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John M. Attah-Baah, Dmitry D. Khalyavin, Pascal Manuel, Nilson S. Ferreira, [Alexei A. Belik](https://orcid.org/0000-0001-9031-2355), Roger D. Johnson

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[Spin reorientation and the interplay of magnetic sublattices in Er<sub>2</sub>CuMnMn<sub>4</sub>O<sub>12</sub>](https://mdr.nims.go.jp/datasets/ff6ad689-af6a-443e-8ae4-6abbde414950)

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Acta Crystallographica Section BStructural Science,Crystal Engineeringand MaterialsISSN 2052-5206© 0000 International Union of CrystallographySpin Reorientation and the Interplay of MagneticSublattices in Er2CuMnMn4O12John M. Attah-Baah,a,b Dmitry D. Khalyavin,c Pascal Manuel,c NilsonS. Ferreira,b Alexei A. Belikd and Roger D. Johnson a,e,f*aDepartment of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT,United Kingdom, bDepartment of Physics, Federal University of Sergipe, São Cristovão 49100-000, SEBrazil, cISIS facility, Rutherford Appleton Laboratory-STFC, Chilton, Didcot OX11 0QX, United King-dom, dResearch Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Sci-ence (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan, eLondon Centre for Nanotechnology, Univer-sity College London, Gower Street, London WC1E 6BT, United Kingdom, and fDiamond Light Source,Rutherford Appleton Laboratory-STFC, Chilton, Didcot OX11 0QX, United Kingdom. Correspondencee-mail: roger.johnson@ucl.ac.ukThrough a combination of magnetic susceptibility, specific heat, and neutron pow-der diffraction measurements we have revealed a sequence of 4 magnetic phasetransitions in the columnar quadruple perovskite Er2CuMnMn4O12. A key featureof the quadruple perovskite structural framework is the complex interplay of mul-tiple magnetic sublattices via frustrated exchange topologies and competing mag-netic anisotropies. We show that in Er2CuMnMn4O12, this phenomenology givesrise to multiple spin-reorientation transitions driven by the competition of easy-axis single ion anisotropy and the Dzyaloshinskii-Moriya interaction; both withinthe manganese B-site sublattice. At low temperature one Er sublattice orders dueto a finite f -d exchange field aligned parallel to its Ising axis, while the otherEr sublattice remains non-magnetic until a final, symmetry-breaking phase transi-tion into the ground state. This non-trivial low-temperature interplay of transitionmetal and rare-earth sublattices, as well as an observed k = (0, 0, 1/2) periodic-ity in both manganese spin canting and Er ordering, raises future challenges todevelop a complete understanding of the R2CuMnMn4O12 family.1. IntroductionSpin-reorientation transitions are characterised by the sponta-neous rotation of ordered magnetic moments [1], and have beenfound to occur in antiferromagnets [2–5], canted antiferromag-netics (weak ferromagnets) [6, 7], ferromagnets [8] and ferri-magnets [9, 10]. This phenomenon is of keen interest, not onlyfrom a fundamental perspective, but also because deterministicmagnetization switching may be utilised in nanoscale functionalspintronic components [11]. In this regard, spin-reorientationtransitions in ferrimagnets are arguably the most appealing, asferrimagnets carry a net magnetization while switching in theultra-fast regime [12]. Spin-reorientation typically occurs dueto competition between different magnetic sublattices with dif-ferent magnetic anisotropies; a typical example is that of therare-earth orthoferrites, in which spin-reorientation is drivenby magnetic f -d exchange interactions between rare-earth andtransition metal sublattices [6].In quadruple perovskites, multiple magnetic sublatticesmay be introduced into the structure, allowing for com-plex frustrated exchange topologies and competing magneticanisotropies. Indeed, many non-trivial magnetic phases havebeen observed in this structural family with properties includ-ing multiferroicity [13–15], low-field magnetoresistance [16],incommensurate magneto-structural coupling [17], and spin-reorientation transitions [9, 10]. The columnar quadruple per-ovskite R2CuMnMn4O12 (R=Dy, Y) undergoes 3 magneticphase transitions, two of which are