature of the rare-earth cation. The magnetic structures are different from the one previously reported for La2NiMnO6, with a ferromagnetic structure involving Mn4+ and Ni2+ moments. This spin alignment can be rationalized taking into account the Goodenough−Kanamori rules. The magnetic ordering temperature (TCM) decreases abruptly as the size of the rare earth decreases, since TCM is mainly influenced by the superexchange interaction between Ni2+ and Mn4+ (Ni2+−O−Mn4+ angle) and this angle decreases with the rare-earth size. The rare-earth magnetic moments participate in the magnetic structures immediately below TCM.

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and Mn4+ ions ordered in a rock-salt configuration, defined in the polar space group C2 at room temperature. In this compound, the presence of 6s2 lone pairs of Bi3+ ions and the covalent Bi−O bonds are responsible for the ferroelectric properties with a ferroelectric Curie temperature (TCE) of 485 K; above this temperature the crystal structure is defined in the centrosymmetric space group P21/n. On the other hand, the superexchange interactions between Ni2+ and Mn4+ via common oxygens lead to ferromagnetism with a ferromagnetic Curie temperature (TCM) of 140 K. In general, according to the Goodenough−Kanamori’s rules,13 the superexchange magnetic interactions between two transition metals, in which one of them possesses half-filled eg orbitals and the other one empty eg orbitals, is ferromagnetic via 180° M−O−M paths. This configuration has also been previously explored in a number of Mn double perovskites, such as La2MMnO6 with M = Co,14−16 Ni,14,15,17−23 and Cu,14,24 in which MO6 and MnO6 octahedra are ordered in a rock-salt configuration; all these oxides are indeed ferromagnets. Of course, although

INTRODUCTION Many important phenomena are driven by charge ordering or charge disproportionation of transition metals of p-block elements in oxides,1 in particular in ABO3 perovskites. Certain exotic conduction effects near the insulator to metal boundary, such as colossal magnetoresistance in manganites (e.g., La0.5Ca0.5MnO3) or superconductivity in K- and Pb-doped BaBiO3,2−4 are motivated by the melting of charge order. Recent examples of disproportionation in oxides include that observed at B-sites of BaBiO35 where Bi4+ separates into Bi3+ and Bi5+, and those concerning high transition-metal valence states, known for a long time in CaFeO3 (CaFe0.53+Fe0.55+O3)6 and RNiO3 (RNi0.52+Ni0.54+O3, for R = Y, Pr−Lu), although the observed charge separations are smaller than expected from the stoichiometric formulas.7−11 High pressure and temperature conditions have recently been used to stabilize some of these compounds containing either charge ordering or charge disproportionation. A paradigmatic example is Bi2NiMnO6, prepared at 6 GPa.12 Very interestingly, this oxide constitutes one of the rare multiferroic oxides, simultaneously exhibiting ferromagnetic and ferroelectric properties. The crystal structure is an extremely distorted superstructure of perovskite with Ni2+ © XXXX American Chemical Society

Received: August 24, 2015

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DOI: 10.1021/acs.inorgchem.5b01951 Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

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La2NiMnO6 (LNMO) and La2CoMnO6 (LCMO) ferromagnetically order at relatively high temperatures (ferromagnetic transition temperatures, TCM = 280 and 230 K, respectively), they do not exhibit ferroelectric ordering and cannot be considered as multiferroics. However, La2NiMnO6 (LNMO) is a ferromagnetic semiconductor and a promising material for spintronics devices, 18 with the advantage of showing ferromagnetic ordering near room temperature. Many other ferromagnetic semiconducting oxides with low TCM’s are thus less appealing for applications. Recently, magnetocapacitance and magnetoresistance near room temperature have also been described for LNMO; furthermore, it has been observed that applying large magnetic fields results in a large change in the dielectric properties of this compound, adding more value as a multifunctional material.19 Nominal La2NiMnO6 was also reported to contain excess oxygen as well as the coexistence of two ferromagnetic phases, monoclinic and rhombohedral, of comparable Curie temperatures.17 Annealing under O2 consistently gave O6+δ; the lowest δ = 0.05(1) was attained for a single P21/n phase. Replacing La3+ by R3+ ions with smaller ionic radius, as in Nd2NiMnO6, was also shown to stabilize the monoclinic phase: excess oxygen is accommodated in the perovskite structure by the creation of cation vacancies, associated with a Ni3+/Ni2+ redox couple.17 In a recent study of the crystal structure of the NdNi1−xMnxO3 series,25 the long-range Ni/Mn ordering in the P21/n space group has been confirmed for the x = 0.5 member, and the magnetic structure has been defined as a canted ferromagnet. In the present work we have prepared four members of the R2NiMnO6 family with smaller R3+ ions. The synthesis involved soft-chemistry procedures followed, when required, by O2 pressure annealing. A neutron powder diffraction (NPD) study at room temperature (RT) and low temperatures (LT) allowed us to unveil the peculiarities of the crystal and magnetic structures, which depend on the nature of the rare-earth ion. Some members of the R2NiMnO6 family of compounds (R = La and rare earths from Pr to Lu) had been previously prepared and their magnetic properties studied.26−33 However, to our knowledge, their magnetic structures were not described, so the magnetic interactions that govern the global magnetization of the samples were still unknown. The replacement of La by a smaller rare-earth cation induces modifications on the crystal structure, and thus, it may drive a change in the sign of the magnetic interactions. In fact, by using first-principles density functional theory (DFT) calculations,31 it has been recently published that the magnetic order in R2NiMnO6 would change from ferromagnetic for R = La and Sm to an E*-type antiferromagnetism for R = Y. The E*-type magnetic structure would break the inversion symmetry, thus allowing a ferroelectric polarization to occur, generating a multiferroic behavior.31 A recent spectroscopic and magnetic study carried out on Tb2NiMnO6 suggests the existence of antiferromagnetic interactions in this compound.33 Moreover, Zhao et al. recently reported on a first-principles-based prediction 34 of a specific class of materials (namely, R2NiMnO6/La2NiMnO6 superlattices) that exhibit an electrical polarization and strong ferromagnetic order near room temperature. Their electrical and ferromagnetic properties can be tuned by means of chemical pressure and/or epitaxial strain, which adds interest to this timely topic. Consequently, the study of the magnetic structure of the R2NiMnO6 family of compounds by NPD is invaluable.

