# Fileset [PhysRevB.109.134111.pdf](https://mdr.nims.go.jp/filesets/a8c0f085-87ff-4ec0-bc8c-25d1fb16b424/download) ## Creator [A. Maia](https://orcid.org/0000-0002-0582-7272), [M. Kempa](https://orcid.org/0000-0002-5902-7780), [V. Bovtun](https://orcid.org/0000-0002-2470-6767), [R. Vilarinho](https://orcid.org/0000-0001-6104-9834), [C. Kadlec](https://orcid.org/0000-0003-2820-4462), [J. Agostinho Moreira](https://orcid.org/0000-0003-4659-7503), [A. A. Belik](https://orcid.org/0000-0001-9031-2355), [P. Proschek](https://orcid.org/0000-0003-2627-3544), [S. Kamba](https://orcid.org/0000-0003-4699-869X) ## Rights [In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Two displacive ferroelectric phase transitions in multiferroic quadruple perovskite

Bi {Mn}_{7} O_{12}

](https://mdr.nims.go.jp/datasets/ebcf9e22-9895-4c7c-a408-1a6dd2d214fa) ## Fulltext Two displacive ferroelectric phase transitions in multiferroic quadruple perovskite ${\rm{BiM}}{{{\rm{n}}}_7}{{{\rm{O}}}_{12}}$PHYSICAL REVIEW B 109, 134111 (2024)Two displacive ferroelectric phase transitions in multiferroic quadruple perovskite BiMn7O12A. Maia ,1 M. Kempa ,1 V. Bovtun ,1 R. Vilarinho ,2 C. Kadlec ,1 J. Agostinho Moreira ,2 A. A. Belik ,3P. Proschek ,4 and S. Kamba 1,*1Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 00 Prague 8, Czech Republic2IFIMUP, Physics and Astronomy Department, Faculty of Sciences, University of Porto,Rua do Campo Alegre 687, s/n 4169-007 Porto, Portugal3Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS),Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan4Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague, Czech Republic(Received 19 December 2023; revised 17 February 2024; accepted 1 April 2024; published 25 April 2024)We report on the microwave, terahertz (THz), infrared, and Raman spectroscopic studies of BiMn7O12ceramics, shedding more light onto the nature of two structural phase transitions and their possible relationwith ferroelectricity in this compound. We observed a softening of one polar phonon in the THz range oncooling towards 460 and 300 K, i.e., temperatures at which BiMn7O12 undergoes subsequent structural phasetransitions from monoclinic I2/m to polar monoclinic Im and triclinic P1 phases. The soft phonon causesdielectric anomalies typical for displacive ferroelectric phase transitions. Microwave measurements performed at5.8 GHz up to 400 K qualitatively confirmed not only the dielectric anomaly at 300 K, but also revealed two otherweak dielectric anomalies near the magnetic phase transitions at 60 and 28 K. This evidences the multiferroicnature of the low-temperature phases, although the relatively high conductivity in the kHz and Hz spectral rangeprevented us from directly measuring the permittivity and ferroelectric polarization. Some Raman modes sensethe magnetic phase transitions occurring near 60 and 25 K, showing that spin-phonon coupling is relevant inthis compound and in this temperature range. The deviation of the Mn-O stretching mode frequency from theanharmonic temperature behavior was successfully explained by the spin correlation function calculated fromthe magnetic contribution to the specific heat.DOI: 10.1103/PhysRevB.109.134111I. INTRODUCTIONA-site ordered quadruple perovskites, AA′3B4O12, exhibitseveral interesting physical and chemical properties [1,2],such as reentrant structural transitions [3], intersite chargetransfer and disproportionation [2], giant dielectric constant[4,5], multiferroicity [6,7], and high catalytic activity [8].AA′3B4O12 has a 12-fold-coordinated A site and a square-planar-coordinated A′ site, while B sites have the usualoctahedral coordination for perovskites. For manganese, it ispossible to have A′ = B, and the composition can be writtenas AMn7O12 in brief. These manganites can have spin, orbital,and charge degrees of freedom depending on the oxidationstate of the A cation [1,3,6,9–12].The quadruple perovskite BiMn7O12 exhibits three struc-tural and two magnetic phase transitions [13]. AboveT1 = 608 K, BiMn7O12 crystallizes in a parent cubic structure,with space group Im3̄. Between 460 and 608 K, BiMn7O12adopts a monoclinic symmetry, with pseudo-orthorhombicmetrics [denoted as I2/m(o)], and orbital order appears belowT1. At T2 = 460 K, BiMn7O12 undergoes a phase transitioninto a polar monoclinic structure, described by the Im spacegroup. Finally, at T3 = 290 K, a triclinic distortion takes*kamba@fzu.czplace and BiMn7O12 transits into another polar structure, de-scribed by the P1 