spin-reorientation transi-tions involving the rotation of a ferrimagnetic magnetizationby 90 degrees [10]. Remarkably, these transitions could notbe explained by the conventional f -d exchange model, andit was proposed that these phenomena originated in the com-petition between single-ion anisotropy and anisotropy due tothe Dzyaloshinskii-Moriya interaction, tuned by spin cantinginduced by frustrated Heisenberg exchange [10].In this paper, we extend previous work on R2CuMnMn4O12,and report the experimental characterization of the magneticphases exhibited by Er2CuMnMn4O12. The crystal structureof Er2CuMnMn4O12 is shown in Figure 1. As is typicalof perovskite-derived structures, the B site manganese ionsare octahedrally coordinated forming a pseudo-cubic corner-sharing framework (Figure 1b and 1e). In the columnar per-ovskite aristotype (space group P 42n mc) [18,19], the MnO6 octa-Acta Cryst. (0000). B00, 000000 LIST OF AUTHORS · (SHORTENED) TITLE 1hedra are severely tilted in an a+a+c− pattern (Glazer nota-tion [20]). These octahedral tilts split the A sites into 3 sym-metry inequivalent sublattices that are typically labelled A, A′,and A′′ (Figure 1a). The A sites are occupied by erbium, andsit within a distorted 10-fold oxygen coordination (Figure 1c).The A′ sites are nominally occupied by copper (labelled Cu1)within a square-planar oxygen coordination, and the A′′ sitesare nominally occupied by manganese (labelled Mn2) within atetrahedral oxygen coordination (Figure 1d).Figure 1The crystal structure of Er2CuMnMn4O12. A single unit cell is shown by thingrey lines, and the cation oxygen coordinations are shaded in panes c-e.The R2CuMnMn4O12 family also support layered charge andferro-orbital ordering [21] that breaks the symmetry betweennearest neighbor MnO6 layers stacked along c, which we labelMn3 and Mn4, respectively. Mn3 ions carry a nominally 3+oxidation state, and the cooperative Jahn-Teller distortions alignd3z2−r2 orbitals approximately parallel to c. The Mn4 ions arenominally 4+ and their octahedral coordination is undistortedto good approximation. A secondary consequence of the chargeand orbital ordering is the splitting of the A sites into two sub-lattices, now related by a pseudo-42 screw, which we label Er1and Er2. The space group of this distorted phase is Pmmn.In this paper, we show that the complex interplay of thenumerous magnetic sublattices described above leads to 4magnetic phase transitions in Er2CuMnMn4O12, characterizedby the onset of ferrimagnetic order, spin-reorientation, spin-canting, and the polarisation of Er ions. The mechanism forspin-reorientation is likely the same as that proposed for otherR2CuMnMn4O12 compounds (R = Dy, Y), which show a sim-ilar sequence of phase transitions [10]. However, the nature ofthe observed low temperature coupling between rare-earth andtransition metal sublattices in Er2CuMnMn4O12, as well as theemergence of k = (0, 0, 1/2) modulations found at low temper-ature for R = Er, Dy, and Y, pose interesting questions for futurestudies.The paper is organized as follows. In Section 2, we describethe experimental methods, and in Sections 3.1, 3.2, and 3.3 wepresent the results of magnetic susceptibility, specific heat, andneutron powder diffraction measurements, respectively. In Sec-tion 3.4, we find an approximate form for the Er crystal electricfield using a simple point charge model, from which we suc-cessfully explain the empirical behavior of the Er ions at lowtemperature. Our results are discussed in Section 4, and finally,we draw conclusions in Section 5.2. ExperimentA sample with the target chemical composition ofEr2.1Cu0.95Mn0.95Mn4O12 was prepared from a stoichiomet-ric mixture of Er2O3, CuO, Mn2O3 and MnO1.839 by a high-pressure, high-temperature method at 6 GPa and about 1650 Kfor 90 min in Pt capsules. The target chemical composition wasslightly shifted from Er2CuMnMn4O12 to eliminate the amountof a ErCu3−xMn4+xO12-type impurity, where magnetic suscep-tibility measurements showed that the magnetic properties ofEr2CuMnMn4O12 and Er2.1Cu0.95Mn0.95Mn4O12 samples werealmost identical except for a weak anomaly near 250 K fromthe impurity phase present in the Er2CuMnMn4O12 sample.We