Article

EXPERIMENTAL SECTION

R2NiMnO6 (R = Tb, Ho, Er, Tm) samples have been prepared from citrate precursors obtained by a soft-chemistry procedure. Stoichiometric amounts of analytical grade of R2O3, Ni(NO3)2·6H2O, and MnCO3 were solved in acid citric by adding several droplets of concentrated HNO3 to favor the solution of rare-earth oxides. The citrate solution was slowly evaporated, leading to organic resin containing a random distribution of the involved cations at an atomic level. These resins were first dried at 120 °C and then slowly decomposed at temperatures up to 600 °C. A subsequent treatment in air at 800 °C for 2 h was carried out in order to eliminate all the organic materials and nitrates. The black precursor powders were heated under 200 bar of oxygen pressure for 12 h at 900 °C. Then, the samples were slowly cooled down to room temperature. The reaction products were characterized by X-ray diffraction (XRD) for phase identification and to assess phase purity. The characterization by XRD was performed using a Bruker-AXS D8 diffractometer (40 kV, 30 mA), controlled by a DIFFRACTplus software, in Bragg−Brentano reflection geometry with Cu Kα radiation (λ = 1.5418 Å). The data were obtained between 10° and 64° 2θ in steps of 0.05°. For the structural refinement, NPD experiments were carried out at room temperature (295 K) at the high resolution D1A neutron diffractometer with λ = 1.910 Å, in the ILLGrenoble, France. Low temperature NPD patterns were collected at the D1B diffractometer with λ = 2.520 Å in a range of temperatures between 2 and 147 K for R = Er, Ho and between 2 and 87 K for R = Tb, Tm. The powder samples were contained in a vanadium cylinder. The refinement of the crystal and magnetic structures was performed by the Rietveld method35 using the FULLPROF refinement program.36 A pseudo-Voigt function was chosen to generate the line shape of the diffraction peaks. The following parameters were refined in the final run of the neutron diffraction data set: scale factor, background coefficients, zero-point error, pseudo-Voigt corrected for asymmetry parameters, positional coordinates, and isotropic displacement factors. The magnetic measurements were performed in a commercial superconducting quantum interference device magnetometer (SQUID). The dc magnetic susceptibility data were collected in the 5−400 K range under an applied magnetic field of 1000 Oe. Isothermal magnetization curves were obtained for magnetic fields going from −5 to 5 T at 5 K.

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RESULTS Crystal Structure. R2NiMnO6 (R = Tb, Ho, Er, Tm) samples were obtained as well-crystallized powders. The XRD patterns are all characteristic of strongly distorted perovskites, showing well-defined superstructure reflections as displayed in Figure 1. No impurity phases were detected from either XRD or NPD data. We observed the presence of additional superstructure reflections that indicate long-range ordering between Ni and Mn cations as in the case of La2NiMnO6. The refinement of the crystallographic structures has been carried out from the NPD patterns acquired at RT. The structural model already reported for LNMO17 with a monoclinic P21/n space group was taken as departure model. In this space group the unit-cell parameters are related to a0 (ideal cubic perovskite, a0 ≈ 3.8 Å) as a ≈ b ≈ √2a0, and c ≈ 2a0. There are two crystallographically independent positions for Ni and Mn cations, 2d (1/200) and 2c (1/201/2), respectively, as well as three kinds of nonequivalent oxygen atoms (O1, O2, O3) all in general 4e (x, y, z) positions, and R cations are also in general 4e (x, y, z) sites. Due to the contrasting neutron scattering lengths of Ni and Mn atoms, we were able to determine the degree of long-range ordering between them by NPD. We observed Ni/Mn ordering of 90.2(1)% for the Tb compound, 88.2(1)% for Ho, 88.0(2)% for Er, and 92.4(2)% for Tm. We B


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have also refined the occupancy factors for oxygen atoms showing no oxygen vacancies in any of the samples within the standard deviations. The final atomic coordinates, unit-cell parameters, and the reliability factors from the refinements at room temperature (RT) are given in Table 1. The monoclinic β angle decreases with the size of the rare-earth cation. Figure 2 shows the good agreement between observed and calculated NPD profiles for R2NiMnO6 (R = Tb, Ho, Er, Tm) perovskites. Table 2 contains some selected bond distances and angles. Figure 3 shows the evolution of the unit-cell parameters and volume with the R3+ size. A monotonic increase of the parameters and volume occurs as the size of the rare-earth ion increases from Tm to Tb. Figure 4a displays the evolution of the mean R−O distances, and Figure 4b shows the variation of ⟨Ni−O⟩ and ⟨Mn−O⟩ distances (listed in Table 3). In terms of distances, the reduction in size of the rare-earth ion mainly affects the R−O distance. Magnetic Measurements. Figure 5a plots the susceptibility versus temperature curves for R2NiMnO6 (R = Tb, Ho, Er, Tm). The curves display, in all cases, a sharp increase

Figure 1. XRD patterns of R2NiMnO6 (R = Tb, Ho, Er, Tm) collected with Cu Kα radiation. All the peaks can be indexed in a monoclinic unit cell with space group P21/n.