space group (assigned as I1 in Ref. [14]).Structural analyses of BiMn7O12 are challenging because ofsevere domain twinning in single crystals, and anisotropicbroadening and diffuse scattering in powder [13]. However,first-principles calculations confirm that noncentrosymmetricstructures are more stable than centrosymmetric ones [13].The energy difference between the Im and P1 models is verysmall, and this fact can explain why the Im to P1 transi-tion is very gradual, and there are no differential scanningcalorimetry (DSC) anomalies associated with this transition[13]. The crystal structure and phase sequence of BiMn7O12are illustrated in Fig. 1.In earlier studies, BiMn7O12 has been shown to exhibittwo magnetic phase transitions at 55 and 25 K [16,17]. Re-cent magnetic and powder neutron diffraction experimentsrevealed three successive magnetic phase transitions [18].Below TN1 = 59 K, B-site Mn cations order antiferromag-netically with propagation vector k1 = (0.5, 0, −0.5), andat TN2 = 55 K the A′-site Mn spins order ferrimagneticallywith k2 =(0, 0, 0) [18]. Both magnetic orderings coincidedown to TN3 = 27 K, below which both the A′-site and B-sitespins reorient with modulation vector k3 =(0, 1, 0). It shouldbe noted that, in contrast to other type II multiferroics, thepolar distortion of the lattice in the P1 structure of BiMn7O12stabilizes the E-type magnetic ordering of Mn at the B-site2469-9950/2024/109(13)/134111(10) 134111-1 ©2024 American Physical Societyhttps://orcid.org/0000-0002-0582-7272https://orcid.org/0000-0002-5902-7780https://orcid.org/0000-0002-2470-6767https://orcid.org/0000-0001-6104-9834https://orcid.org/0000-0003-2820-4462https://orcid.org/0000-0003-4659-7503https://orcid.org/0000-0001-9031-2355https://orcid.org/0000-0003-2627-3544https://orcid.org/0000-0003-4699-869Xhttps://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.109.134111&domain=pdf&date_stamp=2024-04-25https://doi.org/10.1103/PhysRevB.109.134111A. MAIA et al. PHYSICAL REVIEW B 109, 134111 (2024)FIG. 1. Crystal structure of BiMn7O12 at room temperature and schematic representation of its structural (purple) and magnetic (orange)phase sequence. The illustration of the crystal structure was obtained using VESTA software [15].perovskite positions due to trilinear coupling of two magneticorder parameters η1, η2 and polarization P, i.e., η1η2P [18].Conversely, in BiMn3Cr4O12, a different mechanism shouldbe responsible for stabilizing the magnetic structure (probablywith a quadratic coupling η2P or ηP2), because in this materialonly the Cr spins order below TN = TFE [7]. Magnetoelectriccoupling should be induced in both materials via inverse ex-change striction (∝ Si · Sj ). The magnetic phase sequence andthe crystal structure are depicted in Fig. 1 [16–18].The relation between the local crystal structure and thespontaneous electric polarization in BiMn6.96Fe0.04O12 wasrecently studied using 57Fe probe Mössbauer spectroscopy[19,20]. A “dynamic” Born charge model was used to de-velop an algorithm to construct the temperature dependenceof the polarization of the crystal using structural data of thecompound and the experimental values of the quadrupolesplittings of the Mössbauer spectra of the 57Fe probe atoms[19]. The temperature dependence of the electric polarizationobtained from the Mössbauer data points out for a paraelectricto ferroelectric first-order phase transition with Tc ≈ 437 K,close to the I2/m to Im structural transition temperature T2,as well as a considerable increase in the electric polarizationbelow 270 K, with extrapolated T ∗ ≈ 294 K, close to theIm to P1 structural transition at T3 [19]. It has also beendemonstrated that light hole doping of BiMn7O12 with Cu(BiCu0.1Mn6.9O12) can induce incommensurate helical order-ing of electric dipoles [21].Despite BiMn7O12 structural and magnetic properties be-ing extensively studied in the recent past, its dielectricand possible ferroelectric properties have not yet been pub-lished due to its relatively high conductivity above 100 K.BiMn7O12 is sufficiently resistive to perform permittivitymeasurements only below 90 K, revealing dielectric anoma-lies at magnetic phase transitions [22,23]. This evidences formagnetodielectric coupling and the possible multiferroic na-ture of the low temperature magnetic phases. However, directelectric polarization measurements have not yet been pub-lished due to the impossibility of applying a sufficiently highelectric field in the measurement of ferroelectric hysteresisloops, and