note that neutron diffraction cannot distinguish betweenEr and Cu, and refinement of synchrotron X-ray diffractiondata not shown here indicated that the tetrahedral Mn2 siteaccommodates the excess Er. For simplicity, we will use thechemical formula Er2CuMnMn4O12 throughout the paper. ACmagnetometry measurements were performed using a QuantumDesign MPMS-1T with an excitation field of 0.5 Oe, on cool-ing in zero DC field from 225 to 2 K. The measurement wasrepeated for excitation frequencies of 2, 7, 110, 300, and 500Hz. DC magnetometry measurements were performed using aQuantum Design MPMS-XL, having cooled the sample in zeromagnetic field and measured on warming (ZFC), and measuredin field on cooling (FCC), between 300 and 2 K in 100 Oeand between 400 and 2 K in 10 kOe fields. Specific heat datawere collected using a Quantum Design PPMS on cooling inzero applied field, and in applied fields of 1, 2, 5, 10, 30, 50,and 70 kOe. Neutron powder diffraction measurements wereperformed using the WISH diffractometer [22] at ISIS, the UKNeutron and Muon Source. A 1.8 g sample was loaded into a6 mm diameter vanadium can, and mounted within a 4He cryo-stat. Data with high counting statistics (10 µA proton current atISIS) were collected in each magnetic phase including param-agnetic for reference (1.5,9,30,140, and 200 K), and with lowercounting statistics (4 µA proton current) on warming throughthe phases in finer temperature steps (3 -10 K intervals). Crystaland magnetic structure refinements were performed using theFULLPROF suite [23] against data collected in detector banks ataverage 2θ positions of 58.3◦ and 152.8◦.3. Results3.1. Magnetic susceptibilityThe temperature dependence of the real (χ′) and imaginary(χ′′) parts of the AC magnetic susceptibility are plotted in Fig-ures 2a and 2b, respectively. Sharp anomalies in χ′ indicate the2 LIST OF AUTHORS · (SHORTENED) TITLE Acta Cryst. (0000). B00, 000000presence of 4 magnetic phase transitions at TN1 ≃ 172 K, TN2≃ 115 K, TN3 ≃ 17 K, and TN4 ≃ 7 K. We label the respectivephases as CFI’ (TN2 ≤ T ≤ TN1), FI (TN3 ≤ T ≤ TN2),CFI1 (TN4 ≤ T ≤ TN3), and CFI2 (T ≤ TN4). These labels areconsistent with those adopted in Reference [10] where CFI andFI refer to canted and non-canted ferrimagnetic phases, respec-tively. The prime denotes the high temperature CFI phase, whilethe numerical subscripts differentiate the two low temperatureCFI phases. Anomalous behaviour at the phase transition tem-peratures is also seen in χ′′, which shows a strong frequencydependence in the CFI’ phase, indicative of non-trivial mag-netic fluctuations.Figure 2The real (a) and imaginary (b) parts of the AC magnetic susceptibility ofEr2CuMnMn4O12, measured as a function of temperature at different frequency0.5 Oe excitation fields. The static DC field was zero. Four magnetic transitionsare identified in (a), which bound phases CFI’, FI, CFI1, and CFI2 shaded blue,grey, green and purple, respectively.The DC magnetic susceptibility is shown in Figure 3a.Anomalies corroborate the phase transitions observed in theAC susceptibility data, described above. Furthermore, the sharponset of magnetisation below TN1 shows that the CFI’ phaseis characterised by a significant ferromagnetic or ferrimagneticmoment, which is greatly reduced on cooling into the CFI1 andCFI2 phases. The broad anomaly at TN2 was also observed inDy2CuMnMn4O12 and Y2CuMnMn4O12, where it was assignedto a softening of magnetic correlations in the proximity of aspin reorientation transition [10]. The inset to Figure 3a showsthe inverse susceptibility against temperature. Fitting the Curie-Weiss model within the paramagnetic regime (in the temper-ature range 295 to 400 K) gave µeff = 15.40(4)µB/f.u. andθCW = 85(1) K. The positive value for θCW indicates dominantferromagnetic interactions, and the effective moment is close tothe theoretical value of µ = 17.3µB/f.u. (assuming g = 2 fortransition metals).Figure 3a) Temperature dependence of the DC magnetic susceptibility ofEr2CuMnMn4O12 measured under ZFC and FCC conditions in a 100Oe applied field. The inset shows a Curie-Weiss fit (black dashed line) to theinverse susceptibility. b) Specific heat of Er2CuMnMn4O12 measured as