Table 1. Unit-Cell, Positional, and Thermal Parameters and Reliability Factors for the Refinements of R2NiMnO6 Phases (R = Tb, Ho, Er, Tm), in the Monoclinic P21/n Space Group, Z = 4, from NPD Data at 295 K R a (Å) b (Å) c (Å) β V (Å3) R x y z B (Å2) Ni focup Ni/Mn B (Å2) Mn focup Mn/Ni B (Å2) O1 x y z B (Å2) O2 x y z B (Å2) O3 x y z B (Å2) reliability factors χ2 Rp (%) Rwp (%) Rexp (%) RI (%)

Ho

Er

5.2689(1) 5.5424(1) 7.5271(2) 90.135(3) 219.81(1)

Tb

5.2183(1) 5.5445(1) 7.4811(2) 90.206(2) 216.449(9)

5.1998(2) 5.5393(2) 7.4620(3) 90.218(3) 214.93(1)

5.1852(2) 5.5311(2) 7.4439(2) 90.294(2) 213.49(1)

Tm

0.9847(4) 0.0673(3) 0.2508(4) 0.60(4)

0.9831(4) 0.0695(3) 0.2510(3) 0.22(4)

0.9824(5) 0.071(4) 0.2504(4) 0.47(5)

0.9799(5) 0.717(4) 0.2519(4) 0.43(6)

0.902(1)/0.098(1) 0.80(6)

0.882(1)/0.118(1) 0.82(6)

0.880(2)/0.120(2) 1.50(9)

0.924(2)/0.076(2) 0.96(7)

0.902(1)/0.098(1) 0.9(2)

0.882(1)/0.118(1) 0.3(2)

0.880(2)/0.120(2) 0.2(3)

0.924(2)/0.076(2) 0.3(2)

0.0972(5) 0.4683(4) 0.2415(4) 0.78(5)

0.1051(5) 0.4666(5) 0.2439(4) 0.64(6)

0.1074(6) 0.4630(6) 0.2429(5) 0.97(9)

0.1105(5) 0.4590(5) 0.2412(4) 0.39(7)

0.7056(5) 0.3077(6) 0.0484(4) 0.73(7)

0.7045(6) 0.3108(6) 0.0506(4) 0.66(7)

0.7012(7) 0.3123(8) 0.0512(5) 0.89(9)

0.6997(6) 0.3121(6) 0.0529(4) 0.30(8)

0.1847(6) 0.2070(6) 0.9484(5) 1.01(8)

0.1812(6) 0.2059(6) 0.9455(5) 0.91(7)

0.1789(8) 0.2057(7) 0.9446(6) 0.99(9)

0.1778(6) 0.208(6) 0.9413(5) 0.51(8)

1.62 3.13 4.06 3.19 4.39

1.47 2.93 3.77 3.11 4.00

0.95 2.92 3.65 3.74 3.50

1.41 3.28 4.23 3.56 3.92

4e (xyz)

2d (1/200)

2c (1/201/2)

4e (xyz)

4e (xyz)

4e (xyz)

C


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Inorganic Chemistry

temperatures, and we have considered the Curie−Weiss law only between 200 and 300 K. The results obtained for the Weiss constant θWeiss and the paramagnetic effective moment μeff are listed in Table 4. All the paramagnetic temperatures are positive, which suggests that the predominant exchange interactions are ferromagnetic. The values of θWeiss are smaller than the magnetic ordering temperatures (TCM), obtained from magnetic measurements, but their evolutions are similar, increasing with the rare-earth size. The theoretical effective magnetic moments have been determined using the following equation: μeff(calc) = [2μB(R3+)2 + μB(Ni2+)2 + μB(Mn4+)2]1/2. The effective paramagnetic moments in the ground state are 9.5 μB for Tb3+, 10.4 μB for Ho3+, 9.5 μB for Er3+, 7.3 μB for Tm3+, 3.87 μB for Mn4+, and 2.83 μB for Ni2+. The values of the theoretical moments are also listed in Table 4. In all the compounds the experimental effective magnetic moments are comparable to the calculated ones. The isothermal magnetization curves measured at T = 5 K for R2NiMnO6 (R = Tb, Ho, Er, Tm) are displayed in Figure 5b. The magnetization curves present hysteresis loops characteristic of ferromagnetic behavior. They do not reach saturation even at the highest magnetic field. The values of the saturation magnetizations at 5 T are presented in Table 4, corresponding to the magnetic structures described below, where both the transition-metal spins and the rare-earth moments contribute at 5 K. Magnetic Structure Determination. The resolution of the magnetic structures of R2NiMnO6 (R = Tb, Ho, Er, Tm) and the study of their thermal evolutions have been carried out from a set of neutron powder diffraction patterns, sequentially collected below the ordering temperature with a wavelength of λ = 2.52 Å. The NPD patterns were acquired in the temperature intervals 2 < T < 147 K for R = Er, Ho and 2 < T < 87 K for R = Tb, Tm. As an example, Figure 6 shows the thermal variation of the NPD patterns collected for Er2NiMnO6. The evolution of Tb, Ho, and Tm NPD patterns is illustrated in the Supporting Information, Figure S1a−c. Upon cooling below TCM an enhancement of the integrated intensities of some Bragg reflections is observed, which reveals the appearance of magnetic ordering. This can be observed in Figure S2, in which the thermal evolution of some selected Bragg peaks is shown. According to the figure, TCM would be around 85, 80, and 64 K for R = Ho, Er, and Tm, respectively. This result is in good agreement with the TCM’s obtained from the ordered magnetic measurements. For Tb2NiMnO6, the ordering temperature is around 110 K, and the NPD patterns have been obtained below 87 K, where the compound is already magnetically ordered; thus, it was not possible to determine TCM by NPD. Er2NiMnO6 and Ho2NiMnO6 show an important increase in the intensity of some magnetic reflections below 15 and 22 K, respectively (see Figure S2). As it will be shown in the resolution of the magnetic structure, it is associated with an increase of the magnetic moment in the Er3+ and Ho3+ sublattices. Let us point out that, for Tb2NiMnO6, new magnetic peaks appear below T = 6.5 K. As it will be shown, these new magnetic peaks are associated with a spin reorientation of the Tb3+ sublattice. For all the compounds, the magnetic peaks appear at the same positions as the nuclear Bragg reflections, so the magnetic structure is defined by the propagation vector k = 0. The possible magnetic structures compatible with the monoclinic space group P21/n and associated with the propagation vector k