of poling the sample in the paraelectric phase forpyroelectric current studies, due to its high conductivity.Spectroscopic methods that are insensitive to the conduc-tivity of the sample are used to uncover the nature of structuraland possible ferroelectric phase transitions in BiMn7O12. Thatis why we have undertaken a comprehensive temperature de-pendent heat capacity, infrared, THz, Raman, and microwavemeasurements in a broad temperature range, revealing a ferro-electric soft mode driving both ferroelectric phase transitionsnear 460 and 290 K, and optical phonons showing anomaliesnear magnetic phase transitions. In addition, we also observeddielectric anomalies at two magnetic phase transitions, indica-tive of magnetoelectric coupling in multiferroic phases.II. EXPERIMENTAL DETAILSBiMn7O12 polycrystalline samples were synthesized underhigh-pressure and high-temperature conditions from stoi-chiometric mixtures of Bi2O3 and Mn2O3 starting reagents,as detailed in Ref. [13]. Laboratory powder x-ray diffrac-tion (XRD) data were taken at room temperature using aMiniFlex600 diffractometer with CuKα radiation (2θ range10–80 °, a step width of 0.02 °, and a counting speed of1 °/min). XRD data were analyzed by the Rietveld methodwith RIETAN-2000 program [24]. Weight fractions of impuri-ties were estimated by RIETAN-2000 from refined scale factors.The best ceramics contained some impurities, specifically1% of Bi2O2CO3 and 1% Mn2O3. The ceramic disks withdiameter 6 mm had thickness 1–2 mm. Scanning electron134111-2TWO DISPLACIVE FERROELECTRIC PHASE … PHYSICAL REVIEW B 109, 134111 (2024)microscope images of BiMn7O12 ceramics revealed grainswith the size 2–5 µm (see Fig. S1 in the Supplemental Material[25]). The microwave response at 5.8 GHz was measuredusing the composite dielectric resonator method [27,28]. TheTE01δ resonance frequency, quality factor, and insertion lossof the base cylindrical dielectric resonator with and withoutthe sample were recorded during heating from 10 to 400 Kwith a temperature rate of 0.5 K/min in a Janis closed-cycle Hecryostat. The sample without electrodes (2 × 2 mm plate, 0.32mm thick) was placed on top of the base dielectric resonator.The resonators were measured in the cylindrical shieldingcavity using the transmission setup with a weak coupling byan Agilent E8364B network analyzer. The complex refractiveindex n = √εμ of the sample(s) was calculated from theacquired resonance frequencies and quality factors of the baseand composite resonators.The magnetic properties were measured via vibrating sam-ple magnetometer (VSM, Quantum Design) using a QuantumDesign physical properties measurement system (PPMS) invarious temperature ranges (down to 2 K) and magnetic field(up to 9 T). The heat capacity measurements were performedby using the heat capacity option in the PPMS in variousranges of temperature (down to 2 K).The THz complex transmittance was measured usinga custom-made time-domain spectrometer powered by aTi:sapphire femtosecond laser with 35-fs-long pulses centeredat 800 nm. The system is based on coherent generation andsubsequent coherent detection of ultrashort THz transients.The detection scheme consists of an electro-optic sampling ofthe electric field of the transients within a 1-mm-thick, (110)-oriented ZnTe crystal as a sensor [29]. This allows measuringthe time profile of the THz transients transmitted through thesample. The BiMn7O12 sample was highly absorbing in theTHz region due to a strong optical soft mode, therefore weglued it on a sapphire substrate and polished it down to 38µm. The bare sapphire substrate (thickness 0.543 mm) wasmeasured as a reference.Low-temperature unpolarized IR reflectivity measure-ments of one-sided optically polished ceramics (thickness∼1.5 mm) were performed using a Bruker IFS-113v Fourier-transform IR spectrometer equipped with a liquid-He-cooledSi bolometer (1.6 K) serving as a detector. For both the THzcomplex transmittance and IR reflectivity measurements, thetemperature control was done through an Oxford InstrumentsOptistat optical continuous He-flow cryostats with mylarand polyethylene windows, respectively. A commercial high-temperature cell Specac P/N 5850 was used for IR and THzstudies above room temperature. The samples were heated invacuum up to 580 K. We were concerned about heating thesamples to higher temperatures to prevent degradation of thesamples. The IR spectra were fitted using one Lorentz oscilla-tor for each phonon mode. The complex dielectric function isgiven