# Fileset

[Inorganics-V13-315-RMn3Ni2Mn2O12.pdf](https://mdr.nims.go.jp/filesets/4e2e2ac9-aeaf-42d3-bae5-87f0b09f7183/download)

## Creator

[Alexei A. Belik](https://orcid.org/0000-0001-9031-2355), [Ran Liu](https://orcid.org/0000-0002-1659-2325), [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Hidden Magnetic-Field-Induced Multiferroic States in A-Site-Ordered Quadruple Perovskites RMn3Ni2Mn2O12: Dielectric Studies](https://mdr.nims.go.jp/datasets/ae3814cb-706b-484d-a71e-edf865ea4fdb)

## Fulltext

Hidden Magnetic-Field-Induced Multiferroic States in A-Site-Ordered Quadruple Perovskites RMn3Ni2Mn2O12: Dielectric StudiesAcademic Editor: Chiara DionigiReceived: 3 September 2025Revised: 16 September 2025Accepted: 22 September 2025Published: 25 September 2025Citation: Belik, A.A.; Liu, R.;Yamaura, K. HiddenMagnetic-Field-Induced MultiferroicStates in A-Site-Ordered QuadruplePerovskites RMn3Ni2Mn2O12:Dielectric Studies. Inorganics 2025, 13,315. https://doi.org/10.3390/inorganics13100315Copyright: © 2025 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/).ArticleHidden Magnetic-Field-Induced Multiferroic States inA-Site-Ordered Quadruple Perovskites RMn3Ni2Mn2O12:Dielectric StudiesAlexei A. Belik 1,* , Ran Liu 1,2,3 and Kazunari Yamaura 1,21 Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS),Namiki 1-1, Tsukuba 305-0044, Ibaraki, Japan; liu.ran@sanken.osaka-u.ac.jp (R.L.);yamaura.kazunari@nims.go.jp (K.Y.)2 Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku,Sapporo 060-0810, Hokkaido, Japan3 Institute of Scientific and Industrial Research, Osaka University, Mihogaoka 8-1,Ibaraki 567-0047, Osaka, Japan* Correspondence: alexei.belik@nims.go.jpAbstractThe appearance of spin-induced ferroelectric polarization in the so-called type-II mul-tiferroic materials has received a lot of attention. The nature and mechanisms of suchpolarization were intensively studied using perovskite rare-earth manganites, RMnO3, asmodel systems. Later, multiferroic properties were discovered in some RFeO3 perovskitesand possibly in some RCrO3 perovskites. However, R2NiMnO6 double perovskites have fer-romagnetic structures that do not break the inversion symmetry. It was found recently thatmore complex magnetic structures are realized in A-site-ordered quadruple perovskites,RMn3Ni2Mn2O12. Therefore, they have the potential to be multiferroics. In this work,dielectric properties in magnetic fields up to 9 T were investigated for such perovskitesas RMn3Ni2Mn2O12 with R = Ce to Ho and for BiMn3Ni2Mn2O12. The samples withR = Bi, Ce, and Nd showed no dielectric anomalies at all magnetic fields, and the dielec-tric constant decreases with decreasing temperature. The samples with R = Sm to Hoshowed qualitatively different behavior when the dielectric constant started increasingwith decreasing temperature below certain temperatures close to the magnetic orderingtemperatures, TN. This difference could suggest different magnetic ground states. Thesamples with R = Eu, Dy, and Ho still showed no anomalies on the dielectric constant.On the other hand, peaks emerged at TN on the dielectric constant in the R = Sm samplefrom about 2 T up to the maximum available field of 9 T. The Gd sample showed peaks ondielectric constant at TN between about 1 T and 7 T. Transition temperatures increase withincreasing magnetic fields for R = Sm and decrease for R = Gd. These findings suggest thepresence of magnetic-field-induced multiferroic states in the R = Sm and Gd samples withintermediate ionic radii. Dielectric properties at different magnetic fields are also reportedfor Lu2NiMnO6 for comparison.Keywords: A-site-ordered quadruple perovskites; B-site double ordering; multiferroics;dielectric constant1. IntroductionThe appearance of spin-induced ferroelectric polarization in the so-called type-II mul-tiferroic materials has received a lot of attention in the literature [1–7]. Because ferroelectricInorganics 2025, 13, 315 https://doi.org/10.3390/inorganics13100315https://doi.org/10.3390/inorganics13100315https://doi.org/10.3390/inorganics13100315https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/inorganicshttps://www.mdpi.comhttps://orcid.org/0000-0001-9031-2355https://orcid.org/0000-0002-1659-2325https://orcid.org/0000-0003-0390-8244https://doi.org/10.3390/inorganics13100315https://www.mdpi.com/article/10.3390/inorganics13100315?type=check_update&version=1Inorganics 2025, 13, 315 2 of 19polarization appears as a result of a magnetic ordering, there is a strong magnetoelec-tric coupling in such materials, allowing for the control of ferroelectric polarization viaa magnetic field and vice versa [8,9]. The nature and mechanisms of such polarizationwere intensively studied using perovskite-structure rare-earth (R) manganites, RMnO3,as model systems [10–13]. Only some members of the RMnO3 family with specific mag-netic structures develop spin-induced ferroelectric polarization, for example, in RMnO3(R = Tb to Dy) with modulated sinusoidal/spiral antiferromagnetic (AFM) ordering andin RMnO3 (R = Ho to Lu) with the so-called E-type magnetic ordering. Multiferroic prop-erties were discovered in some RFeO3 perovskites [14–20] and possibly in some RCrO3perovskites [21–23]. While the multiferroic properties of RFeO3 at very low temperatures,where they are caused by additional magnetic orderings of the R3+ sublattice, are wellestablished [14–16], the existence of ferroelectric polarization at higher temperatures inRFeO3 and RCrO3 is still under debate [18,19,24].All R2NiMnO6 double perovskites [25–41] have simple ferromagnetic (FM) structures(in the first approximation), which do not break inversion centers and do not produce spin-induced ferroelectric polarization. Nevertheless, there are a few reports with claims of spin-induced ferroelectric properties in R2NiMnO6 double perovskites [25,26]. However, suchclaims were not confirmed [27], and therefore, they are still controversial. The use of cationssmaller than Lu3+ (rXIII(Lu3+) = 0.977 Å [42]) at the R sites (such as Sc3+ with rXIII(Sc3+) =0.870 Å and In3+ with rXIII(In3+) = 0.92 Å [42]) further reduces Ni–O–Mn bond angles inthe R2NiMnO6 series, weakens the strength of direct FM Ni–Mn exchange interactions,and stabilizes complex AFM structures. For example, Sc2NiMnO6 demonstrates two AFMtransitions [43]. The dielectric constant of Sc2NiMnO6 starts increasing with decreasingtemperature when approaching TN1 = 35 K and shows a sharp drop below TN2 = 17 K.On the other hand, pyroelectric current measurements did not show the development ofspin-induced ferroelectric polarization [43]. One AFM transition with an incommensuratestructure was found in In2NiMnO6 at TN = 26 K [44,45], and this compound