Non-collinear magnetic structure of manganese quadruple perovskite CdMn₇O₁₂

Abstract

We report on the magnetic structure of CdMn₇O₁₂ determined by powder neutron diffraction. We were able to measure the magnetic structure of this Cd containing and highly neutron absorbing material by optimizing the sample geometry and by blending the CdMn₇O₁₂ with Aluminum powder. Below its Néel temperature T_N1 all magnetic reflections can be indexed by a single commensurate propagation vector k = (0, 0, 1). This is different to the case of CaMn₇O₁₂ where the propagation vector is incommensurate and where an in-plane helical magnetic structure has been found. We observe a commensurate non-collinear magnetic structure in CdMn₇O₁₂ with in-plane aligned magnetic moments resembling the ones in CaMn₇O₁₂. However, the commensurate propagation vector prevents the appearance of a helical magnetic structure in CdMn₇O₁₂. Finally, we also observe a third structural phase transition below ~60 K that can be attributed to phase separation.

Introduction

The coexistence of ferroelectricity (FE) and magnetic ordering in multiferroic materials has attracted enormous attention in the past¹. Especially the magnetoelectric coupling in these materials is of interest for possible technical applications. Multiferroics with spin induced ferroelectric properties seem to have the highest potential for sizeable magnetoelectric effects. Several possible mechanisms are able to induce FE by magnetic ordering, e.g. the inverse Dzyaloshinskii-Moriya interaction², the exchange striction³ or the spin current⁴ and d − p hybridization effect^5,6. The electric polarization ( P ) in these materials is, however, usually smaller than in conventional ferroelectrics and the magnetic transition temperature not very high⁷. Hence, the observation of a comparably large P of 2870 μC/m² in single crystalline CaMn₇O₁₂ has generated intense interest in this series of manganites^{8,9,10,11,12,13,14,15,16,17}.

Multiferroic CaMn₇O₁₂^8,14 belongs to the quadruple perovskite family with general formula ()B₄O₁₂. The A site is 12-fold coordinated and A′ site is square-coordinated, while the B site is octahedrally coordinated. The A′ site is occupied by Mn³⁺ ions and the B site by mixed valent Mn^3.25+ ions. Below ~440 K, CaMn₇O₁₂ undergoes a structural transition from cubic () to rhombohedral ()^18,19. The A′ ions are located at Wyckoff position 9e in space group , and the B site Mn³⁺ and Mn⁴⁺ ions are located at Wyckoff positions 9d and 3b. CaMn₇O₁₂ undergoes two successive magnetic transitions at T_N1 ~ 90 K and T_N2 ~ 48 K. In the temperature range T_N2 < T < T_N1 the magnetic structure is modulated along the c-direction with propagation vector k = (0, 0, 1.037)⁸. The magnetic structure below T_N2 becomes more complicated due to the appearance of multiple propagation vectors¹⁷.

Except for CaMn₇O₁₂, the other quadruple perovskite manganites have to be synthesized under high pressure and high temperature conditions rendering the sample availability more difficult. A recent study on its analogue, CdMn₇O₁₂, has shown similar physical properties¹¹. For example, CdMn₇O₁₂ also exhibits a structural transition at T_s1 ~ 493 K and two successive magnetic transitions at T_N1 = 88 K and T_N2 = 33 K. Moreover, the magnetic transition at T_N1 is robust against external magnetic fields, while T_N2 can be gradually suppressed with applied magnetic field. The crystal structure of CdMn₇O₁₂ at room temperature is trigonal (space group ). Around T_s2 ~ 254 K a commensurate structural modulation has been reported recently¹⁵.

In this paper, we report the magnetic structure of CdMn₇O₁₂ determined by powder neutron diffraction (PND). We focus on the temperature range T_N2 < T < T_N1, where the magnetic peaks can be indexed by a single propagation vector like in CaMn₇O₁₂. However, for CdMn₇O₁₂ the propagation vector amounts to k = (0, 0, 1) which is in contrast to CaMn₇O₁₂ where an incommensurate propagation vector along the c-direction has been observed. The magnetic structure of CdMn₇O₁₂ is non-collinear.