afunction of temperature. The inset highlights the magnetic field dependence onthe low temperature anomalies. Phases CFI’, FI, CFI1, and CFI2 are shadedblue, grey, green and purple, respectively.3.2. Specific heatThe temperature dependence of the specific heat is shown inFigure 3b. Clear anomalies are observed at each phase transi-tion, with sharp peaks seen at TN3 and TN4. We will later showthat these transitions are associated with the ordering of Er3+moments. Hence, these low temperature peaks in specific heatlikely originate in the sequential splitting of Er3+ ground statedoublets. Unfortunately, quantitative analysis of the entropywas not possible due to poor thermal conductivity from thepressed polycrystalline sample. However, the field dependentbehaviour shown in the inset to Figure 3b is consistent withActa Cryst. (0000). B00, 000000 LIST OF AUTHORS · (SHORTENED) TITLE 3a gradual, powder averaged field-induced splitting of the Er3+ground state resulting in a ‘smearing’ of the peak in specificheat.3.3. Neutron powder diffractionThe crystal structure of Er2CuMnMn4O12 was refined againstneutron powder diffraction data measured in the paramagneticphase at 200 K. The structure of Y2CuMnMn4O12 [10], withY replaced by Er, was taken as a starting model. The crys-tal structure parameters are given in Table 1, and the fit tothe data is shown in Figure 4a. Excellent agreement betweenmodel and data was achieved (R = 4.58%, wR = 3.28%, andRBragg = 6.0%).Table 1Crystal structure parameters of Er2CuMnMn4O12(space group Pmmn) refinedat 200 K. The lattice parameters were determined to be a = 7.2640(1) Å, b =7.3187(1) Å, and c = 7.7764(1) Å. Atomic Wyckoff positions are Er1,Er2: 2a[1/4,1/4,z]; Cu1,Mn2: 2b [3/4,1/4,z]; Mn3: 4c [0,0,0]; Mn4: 4d [0,0,1/2]; O1:8g [x,y,z]; O2,O4: 4f [x,1/4,z]; and O3,O5: 4e [1/4,y,z]. Bond valence sums(BVS) were calculated using the parameters, R0(Er3+) = 1.99, R0(Cu2+) = 1.68,R0(Mn2+) = 1.79, R0(Mn3+) = 1.76, R0(Mn4+)= 1.75, and B = 0.37, where thebond valence, BV = exp((Ro −R)/B). N.B. For mixed occupancy sites we givethe BVS of the majority cation.Atom Frac. coord. Uiso (×10−2Å2) BVS (|e|) OccupationEr1 z = 0.7785(6) 1.21(11) +2.86 ErEr2 z = 0.2834(6) 0.74(10) +2.90 ErCu1 z = 0.7308(9) 0.98(2) +1.98 76%Cu, 24% MnMn2 z = 0.2410(6) 1.5(8) +1.93 76%Mn, 24% CuMn3 - 0.72(2) +3.27 MnMn4 - 0.45(2) +3.74 MnO1 x = 0.4388(2) 0.90(7) - Oy = -0.0624(3)z = 0.2669(3)O2 x = 0.0587(4) 0.97(10) - Oz = 0.0413(3)O3 y = 0.5335(4) 0.59(9) - Oz = 0.9218(4)O4 x = 0.5343(4) 0.74(10) - Oz = 0.4188(4)O5 y = 0.4353(4) 0.82(9) - Oz = 0.5414(4)On cooling through TN1, new Bragg intensities appear inthe neutron powder diffraction data (see Figure 4b). Given thecoincidence with the magnetic susceptibility anomaly we canreasonably assume these new intensities originate in magneticorder. The magnetic peaks have a similar width to the nuclearpeaks, indicating long-range magnetic correlations. The mag-netic intensities appear in the same positions as nuclear intensi-ties, and therefore index by the Γ-point propagation vector, k =(0, 0, 0). We refer the reader to the complete symmetry analysisof Γ-point magnetic structures in the Pmmn R2CuMnMn4O12columnar perovskites published in the Supplemental Material ofReference [10]. It was shown that the magnetic representationdecomposes into 8 irreducible representations, of which only 4allow for a net ferromagnetic moment observed in the DC mag-netic susceptibility data; they are mΓ+1 , mΓ+2 , mΓ+3 , and mΓ+4 .Magnetic structure models also detailed in the SupplementalMaterial of Reference [10] constrained to each symmetry weresystematically refined against the neutron powder diffractiondata measured at 140 K, representative of phase CFI’. The onlymodel compatible with the diffraction data was that transform-ing as mΓ+4 . Within this symmetry, all magnetic sublattices (Er1,Er2, Cu1, Mn2, Mn3, and Mn4) can adopt ferromagnetic orderpolarised along ±b, with the addition of Mn3 and Mn4 anti-ferromagnetic A- and Y-type modes polarised along a and c,respectively [10]. The linear combination of ferromagnetic andantiferromagnetic modes leads to spin canting.4 LIST OF AUTHORS · (SHORTENED) TITLE Acta Cryst. (0000). B00, 