byε(ω) = ε∞ +∑j ε jω20 jω20 j − ω2 − iγ jω, (1)where ε∞ is the contribution from electronic transitions tothe dielectric function, and the jth phonon is describedby an eigenfrequency ω0 j , an oscillator strength ε j , anddamping γ j . These parameters were fitted so that the re-flectivity at normal incidence, given by R(ω) = |√ε(ω)−1√ε(ω)+1|2,matches the experimental data. The eigenfrequencies ω0 jcorrespond to the transverse optical phonon frequencies.The high-frequency permittivity ε∞ was obtained fromthe room-temperature frequency-independent reflectivity tailabove the phonon frequencies and was assumed temperatureindependent.Unpolarized Raman spectra were recorded using a Ren-ishaw inVia Qontor spectrometer with a 785-nm linearlypolarized diode-pumped laser and an edge filter. Measure-ments were done at fixed temperatures from 10 to 600 K usinga THMS600 Linkam stage cooled by a nitrogen flow down to80 K and a custom-made closed-cycle helium cryostat downto 10 K. The laser power (2.3 mW) was chosen adequatelyto prevent heating the sample. The wave number at a giventemperature ω(T ) of each Raman mode is obtained by the bestfit of the Raman spectra with a sum of damped oscillators [30]:I (ω, T ) = [1 + n(ω, T )]∑jA0 j�20 j�0 jω(�20 j − ω2)2 + �20 jω2, (2)where n(ω, T ) is the Bose-Einstein factor and A0 j, �0 j, �0 jare the strength, wave number, and damping coefficient of thejth oscillator, respectively. In the temperature range where noanomalous behavior is observed, the temperature dependenceof the wave number of the phonon frequencies is well de-scribed by the normal anharmonic temperature effect due tovolume contraction as temperature decreases [31]:ω(T ) = ω0 + C[1 + 2ex − 1]+ D[1 + 3ey − 1+ 3(ey − 1)2](3)with x ≡ h̄ω0/2kBT , y ≡ h̄ω0/3kBT, and where ω0, C, andD are model constants, h̄ is the reduced Planck constant, andkB is the Boltzmann constant.Deviations to the normal anharmonic temperature effectwere interpreted on the basis of the spin-phonon couplingas [32] ω(T ) = ω(T ) − ω0 ∝ ∂2J∂u2〈Si · Sj〉 ≈ R〈Si · Sj〉 (4)where J is the magnetic exchange integral, u is the normalcoordinate of the vibrational mode, and R is the difference ofthe second derivatives of the ferro- and antiferromagnetic ex-change integrals with respect to the normal coordinate, wherethe approximation assumes the same spin correlation function,〈Si · Sj〉, for both.III. RESULTS AND DISCUSSIONA. Polar soft phonon in the THz rangeFigures 2(a) and 2(b) show the real and imaginary parts ofthe complex dielectric spectra, ε′(ω) and ε′′(ω) of BiMn7O12,respectively, measured at several fixed temperatures in theTHz spectral range. At 580 K, only one polar phonon is ob-served at 28 cm−1. As the temperature decreases towards T2 =460 K, the phonon frequency shifts towards lower frequen-cies, while the static permittivity increases, and on further134111-3A. MAIA et al. PHYSICAL REVIEW B 109, 134111 (2024)320 K350 K380 K400 K420 K460 K500 K580 K10 K50 K70 K100 K150 K200 K250 K295 K320 K350 K380 K400 K420 K460 K500 K580 K10 K50 K70 K100 K150 K200 K250 K295 K10 20 30 40 50 60 70 80 90020406080100120140320 K350 K380 K400 K420 K460 K500 K580 K10 K50 K70 K100 K150 K200 K250 K295 K-20020406080100120140320 K350 K380 K400 K420 K460 K500 K580 K10 K50 K70 K100 K150 K200 K250 K295 KBiMn7O12(a)(b)’’’Wave number (cm-1)FIG. 2. (a) ε′(ω) and (b) ε′′(ω) spectra of BiMn7O12 obtained byTHz time-domain spectroscopy at several temperatures.cooling to 380 K, the phonon hardens. This temperature be-havior is typical of a polar soft phonon driving a displaciveferroelectric phase transition. Below 380 K, the phonon soft-ens once again down to 300 K. This phonon anomaly at 300K is in the vicinity of the structural phase transition from theIm to P1 structure, in which the ferroelectric polarization ispredicted to move out of the ac plane [18]. Below 300 K,the phonon frequency smoothly increases down to 10 K. Thisbehavior is best seen in the temperature dependence of thesoft mode wave number and its dielectric strength, depictedin Figs. 3(a) and 3(b), respectively. The dielectric strength ofthe soft phonon, εSM (T ), considerably increases on coolingfrom 580 K towards 460 K [see Fig. 3(b)] due to the conser-vation law of the oscillator strength f j = ε j (T )ω20 j (T ) =const (valid for all uncoupled polar phonons, including thesoft mode). It is noteworthy that at 580 K, εSM consti-tutes approximately 90% of the static electric permittivityin the THz range: ε0 = ε∞ + ∑j ε j . Cooling from 380 K, εSM (T ) decreases and exhibits a broad plateaulike behaviordown to 300 K, below which it smoothly decreases down to20% of the static electric permittivity at the lowest measuredtemperature.The temperature dependence of the relative changes of realand imaginary parts of the dielectric permittivity measured atFIG. 