Results and Discussion

Figure 1 shows the Rietveld fit of the room temperature crystal structure measured both by PND and XRD (space group ). In Fig. 1(a), the few peaks of the Al powder did not interfere significantly with sample reflections and a reliable refinement of the crystal structure of CdMn₇O₁₂ could be obtained. The structural parameters are listed in Table 1. The refined volume fractions of Al and CdMn₇O₁₂ amount to 69.7(5)% and 30.3(2)% respectively.

Figure 1

Rietveld fit of the room-temperature crystal structure of CdMn₇O₁₂ measured by (a) powder neutron diffraction at the D2B diffractometer with wavelength λ = 1.59 Å and (b) x-ray powder diffraction with wavelength λ = 1.5406 Å.

Table 1 Atomic position of CdMn₇O₁₂ at room-temperature obtained from Rietveld refinement of the PND pattern measured at D2B.

Note, that indications for a structural transition  →  at T_s2~ 254 K have been reported recently¹⁵.

We performed temperature dependant powder X-ray diffraction experiments down to 12 K and were able to observe an additional structural transition at T_s3 ~ 60 K. Note, that there is a small anomaly at ~60 K in specific heat measurements at high magnetic fields of 9 T, whereas no obvious anomaly could be observed in zero field measurements¹¹. Our measurements are indicative for the occurrence of phase separation below T_s3 similar as observed in other transition metal oxides like SrCrO₃²⁰. Below T_s3, the intensity of the main peaks related to the phase decreases and additional peaks appear which belong to a lower symmetry phase, see Fig. 2. This would be consistent with a scenario where phase separation occurs below T_s3 and where only a certain volume fraction of the compound undergoes the structural transition (that might be enhanced by applying magnetic fields of 9 T). The origin of this structural transition requires further studies. Here, we focus mainly on the magnetic structure determination of CdMn₇O₁₂ slightly above or around T_s3.

Figure 2: Temperature dependence of the XRD patterns measured at 60 K, 50 K, 40 K, 30 K, 20 K and 12 K.

As can be seen, additional peaks appear below T_s3 ~ 60 K. These additional peaks are indicative for phase separation and can be attributed to a second phase appearing below T_s3. (The patterns are shifted for clarity).

We determined the lattice parameters of the and phases in the entire measured temperature range, see Fig. 3. The lattice parameters show an anisotropic thermal expansion. The a lattice constant decreases continuously with decreasing temperature until T_N2. A small kink can be observed at T_s2 while no obvious anomaly can be found at T_N1. Then, below T_N2, a starts to increase with decreasing temperature. On the other hand, the c lattice constant exhibits distinct anomalies at T_s2 and also at 100 K and 50 K. This behaviour is similar to the one in CaMn₇O₁₂²¹. The temperatures of 100 K and 50 K are somewhat higher than the magnetic transition temperatures T_N1 and T_N2, suggesting that the magnetic transitions follow the structural ones.

Figure 3

Temperature dependence of the lattice constant (space groups and) determined by x-ray powder diffraction.

We studied the crystal structure of CdMn₇O₁₂ at 40 K by means of powder neutron diffraction at the D2B diffractometer. The peak-splitting that has been observed in our high-resolution XRD measurements could not be resolved in our neutron measurements with less resolution. In Fig. 4(a) a refinement of the crystal structure with one single phase (space group ) is shown. For comparison, the pattern refined with space group is also shown in Fig. 4(b). The additional peaks indicated by the arrows cannot be described by space group . The structural parameters are listed in Table 2.

Figure 4: Rietveld fit of the powder neutron diffraction patterns measured at D2B diffractometer with wavelength λ = 1.59 Å at 40 K.