shows spin-induced ferroelectric polarization [45]. Ferroelectric polarization is suppressed by magneticfields above 6 T. The dielectric constant of In2NiMnO6 basically decreases with decreasingtemperature between 5 K and 300 K, and a sharp peak is only observed at TN [45]. It turnedout that Lu2NiMnO6 is located near a phase boundary between FM and AFM states on thephase diagram of the R2NiMnO6 double perovskites, and a moderate pressure can inducea transition from an FM state to an incommensurate AFM state [35].The R2NiMnO6 family of B-site-ordered double perovskites was recently extendedfurther to a subfamily of A-site-ordered quadruple perovskites [46–51] with the compo-sition of RMn3Ni2Mn2O12 with R = Bi [52], La [53,54], Ce [52], Nd [55], Sm [55], Gd [55],Dy [55], and Ho [52]. RMn3Ni2Mn2O12 behaves differently from R2NiMnO6. For example,LaMn3Ni2Mn2O12 has two magnetic transitions at TN = 46 K and TC = 34 K [53] (similar toSc2NiMnO6 and in comparison with other members of the R2NiMnO6 family (R = La to Lu)).Complex magnetic structures are realized in LaMn3Ni2Mn2O12 [53]. NdMn3Ni2Mn2O12 al-ready shows one magnetic transition at TN = 26 K [55]. Net FM components are developedat the ground states of RMn3Ni2Mn2O12 with R = La and Nd. On the other hand, AFMground states are basically realized in RMn3Ni2Mn2O12 with R = Sm to Ho. Complex AFMground states are promising for the realization of spin-induced ferroelectric polarization.However, detailed dielectric studies of the RMn3Ni2Mn2O12 perovskites have not beenperformed yet.Therefore, in this work, we investigated nearly all members of the RMn3Ni2Mn2O12family by performing detailed measurements of dielectric constant in different magneticfields up to 9 T. While no dielectric constant anomalies were found at a zero magneticfield in all samples, peaks emerge in the dielectric constant in the R = Sm and Gd samplesInorganics 2025, 13, 315 3 of 19in intermediate ranges of the magnetic field. These observations suggest the presence ofmagnetic-field-induced multiferroic states in the R = Sm and Gd samples. Basic physicalproperties of EuMn3Ni2Mn2O12 and dielectric properties at different magnetic fields forLu2NiMnO6 are also reported for comparison.2. Results and Discussion2.1. R = Bi, Ce, and NdTemperature dependence of dielectric constant and loss tangent of BiMn3Ni2Mn2O12in different magnetic fields is shown in Figure 1. Very weak effects of magnetic fields ondielectric constant values were observed in agreement with the reported weak effects ofmagnetic fields on specific heat values [52]. No dielectric constant anomalies were observedat TN = 36 K [52] of BiMn3Ni2Mn2O12.2302402502602702802900 10 20 30 40 500 T, cooling0 T, heating1 T, cooling1 T, heating5 T, cooling5 T, heating2302502702900 10 20 30 40 50100 Hz 301 Hz903 Hz 2.71 kHz8.16 kHz 24.5 kHz73.7 kHz 221 kHz665 kHz0.0000.0030.0060.0090 10 20 30 40 500 T, cooling 0 T, heating1 T, cooling 1 T, heating5 T, cooling 5 T, heatingTemperature (K) Dielectric constant, εLoss tangent (a) (b) f = 665 kHz BiMn3Ni2Mn2O12 TN = 36 K 0.0030.0060 10 20 30 40 50100 Hz 301 Hz903 Hz 2.71 kHz8.16 kHz 24.5 kHz73.7 kHz 221 kHz665 kHzFigure 1. (a) Temperature dependence of dielectric constant of BiMn3Ni2Mn2O12 at one frequency of665 kHz and different magnetic fields of 0, 1, and 5 T on cooling and heating. The inset shows thetemperature dependence of the dielectric constant at different frequencies at H = 0 T (on cooling).The arrow shows a magnetic transition temperature [52]. (b) Temperature dependence of loss tangentof BiMn3Ni2Mn2O12 at one frequency of 665 kHz and different magnetic fields of 0, 1, and 5 T oncooling and heating. The inset shows the temperature dependence of the loss tangent at differentfrequencies at H = 0 T (on cooling).The temperature dependence of the dielectric constant and loss tangent ofCeMn3Ni2Mn2O12 (Figure 2) and NdMn3Ni2Mn2O12 (Figures 3 and S1) were qualita-Inorganics 2025, 13, 315 4 of 19tively similar. The dielectric constant slightly decreased with decreasing temperature, andweak effects of magnetic fields on dielectric constant values were observed below about60 K. Loss tangent of both samples showed broad anomalies below about 15 K (at thefrequency of 665 kHz). No dielectric constant anomalies were observed at their magnetictransition temperatures of 27 K and 33 K (for R = Ce [52]) and 26 K (for R = Nd [55]). Indielectric insulator materials without any ferroelectric or ferroelectric-like transitions, thedielectric constant is usually temperature independent or slightly decreases with decreasingtemperature. Therefore, the temperature dependence of the dielectric constant of the R = Ceand Nd samples is typical for ordinary insulators.0.0000.0010.0020.0030.0040.0050 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heating22.723.023.323.623.90 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heatingTemperature (K) Dielectric constant, εLoss tangent (a) (b) f = 665 kHz CeMn3Ni2Mn2O12 TN1 = 33 K TN2 = 27 K Figure 2. (a) Temperature dependence of dielectric constant of CeMn3Ni2Mn2O12 at one frequency of665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating. Arrows show mag-netic transition temperatures [52]. (b) Temperature dependence of loss tangent of CeMn3Ni2Mn2O12at one frequency of 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating.2.2. R = SmThe temperature dependence of the dielectric constant of RMn3Ni2Mn2O12 withR = Sm to Ho was qualitatively different from that of RMn3Ni2Mn2O12 with R = Bi, Ce,and Nd because the dielectric constant started increasing with decreasing temperaturebelow about 30–40 K. The increase of the dielectric constant suggests the development ofpolar correlations. This change in the behavior of the dielectric constant also correlateswith the changes in the magnetic properties because net FM components were observed atthe ground states of RMn3Ni2Mn2O12 with R = Ce and Nd, while AFM ground states areInorganics 2025, 13, 315 5 of 19basically realized in RMn3Ni2Mn2O12 with R = Sm to Ho. This change in the behavior ofthe dielectric constant could reflect different magnetic structures.0.0000.0010.0020.0030.0040.0050 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heating36.537.037.538.038.539.039.50 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heatingTemperature (K) Dielectric constant, εLoss tangent (a) (b) f = 665 kHz NdMn3Ni2Mn2O12 TN = 26 K -0.001Figure 3. (a) Temperature dependence of dielectric constant of NdMn3Ni2Mn2O12 at one frequencyof 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating. The arrowshows a magnetic transition temperature [55]. (b) Temperature dependence of loss tangent ofNdMn3Ni2Mn2O12 at one frequency