3. (a) Temperature dependence of the frequency of twocomponents of the soft mode in BiMn7O12, ω02 = ωSM and ω01,where the latter is discernable only below room temperature. (b)Temperature dependence of dielectric strength of the soft mode andthe sum of the contributions of all phonons to the static permittivity.The dashed lines are a guide for the eye. Inset: Contribution (in %)of the SM to the total static permittivity.5.8 GHz, is shown in Figs. 4(a) and 4(b), respectively. A broadanomaly at 300 K is clearly visible, which is qualitatively con-sistent with the phonon anomaly in Fig. 3 near T3. Its absolutevalue is smaller than ε in Fig. 3, most likely due to loweraccuracy of the microwave (MW) measurements, because therectangular sample plate is much smaller than base dielectricresonator while the exact calculation of ε requires the samediameter of the cylindrical sample and base resonator [27].The anomalies seen at magnetic phase transitions near 60 and28 K (see also our magnetic moment measurements in Fig. S2[25]) can come from both magnetic permeability μ and elec-tric permittivity ε, but it should be mentioned that dielectricmeasurements at 100 kHz revealed similar anomalies in ε(T)[23] and also in the Hz frequency range (see Fig. S3 of theSupplemental Material [25]), so we assume that the anomaliesobserved at low temperatures in Fig. 4 also come from ε(T)and not from μ(T). The existence of dielectric anomalies atthe magnetic phase transition temperatures is also in agree-ment with Ref. [18] which, based on a detailed analysis of134111-4TWO DISPLACIVE FERROELECTRIC PHASE … PHYSICAL REVIEW B 109, 134111 (2024)1.001.051.101.151.200 50 100 150 200 250 300 350 40006121824303642ε'(T)/ε'(10K)BiMn7O125.8 GHz(a)(b)ε''(T)/ε''(10K)Temperature (K)20 40 60 80 1001.0051.0101.015ε'(T)/ε'(10K)Temperature (K)20 40 60 80 1001.42.84.25.6ε''(T)/ε''(10K)Temperature (K)FIG. 4. Relative changes of the (a) real and (b) imaginary partsof the dielectric permittivity measured at 5.8 GHz.neutron powder diffraction data, revealed that the magneto-electric coupling via inverse exchange striction, expressed bytrilinear coupling of the order parameters, uniquely stabilizesa polar collinear magnetic structure.It should be mentioned that the dielectric anomalies seenat the magnetic phase transitions in the temperature depen-dence of permittivity, both in the microwave (Fig. 4) andlow-frequency spectral range (Fig. S3 [25]), are not detectedin the THz spectra, as the measurements were performed each10 K, not exactly coinciding with the temperatures of the mag-netic phase transitions. Moreover, the permittivity anomalieshave values of 1–2 (see Fig. S3 [25]), which are comparableto the accuracy of the THz measurements.Unfortunately, due to the experimental limitations of ourMW setup, it was not possible to measure above 400 K, so theeffect of the higher temperature structural transitions (T1 andT2) in the MW permittivity are not ascertained [15]. The originof the small anomaly around 95 K is unknown, but it shouldbe noted that, at the same temperature, a small anomaly in thetemperature dependence of the magnetization was observed(see Fig. S2b [25]), but no anomaly in specific heat was seennear 95 K (see Fig. 7).B. Polar phononsTo better describe the temperature dependence of the polarsoft phonon and its contribution to the total permittivity, we0 100 200 300 400 500 6000.10.20.30.40.50.60.70.8BiMn7O12 500 K300 K20 KFrequency (cm-1)ReflectivityFIG. 5. Unpolarized IR reflectivity spectra of BiMn7O12 ceram-ics recorded at 20, 300, and 500 K. The corresponding fits are shownas dotted lines. The reflection band below 50 cm−1 corresponds tothe soft mode.FIG. 6. (a) ε′ and (b) ε′′ (in logarithmic scale) spectra ofBiMn7O12 obtained from fitting the IR reflectivity at severaltemperatures.134111-5A. MAIA et al. PHYSICAL REVIEW B 109, 134111 (2024)TABLE I. Factor-group analysis of the �-point phonons in BiMn7O12 [33–35]. The Wyckoff positions were taken from Ref. [13].Temperature Space group IR-active modes Raman-active modes Silent modes Acoustic modesT > T1 Im3̄ 13Tu 3Ag ⊕ 3Eg ⊕ 7Tg 3Au ⊕ 3Eu 1TuT2 < T < T1 I2/m 19Au ⊕ 23Bu 13Ag ⊕ 11Bg 1Au ⊕ 2BuT3 < T < T2 Im 32A′ ⊕ 25A′′ 32A′ ⊕ 25A′′ 2A′ ⊕ 