Figure 2. Comparison of the observed (+), calculated (solid line), and difference (at the bottom) NPD patterns at room temperature, collected at the high resolution D1A-ILL diffractometer (λ = 1.91 Å). The tick marks correspond to the position of the allowed Bragg reflections.

characteristic of the spontaneous ferromagnetic ordering below TCM around 100 K. TCM increases with the size of the rare-earth ion, as is shown in the lower inset of Figure 5a. At low temperatures, another magnetization anomaly is observed, due to the magnetic contribution of the rare earths. In the case of Tb2NiMnO6 the susceptibility increases below ∼60 K and reaches a plateau at very low temperatures. In the case of Er2NiMnO6, the curve has a maximum around 40 K and then abruptly decreases. The same behavior is presented by Ho2NiMnO6 and Tm2NiMnO6 samples where a fair decrease of the susceptibility happens around 20 K. All the samples present thermomagnetic irreversibilities between the zero-field cooling (ZFC) and field cooling (FC) curves. As an example, both curves for Ho2NiMnO6 are shown in the upper inset of Figure 5a. This divergence suggests the competition between different magnetic interactions or spin geometric frustrations. In all the cases Mn and Ni spins order in the (a,c) plane but with different orientations, in noncollinear magnetic structures; thus, it is expected that both spins are frustrated within this plane even above the magnetic ordering temperature of the rare earth, which could even enhance more this frustration. A similar frustration effect has been shown in other perovskites as Sr2NiReO6.37 Above the magnetic ordering temperature the reciprocal susceptibilities of the samples present a linear behavior. Only in the case of Ho2NiMnO6 the linearity disappears at high D


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Inorganic Chemistry

Table 2. Main Bond Distances (Å) and Selected Angles (deg) for Monoclinic R2NiMnO6 (R = Tb, Ho, Er, Tm), Determined from NPD at 295 K R

Tb

Ni−O1 (×2) Ni−O2 (×2) Ni−O3 (×2) ⟨Ni−O⟩ Δd × 104

2.021(3) 2.052(3) 2.056(3) 2.043(3) 0.59

Mn−O1 (×2) Mn−O2 (×2) Mn−O3 (×2) ⟨Mn−O⟩ Δd × 104 Ni−O1−Mn Ni−O2−Mn Ni−O3−Mn

1.896(3) 1.918(3) 1.933(3) 1.916(3) 0.63 147.9(1) 148.8(1) 146.9(1)

R−O1 R−O1 R−O1 R−O2 R−O2 R−O2 R−O3 R−O3 R−O3 ⟨R−O⟩short ⟨R−O⟩

2.301(3) 3.115(3) 2.271(3) 2.500(4) 2.317(4) 2.615(4) 2.627(5) 2.313(4) 2.508(4) 2.432(4) 2.507(4)

R Ni1 Mn1 O1 O2 O3

+2.905(11) +2.099(7) +3.872(17) −2.053(8) −1.928(8) −1.893(9)

Ho

Er

NiO6 Octahedra 2.003(3) 2.061(3) 2.057(3) 2.040(3) 1.68 MnO6 Octahedra 1.912(3) 1.904(3) 1.929(3) 1.915(3) 0.30 145.6(1) 147.5(1) 145.5(1) RO9 Polyhedra 2.293(3) 3.122(3) 2.224(3) 2.477(4) 2.287(4) 2.604(4) 2.623(4) 2.284(4) 2.483(4) 2.409(4) 2.488(4) BVS +3.051(11) +2.116(7) +3.871(13) −2.103(9) −1.985(8) −1.934(9)

Tm

2.011(4) 2.057(4) 2.062(4) 2.043(4) 1.26

2.025(3) 2.050(3) 2.057(3) 2.044(3) 0.45

1.906(4) 1.909(4) 1.923(4) 1.913(4) 0.15 144.6(2) 146.6(2) 144.8(2)

1.895(3) 1.915(3) 1.936(3) 1.915(3) 0.76 143.3(1) 145.9(1) 143.3(1)

2.267(4) 3.125(4) 2.216(4) 2.473(5) 2.274(5) 2.594(5) 2.612(5) 2.272(5) 2.477(5) 2.398(5) 2.479(5)

2.24884) 3.125(4) 2.213(4) 2.460(4) 2.249(4) 2.590(4) 2.636(5) 2.243(4) 2.454(4) 2.387(4) 2.469(5)

+2.85(1) +2.100(9) +3.899(17) −2.05(1) −1.91(1) −1.87(1)

+3.067(12) +2.092(7) +3.872(13) −2.115(9) −1.987(9) −1.934(9)

Figure 3. Variation of unit-cell parameters and volume with the R3+ ionic radii. Data for R = La, Nd, and Sm have been taken for comparison from refs 20, 25, and 34, respectively.