of 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T oncooling and heating.The dielectric constant and loss tangent of SmMn3Ni2Mn2O12 are shown in Figures 4and S2–S4. At H = 0 T, the dielectric constant and loss tangent of SmMn3Ni2Mn2O12showed no detectable anomalies. However, at H = 2 T, a small kink appears on thedielectric constant, and a peak is visible on the loss tangent near TN = 23 K. At highermagnetic fields (4–8 T), a small kink on the dielectric constant transforms to a small peak.Peaks on both dielectric constant and loss tangent are moving to higher temperatures withincreasing magnetic field in agreement with the similar shift of specific heat anomalies(Figure 5a), confirming their common magnetic origin. Peaks on loss tangent were observedat 20.5 K (at 2 T), 21.5 K (at 4 T), 23.0 K (at 6 T), 24.5 K (at 8 T), and 25.2 K (at 9 T). Almost nohysteresis in the peak positions was observed during cooling and heating. Therefore, theappearance of peaks on both dielectric constant and loss tangent at magnetic fields of 2–9 Tsuggests the development of spin-induced ferroelectric polarization in SmMn3Ni2Mn2O12at such magnetic fields.Inorganics 2025, 13, 315 6 of 1954.054.555.055.556.056.557.00 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heating0.0010.0030 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heatingTemperature (K) Dielectric constant, εLoss tangent (a) (b) f = 665 kHz SmMn3Ni2Mn2O12 TN = 23 K 0.0000.00110 20 30 409 T, cooling9 T, heating54.454.955.410 20 30 40 509 T, cooling9 T, heating-0.001-0.001Figure 4. (a) Temperature dependence of dielectric constant of SmMn3Ni2Mn2O12 at one frequencyof 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating. The arrow showsa magnetic transition temperature at H = 0 T [55]. (b) Temperature dependence of loss tangent ofSmMn3Ni2Mn2O12 at one frequency of 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T oncooling and heating. The insets show data at a magnetic field of 9 T.2.3. R = EuAs EuMn3Ni2Mn2O12 has not been reported yet, we start with the basic character-ization of this compound by other methods. EuMn3Ni2Mn2O12 crystallized in a cubicstructure of the A-site-ordered quadruple perovskite family [46–51] with a = 7.3430(1) Å.The quality of the standard laboratory X-ray diffraction data (with a measurement speed of3◦/min) did not allow detection of superstructure reflections related to (partial) orderingof Ni2+ and Mn4+ cations and, therefore, to assign the Im-3 or Pn-3 space groups. Therefore,we measured X-ray diffraction data with a speed of 0.1◦/min between 38◦ and 44◦ andcould detect a very weak (311) superstructure reflection. This fact suggests that there isa partial ordering of Ni2+ and Mn4+ cations, and the space group is Pn-3, similar to someother members of the RMn3Ni2Mn2O12 family [55]. Laboratory X-ray diffraction data alsoshowed the presence of some amounts of (Eu1−xMnx)MnO3 impurity (space group Pnmawith a = 5.5357 Å, b = 7.5834 Å, c = 5.3196 Å; about 6.7 wt. %) and NiO impurity (spacegroup R-3m with a = 2.9597 Å and c = 7.2374 Å; about 2.5 wt. %). The (Eu1−xMnx)MnO3impurity has a ferrimagnetic transition near 140 K.Inorganics 2025, 13, 315 7 of 190.00.51.01.52.00 20 40 60 800 T9 T0.40.91.41.90 10 20 30 40 500 T 2 T 4 T6 T 8 T0.00.51.01.52.00 20 40 60 800 T9 TC p / T (J×K−2 ×mol−1 ) SmMn3Ni2Mn2O12 Temperature (K) C p / T (J×K−2 ×mol−1 ) 0.40.91.41.90 10 20 30 40 500 T 3 T6 T 9 TGdMn3Ni2Mn2O12 (a) (b) Figure 5. (a) Cp/T vs. T curves of SmMn3Ni2Mn2O12 measured at H = 0 and 9 T on cooling. Theinset shows Cp/T vs. T curves at H = 0, 2, 4, 6, and 8 T. (b) Cp/T vs. T curves of GdMn3Ni2Mn2O12measured at H = 0 and 9 T on cooling. The inset shows Cp/T vs. T curves at H = 0, 3, 6, and 9 T.Temperature dependence of specific heat and magnetic susceptibilities ofEuMn3Ni2Mn2O12 is shown in Figure 6. Specific heat data clearly showed the presence ofone magnetic transition at TN = 33 K; the specific heat anomaly was slightly dependent onmagnetic fields. χ vs. T curves showed a very small kink at TN = 33 K. On the other hand,differential dχT/dT vs. T curves allowed detecting the magnetic anomaly more clearly (theinset of Figure 6b). At high temperatures, inverse magnetic susceptibilities followed theCurie–Weiss law (Figure S5), and the obtained Curie–Weiss parameters (using the 7 T FCCcurve in a temperature range of 250–350 K) were µeff = 11.216µB (the experimental effectivemagnetic moment) and θ = +0.1 K (the Curie–Weiss temperature). The µeff value was closeto the expected calculated value of µcalc = 11.382µB (taking 3.4µB for Eu3+ [56]).Inorganics 2025, 13, 315 8 of 190.00.10.20.30 50 100 150 200 250 300 350ZFC, 7 TFCC, 7 T0.220.320.420.520 10 20 30 40 50 600.10.20.3ZFC, 1 TFCC, 1 TZFC, 7 T0.00.51.01.50 20 40 60 80 1000 T 1 T 3 T5 T 7 T 9 T0.00.51.01.50 10 20 30 40 50C p / T (J×K−2 ×mol−1 ) Temperature (K) TN = 33 K EuMn3Ni2Mn2O12 χ (emu×mol−1 ×Oe−1 ) dχT/dT  Temperature (K) TN = 33 K (a) (b) Figure 6. (a) Cp/T vs. T curves of EuMn3Ni2Mn2O12 measured at H = 0, 1, 3, 5, 7, and 9 T oncooling. The inset shows Cp/T vs. T curves at H = 0 and 9 T. The arrow shows a magnetic transitiontemperature. (b) ZFC (filled symbols) and FCC (empty symbols) dc magnetic susceptibility curves(χ = M/H) of EuMn3Ni2Mn2O12 measured at H = 7 T. The inset shows ZFC and FCC dχT/dT vs. Tcurves at H = 1 T and 7 T.Isothermal magnetization curves (M vs. H) showed nearly linear behavior atT = 5–200 K above about 1 T (Figure S5). The S-type shape was observed near the ori-gin without any significant hysteresis originating from the impurity contribution with softFM-like properties. Nearly the same S-type contribution was observed at T = 5–100 K,that is, below and above TN = 33 K of EuMn3Ni2Mn2O12. On the other hand, the S-typeshape near the origin disappeared at 200 K, that is, above the ferrimagnetic transition of the(Eu1−xMnx)MnO3 impurity. Therefore, the χ vs. T and M vs. H curves give evidence that apurely AFM transition takes place in EuMn3Ni2Mn2O12 without any net FM-like moments.Temperature dependence of the dielectric constant and loss tangent of EuMn3Ni2Mn2O12(Figure 7) at different magnetic fields (0–8 T) showed no anomalies at TN = 33 K, suggestingthe absence of any detectable (spin-induced) ferroelectric polarization.Inorganics 2025, 13, 315 9 of 19 0.0000.0020.0040 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heating43444546470 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heatingTemperature (K) Dielectric constant, ε Loss tangent (a) (b) f = 665 kHz EuMn3Ni2Mn2O12 TN = 33 K Figure 7. (a) Temperature dependence of dielectric constant of EuMn3Ni2Mn2O12 at one frequency of665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating. The