1A′′T < T3 P1 57A 57A 3Ahave also probed the higher energy polar lattice excitationsthrough temperature dependent unpolarized Fourier transforminfrared spectroscopy. Representative unpolarized reflectivityspectra, recorded at 20, 300, and 500 K, are shown in Fig. 5.The MIR spectrum at 300 K is shown in Fig. S4, and the fitparameters are listed in Table SI of the Supplemental Material[25]. The spectra of the real and imaginary parts of permit-tivity, calculated from fitting the IR reflectivity spectra usingEq. (1), are also shown in Figs. 6(a) and 6(b), respectively.The factor-group analysis and the optical activity ofphonons for the different structural phases is presented inTable I. The primitive cell contains only one formula unitBiMn7O12 in all crystal phases. From a symmetry point ofview, 15 new polar modes and 33 new Raman modes becomeactive due to a change of symmetry from monoclinic I2/m tothe lower symmetry monoclinic Im at 460 K. When changingfrom Im symmetry to P1 at 300 K, no new IR or Raman modesare expected. However, it should be emphasized that in theferroelectric Im and P1 phases all phonons are both IR andRaman active.It should be noted that the I2/m structure contains 69 modes(including acoustic modes), although there are only 60 modesin the Im and P1 phases, at lower temperatures. This apparentdiscrepancy is due to the Bi cation being at Wyckoff position8 j with 1/4 occupancy in the I2/m phase [13], so nine moremodes are allowed than at lower temperatures. According toRef. [13], in the cubic phase the Bi cation is in the Wyckoffposition 16 f with an occupation of only 1/8 and is thereforealso predicted to have a higher number of degrees of freedom,and modes, than at lower temperatures. The partial occupationof atomic positions influences the increased damping of thecorresponding phonons in the high-temperature phases.The significant increase in the number of polar modes withcooling can be seen both in Figs. 5 and 6. Experimentally, wedetected 41 IR-active modes at 20 K (P1 phase), 31 modes at300 K (Im phase), and 28 modes at 500 K (I2/m phase). Thisis below the number of modes expected from the factor-groupanalysis. Both the high number of modes and the temperatureranges of the phase transitions leading to a higher dampingof the modes explain the lower number of detected modes.Furthermore, many of those modes can have an intensity thatis below our detection limit.The soft mode should have Tu symmetry in the cubic phaseand should split in the monoclinic I2/m phase below 608K into three components with Au + 2Bu symmetries. SinceBiMn7O12 chemically decomposes at high temperatures, itwas possible to perform THz measurements only up to 580 K,when the soft mode must already be split into three compo-nents. The phonons with frequencies ω01–ω03 are very likelythe three components of the soft mode, although the mode ω03is not seen at 500 K (see Table SI [25]) due to its low strengthand strong damping and only resolves below 380 K in Imphase. The two components of the soft mode with frequenciesω01 and ω02 lie below 30 cm−1, but are overlapped above T3,so that they can only be resolved in the P1 phase below 300 K,when they harden and their damping decreases with cooling(see Fig. 3).C. Specific heatThe specific heat, divided by temperature, as a function oftemperature, is shown in Fig. 7. Two anomalies are clearlyobserved in the temperature dependence of the specific heatat 59 and at 24 K, respectively. The temperatures at whichthese anomalies occur are in good agreement with the re-ported values of the critical temperatures of the magneticphase transitions occurring at TN1 = 59 K and at TN3 = 23 K,respectively, associated with the paramagnetic to the E-typeantiferromagnetic ordering of the B-site Mn3+ spins, and achange of spin ordering of both A′- and B-site Mn sublattices.As in previous reports, the specific heat does not reveal anyanomalous temperature dependence at TN2 nor at the structuralphase transitions occurring below 300 K. The analysis ofthe specific heat versus temperature, by means of the fittingof Debye´s equation to the experimental data, enabled us tocalculate the magnetic contribution to the specific heat, shownin Fig. 7 (neglecting the electronic contribution only relevant0 50 100 150 2000123CT/TCpho/TCmag/TC/T(Jmol-1K-2)T (K)FIG. 7. Temperature dependence of the specific heat divided bytemperature of BiMn7O12. Solid red line was determined by the bestfit of Debye equation to the experimental data recorded above 120 K.Temperature