= 0 have been deduced by following the representation analysis technique of the group theory described by Bertaut.38 The irreducible representations of the small group, Gk, that coincides with the space group P21/n for k = 0, and the corresponding basis vectors for the Mn4+, Ni2+, and R3+ sublattices have been generated with the help of the program Basireps included in Fullprof.36 The irreducible representations

Figure 4. Evolution of the bond lengths along the R2NiMnO6 series. Data for R = La, Nd, and Sm have been taken for comparison from refs 20, 25, and 34, respectively.

E


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Inorganic Chemistry

Table 3. Mean Tilting Angles of NiO6 Octahedra (deg), Mean Ni/Mn−O and R−O Distances (Å), Tolerance Factors (t), and Unit-Cell Volumes (Å3) for R2NiMnO6 Perovskites R

⟨φ⟩

⟨Ni−O⟩

⟨Mn−O⟩

⟨R−O⟩

t

V

Tb Ho Er Tm

16.1 16.9 17.3 17.9

2.043(3) 2.040(3) 2.043(4) 2.044(3)

1.916(3) 1.915(3) 1.913(4) 1.915(3)

2.432(4) 2.409(4) 2.398(5) 2.387(4)

0.869 0.861 0.857 0.852

219.81(1) 216.449(9) 214.93(1) 213.49(1)

Figure 6. Thermal evolution of NPD patterns collected for Er2NiMnO6 at D1B-ILL diffractometer.

Table 5. Irreducible Representations of the Small Group Gk for k = 0 in Kovalev’s Notation Γ Γ2 Γ3 Γ4 1

Figure 5. (a) Temperature dependence of the dc susceptibility for R2NiMnO6 (R = Tb, Ho, Er, Tm). Upper inset: Field cooling (FC) and zero field cooling (ZFC) curves for Ho2NiMnO6. Lower inset: Evolution of the magnetic ordering temperature with R3+ ionic radii. (b) Magnetization vs magnetic field isotherms at T = 5 K for R2NiMnO6 (R = Tb, Ho, Er, Tm).

h1

h2/(1/2, 1/2, 1/2)

h25

h27/(1/2, 1/2, 1/2)

1 1 1 1

1 1 −1 −1

1 −1 1 −1

1 −1 −1 1

features, although in all cases R3+, Mn4+, and Ni2+ sublattices simultaneously order below TCM. Figure 7 shows the variation of the magnetic moments for Er2NiMnO6. The spins are defined on the (a, c) plane for the Mn4+ and Ni2+ sublattices and along the c-axis for the Er3+ moments. We define Θ (deg) as the angle between the magnetic moment on the (a, c) plane and the a-axis direction. According to the inset of Figure 7a, for Mn4+ spins the angle with the a-axis remains nearly constant down to 2 K; however, for the Ni2+ spins (inset of Figure 7b), there is a spin reorientation on the (a,c) plane, finally lying along the a-axis below 25 K. As regarding the Er3+ sublattice, as it is shown in Figure 7c, the magnetic moment begins to increase below 15 K, reaching a magnitude of 5.07(9) μB at 2 K. For Ho2NiMnO6, Figure 8a,b shows that the Mn4+ and Ni2+ spins are also defined on the (a,c) plane, with the Mn4+ spin

are given in Table 5 and the basis vectors in Table 6. For Table 6, the Mn atoms at the 2c site are denoted as 1 (0, 1/2, 0) and 2 (1/2, 0, 1/2), the Ni atoms at the 2d site are labeled as 3 (1/2, 0, 0) and 4 (0, 1/2, 1/2) and the notation for the rare-earth atoms, R, at the 4e site are 5 (x, y, z), 6 (−x + 1/2, y + 1/2, −z + 1/2), 7 (−x, −y, −z), and 8 (x + 1/2, −y + 1/2, z + 1/2). After checking the different solutions given in Table 6, for all the compounds the best agreement with the experimental data is obtained if the magnetic structure is given by the basis vectors associated with Γ3. Nevertheless, it is remarkable that the magnetic structure of each compound presents different

Table 4. Magnetic Parameters for R2NiMnO6 from the Magnetic Susceptibility Dataa Tb2NiMnO6 Ho2NiMnO6 Er2NiMnO6 Tm2NiMnO6 a

MS (μB/fu)

TCM (K)

θWeiss (K)

μeff (μB/fu)

μcalc (μB/fu)

14.2 13.5 12.6 9.0

114 85 74 62

64.515(1) 31.035(2) 25.33(3) 23.99(1)

13.536(4) 14.700(6) 16.281(9) 11.351(4)

14.26 15.47 14.26 11.38

The TCM is obtained from the derivative of the field-cooled curve and MS from the saturation of the hysteresis curve. F


Article

Inorganic Chemistry Table 6. Basis Vectors of the Sublattices Mn4+ (2c), Ni2+ (2d), and R3+ (4e) Mn4+ (2c) Γ1 Γ2 Γ3 Γ4

Ni2+ (2d)

R3+ (4e)

1

2

3

4

(u, v, w)

(u,̅ v, w̅ )

(u, v, w)

(r, s, t)

5

(u, v, w)

(u, v,̅ w)

(r, s, t)

(r, s,̅ t)

(o, (o, (o, (o,

p, p, p, p,

6 q) q) q) q)

(o,̅ (o,̅ (o, (o,

p, p, p,̅ p,̅

7 q)̅ q)̅ q) q)

(o, (o,̅ (o, (o,̅

p, p,̅ p, p,̅

8 q) q)̅ q) q)̅

(o,̅ (o, (o, (o,̅

p, p,̅ p,̅ p,

q)̅ q) q) q)̅

Figure 7. Thermal evolution of the ordered magnetic moment of the (a) Mn4+ sublattice, (b) Ni2+ sublattice, and (c) Er3+ sublattice in Er2NiMnO6. Insets in parts a and b show the thermal evolution of the angle of the magnetic moment with the a-axis.