arrow shows amagnetic transition temperature. (b) Temperature dependence of loss tangent of EuMn3Ni2Mn2O12at one frequency of 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating.2.4. R = GdThe dielectric constant of GdMn3Ni2Mn2O12 showed a small kink near TN = 22 K atH = 0 T (Figures 8 and S6). The kink transforms to a weak peak already at H = 1 T. Themost pronounced peaks on dielectric constant and loss tangent were observed at H = 5 T(Figures 8 and 9). Peaks on the dielectric constant disappear at H = 8 and 9 T. Peaks onthe dielectric constant clearly move to lower temperatures with increasing magnetic fields(peaks were observed at 23.2 K at 1 T, 23.0 K at 2 T, 22.5 K at 3 T, 21.5 K at 4 T, 20.5 K at 5 T, and19.2 K at 6 T) in agreement with specific heat measurements (Figure 5b), confirming theircommon magnetic origin. Therefore, GdMn3Ni2Mn2O12 exhibits spin-induced ferroelectricpolarization at about H = 1–7 T.2.5. R = DyThe temperature dependence of the dielectric constant and loss tangent ofDyMn3Ni2Mn2O12 between H = 0 T and H = 8 T (Figure 10) was close to those ofEuMn3Ni2Mn2O12 (Figure 6). No anomalies were observed at the magnetic transitiontemperatures of 36 K and 10 K [55].Inorganics 2025, 13, 315 10 of 19 43.443.744.00 10 20 30 40 505 T, cooling 5 T, heating6 T, cooling 6 T, heating7 T, cooling 7 T, heating8 T, cooling 8 T, heating9 T, cooling 9 T, heating43.443.744.044.344.644.945.20 10 20 30 40 500 T, cooling 0 T, heating1 T, cooling 1 T, heating2 T, cooling 2 T, heating3 T, cooling 3 T, heating4 T, cooling 4 T, heatingTemperature (K) Dielectric constant, ε (a) (b) f = 665 kHz GdMn3Ni2Mn2O12 Dielectric constant, ε TN = 22 K Figure 8. (a) Temperature dependence of dielectric constant of GdMn3Ni2Mn2O12 at one frequencyof 665 kHz and different magnetic fields of 0, 1, 2, 3, and 4 T on cooling and heating. The arrow showsa magnetic transition temperature at H = 0 T [55]. (b) Temperature dependence of dielectric constantof GdMn3Ni2Mn2O12 at one frequency of 665 kHz and different magnetic fields of 5, 6, 7, 8, and 9 Ton cooling and heating.2.6. R = HoTemperature dependence of dielectric constant and loss tangent of HoMn3Ni2Mn2O12between 0 T and 9 T is shown on Figures 11 and 12. Both dielectric constant and losstangent showed small peaks near 36 K; this temperature matches with the magnetic transi-tion temperature of HoMn3Ni2Mn2O12 [52], which was unambiguously determined withspecific heat and magnetization measurements [52]. On the other hand, this temperatureis also close to the magnetic and ferroelectric transition temperature of the HoMn2O5impurity [57–60], which shows very strong and sharp anomalies on both dielectric constantand loss tangent [57–59]. The positions and intensities of the peaks remained nearly thesame in all magnetic fields in HoMn3Ni2Mn2O12; and there was small hysteresis in thepositions of the peaks on cooling and heating. Exactly the same behavior was observedin HoMn2O5 [57–59]. On the other hand, no hysteresis was observed on the temperaturedependence of magnetic susceptibilities of HoMn3Ni2Mn2O12 [52] (we note that almost noanomalies were observed on magnetic susceptibilities of HoMn2O5 [59,60]). Therefore, webelieve that there is a high probability that the observed anomalies on dielectric constantand loss tangent are caused by the HoMn2O5 impurity even though its amount was quitesmall (about 3 weight % [52]). Therefore, the intrinsic dielectric constant and loss tangentInorganics 2025, 13, 315 11 of 19of HoMn3Ni2Mn2O12 are very close to those of DyMn3Ni2Mn2O12; that is, there are nodetectable anomalies at the magnetic transition temperature between 0 T and 9 T. 0.00200.00230.00260.00290.00320 10 20 305 T, cooling 5 T, heating6 T, cooling 6 T, heating7 T, cooling 7 T, heating8 T, cooling 8 T, heating9 T, cooling 9 T, heating0.00200.00230.00260.00290 10 20 300 T, cooling 0 T, heating1 T, cooling 1 T, heating2 T, cooling 2 T, heating3 T, cooling 3 T, heating4 T, cooling 4 T, heatingTemperature (K) (a) (b) f = 665 kHz GdMn3Ni2Mn2O12 Loss tangent Loss tangent Figure 9. (a) Temperature dependence of loss tangent of GdMn3Ni2Mn2O12 at one frequency of665 kHz and different magnetic fields of 0, 1, 2, 3, and 4 T on cooling and heating. (b) Temperaturedependence of loss tangent of GdMn3Ni2Mn2O12 at one frequency of 665 kHz and different magneticfields of 5, 6, 7, 8, and 9 T on cooling and heating.2.7. Lu2NiMnO6For comparison, we report here the dielectric properties of one member of theR2NiMnO6 family with the smallest R3+ cation of R = Lu. Specific heat measurementsconfirmed the presence of one FM transition at TC = 41 K (the inset of Figures 13b and S7).Dielectric properties of different members of the R2NiMnO6 family were reported in theliterature [39,40], and no dielectric anomalies were usually observed. On the other hand,very detailed studies in the vicinity of TC demonstrated very weak kink-like anomaliesat TC [25,36]; however, effects of magnetic fields have not been studied. Temperaturedependence of the dielectric constant and loss tangent of our Lu2NiMnO6 sample, preparedby a high-pressure high-temperature method at 6 GPa, is shown in Figure 13. At H = 0 T,we observed a very weak kink-like anomaly at TC similar to the previous reports [25,36].The kink-like anomaly could originate from magnetostriction effects because Lu2NiMnO6is a ferromagnet [61,62]. High magnetic fields smeared kink-like anomalies; for example,at H = 7 T and 9 T, no visible dielectric anomalies were detected near TC. Therefore,Lu2NiMnO6 does not develop ferroelectric polarization between 0 T and 9 T. The dielectricInorganics 2025, 13, 315 12 of 19constant decreases with decreasing temperature between 3 K and 300 K, as for ordinaryinsulators/dielectrics.0.0000.0020.0040.0060.0080.0100 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heating454749515355570 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heating6 T, cooling 6 T, heating8 T, cooling 8 T, heatingTemperature (K) Dielectric constant, ε Loss tangent (a) (b) f = 665 kHz DyMn3Ni2Mn2O12 TN1 = 36 K TN2 = 10 K Figure 10. (a) Temperature dependence of dielectric constant of DyMn3Ni2Mn2O12 at one frequencyof 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T on cooling and heating. The arrows showthe magnetic transition temperatures at H = 0 T [55]. (b) Temperature dependence of loss tangent ofDyMn3Ni2Mn2O12 at one frequency of 665 kHz and different magnetic fields of 0, 2, 4, 6, and 8 T oncooling and heating.52.054.056.058.060.062.00 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heatingDielectric constant, ε(a) f = 665 kHz TN1 = 36 K 52.452.953.453.930 33 36 39 42TN2 = 10 K Figure 11. Cont.Inorganics 2025, 