000000Figure 4Neutron powder diffraction data measured in 5 phases; a) paramagnetic, b)CFI’, c) FI, d) CFI1, and e) CFI2. Data are shown as red points, the fitted patternas black lines, and the difference curve Iobs − Icalc as a blue line at the bottomof the panes. The top and bottom row of green tick marks in each pane indicatethe position of nuclear and magnetic Bragg peaks, respectively.Our starting model had 10 free parameters (mode ampli-tudes), but after initial refinement the Er1, Er2, and Cu1 modeamplitudes could be set to zero. It is not surprising that the Er1and Er2 moments are zero at this temperature, as A-site rare-earth ions in perovskite manganites typically order below lowtemperature phase transitions due to relatively weak f -d inter-actions. The absence of a moment at the Cu1 site is either due tothe ordered moment being below the sensitivity of the diffrac-tion experiment (approximately < 0.1µB), or due to the mixed76% Cu and 24% Mn cation occupation of that site refinedagainst the paramagnetic data (see Table 1): If first we assumethe random distribution of A′′ Cu and Mn ions carry magneticmoments of 1 and 3 µB, respectively, and second, we assume theA′′ Cu and Mn moments are aligned in opposite directions withrespect to the nearest neighbour Mn3 and Mn4 sublattices dueto opposite sign Cu-Mn and Mn-Mn A′′-B exchange interac-tions, then the average moment at the Cu1 site is approximatelyzero.Table 2Magnetic structure parameters of Er2CuMnMn4O12. The F and A labels denoteferromagnetic and Néel-type antiferromagnetic modes, respectively. The Ylabel denotes an Mn3/Mn4 mode of ferromagnetic stripes along a, coupledantiferromagnetically along b [10]. The subscripts indicate the polarisation ofthe modes. Freely refined and fixed values are given with and without stan-dard uncertainties, respectively, and dashes indicate that the component is notallowed by the symmetry of the respective phase.mΓ+2 mΓ+4 mZ+4 mZ+3Atom Fz (µB) Fy (µB) Ax (µB) Ax (µB) Yz (µB) Ax (µB)CFI’ phase at 140 KEr1 - 0 - - - -Er2 - 0 - - - -Cu1 - 0 - - - -Mn2 - -2.15(4) - - - -Mn3 - 2.28(3) 0.19(2) - - -Mn4 - 1.31(3) 0 - - -FI phase at 40 KEr1 0 - - - - -Er2 0 - - - - -Cu1 0 - - - - -Mn2 -3.14(4) - - - - -Mn3 3.22(4) - - - - -Mn4 2.27(3) - - - - -CFI1 phase at 9 KEr1 - 0 - - - -Er2 - -5.02(4) - - - -Cu1 - 0 - - - -Mn2 - -3.23(6) - - - -Mn3 - 1.91(3) 0 2.28(2) 0.93(3) -Mn4 - 2.70(3) 0 - - -CFI2 phase at 1.5 KEr1 - 0 - 0 - -3.96(4)Er2 - -7.35(4) - 0 - 0Cu1 - 0 - 0 - 0Mn2 - -3.23 - 0 - 0Mn3 - 1.91 0 2.28 0.93 -Mn4 - 2.70 0 - - -Further refinement indicated that the Y-type mode ampli-tudes should also be set to zero, while an additional A-typemode was required to properly account for the diffraction inten-sities. We note, however, that it was not possible to deter-mine whether this mode resided on the Mn3 or Mn4 sublat-tice. Here, we propose a model in which spin canting occurs onthe Mn3 sites — consistent with the low temperature structure.The final refinement of just 4 free parameters (given in Table2) gave excellent agreement with the data (Rmag = 2.00%).The refinement is shown in Figure 4b, and the evolution ofthe magnetic moment components as a function of tempera-ture is shown in Figure 5. The magnetic space group for phaseCFI’ is Pmm′n′ (#59.410, basis={[0, 1, 0], [−1, 0, 0], [0, 0, 1]},origin=[1/2, 1/2, 0], see supplementary mcif for full descrip-tion).Acta Cryst. (0000). B00, 000000 LIST OF AUTHORS · (SHORTENED) TITLE 5Figure 5Temperature dependence of the ±Fi magnetic moments on the a) Mn2, b) Mn3,and c) Mn4 sublattices, where the blue and red data correspond to Γ+4 (Fy) andΓ+2 (Fz) order, respectively. Pane d shows the antiferromagnetic componentsthat lead to spin canting on the Mn3 sublattice.Cooling through TN2 gave rise to a redistribution of intensityamongst the Γ-point magnetic Bragg peaks consistent with areorientation of the ferromagnetic modes from parallel to ±b, toparallel to ±c. Hence, the transition at TN2 is identified as a spinreorientation transition, from a structure transforming as mΓ+4to one transforming as mΓ+2 . The reoriented magnetic structure(maintaining zero moment on the Er1, Er2, and Cu1 sublattices)was refined against data measured