Figure 8. Thermal evolution of the ordered magnetic moment of the (a) Mn4+ sublattice, (b) Ni2+ sublattice, and (c) Ho3+ sublattice in Ho2NiMnO6. Insets in parts a and b show the thermal evolution of the angle of the magnetic moment with the a-axis.

nearly parallel to the c-axis. As in Er2NiMnO6, the coupling between the components for Mn4+ and Ni2+ spins along the caxis is antiferromagnetic. Concerning the Ho3+ sublattice, as it is shown in Figure S3, the magnetic moment is initially on the (a, c) plane, but below ∼22 K, on decreasing the temperature, a component of the magnetic moment along the b-axis appears (Figure S3b), in good agreement with the notable increase of the magnetic moment of the Ho3+ sublattice, as is shown in Figure 8c. Regarding Tm2NiMnO6 (Figure S4), the Mn4+ moment is initially parallel to the c-axis, but at around 60 K there is a spin reorientation and at ∼20 K Mn4+ spins lie along the a-axis (Figure S4a). For the Ni2+ and Tm3+ sublattices (Figure S4b,c), the magnetic moments are oriented along the c-axis, and the coupling between both moments is antiferromagnetic. Another interesting feature is that Tm3+ moments do not undergo an important change in its magnitude at low temperature in contrast with Er3+ and Ho3+ perovskites. The case of Tb2NiMnO6 is singular: between TCM and 6.5 K, it presents a commensurate magnetic order arrangement similar to that of the other members of the family, defined by a propagation vector k = 0, but below 6.5 K, new magnetic peaks

appear, associated with an incommensurate propagation vector k = (0, 0.11, 0.04). This behavior is often observed in Tbcontaining compounds, prone to adopt helicoidal structures at very low temperatures.39 As it is shown in Figure S5a, Mn4+ spins lie on the (a, c) plane in the entire temperature range (inset of Figure S5a). As regarding Ni2+ and Tb3+ sublattices (Figure S5b,c), the magnetic moments are directed along the caxis, but antiferromagnetically coupled. The magnetic moments and the reliability factors obtained from the fitting at T = 2 K for R = Er, Ho, and Tm and T = 10.3 K for Tb sample are presented in Table 7. The good agreement between calculated and observed NPD patterns is shown in Figure 9. A plot of the magnetic structures is depicted in Figure 10 for the commensurate structures.

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DISCUSSION As has been reported for other similar double perovskites such as La2NiMnO617 and Nd2NiMnO6,25 the present perovskites crystallize in a B-ordered network with a pseudocubic structure (monoclinic P21/n space group) in which NiO6 and MnO6 octahedra are long-range ordered in a rock-salt configuration. The oxidation state of Ni and Mn in La2NiMnO6 has been G


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Table 7. Magnetic Moments and Reliability Factors for R2NiMnO6 Obtained in the Fitting of the NPD Pattern at T = 2 K (R = Ho, Er, Tm) and T = 10.3 K (R = Tb) R3+

Tb3+

Ho3+

Er3+

Tm3+

R mx, my, mz (μB) R3+ |m| (μB) Mn4+ mx, my, mz (μB) Mn4+ |m| (μB) Ni2+ mx, my, mz (μB) Ni2+ |m| (μB) RBragg (%) RMagn (%) χ2

0, 0, 2.31(9) 2.31(9) 1.5(3), 0, 2.1(1) 2.6(2) 0, 0, −1.1(3) 1.1(3) 7.0 8.5 2.5

3.1(1), 4.40(7), 1.7(2) 5.63(9) −0.3(3), 0, −2.2(4) 2.3(4) 1.1(4), 0, 1.1(3) 1.6(3) 4.1 6.8 6.4

0, 0, 5.07(9) 5.07(9) 0.7(7), 0, −2.8(5) 2.9(6) 2.2(7), 0, −0.0(5) 2.2(7) 3.9 4.1 3.4

0, 0, 1.83(10) 1.83(10) −2.6(2), 0, −0.1(2) 2.6(2) 0, 0, −1.7(3) 1.7(3) 6.6 7.9 1.7

3+

Figure 10. View of the low temperature magnetic structure of (a) Tb 2 NiMnO 6 , (b) Ho 2 NiMnO 6 , (c) Er 2 NiMnO 6 , and (d) Tm2NiMnO6.

for the ordering, but also for the attractive physical properties of this compound. We have performed NPD at RT to determine the structural parameters of R2NiMnO6: the positions, distances, and angles. Figure 3 depicts the evolution of the unit-cell dimensions and volume with the ionic R3+ size, taken from Shannon for 8-fold oxygen coordination.42 Although all the cell parameters increase with the size of the rare-earth ion, the variation of the b parameter is smaller compared to that of a and c; it is due to the tilting scheme of NiO6 and MnO6 octahedra in P21/n perovskites, of the type a−a−c+ in Glazer’s nomenclature,43 in which the distortion driven by the reduction of the R3+ size leaves b almost unchanged.44 The observed increase in unit-cell volume scales with the R3+ size. It is worth mentioning that, in all cases, c/√2 lies between a and b. This is characteristic of the so-called O structure and constitutes the usual situation in perovskites where the primary distorting effect is steric, driven by the reduction in size of R3+ cations. The β angle diverges from 90° as the size of R decreases (Table 1), indicating the lower pseudocubic character of the cell, as the distortion of the perovskite structure increases. As is expected, the ⟨R−O⟩ distance decreases with the size of the rare-earth ion. However, the average ⟨Ni−O⟩ and ⟨Mn−O⟩