13, 315 13 of 1952.054.056.058.060.062.00 10 20 30 40 506 T, cooling6 T, heating8 T, cooling8 T, heating9 T, cooling9 T, heatingTemperature (K) (b) Dielectric constant, ε52.352.853.330 35 40 45HoMn3Ni2Mn2O12 Figure 11. (a) Temperature dependence of dielectric constant of HoMn3Ni2Mn2O12 at one frequencyof 665 kHz and different magnetic fields of 0, 2, and 4 T on cooling and heating. The arrows showthe magnetic transition temperatures [52]. (b) Temperature dependence of the dielectric constantof HoMn3Ni2Mn2O12 at one frequency of 665 kHz and different magnetic fields of 6, 8, and 9 T oncooling and heating. The insets show magnified parts.0.0000.0010.0020.0030.0040.0050.0060 10 20 30 40 506 T, cooling 6 T, heating8 T, cooling 8 T, heating9 T, cooling 9 T, heating0.0000.0010.0020.0030.0040.0050.0060 10 20 30 40 500 T, cooling 0 T, heating2 T, cooling 2 T, heating4 T, cooling 4 T, heatingTemperature (K) (a) (b) f = 665 kHz HoMn3Ni2Mn2O12 Loss tangent Loss tangent TN1 = 36 K TN2 = 10 K Figure 12. (a) Temperature dependence of loss tangent of HoMn3Ni2Mn2O12 at one frequency of665 kHz and different magnetic fields of 0, 2, and 4 T on cooling and heating. The arrows show theInorganics 2025, 13, 315 14 of 19magnetic transition temperatures [52]. (b) Temperature dependence of loss tangent of HoMn3Ni2Mn2O12at one frequency of 665 kHz and different magnetic fields of 6, 8, and 9 T on cooling and heating.0.0010.0020.0030 20 40 60 800 T, cooling0 T, heating7 T, cooling9 T, heating1820222426280 50 100 150 200 250 3000 T7 T9 T18.719.219.70 20 40 60 80 100 120 1400 T7 T9 TTemperature (K) (b) (a) Loss tangent Dielectric constant, εLu2NiMnO6 f = 986 kHz TC = 41 K 0.00.20.40.60.80 20 40 60 800 T9 TCp / T (J×K−2 ×mol−1 ) T (K) Figure 13. Temperature dependence of (a) dielectric constant and (b) loss tangent at one frequency of986 kHz in Lu2NiMnO6 at H = 0, 7, and 9 T in different temperature ranges. The inset in the panel (a)shows details below 150 K, where the arrow shows a ferromagnetic transition temperature. The insetin the panel (b) shows Cp/T vs. T curves of Lu2NiMnO6 at H = 0 and 9 T.3. Materials and MethodsRMn3Ni2Mn2O12 samples with R = Bi, Ce, Nd, Sm, Eu, Gd, Dy, and Ho were preparedfrom stoichiometric mixtures of Bi2O3 (Rare Metallic Co., Tokyo, Japan, 99.9999%), CeO2(Rare Metallic Co., Tokyo, Japan, 99.99%), R2O3 (Rare Metallic Co., Tokyo, Japan, 99.9%),Mn2O3 (Rare Metallic Co., Tokyo, Japan, 99.99%), MnO2 (Alfa Aesar, Ward Hill, MA, USA,99.99%), and NiO (Rare Metallic Co., Tokyo, Japan, 99.9%). Single-phase Mn2O3 wasprepared from a commercial MnO2 chemical (Rare Metallic Co., Tokyo, Japan, 99.99%) byannealing in air at 923 K for 24 h. The synthesis was performed at about 6 GPa and at about1500 K for 2 h in sealed Au capsules using a belt-type HP instrument. After annealing at1500 K, the samples were cooled down to room temperature by turning off the heatingcurrent, and the pressure was slowly released.Inorganics 2025, 13, 315 15 of 19The Lu2NiMnO6 sample was prepared from stoichiometric mixtures of Lu2O3 (RareMetallic Co., Tokyo, Japan, 99.9%), MnO2 (Alfa Aesar, Ward Hill, MA, USA, 99.99%),and NiO (Rare Metallic Co., Tokyo, Japan, 99.9%) by the high-pressure high-temperaturemethod at about 6 GPa and at about 1700 K for 2 h in a sealed Pt capsule. We note thatthe oxygen content and purity of MnO2 (Alfa Aesar, Ward Hill, MA, USA, 99.99%) wereconfirmed before its use by the thermogravimetric analysis and X-ray powder diffraction.The refined lattice parameters of Lu2NiMnO6 (space group P21/n with a = 5.1490(1) Å,b = 5.5123(1) Å, c = 7.4073(1) Å, and β = 90.441(1)◦) were close to the reported values [35].X-ray powder diffraction data of EuMn3Ni2Mn2O12 were collected at room tempera-ture on a MiniFlex600-C diffractometer (Rigaku, Tokyo, Japan) using CuKα radiation (a2θ range of 10–120◦, a step width of 0.02◦, and a scan speed of 3◦/min; and a 2θ range of38–44◦, a step width of 0.02◦, and a scan speed of 0.1 ◦/min) (Figure S8). The Rietveld analy-sis of all X-ray powder diffraction data was performed using the RIETAN-2000 program [63].The crystallographic characterization of other samples was reported in [52,55].Magnetic measurements of EuMn3Ni2Mn2O12 were performed on SQUID magnetome-ters (Quantum Design MPMS3, San Diego, CA, USA) between 2 K and 350 K (and between330 K and 750 K) in applied fields of 0.01 T, 1 T, and 7 T under both zero-field-cooled (ZFC)and field-cooled on cooling (FCC) conditions. Magnetic-field dependence was measuredat different temperatures between −7 T and +7 T. Specific heat, Cp, of RMn3Ni2Mn2O12was measured on cooling from 100 K to 2 K at different magnetic fields from 0 T to 9 T bya pulse relaxation method using a commercial calorimeter (Quantum Design PPMS, SanDiego, CA, USA).Dielectric properties were measured using an Alpha-A High Performance FrequencyAnalyzer (NOVOCONTROL Technologies, Montabaur, Germany) on cooling and heatingin a temperature range between 3–5 K and 70–300 K and a frequency range from 100 Hzto 665 kHz (or 986 kHz) at different magnetic fields from 0 T to 9 T. Pieces of pellets wereused in all magnetic, specific heat, and dielectric measurements.4. ConclusionsDielectric properties of the A-site-ordered quadruple perovskites, RMn3Ni2Mn2O12with R = Bi, Ce, Nd, Sm, Eu, Gd, Dy, and Ho, were investigated at different magnetic fieldsbetween 0 T and 9 T. A principal difference in the temperature dependence of the dielectricconstant was observed for R = Bi, Ce, and Nd and for R = Sm, Eu, Gd, Dy, and Ho. Thedielectric constant of the former group decreases with decreasing temperature down tothe lowest temperature. The dielectric constant of the latter group starts increasing withdecreasing temperature when approaching magnetic transition temperatures, suggestingdifferent magnetic ground states. Peak-like anomalies were found on dielectric constantand loss tangent in intermediate magnetic-field ranges for the R = Sm and Gd samples, sug-gesting the existence of “hidden” [64] magnetic-field-induced multiferroic states. Physicalproperties of a new compound, EuMn3Ni2Mn2O12, were also investigated with specificheat and magnetization measurements. Dielectric properties of Lu2NiMnO6 at differentmagnetic fields are reported for comparison.Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/inorganics13100315/s1. Figure S1: Temperature dependenceof (a) dielectric constant and (b) loss tangent of NdMn3Ni2Mn2O12 at different frequencies from100 Hz to 665 kHz. Measurements were performed on cooling at H = 0 T; Figure S2: Temperaturedependence of dielectric constant of SmMn3Ni2Mn2O12 at different frequencies from 100 Hz to665 kHz. Measurements were performed on cooling at (a) H = 0 T and at (b) H = 8 T; Figure S3:Temperature dependence of loss tangent of SmMn3Ni2Mn2O12 at different frequencies from 100 Hzto 665 kHz. Measurements were performed on cooling at (a) H = 0 T and at (b) H = 8 T; Figure S4:https://www.mdpi.com/article/10.3390/inorganics13100315/s1https://www.mdpi.com/article/10.3390/inorganics13100315/s1Inorganics 2025, 13, 315 16 of 19Temperature dependence of dielectric constant of SmMn3Ni2Mn2O12 at one frequency of 665 kHzand different magnetic fields of (a) 0, 1, 2, 3, and 4 T and (b) 5, 6, 7, 8, and 9 T on cooling and heating.Different measurements (from Figure 4 in the main text and from Figures S2 and S3) are reported.Temperature dependence of loss tangent of SmMn3Ni2Mn2O12 at one frequency of 665 kHz anddifferent magnetic fields of (c) 0, 1, 2, 3, and 4 T and (d) only at 0 and 1 T (to emphasize the absence ofanomalies) on cooling and heating. (e) Temperature dependence of loss tangent of SmMn3Ni2Mn2O12at one frequency of 665 kHz and different magnetic fields of 5, 6, 7, 8, and 9 T; Figure S5: (a) M vs.H curves of EuMn3Ni2Mn2O12 at T = 5 K, 20 K, 40 K, 60 K, 100 K, and 200 K. The inset shows amagnified part of the M vs. H curves at T = 5 K and 20 K. (b) M vs. H curves of EuMn3Ni2Mn2O12at T = 5 K and 20 K, below its TN = 33 K. The S-type shape of the M vs. H curves near the origincomes from a contribution from the ferrimagnetic impurity (Eu1−xMnx)MnO3 (space group Pnma);otherwise, the M vs. H curves were linear without hysteresis. (c) Inverse magnetic susceptibilitiesof EuMn3Ni2Mn2O12 measured at magnetic fields of H = 100 Oe, 10 kOe, and 70 kOe in the low-temperature (LT) region of 2–350 K and in the high-temperature (HT) region of 330–750 K. Red linesshow the Curie–Weiss fittings of the LT and HT data at H = 70 kOe; fitting parameters are shownon this figure. The anomaly near 140 K on the LT region originates from the ferrimagnetic impurity(Eu1−xMnx)MnO3. A very weak anomaly near 400 K, seen on the HT data at H = 100 Oe, couldoriginate from traces of NiMnO3 impurity observed in some other samples of RMn3Ni2Mn2O12with R = Bi, Ce, and Ho. Magnetic measurements showed that the amount of a possible NiMnO3impurity was very small, well below the detection limit of laboratory X-ray diffraction; Figure S6:Temperature dependence of dielectric constant of GdMn3Ni2Mn2O12 at different frequencies from100 Hz to 665 kHz. Measurements were performed on heating at (a) H = 0 T and at (b) H = 5 T;Figure S7: Cp/T vs. T curves of Lu2NiMnO6 at different magnetic fields of H = 0, 0.2, 1, 2, 3, 5, and 9 T.Measurements were performed on cooling; Figure S8: (a) Experimental (black crosses), calculated (redline), and difference (blue line at the bottom) room-temperature laboratory X-ray powder diffractionpatterns of EuMn3Ni2Mn2O12 (space group Pn−3) in a 2θ range of 16◦ and 120◦. The tick marksshow possible Bragg reflection positions for the main phase (brown), (Eu1−xMnx)MnO3 impurity(blue), and NiO impurity (green) (from top to bottom). (b) A magnified part of the experimental andcalculated patterns in a 2θ range of 38◦ and 44◦, emphasizing the presence of the (311) reflection fromthe (partial) B-site ordering. The data between 38◦ and 44◦ were measured with a speed of 0.1◦/minand scaled to match with other data (panel (a)) measured with a speed of 3◦/min; because of scaling,the background on panel (b) was not fitted well.Author Contributions: Conceptualization, A.A.B.; methodology, A.A.B.; validation, A.A.B.; formalanalysis, A.A.B.; investigation, A.A.B., R.L., and K.Y.; resources, K.Y.; data curation, A.A.B.; writing—original draft preparation, A.A.B.; writing—review and editing, A.A.B.; supervision, A.A.B. and K.Y.;project administration, A.A.B.; funding acquisition, K.Y. All authors have read and agreed to thepublished version of the manuscript.Funding: This work was partially supported by a Grant-in-Aid for Scientific Research (No. JP25K01657)from the Japan Society for the Promotion of Science.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: The original data presented in this study are openly available onZenodo at https://doi.org/10.5281/zenodo.17131358.Acknowledgments: MANA was supported by the World Premier International Research CenterInitiative (WPI), MEXT, Japan.Conflicts of Interest: The author declares no conflicts of interest.References1. Schmid, H. Multi-ferroic magnetoelectrics. Ferroelectrics 1994, 162, 317–338. [CrossRef]2. Eerenstein, W.; Mathur, N.; Scott, J.F. Multiferroic and magnetoelectric materials. Nature 2006, 442, 759–765. [CrossRef]https://doi.org/10.5281/zenodo.17131358https://doi.org/10.1080/00150199408245120https://doi.org/10.1038/nature05023Inorganics 2025, 13, 315 17 of 193. Khomskii, D.I. Multiferroics: Different ways to combine magnetism and ferroelectricity. J. Magn. Magn. Mater. 2006, 306, 1–8.[CrossRef]4. Cheong, S.-W.; Mostovoy, M. Multiferroics: A magnetic twist for ferroelectricity. Nat. Mater. 2007, 6, 13–20. [CrossRef]5. Khomskii, D. Classifying multiferroics: Mechanisms and effects. Physics 2009, 2, 20. [CrossRef]6. Tokura, Y.; Seki, S.; Nagaosa, N. Multiferroics of spin origin. Rep. Prog. Phys. 2014, 77, 076501. [CrossRef]7. Fiebig, M.; Lottermoser, T.; Meier, D.; Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 2016, 1, 16046. [CrossRef]8. Heron, J.T.; Trassin, M.; Ashraf, K.; Gajek, M.; He, Q.; Yang, S.Y.; Nikonov, D.E.; Chu, Y.; Salahuddin, H.S.; Ramesh, R.Electric-field-induced magnetization reversal in a ferromagnet-multiferroic heterostructure. Phys. Rev. Lett. 2011, 107, 217202.[CrossRef]9. Ueland, B.G.; Lynn, J.W.; Laver, M.; Choi, Y.J.; Cheong, S.-W. Origin of electric-field-induced magnetization in multiferroicHoMnO3. Phys. Rev. Lett. 2010, 104, 147204. [CrossRef]10. Kimura, T.; Goto, T.; Shintani, H.; Ishizaka, K.; Arima, T.; Tokura, Y. Magnetic control of ferroelectric polarization. Nature 2003,426, 55–58. [CrossRef] [PubMed]11. Kenzelmann, M.; Harris, A.B.; Jonas, S.; Broholm, C.; Schefer, J.; Kim, S.B.; Zhang, C.L.; Cheong, S.-W.; Vajk, O.P.; Lynn, J.W.Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3. Phys. Rev. Lett. 2005, 95, 087206. [CrossRef]12. Pomjakushin, V.Y.; Kenzelmann, M.; Dönni, A.; Harris, A.B.; Nakajima, T.; Mitsuda, S.; Tachibana, M.; Keller, L.; Mesot, J.;Kitazawa, H.; et al. Evidence for large electric polarization from collinear magnetism in TmMnO3. New J. Phys. 2009, 11, 043019.