at 40 K (see Figure 4c), anexcellent fit was achieved (Rmag = 1.98%), and the mode ampli-tudes are given in Table 2. We note that an A-type canting modeis not allowed within mΓ+2 symmetry, and other symmetry-allowed Mn3 and Mn4 canting modes were found to be zero.The magnetic space group for phase FI is Pm′m′n (#59.409,basis={[1, 0, 0], [0, 1, 0], [0, 0, 1]}, origin=[1/2, 1/2, 0], see sup-plementary mcif for full description).Below TN3 the Γ-point magnetic intensities change oncemore. Modelling of the diffraction pattern showed that the Mn2,Mn3, and Mn4 Γ-point magnetic structure returned to beingpolarised parallel to ±b. Furthermore, an additional ferromag-netic mode on the Er2 sublattice, also polarised parallel to ±b,was required to fully account for the Γ-point intensities (seeFigure 6). This Er2 mode transformed by the same mΓ+4 irrep asthe transition metal sublattices. Systematic tests against the datashowed that no additional Γ-point modes appeared on any othersublattice, including Er1. The temperature dependence of thetransition metal moments (Figure 5) showed that all momentsapproached saturation at the Γ-point, with the exception of theMn3 sublattice, which showed a large drop in the Γ-point com-ponent through TN3.Figure 6Temperature dependence of the Er1 and Er2 moments, whose respective mag-netic modes transform a mZ+3 (antiferromagnetic, m||a), and mΓ+4 (ferromag-netic, m||b), respectively. Fits to a simple magnetisation model for a 2-levelsystem are shown by red lines (see text for details).In addition to the above changes, new diffraction peaksappeared below TN3, which could be indexed with the Z-pointpropagation vector k = (0, 0, 1/2). Symmetry analysis reportedin the Supplemental Material of reference [10] identified 8 pos-sible Z-point symmetries. All were tested against the diffrac-tion data, and it was found that the new Z-point intensitiescould be uniquely accounted for by A- and Y-type antiferro-magnetic modes on the Mn3 sublattice, polarised along ±a and±c, respectively. These modes transform by the mZ+4 irrep,and correspond to a canting of the Mn3 moment, which, inany given layer, is similar to that found in phase CFI’ albeitwith a small additional Y mode. The main difference is thatin the low temperature CFI1 phase the relative sign of thecanting alternates from one unit cell to the next along ±cin accordance with the Z-point propagation vector. We notethat this additional antiferromagnetic mode is consistent with6 LIST OF AUTHORS · (SHORTENED) TITLE Acta Cryst. (0000). B00, 000000the observed reduction in the Mn3 moment at the Γ-point. Afinal refinement of the combined Γ-point and Z-point struc-tures gave excellent agreement with the data (Rmag = 3.13%)as shown in Figure 4d, and the refined sublattice momentsare given in Table 2. The magnetic space group for phaseCFI1 is Pmm′n′ (#59.410, basis={[0, 1, 0], [−1, 0, 0], [0, 0, 2]},origin=[1/2, 1/2, 0], see supplementary mcif for full descrip-tion).Figure 7The magnetic structures of Er2CuMnMn4O12in each ordered phase. Er1, Er2,Cu1, Mn2, Mn3, and Mn4 sublattices are coloured red, green, black, purple,cyan and maroon, respectively (see Figure 1).Finally, below TN4 additional intensity appears at the Z-point Bragg peaks. Systematic tests of magnetic structures con-strained by the CFI1 phase magnetic symmetry (mZ+4 ) failedto account for this additional intensity, implying a symme-try breaking admixture of another Z-point irrep — consistentwith the observation of a sharp phase transition. Expanding themagnetic structure tests to models transforming by all Z-pointirreps, we identified an antiferromagnetic mode on the Er1 sub-lattice polarised parallel to ±a (perpendicular to Er2 moments),transforming as mZ+3 , that uniquely accounted for the changesin neutron powder diffraction observed below TN2 (see Figure6 for the temperature dependence of the Er moment). Unfortu-nately, peak overlap now led to excessive correlation betweenfreely refining parameters, so it was necessary to fix the CFI1magnetic structure in refinements within the lower tempera-ture CFI2 phase. Still, excellent agreement with the data wasachieved (Rmag = 3.82%, Figure 4e), and the parameters aresummarised