Figure 9. Comparison of the observed (+) and calculated (solid line) NPD patterns after the fitting at low temperature for (a) Tb2NiMnO6, (b) Ho2NiMnO6, (c) Er2NiMnO6, and (d) Tm2NiMnO6, collected at the D1B-ILL diffractometer (λ = 2.52 Å). The first series of vertical lines corresponds to the nuclear Bragg peaks and the second one to the magnetic reflections. The continuous line below the reflections corresponds to the difference between the observed and calculated patterns.

widely studied, since it could be Ni3+/Mn3+ or Ni2+/Mn4+. The rock-salt ordering between Ni3+ and Mn3+ would be derived from the Jahn−Teller character of Mn3+, while Ni2+/Mn4+ order would be due to charge ordering. Different studies using NMR and X-ray absorption spectroscopy26,40,41 reveal that the actual oxidation states of the transition metals are Ni2+ and Mn4+, and this charge ordering would be responsible not only H


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Inorganic Chemistry

theoretical saturation magnetizations of about 24 μB/fu for Tb2NiMnO6, 26 μB/fu for Ho2NiMnO6, 24 μB/fu for Er2NiMnO6, and 20 μB/fu for Tm2NiMnO6. Those values are in all cases much higher than the experimental ones. In fact, our studies of the magnetic structure show that in all cases we are not in the presence of collinear arrangements but heavily canted structures regarding the transition-metal spins, and the rare-earth moments are not fully developed at low temperature (Figure 10), exhibiting values much smaller than expected. The magnetic ordering temperature (TCM) remarkably depends on the nature of the rare-earth ion; similar TCM values have been recently reported for R2NiMnO6 perovskite growth as thin films.34 TCM values monotonically decrease with the size of R3+ (inset Figure 5a), and the octahedral tilting increases. Therefore, TCM is mainly influenced by the superexchange interaction between Ni2+ and Mn4+, which means that the decrease of TCM is not directly related to the magnetic interactions involving rare earths. Since Ni−O and Mn−O bond lengths do not significantly evolve along the series, the ⟨Ni−O−Mn⟩ angle (Table 2) is responsible for the evolution of TCM. However, since the variation of TCM is better fitted to the evolution of the rare-earth size than to the evolution of the Ni−O−Mn angle, it seems that there is something else that affects TCM. NMR hyperfine magnetic field studies28 have suggested that the decrease of the covalency of Ni−O and Mn−O bonds as the size of the rare earth decreases is also a responsibility of the decrease of the magnetic ordering temperature, TCM. Regarding the magnetic structures of R2NiMnO6 determined by NPD (Figure 10), it is remarkable that, while La2NiMnO6 presents a collinear ferromagnetic structure concerning Mn4+ and Ni2+ spins,19 in R2NiMnO6 (R= Tb, Ho, Er, Tm) there is a canted arrangement of Mn4+ and Ni2+ spins, giving rise to a net ferrimagnetic structure. This different alignment of the spins can be explained taking into account the Goodenough− Kanamori rules. The direct superexchange interaction in octahedral sites via half-filled eg orbitals and empty eg orbitals is ferromagnetic via 180° Ni2+(d8)−O−Mn4+(d3) paths, and the sign of the interaction changes from ferromagnetic to antiferromagnetic as the angle becomes closer to 90°.13 Therefore, as the size of the rare-earth ion decreases, the angle also decreases, and therefore, the interactions evolve from ferro- to antiferromagnetic, adopting an intermediate state in the present cases. It could also explain in some way the decrease of the TCM, since the magnetic interactions between perfectly parallel or antiparallel moments through oxygen atoms are stronger than between cations with the spins in different directions. Indeed, it could explain why the reduction of TCM is so large for all our compounds compared to the La sample, although it is comparable among them. The magnetic moments obtained by NPD for Mn4+ and Ni2+ positions fit very well with the theoretical values of 3.0 μB and 2.0 μB expected for Mn4+ and Ni2+ cations for R = Er (see Table 7) as also found for La2NiMnO6 and Nd2NiMnO6.19,25 However, they adopt lower values for the remaining rareearth perovskites, indicating that the long-range ordering is more perfectly reached for R2NiMnO6, R= La, Nd, Er, and there are different degrees of frustration for R = Tb, Ho, and Tm. The rare-earth moments are significantly smaller than those expected for a full long-range magnetic ordering, which is consistent with the divergence between ZFC and FC curves indicating some magnetic frustration or partial cluster-glass behavior as commented before.