(a) The nuclear structure is refined in the high 2θ range with space group . (b) Comparison of the pattern refined by using the space group and . Arrows indicate the peaks which cannot be described by the space group .

Table 2 Atomic positions of CdMn₇O₁₂ at 40 K as obtained from Rietveld refinement of the PND pattern measured at the D2B diffractometer.

We next focus on the magnetic structure refinement. We have measured the magnetic structure of CdMn₇O₁₂ between 2 K and 120 K at the D1B diffractometer using an incident neutron wavelength of 2.52 Å. Only two peaks from the Aluminum powder appear in the entire diffraction pattern. Thus, the dilution with fine Aluminum powder does not cause any interference with magnetic reflections that appear below the Néel temperature of CdMn₇O₁₂. As can be seen in Fig. 5 all peaks that appear at low temperature and that can not be indexed with space group vanish at the Néel temperature of CdMn₇O₁₂. Hence, these reflections are magnetic in origin and can not be connected to the structural transition that takes place at 254 K. For T_N2 < T < T_N1 all magnetic peaks can be indexed with a single propagation vector k = (0, 0, 1), which is different from the incommensurate case in CaMn₇O₁₂. Below T_N2 the magnetic structure is more complicated and multiple propagation vectors are necessary for describing the magnetic structure. Here, we will focus on the magnetic structure for T_N2 < T < T_N1 only. Due to the structural transition from to , the three Mn sites split into six different sites below about 200 K. Instead of a refinement with that many independent magnetic moments and moment sizes we were also able to describe the magnetic neutron scattering intensities properly in a refinement based on irreducible representations for the high symmetry crystal structure which is similar to a refinement in with certain constraints to the moments. Since the structural distortions below the structural phase transition are negligible for the magnetic structure these constraints appear reasonable. Figure 6 shows the results of our refinements for temperatures of (a) 75 K and (b) 40 K.

Figure 5

Temperature dependence of magnetic peaks observed in our PND patterns (λ = 2.52 Å).

Figure 6: Rietveld refinement of the magnetic structure measured at the D1B diffractometer (λ = 2.52 Å).

The magnetic structure at (a) 75 K (above T_s3) and (b) 40 K (below T_s3) can be described both by the IR Γ₃. In (a), additionally, the 120 K data is shown as a reference. In (b) the two asterisks mark the nuclear peak positions that become broader and stronger due to the structural transition below T_s3. However, the overall magnetic peak intensities can be still described by IR Γ₃.

The magnetic reducible representation Γ of site 9e and 9d is decomposed into three irreducible representations (IRs) with dimension one, as

For site 3b, it is also decomposed into three IR with dimension one, as

The basis vectors (ψ_i) of the IRs are listed in Tables 3 and 4 for the 3b and for the 9e(9d) site respectively.

Table 3 Basis vectors of the irreducible representations of the space group for sites 3b with propagation vector k = (0, 0, 1).

Table 4 Basis vectors of the irreducible representations of the space group for sites 9e and 9d with propagation vector k = (0, 0, 1).

Since there are three different Mn sites in the unit cell, magnetic couplings between Mn ions at different sites require the Mn ions order according to the same IR in the first order approximation²². From Table 3, it can be seen that the IR Γ₁ constrains the magnetic moments at site 3b along the c-direction, while for IR Γ₂ and Γ₃, the real and imaginary components are perpendicular to each other with the same length, thus, giving rise to a non-collinear magnetic structure with moments that have the same size and that are aligned within the ab plane. Earlier PND studies on CaMn₇O₁₂ suggested a ferrimagnetic ordering with magnetic moments along the c-axis²³. However, the observation of the (0 0 2) peak at 2Θ ~ 47° is not indicative for this scenario based on IR Γ₁. Also if ab components of Mn ions at 9e and 9d sites are included for the refinement based on IR Γ₁ no satisfactory description of the measured data could be obtained. Since CdMn₇O₁₂ is a quite localized system, we also assume no modulations of the ordered moment sizes for the 9e and 9d sites. This can be realized by a linear combination of the basis vectors as follows:

Thus, the IR Γ₂ gives rise to a 120°-type noncollinear structure, while the magnetic moments are parallel to each other within the same layer for Γ₃. The former will lead to the extinction of the (0 0 l + k_z) reflection, which is not in agreement with our experimental observations (Fig. 6(a)). For these reasons the magnetic structure of CdMn₇O₁₂ can be described by the IR Γ₃. The refinable parameters are the amplitudes of the moments at three sites and the phases between them. In our refinements the phase difference between Mn1/Mn2 and Mn3 turned out to be always close to π. Therefore, we fixed the phase to this value and only the amplitude of the moments was, finally, refined. The best refinement is shown in Fig. 6(a). As can be seen, all magnetic reflections can be described in a satisfactory manner; the magnetic R factor amounts to 22.5%. The magnetic structure is plotted in Fig. 7. Within the same sublattice the moments are parallel to each other within the same layer (same value of z) and rotate by 2π/3 and 4π/3 when going from one layer to the next according to the centering translations (2/3, 1/3, 1/3) and (1/3, 2/3, 2/3) respectively. The net moment in the unit cell is zero, which is consistent with the magnetization measurements between T_N1 and T_N2, showing linear curve of M vs. H. The magnetic structure resembles the one of CaMn₇O₁₂^8,24. However, the magnetic structure of CaMn₇O₁₂ is incommensurate whereas the propagation vector is commensurate in the case of CdMn₇O₁₂.

Figure 7: Magnetic structure of CdMn₇O₁₂ (T_N2 < T < T_N1) projected along the c-direction. The red, green and blue arrows represent the magnetic moment of Mn1, Mn2 and Mn3 at the crystallographic 9e, 9d and 3b sites respectively.

The light and dark color represent Mn ions in different layers along the c-direction.

The temperature dependence of the ordered magnetic moments for the distinct Mn sites is shown in Fig. 8. Below TN1, the ordered moment size starts to increase. Then, at T_s3, the moments at the Mn1 site exhibit an anomalous decrease whereas the Mn2 and Mn3 sites continue their increase. Note, that the size of the magnetic moments of Mn³⁺ ions at the 9e (Mn1) and 9d (Mn2) sites (the 9e site is square coordinated, while the 9d site is octahedrally coordinated by O ions) is very similar for CaMn₇O₁₂ which is in contrast to the case of CdMn₇O₁₂.

Figure 8

Temperature dependence of the magnetic moments for the distinct Mn sites.

In summary, the magnetic structure of CdMn₇O₁₂ below its Néel temperature has been determined by PND. We observe a non-collinear magnetic structure with Mn spins that are aligned within the ab plane. The magnetic propagation vector is commensurate with k = (0, 0, 1) which prevents the occurrence of a helical structure. This is different to the case of CaMn₇O₁₂.

Methods

Polycrystalline samples of CdMn₇O₁₂ were synthesized by high pressure method as described elsewhere¹¹.

Powder neutron diffraction (PND) measurements were performed at the D1B and D2B diffractometers at the Institut Laue-Langevin (ILL), France with a neutron wave length λ of 2.52 Å and 1.59 Å respectively. In order to reduce the absorption of neutrons by Cd nuclei, the CdMn₇O₁₂ powder was mixed with larger amount of Al powder and filled into the outer space of a hollow vanadium cylinder. This technique that we initially developed for SmFeO₃²⁵ enabled us to obtain excellent and fully evaluable neutron data of this highly neutron absorbing material (irrespective of the chosen neutron wavelength ~2.5 Å or ~1.6 Å). The PND patterns were analyzed by the Rietveld method using the Fullprof software.

In addition, temperature dependent x-ray diffraction (XRD) measurements were also performed on a Bruker D8 Discover A25 diffractometer using Cu radiation. A closed cycle helium cryostat (Phenix of Oxford Cryosystems) was used for cooling the flat plate powder sample.