dependence of the magnetic contribution to the specificheat, calculated from the difference of the experimental data andthe extrapolated lattice contribution described by Debye behavior,extrapolated to 2 K.134111-6TWO DISPLACIVE FERROELECTRIC PHASE … PHYSICAL REVIEW B 109, 134111 (2024)100 200 300 400 500 600 700 800400 K320 K280 K240 K200 K160 K120 K80 K600 KIntensity(arb.units)Raman Shift (cm-1)500 KFIG. 8. Unpolarized Raman spectra of BiMn7O12 ceramicsrecorded at several fixed temperatures. The spectra are verticallyoffset from each other for better resolution.below 10 K) [25]. The magnetic contribution to the specificheat increases just below 150 K, due to precursor magneticeffects. The existence of precursor effects well above themagnetic phase transition has been observed also in rare-earthorthomanganites, like GdMnO3 [36].D. Raman scattering and spin-phonon couplingFigure 8 shows the unpolarized Raman spectra recordedat different fixed temperatures, in the 100–850 cm−1 spec-tral range. The energies of the Raman modes determined inthree crystal phases are listed in Table SII [25]. The hightemperature Raman spectra reveal rather broad bands, due tothermal effects. The Raman spectrum recorded at 600 K isproperly simulated with seven bands in this spectral range.According to group theory arguments and published crystal-lographic data [13], in the Im3̄ cubic symmetry only phononsinvolving vibrations of oxygen atoms are Raman active. Asexpected, on cooling, the Raman bands become narrower andshift towards higher wave numbers, according to Eq. (3).The phase transition at T1 = 608 K impacts certain spectralfeatures, with the most evident being the splitting of the bandlocated at 175 and 633 cm−1, at 600 K, and the appearance ofsharp bands at 158 cm−1 in the spectrum recorded at 380 K.The spectrum recorded at 400 K is described by 12 bands.The structural phase transition from Im to P1, at 290 K isrevealed by the appearance of weak bands, better observedin the 470–550 cm−1 range. However, the number of newbands is smaller than the number of predicted new modes inthe Raman spectra recorded in the monoclinic and triclinicphases; this discrepancy is explained by a weak intensity ofmodes and partial/total band overlap. Nevertheless, a detailedanalysis of the temperature dependencies of the frequencyof some phonons reveals interesting results, which we willaddress in the following.Figure 9(a) shows the temperature dependence of thephonon frequency, observed at 153 cm−1 at 440 K. Thisphonon is only observed below T2 = 460 K, and its frequencyexhibits a cusplike anomaly at ∼294 K, exactly at the Im to P1structural phase transition. In rare-earth orthomanganites andrare-earth orthoferrites, low frequency phonons lying in thisspectral range are assigned to the A-site atomic vibrations. Theappearance of this band at the cubic (Im3̄) to the monoclinic(I2/m) phase transition at T2 reveals the Raman activationof vibrations involving other than just oxygen movements.Although no mode assignment is available to the best ofour knowledge, we tentatively assign the phonon seen near150 cm−1 to the A- or A′-site cation vibration, likely asso-ciated with Mn oscillations. This mode assignment is alsosupported by the current interpretation of the Raman spectrarecorded in LaMn7O12 [37]. The ferroelectric polarization iscaused mainly by displacement of Bi cations, but in the Aperovskite positions there is not only Bi, but also three Mncations which should sense the displacement of Bi cations,and therefore, the vibration of these Mn cations could alsoshow a change in frequency at the ferroelectric phase transi-tion from the Im to the P1 phase. The same phonon displays,above room temperature, an increasing damping when heatingto T2 = 460 K (Fig. S6 [25]). Since this phonon is highlydamped above T2, it is not possible to accurately determine itsfrequency in the I2/m phase. A mode with a similar frequencyis seen in the IR spectra, but its value shows a strong increasewith heating (Fig. S6 [25]). Also, its attenuation is high at hightemperatures, so its frequency is burdened with a large error,making it impossible to determine whether it is the same modeas in the Raman spectra (which is allowed by the selectionrules in Table I) or a different mode entirely.The magnetic phase transition occurring at TN1 = 59 Kis also reflected by the anomalous temperature dependenceof some internal vibrations. As a representative example, wepresent in Figs. 9(a) and 9(b) the temperature dependenceof