values do not significantly evolve with this size (Figure 4); for instance, ⟨Ni−O⟩ spans from 2.040 Å for Ho to 2.043 Å for R = Tm. Nevertheless, if we compare with the end member of the series, for the perovskite with the largest rare-earth ion La2NiMnO645 a difference concerning ⟨Ni−O⟩ and ⟨Mn−O⟩ is observed. The Ni−O and Mn−O mean distances are 2.026 and 1.921 Å for La2NiMnO6; when a smaller R cation is introduced (Table 2), ⟨Ni−O⟩ distances are substantially higher whereas ⟨Mn−O⟩ distances are smaller. This suggests a higher charge difference between Ni and Mn cations: it would seem that smaller rare earths are more effective in stabilizing the charge disproportionation between Ni2+ and Mn4+, as happens in the perovskite series RNiO3, where disproportionation of Ni3+δ and Ni3‑δ is observed below the characteristic metal−insulator transitions,9 with δ being larger for the heavier lanthanides.46 An appealing piece of information concerning the oxidation states of Ni and Mn elements was determined by bond-valence calculations using the Brown’s model, where the valences are calculated as si = exp[(r0 − ri)/B], where B = 0.37, and r0 = 1.654 Å for the Ni−O pair, r0 = 1.753 Å for Mn−O, r0 = 2.032 Å for Tb−O, r0 = 2.025 Å for Ho−O, r0= 1.988 Å for Er−O, and r0= 2.000 Å for Tm−O from Brese et al.47 Individual average R−O, Ni−O, and Mn−O distances (ri) are taken from Table 2; determined BVS values are also included in this table. As expected, Ni1 is divalent, and Mn1 is tetravalent for all the compounds, accounting for the long-distance ordering observed between such cations in the monoclinic lattice. There is no clear trend in the evolution of the Ni and/or Mn valences along the series. The small deviations found in the oxidation states could be related to the small degree of disorder between Ni and Mn. In order to quantify the relative distortion of the octahedra we define the Δd⟨M−O⟩ parameter, concerning the deviation of M−O distances with respect to the average ⟨M−O⟩ value, as Δd⟨M−O⟩= (1/3)∑n=1,3[(dn − ⟨d⟩)/⟨d⟩]2 for Ni−O and Mn−O distances (Table 2). This is particularly interesting for MnO6 octahedra, where a significant amount of Mn3+ would lead to a conspicuous distortion. For La2NiMnO6, Δd⟨Mn−O⟩= 3.7 × 10−5, which is comparable to the values obtained for the rest of the rare earths (6.0 × 10−5 for Tb, 3.0 × 10−5 for Ho, 1.5 × 10−5 for Er, and 7.6 × 10−5 for Tm) indicating a negligible Mn octahedral distortion. In all cases, the distortion parameter is much smaller than those observed in other perovskite series like RMnO3, where the Jahn−Teller character of Mn3+ originates a dramatic electronic-driven distortion; for instance, Δd = 49.7 × 10−4 for DyMnO3 at room temperature.48 Therefore, this parameter points out a Mn4+ oxidation state for the Mn cations in R2NiMnO6 (R = Tb, Ho, Er, Tm). The Ni−O−Mn tilting angle between the octahedra can be obtained from the ⟨Ni−O−Mn⟩ bond angles as φ = 180 − ⟨Ni−O−Mn⟩/2. A progressive increase of the tilting angle is observed as the R3+ size decreases, from φ = 16.1° for R= Tb, to φ = 16.9° for Ho, to φ = 17.3° for Er, to φ = 17.9° for Tm (Table 3). This evolution also suggests that the increase of the distortion of the cell, as β progressively deviates from 90°, is primarily driven by the tilting of the octahedra. The decrease of φ is a general characteristic of the RMO3 perovskites.49 Regarding the magnetic properties, Table 4 shows the saturation magnetization measured at 5 T for R2NiMnO6 (R= Tb, Ho, Er, Tm). A hypothetical collinear structure where all the Ni2+ (S = 2/2) and Mn4+ (S = 3/2) spins and the rare-earth magnetic moments were ferromagnetically coupled would give I


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Inorganic Chemistry

grateful to the Institut Laue-Langevin for making all facilities available.

Surprisingly, theoretical calculations predicted an antiferromagnetic coupling between Mn and Ni cations for the R2NiMnO6 perovskite series.31 Our experimental work reporting the magnetic structures of R2NiMnO6 for the strongly paramagnetic rare-earth cations unveils that there is, indeed, an antiferromagnetic component in the canted magnetic structures, but the most significant features, including the presence of substantial ferromagnetic interactions (as already anticipated by the positive θWeiss figures), were not taken into account. The possibility that the full antiferromagnetic alignment between Mn and Ni cations would produce a rupture of the inversion symmetry generating a multiferroic compound has not been realized. This is not the case for ferrimagnetic R2NiMnO6 (R = Tb, Ho, Er, Tm); however, a further study of the magnetic structure of the rest of the R2NiMnO6 members is still a pending issue.

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CONCLUSIONS We have synthesized the series of double perovskites R2MnNiO6 (R = Tb, Ho, Er, Tm) with almost a full longrange structural order between Ni2+ and Mn4+ cations. The samples crystallize in a monoclinic P21/n structure. The cell parameters, volume, and superexchange angles decrease with the size of the rare-earth ions. The magnetic properties are also strongly influenced by the nature of R3+, observing a reduction of the ferrimagnetic ordering temperature as the rare earth decreases in size and also changing the magnetic interactions. It has been found that, while La2NiMnO6 presents a collinear ferromagnetic structure with Mn4+ and Ni2+ moments aligned parallel, the magnetic structures for R = Tb, Ho, Er, Tm are strongly canted, resulting in a net ferrimagnetic structure. This different alignment of the spins can be explained taking into account the Goodenough−Kanamori rules. We have also found that the magnetic moments of the rare earths participate in the magnetic structures at low temperature but are not fully longrange ordered, probably as a result of magnetic frustration.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.5b01951. Thermal evolution of NPD patterns for R2NiMnO6 (R = Tb, Ho and Tm) and thermal evolution of the magnetic moments for R2NiMnO6 (R = Tb, Ho, Er, and Tm) from NPD (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness through the projects MAT2013-41099-R and CSD2007-00045 and funding of the Universidad Complutense de Madrid and Banco Santander through the project UCM2014-971703. J.S.-B. acknowledges receipt of a Ramón y Cajal Fellowship (RyC-2010-06276) from the Spanish Ministry of Economy and Competitiveness. We are J


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