Non-collinear magnetic structure of manganese quadruple perovskite CdMn7O12

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 TN1 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.

The coexistence of ferroelectricity (FE) and magnetic ordering in multiferroic materials has attracted enormous attention in the past 1 . 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 interaction 2 , the exchange striction 3 or the spin current 4 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 high 7 . Hence, the observation of a comparably large P of 2870 μC/m 2 in single crystalline CaMn 7 O 12 has generated intense interest in this series of manganites [8][9][10][11][12][13][14][15][16][17] . Multiferroic CaMn 7 O 12 8,14 belongs to the quadruple perovskite family with general formula ( ′ AA 3 )B 4 O 12 . 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 Mn 3+ ions and the B site by mixed valent Mn 3.25+ ions. Below ~440 K, CaMn 7 O 12 undergoes a structural transition from cubic (Im3) to rhombohedral (R3) 18,19 . The A′ ions are located at Wyckoff position 9e in space group R3, and the B site Mn 3+ and Mn 4+ ions are located at Wyckoff positions 9d and 3b. CaMn 7 O 12 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 vectors 17 .
Except for CaMn 7 O 12 , 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, CdMn 7 O 12 , has shown similar physical properties 11 . For example, CdMn 7 O 12 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 CdMn 7 O 12 at room temperature is trigonal (space group R3). Around T s2 ~ 254 K a commensurate structural modulation → R P 3 3 has been reported recently 15 . In this paper, we report the magnetic structure of CdMn 7 O 12 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 CaMn 7 O 12 . However, for CdMn 7 O 12 the propagation vector amounts to k = (0, 0, 1) which is in contrast to CaMn 7 O 12 where an incommensurate propagation vector along the c-direction has been observed. The magnetic structure of CdMn 7 O 12 is non-collinear. Figure 1 shows the Rietveld fit of the room temperature crystal structure measured both by PND and XRD (space group R3). 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 CdMn 7 O 12 could be obtained. The structural parameters are listed in Table 1. The refined volume fractions of Al and CdMn 7 O 12 amount to 69.7(5)% and 30.3(2)% respectively.   15 . 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 measurements 11 . Our measurements are indicative for the occurrence of phase separation below T s3 similar as observed in other transition metal oxides like SrCrO 3 20 . Below T s3 , the intensity of the main peaks related to the P3 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 CdMn 7 O 12 slightly above or around T s3 .

Results and Discussion
We determined the lattice parameters of the R3 and P3 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 CaMn 7 O 12 21 . 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.  We studied the crystal structure of CdMn 7 O 12 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 P3) is shown. For comparison, the pattern refined with space group R3 is also shown in Fig. 4(b). The additional peaks indicated by the arrows cannot be described by space group R3. The structural parameters are listed in Table 2.
We next focus on the magnetic structure refinement. We have measured the magnetic structure of CdMn 7 O 12 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 CdMn 7 O 12 . As can be seen in Fig. 5 all peaks that appear at low temperature and that can not be indexed with space group R3 vanish at the Néel temperature of CdMn 7 O 12 . 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 CaMn 7 O 12 . 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 R3 to P3, 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 R3 which is similar to a refinement in P3 with certain constraints to the moments. Since the structural distortions below the structural phase transition → R P 3 3 are negligible for the magnetic Comparison of the pattern refined by using the space group R3 and P3. Arrows indicate the peaks which cannot be described by the space group R3.
Scientific RepoRts | 7:45939 | DOI: 10.1038/srep45939 structure these constraints appear reasonable. Figure 6 shows the results of our refinements for temperatures of (a) 75 K and (b) 40 K. 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. 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 approximation 22 . From Table 3, it can be seen that the IR Γ 1 constrains the magnetic moments at site 3b along the c-direction, while for IR Γ 2 and Γ 3 , 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 CaMn 7 O 12 suggested a ferrimagnetic ordering with magnetic moments along the c-axis 23 . However, the observation of the (0 0 2) peak at 2Θ ~ 47° is not indicative for this scenario based on IR Γ 1 . Also if ab components of Mn ions at 9e and 9d sites are included for the refinement based on IR Γ 1 no satisfactory description of the measured data could be obtained. Since CdMn 7 O 12 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: 1 2 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 Γ 3 . 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 Γ 3 . Table 3. Basis vectors of the irreducible representations of the space group R3 for sites 3b with propagation vector k = (0, 0, 1). Thus, the IR Γ 2 gives rise to a 120°-type noncollinear structure, while the magnetic moments are parallel to each other within the same layer for Γ 3 . 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 CdMn 7 O 12 can be described by the IR Γ 3 . 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 CaMn 7 O 12 8,24 . However, the magnetic structure of CaMn 7 O 12 is incommensurate whereas the propagation vector is commensurate in the case of CdMn 7 O 12 .

Mn3 (3b)
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 Mn 3+ 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 CaMn 7 O 12 which is in contrast to the case of CdMn 7 O 12 .
In summary, the magnetic structure of CdMn 7 O 12 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 CaMn 7 O 12 .

Methods
Polycrystalline samples of CdMn 7 O 12 were synthesized by high pressure method as described elsewhere 11 . 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 CdMn 7 O 12 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 SmFeO 3 25 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 α K 1 radiation. A closed cycle helium cryostat (Phenix of Oxford Cryosystems) was used for cooling the flat plate powder sample.