in Table 2. The magnetic space group for phaseCFI2 is P2′/c′ (#13.69, basis={[−1, 0, 0], [0, 0, 2], [1, 1, 0]},origin=[1/2, 1/2, 0], see supplementary mcif for full descrip-tion).3.4. Er3+ crystal electric fieldThe site point symmetry of both Er ions is mm2, with pairsof Er1 and Er2 ions related by a pseudo-42 screw parallel to c(as present in the P4/nmc columnar perovskite aristotype [19]).Hunds rules gives J = 15/2 and gJ = 6/5 for the free Er3+ion. In an orthorhombic mm2 crystal electric field (CEF), thedegeneracy of states |J,mJ⟩ will be lifted to 8 Kramers doublets.Assuming the energy gap between the ground state doublet andall others is >> kBT , the magnetisation of a given Er ion in aneffective f -d exchange field, Beff, will then be described by thatof a two level system;m = µ.tanh(µBeffkBT)(1)where µ is the available Er moment dependent on the groundstate wavefunctions. The red lines in Figure 6 show fits of Equa-tion 1 to the temperature dependence of the Er moments. Thevalue of µ was constrained to be the same for both Er1 andEr2, and reasonable agreement is found for refined parametersµ = 7.2(1)µB, BEr1eff = 0.20(2) T, and BEr2eff = 1.6(1) T.The ground state wavefunctions for Er1 and Er2 were esti-mated using a point charge model for the CEF. The Hamiltonianfor a given Er ion is writtenH =∑nn∑m=−nBmn Omn + gJµBJ · Beff, (2)The second term is the Zeeman energy, and the first term is theCEF energy, where Omn are Stevens operator equivalents [24]and the CEF parametersBmn = Amn ⟨rn⟩Θn. (3)Here, Θn are the Stevens factors [24], ⟨rn⟩ are radial expectationvalues for Er3+ [25], and in the point charge approximationAmn =−|e|2(2n + 1)ϵ0Cmn∑iqirn+1iZmn (θi, ϕi). (4)The summation is taken over i nearest neighbour atoms ofcharge qi and position (ri, θi, ϕi). Zmn is a tesseral harmonic withnumerical factor Cmn , and ϵ0 is the permittivity of free space. Foreach Er site, twelve oxygen ions were taken as nearest neigh-bours, with positions refined against the paramagnetic neutronpowder diffraction data (described above). The calculated val-ues of symmetry allowed Bmn are given in Table 3.Acta Cryst. (0000). B00, 000000 LIST OF AUTHORS · (SHORTENED) TITLE 7Table 3Crystal electric field parameters for Er1 and Er2 in units µeV (3.s.f.).Atom Crystal field parametersB02 B22 B04 B24 B44Er1 340 -259 -0.138 -1.34 0.490Er2 260 255 -0.0973 1.08 0.635B06 B26 B46 B66Er1 -0.00145 0.00703 0.0238 -0.0207Er2 -0.00148 -0.0111 0.0240 0.0226The CEF parameter magnitudes are similar for Er1 and Er2with a sign change for B22, B24, B26, and B66, which is expected ifthey are related by pseudo-42 screw. The Hamiltonian was diag-onalized for both Er ions, with small magnetic fields systemati-cally applied parallel to a, b, and c to lift the doublet degeneracy.Evaluating the expectation value of the total angular momentumoperators for the ground state wavefunctions showed that Er1has a strong Ising-like single ion anisotropy parallel to a, andEr2 has a strong Ising-like single ion anisotropy parallel to b, inaccordance with the empirical moment directions refined at lowtemperature.4. DiscussionA similar sequence of phase transitions was observed inR2CuMnMn4O12 (R = Y and Dy), where it was understoodthat frustrated Heisenberg exchange stabilised large spin cant-ing (specifically the admixture of F and A modes) on theMn3 sublattice in the CFI’ and CFI phases. This spin cantingintroduced magnetic anisotropy via the Dzyaloshinskii-Moriya(DM) interaction, which could then compete with Mn3 single-ion-anisotropy (SIA). In Y2CuMnMn4O12, this scenario pro-vided a mechanism for both high and low temperature spin-reorientation transitions at TN2 and TN3, even in the absenceof f -d exchange. In Dy2CuMnMn4O12, both phase transitionssimilarly occurred, but at TN3 the spin canting was not accom-panied by spin-reorientation on account of the dominant DySIA parallel to c introduced via f -d exchange. In both R = Dyand Y compounds the low temperature spin canting was associ-ated with a Z-point antiferromagnetic mode, as observed in thepresent study, and the origin of this doubled periodicity along chad not been explained [10].The spin-reorientation transitions observed inEr2CuMnMn4O12 