the modes at 559 cm−1 (value at 400 K) and 633 cm−1(value at 600 K), respectively. These two modes are known toinvolve the oxygen vibrations and, consequently, they accountfor the changes in bond angle O-Mn-O and length Mn-O,respectively. Therefore, these vibrations probe the magneticexchange interactions. On cooling, the wave number of thesetwo modes increases, following the anharmonic temperaturebehavior described by the solid lines, determined by the fit ofEq. (3) to the experimental data above 200 K and extrapolatedto low temperatures. No clear anomalies are ascertained inthe structural phase transitions, but a detailed inspection ofthe temperature dependence of the wave number of thesetwo modes shows a clear deviation from the extrapolatedanharmonic temperature behavior. The deviation is clear atTN1 = 59 K; for further cooling, an anomalous increase isobserved, due to spin-phonon coupling in this compound. Asrepresentative example, we focus on the Mn-O vibration at134111-7A. MAIA et al. PHYSICAL REVIEW B 109, 134111 (2024)FIG. 9. (a),(b) Temperature dependence of the wave number of selected Raman modes. The best fit with Eq. (3) in the paraelectric phaseis represented by a solid line and is extrapolated down to 0 K. (c) The deviation, ω, of the highest phonon frequency seen near 650 cm−1from the anharmonic temperature behavior [Eq. (3)] as a function of the spin-spin correlation function, 6J〈Si · Sj〉, obtained from integratingthe magnetic contribution to the specific heat, shown in Fig. 7. Inset: temperature dependencies of ω and 6J〈Si · Sj〉.∼559 cm−1 (value at 400 K), shown in Fig. 9(a), which bettersenses the magnetic phase transition at TN1. According to spin-phonon coupling theory presented in Eq. (4), the anomaloustemperature dependence of the wave number must be a linearfunction of the spin-spin correlation function, 〈Si · Sj〉, whichcan be calculated from the integral of the magnetic contribu-tion to the specific heat shown in Fig. 9 [32]. In this case,the anomalous temperature dependence of the wave numberof the aforementioned Mn-O vibration is a linear functionof the spin-spin correlation function, as shown in Fig. 9(c),providing clear evidence for the coupling between lattice vi-brations and the magnetic momenta in BiMn7O12. Note thatthe spin-spin correlation function calculated from the mag-netic contribution to the specific heat increases linearly belowTN1 and saturates at low temperatures below 10 K [see inset ofFig. 9(c)].The detailed temperature dependence of other Raman-active phonons is shown in Fig. S5 [25]. The classicalanharmonic behavior, according to Eq. (3), is observed formost phonons, except the mode at 340 cm−1 which exhibitsan anomalous temperature behavior, likely caused by a short-range magnetic order above TN1.IV. CONCLUSIONSWe observed the softening of a phonon in the THz rangeon cooling towards T2 = 460 K, a temperature at whichBiMn7O12 undergoes a structural phase transition from mon-oclinic I2/m to a noncentrosymmetric monoclinic Im phase.At 300 K, this phonon also has an anomaly coinciding withanother structural phase transition to the P1 phase, in whichthe polarization is predicted to move out of the ac plane.The observed behavior of the optical phonon is typical for134111-8TWO DISPLACIVE FERROELECTRIC PHASE … PHYSICAL REVIEW B 109, 134111 (2024)displacive ferroelectric phase transitions. Also, the microwavepermittivity shows a peak at T3 = 290 K, indicating the fer-roelectric nature of the phase transition at this temperature.For experimental reasons, it was not possible to measure themicrowave permittivity above 400 K, i.e., not near T2 or T1.Unfortunately, neither the polarization hysteresis loops nor thepyrocurrent could be measured due to the conductivity of thesample above 100 K, but the soft mode in THz and IR spectraclearly indicates signs of successive displacive ferroelectricphase transitions in the two polar phases Im and P1.The results here presented are consistent with the recentlyreported temperature dependence of the polarization calcu-lated from Mössbauer data for BiMn6.96Fe0.04O12, showing aparaelectric to ferroelectric phase transition around 437 K, anda considerable increase in polarization below 270 K, with anextrapolated Curie temperature of 294 K [19].The dielectric anomalies, measured at 5.8 GHz and in the1–10 Hz range, observed near TN1 and TN3 are indicativeof a strong magnetoelectric coupling at the magnetic phasetransitions. 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