[CrossRef]13. Mukherjee, S.; Dönni, A.; Nakajima, T.; Mitsuda, S.; Tachibana, M.; Kitazawa, H.; Pomjakushin, V.; Keller, L.; Niedermayer, C.;Scaramucci, A.; et al. E-type noncollinear magnetic ordering in multiferroic o-LuMnO3. Phys. Rev. B 2017, 95, 104412. [CrossRef]14. Tokunaga, Y.; Iguchi, S.; Arima, T.; Tokura, Y. Magnetic-field-induced ferroelectric state in DyFeO3. Phys. Rev. Lett. 2008, 101,097205. [CrossRef] [PubMed]15. Tokunaga, Y.; Taguchi, Y.; Arima, T.H.; Tokura, Y. Electric-field-induced generation and reversal of ferromagnetic moment inferrites. Nat. Phys. 2012, 8, 838–844. [CrossRef]16. Bousquet, E.; Cano, A. Non-collinear magnetism in multiferroic perovskites. J. Phys. Condens. Matter 2016, 28, 123001. [CrossRef][PubMed]17. Lee, J.-H.; Jeong, Y.K.; Park, J.H.; Oak, M.-A.; Jang, H.M.; Son, J.Y.; Scott, J.F. Spin-canting-induced improper ferroelectricity andspontaneous magnetization reversal in SmFeO3. Phys. Rev. Lett. 2011, 107, 117201. [CrossRef]18. Johnson, R.D.; Terada, N.; Radaelli, P.G. Comment on “Spin-canting-induced improper ferroelectricity and spontaneous magneti-zation reversal in SmFeO3”. Phys. Rev. Lett. 2012, 108, 219701. [CrossRef] [PubMed]19. Kuo, C.-Y.; Drees, Y.; Fernández-Díaz, M.T.; Zhao, L.; Vasylechko, L.; Sheptyakov, D.; Bell, A.M.T.; Pi, T.W.; Lin, H.-J.; Wu, M.-K.;et al. k = 0 magnetic structure and absence of ferroelectricity in SmFeO3. Phys. Rev. Lett. 2014, 113, 217203. [CrossRef]20. Rajeswaran, B.; Sanyal, D.; Chakrabarti, M.; Sundarayya, Y.; Sundaresan, A.; Rao, C.N.R. Interplay of 4f-3d magnetism andferroelectricity in DyFeO3. EPL 2013, 101, 17001. [CrossRef]21. Saha, R.; Sundaresan, A.; Rao, C.N.R. Novel features of multiferroic and magnetoelectric ferrites and chromites exhibitingmagnetically driven ferroelectricity. Mater. Horiz. 2014, 1, 20–31. [CrossRef]22. Oliveira, G.N.P.; Teixeira, R.C.; Moreira, R.P.; Correia, J.G.; Araújo, J.P.; Lopes, A.M.L. Local inhomogeneous state in multiferroicSmCrO3. Sci. Rep. 2020, 10, 4686. [CrossRef]23. Zvezdin, A.K.; Gareeva, Z.V.; Chen, X.M. Multiferroic order parameters in rhombic antiferromagnets RCrO3. J. Phys. Condens.Matter 2021, 33, 385801. [CrossRef]24. Prado-Gonjal, J.; Schmidt, R.; Romero, J.-J.; Ávila, D.; Amador, U.; Morán, E. Microwave-assisted synthesis, microstructure, andphysical properties of rare-earth chromites. Inorg. Chem. 2013, 52, 313–320. [CrossRef]25. Zhang, C.; Zhang, T.; Ge, L.; Wang, S.; Yuan, H.; Feng, S. Hydrothermal synthesis and multiferroic properties of Y2NiMnO6. RSCAdv. 2014, 4, 50969–50974. [CrossRef]26. Su, J.; Yang, Z.; Lu, X.; Zhang, J.; Gu, L.; Lu, C.; Li, Q.; Liu, J.; Zhu, J. Magnetism-driven ferroelectricity in double perovskiteY2NiMnO6. ACS Appl. Mater. Interfaces 2015, 7, 13260–13265. [CrossRef]27. Nhalil, H.; Nair, H.S.; Kumar, C.M.N.; Strydom, A.M.; Elizabeth, S. Ferromagnetism and the effect of free charge carriers onelectric polarization in the double perovskite Y2NiMnO6. Phys. Rev. B 2015, 92, 214426. [CrossRef]28. Sánchez-Benítez, J.; Martínez-Lope, M.J.; Alonso, J.A.; García-Muñoz, J.L. Magnetic and structural features of the NdNi1−xMnxO3perovskite series investigated by neutron diffraction. J. Phys. Condens. Matter 2011, 23, 226001. [CrossRef] [PubMed]29. Retuerto, M.; Muñoz, Á.; Martínez-Lope, M.J.; Alonso, J.A.; Mompeán, F.J.; Fernández-Díaz, M.T.; Sánchez-Benítez, J. Magneticinteractions in the double perovskites R2NiMnO6 (R = Tb, Ho, Er, Tm) investigated by neutron diffraction. Inorg. Chem. 2015, 54,10890–10900. [CrossRef] [PubMed]https://doi.org/10.1016/j.jmmm.2006.01.238https://doi.org/10.1038/nmat1804https://doi.org/10.1103/Physics.2.20https://doi.org/10.1088/0034-4885/77/7/076501https://doi.org/10.1038/natrevmats.2016.46https://doi.org/10.1103/PhysRevLett.107.217202https://doi.org/10.1103/PhysRevLett.104.147204https://doi.org/10.1038/nature02018https://www.ncbi.nlm.nih.gov/pubmed/14603314https://doi.org/10.1103/PhysRevLett.95.087206https://doi.org/10.1088/1367-2630/11/4/043019https://doi.org/10.1103/PhysRevB.95.104412https://doi.org/10.1103/PhysRevLett.101.097205https://www.ncbi.nlm.nih.gov/pubmed/18851654https://doi.org/10.1038/nphys2405https://doi.org/10.1088/0953-8984/28/12/123001https://www.ncbi.nlm.nih.gov/pubmed/26912212https://doi.org/10.1103/PhysRevLett.107.117201https://doi.org/10.1103/PhysRevLett.108.219701https://www.ncbi.nlm.nih.gov/pubmed/23003315https://doi.org/10.1103/PhysRevLett.113.217203https://doi.org/10.1209/0295-5075/101/17001https://doi.org/10.1039/C3MH00073Ghttps://doi.org/10.1038/s41598-020-61384-6https://doi.org/10.1088/1361-648X/ac0dd6https://doi.org/10.1021/ic302000jhttps://doi.org/10.1039/C4RA07099Bhttps://doi.org/10.1021/acsami.5b00911https://doi.org/10.1103/PhysRevB.92.214426https://doi.org/10.1088/0953-8984/23/22/226001https://www.ncbi.nlm.nih.gov/pubmed/21572231https://doi.org/10.1021/acs.inorgchem.5b01951https://www.ncbi.nlm.nih.gov/pubmed/26513539Inorganics 2025, 13, 315 18 of 1930. Booth, R.J.; Fillman, R.; Whitaker, H.; Nag, A.; Tiwari, R.M.; Ramanujachary, K.V.; Gopalakrishnan, J.; Lofland, S.E. Aninvestigation of structural, magnetic and dielectric properties of R2NiMnO6 (R = rare earth, Y). Mater. Res. Bull. 2009, 44,1559–1564. [CrossRef]31. Nasir, M.; Kumar, S.; Patra, N.; Bhattacharya, D.; Jha, S.N.; Basaula, D.R.; Bhatt, S.; Khan, M.; Liu, S.-W.; Biring, S.; et al. Role ofantisite disorder, rare-earth size, and superexchange angle on band gap, Curie temperature, and magnetization of R2NiMnO6double perovskites. ACS Appl. Electron. Mater. 2019, 1, 141–153. [CrossRef]32. Asai, K.; Fujiyoshi, K.; Nishimori, N.; Satoh, Y.; Kobayashi, Y.; Mizoguchi, M. Magnetic properties of REMe0.5Mn0.5O3 (RE = rareearth element, Me = Ni, Co). J. Phys. Soc. Jpn. 1998, 67, 4218–4228. [CrossRef]33. Sobolev, A.V.; Glazkova, I.S.; Akulenko, A.A.; Sergueev, I.; Chumakov, A.I.; Yi, W.; Belik, A.A.; Presniakov, I.A. 61Ni nuclearforward scattering study of magnetic hyperfine interactions in double perovskites A2NiMnO6 (A = Sc, In, Tl). J. Phys. Chem. 2019,123, 23628–23634. [CrossRef]34. Ding, L.; Khalyavin, D.D.; Manuel, P.; Blake, J.; Orlandi, F.; Yi, W.; Belik, A.A. Colossal magnetoresistance in the insulatingferromagnetic double perovskites Tl2NiMnO6: A neutron diffraction study. Acta Mater. 2019, 173, 20–26. [CrossRef]35. Terada, N.; Colin, C.V.; Qureshi, N.; Hansen, T.; Matsubayashi, K.; Uwatoko, Y.; Belik, A.A. Pressure-induced incommensurateantiferromagnetic order in a ferromagnetic B-site ordered double-perovskite Lu2NiMnO6. Phys. Rev. B 2020, 102, 094412.[CrossRef]36. Zhang, C.; Zhu, W.; Yuan, L.; Yuan, H. B-site ordering, magnetic and dielectric properties of hydrothermally synthesizedLu2NiMnO6. J. Alloys Compd. 2018, 744, 395–403. [CrossRef]37. Chanda, S.; Saha, S.; Dutta, A.; Murthy, J.K.; Venimadhav, A.; Shannigrahi, S.; Sinha, T.P. Magnetic ordering and conductionmechanism of different electroactive regions in Lu2NiMnO6. J. Appl. Phys. 2016, 120, 134102. [CrossRef]38. Zhang, L.; Shi, T.L.; Cao, J.J.; Yan, S.M.; Fang, Y.; Han, Z.D.; Qian, B.; Jiang, X.F.; Wang, D.H. Critical behavior and magnetocaloriceffect in the multiferroic double perovskite Lu2NiMnO6. J. Alloys Compd. 