at TN2 and TN3 can be explained by the samemechanism proposed for Y2CuMnMn4O12. In addition, theEr2 moment becomes polarised below TN3 due to a finite f -dexchange field parallel to its Ising axis after spin-reorientation.To the contrary, the Er1 ions do not develop a moment at thistemperature due to their Ising axis being perpendicular to themagnetization of the transition metal sublattice. Further, theEr1 Z-point symmetry-adapted mode for irrep mZ+4 is polarisedalong b [10], hence coupling to the mZ+4 Mn3 A mode is alsoprevented by the Er1 Ising anisotropy. Instead, the Er1 ionsremain unpolarised, introducing a low temperature instabilitythat leads to the symmetry breaking phase transition at TN4. Wefind that below TN4, the Er1 moments develop a finite polari-sation parallel to their Ising axis, with their long-range ordertransforming by the mZ+3 irrep. This irrep is different to that ofthe Mn3 canting (mZ+4 ), which is consistent with the symmetrybreaking transition but leads to questions regarding the natureof the coupling between Er1 and transition metal spins. We pro-pose two possible scenarios. Firstly, that the transition at TN4is magnetostructural (akin to a spin-Jahn-Teller transition [26])whereby a spontaneous symmetry-breaking structural distortionfacilitates coupling between the mZ+3 A mode at the Er1 sub-lattice and the mZ+4 A mode at the Mn3 sublattice. Secondly,the Mn3 canting may adopt an additional mZ+3 mode, whichthen couples directly to the Er1 sublattice. In the former casethe primary energy cost associated with the transition is elastic,while in the latter case the primary energy cost is in magneticexchange.Finally, we note that the above behaviour is consistent withthe refined parameters of our two level system fitted to the Er1and Er2 moment temperature dependencies. Both Er1 and Er2can develop the same size moment in the ground state (belowthe base temperature of the neutron powder diffraction exper-iment), but the Er1 moment reduces rapidly on warming dueto the weaker f -d exchange field while the Er2 moment is sus-tained to higher temperatures by a larger field. This is consistentwith the sequence of phase transitions, and exactly what onewould expect if the Er1 moment is coupled to an antiferromag-netic mode of the single Mn3 sublattice while the Er2 momentis coupled to multiple ferromagnetic sublattices.5. ConclusionsIn summary, we have shown that Er2CuMnMn4O12 undergoes4 magnetic phase transitions. Below TN1 ≃ 172 K, the sys-tem adopts ferrimagnetic order of transition metal ions polar-ized along ±b, with antiferromagnetic canting on the Mn3B site sublattice. A spin-reorientation transition occurs at TN2≃ 115 K, where the ferrimagnetic order rotates to be polar-ized along ±c. The antiferromagnetic canting vanishes in thisphase in accordance with magnetic symmetry. A second spin-reorientation transition occurs at TN3 ≃ 17 K, where the ferri-magnetic order returns to ±b. Mn3 sublattice antiferromagneticcanting also reappears at TN3, but now with a doubled periodic-ity along c (k = (0, 0, 1/2)). Furthermore, the transition metalferrimagnetic order is now accompanied by a moment at theEr2 sublattice, which has an Ising axis parallel to the ferrimag-netic magnetization. To the contrary, the Er1 sublattice remainsnon-magnetic in this phase as its Ising axis is perpendicular tothe ferrimagnetic magnetization. As a result, a fourth and finalsymmetry-breaking phase transition occurs at TN4 ≃ 7 K char-acterized by the k = (0, 0, 1/2) ordering of the Er1 momentsthat couple to the pre-existing antiferromagnetic spin cantingof the Mn3 sublattice. The mechanism for spin-reorientationis likely the same as that proposed for other R2CuMnMn4O12compounds, which show a similar sequence of phase transi-tions [10]. However, the nature of the low temperature couplingbetween Er1 and Mn3 sublattices is not clear from our elasticdiffraction data or symmetry analysis. We have proposed twoscenarios based on elastic and magnetic energies, and it wouldbe interesting to differentiate these two mechanisms in future8 LIST OF AUTHORS · (SHORTENED) TITLE Acta Cryst. (0000). B00, 000000studies. 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