2018, 763, 613–621. [CrossRef]39. Katari, V.; Babu, P.D.; Mishra, S.K.; Mittal, R.; Bevara, S.; Achary, S.N.; Deshpande, S.K.; Tyagi, A.K. Effect of preparationconditions on magnetic and dielectric properties of Y2MMnO6 (M = Co, Ni). J. Am. Ceram. Soc. 2016, 99, 499–506. [CrossRef]40. Kakarla, D.C.; Jyothinagaram, K.M.; Das, A.K.; Adyam, V. Dielectric and magnetodielectric properties of R2NiMnO6 (R = Nd, Eu,Gd, Dy, and Y). J. Am. Ceram. Soc. 2014, 97, 2858–2866. [CrossRef]41. Zhang, C.Y.; Wang, Z.Z.; Yuan, L.; Ti, R.X.; Wu, H.R.; Yuan, H.M. Double perovskites R2NiMnO6 with small R3+ cations: Magneticinteractions tuned by R3+ ionic radius and the role of orbital ordering. J. Alloys Compd. 2025, 1039, 182997. [CrossRef]42. Shannon, R.D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. ActaCrystall. A 1976, 32, 751–767. [CrossRef]43. Yi, W.; Princep, A.J.; Guo, Y.F.; Johnson, R.D.; Khalyavin, D.D.; Manuel, P.; Senyshyn, A.; Presniakov, I.A.; Sobolev, A.V.;Matsushita, Y.; et al. Sc2NiMnO6: A double-perovskite with a magnetodielectric response driven by multiple magnetic orders.Inorg. Chem. 2015, 54, 8012–8021. [CrossRef] [PubMed]44. Yi, W.; Liang, Q.F.; Matsushita, Y.; Tanaka, M.; Belik, A.A. High-pressure synthesis, crystal structure, and properties of In2NiMnO6with antiferromagnetic order and field-induced phase transition. Inorg. Chem. 2013, 52, 14108–14115. [CrossRef] [PubMed]45. Terada, N.; Khalyavin, D.D.; Manuel, P.; Yi, W.; Suzuki, H.S.; Tsujii, N.; Imanaka, Y.; Belik, A.A. Ferroelectricity induced byferriaxial crystal rotation and spin helicity in a B-site-ordered double-perovskite multiferroic In2NiMnO6. Phys. Rev. B 2015, 91,104413. [CrossRef]46. Vasil’ev, A.N.; Volkova, O.S. New functional materials AC3B4O12 (Review). Low Temp. Phys. 2007, 33, 895–914. [CrossRef]47. Long, Y. A-site ordered quadruple perovskite oxides AA′3B4O12. Chin. Phys. B 2016, 25, 078108. [CrossRef]48. Yamada, I. Novel catalytic properties of quadruple perovskites. Sci. Technol. Adv. Mater. 2017, 18, 541–548. [CrossRef]49. Belik, A.A.; Johnson, R.D.; Khalyavin, D.D. The rich physics of A-site-ordered quadruple perovskite manganites AMn7O12.Dalton Trans. 2021, 50, 15458–15472. [CrossRef]50. Solana-Madruga, E.; Arevalo-Lopez, A.M. High-pressure A-site manganites: Structures and magnetic properties. J. Solid StateChem. 2022, 315, 123470. [CrossRef]51. Ding, J.; Zhu, X.H. Research progress on quadruple perovskite oxides. J. Mater. Chem. C 2024, 12, 9510–9561. [CrossRef]52. Belik, A.A. A site-ordered quadruple perovskites, RMn3Ni2Mn2O12 with R = Bi, Ce, and Ho, with different degrees of B siteordering. Molecules 2025, 30, 1749. [CrossRef]53. Yin, Y.Y.; Liu, M.; Dai, J.H.; Wang, X.; Zhou, L.; Cao, H.; Cruz, C.D.; Chen, C.T.; Xu, Y.; Shen, X.; et al. LaMn3Ni2Mn2O12: AnA-and B-site ordered quadruple perovskite with A-site tuning orthogonal spin ordering. Chem. Mater. 2016, 28, 8988–8996.[CrossRef]54. Liu, M.; Hu, C.-E.; Cheng, C.; Chen, X.R. A–B-intersite-dependent magnetic order and electronic structure of LaMn3Ni2Mn2O12:A first-principles study. J. Phys. Chem. C 2018, 122, 1946–1954. [CrossRef]55. Belik, A.A.; Liu, R.; Tanaka, M.; Yamaura, K. B-site-ordered and disordered structures in A-site-ordered quadruple perovskitesRMn3Ni2Mn2O12 with R = Nd, Sm, Gd, and Dy. Molecules 2024, 29, 5488. [CrossRef]https://doi.org/10.1016/j.materresbull.2009.02.003https://doi.org/10.1021/acsaelm.8b00062https://doi.org/10.1143/JPSJ.67.4218https://doi.org/10.1021/acs.jpcc.9b06621https://doi.org/10.1016/j.actamat.2019.04.044https://doi.org/10.1103/PhysRevB.102.094412https://doi.org/10.1016/j.jallcom.2018.02.104https://doi.org/10.1063/1.4963824https://doi.org/10.1016/j.jallcom.2018.06.001https://doi.org/10.1111/jace.13975https://doi.org/10.1111/jace.13039https://doi.org/10.1016/j.jallcom.2025.182997https://doi.org/10.1107/S0567739476001551https://doi.org/10.1021/acs.inorgchem.5b01195https://www.ncbi.nlm.nih.gov/pubmed/26241691https://doi.org/10.1021/ic401917hhttps://www.ncbi.nlm.nih.gov/pubmed/24299461https://doi.org/10.1103/PhysRevB.91.104413https://doi.org/10.1063/1.2747047https://doi.org/10.1088/1674-1056/25/7/078108https://doi.org/10.1080/14686996.2017.1350557https://doi.org/10.1039/D1DT02992Dhttps://doi.org/10.1016/j.jssc.2022.123470https://doi.org/10.1039/D4TC01467Ghttps://doi.org/10.3390/molecules30081749https://doi.org/10.1021/acs.chemmater.6b03785https://doi.org/10.1021/acs.jpcc.7b10591https://doi.org/10.3390/molecules29235488Inorganics 2025, 13, 315 19 of 1956. Kittel, C.; McEuen, P. Introduction to Solid State Physics; John Wiley & Sons, Inc.: New York, NY, USA, 2005.57. Higashiyama, D.; Miyasaka, S.; Tokura, Y. Magnetic-field-induced polarization and depolarization in HoMn2O5 and ErMn2O5.Phys. Rev. B 2005, 72, 064421. [CrossRef]58. Mihailova, B.; Gospodinov, M.M.; Güttler, B.; Yen, F.; Litvinchuk, A.P.; Iliev, M.N. Temperature-dependent Raman spectra ofHoMn2O5 and TbMn2O5. Phys. Rev. B 2005, 71, 172301. [CrossRef]59. Radulov, I.; Nizhankovskii, V.I.; Lovchinov, V.; Dimitrov, D.; Apostolov, A. Colossal magnetostriction effect in HoMn2O5. Eur.Phys. J. B 2006, 52, 361–364. [CrossRef]60. Tzankov, D.; Skumryev, V.; Aroyo, M.; Puzniak, R.; Kuz’min, M.D.; Mikhov, M. Magnetic anisotropy of multiferroic HoMn2O5single crystal. Solid State Commun. 2008, 147, 212–216. [CrossRef]61. Boldrin, M.; Bagri, A.; Barlettani, D.; Teather, E.; Squillante, L.; de Souza, M.; Pontes, R.B.; Silva, A.G.; Mori, T.J.A.; Perry, R.; et al.Magnetostriction as the origin of the magnetodielectric effect in La2CoMnO6. Phys. Rev. Mater. 2025, 9, 094403. [CrossRef]62. Manikandan, M.; Ghosh, A.; Mahendiran, R. Giant magnetostriction in La2CoMnO6 synthesized by microwave irradiation. Appl.Phys. Lett. 2023, 123, 022403. [CrossRef]63. Izumi, F.; Ikeda, T. A Rietveld-analysis program RIETAN-98 and its applications to zeolites. Mater. Sci. Forum 2000, 321–324,198–205. [CrossRef]64. Kumar, R.; Sundaresan, A. Unveiling a hidden multiferroic state under magnetic fields in BaHoFeO4. Phys. Rev. B 2023, 107,184420. [CrossRef]Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.https://doi.org/10.1103/PhysRevB.72.064421https://doi.org/10.1103/PhysRevB.71.172301https://doi.org/10.1140/epjb/e2006-00318-3https://doi.org/10.1016/j.ssc.2008.05.015https://doi.org/10.1103/sjr4-6kdphttps://doi.org/10.1063/5.0153838https://doi.org/10.4028/www.scientific.net/MSF.321-324.198https://doi.org/10.1103/PhysRevB.107.184420 Introduction  Results and Discussion  R = Bi, Ce, and Nd  R = Sm  R = Eu  R = Gd  R = Dy  R = Ho  Lu2NiMnO6  Materials and Methods  Conclusions  References