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H. Tamatsukuri, T. Uchihara, S. Mitsuda, [Y. Ishii](https://orcid.org/0000-0002-8957-5833), H. Nakao, [K. Takehana](https://orcid.org/0000-0001-6386-1746), [Y. Imanaka](https://orcid.org/0000-0003-2804-4438)

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[Magnetoferroelectric phase transition induced by latent spin-lattice coupling in the geometrically frustrated magnet <math>  <mrow>    <msub>      <mi>CuFe</mi>      <mrow>        <mn>0.95</mn>      </mrow>    </msub>    <msub>      <mi>Al</mi>      <mrow>        <mn>0.05</mn>      </mrow>    </msub>    <msub>      <mi>O</mi>      <mn>2</mn>    </msub>  </mrow></math>](https://mdr.nims.go.jp/datasets/fd2b2006-10ae-426b-b2eb-324c00aea3ba)

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Magnetoferroelectric phase transition induced by latent spin-lattice coupling in thegeometrically frustrated magnet CuFe0.95Al0.05O2H. Tamatsukuri,1, ∗ T. Uchihara,2 S. Mitsuda,2 Y. Ishii,3 H. Nakao,4 K. Takehana,5 and Y. Imanaka51Materials and Life Science Division, J-PARC Center,Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan2Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo 162-8601, Japan3National Institute for Materials Science, Center for Basic Research on Materials (CBRM),Synchrotron Radiation Imaging Group, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0003, Japan4Photon Factory, Institute of Materials Structure Science,High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan5National Institute for Materials Science, Center for Basic Research on Materials (CBRM),High Magnetic Field Physics Group, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan(Dated: March 18, 2025)In multiferroic CuFe0.95Al0.05O2, applying uniaxial pressure p generates a magnetoferroelectricphase distinct from the well-studied spin-driven ferroelectric phase associated with helical magneticordering in this system. Using a four-circle neutron diffractometer, the magnetic structure of thep-induced magnetoferroelectric phase is determined as the collinear sinusoidal type, which itselfdoes not break the inversion symmetry in this system. Additionally, synchrotron radiation x-raydiffraction experiments are conducted to investigate how the triangular lattice in CuFe0.95Al0.05O2is distorted by applied p. Although lattice distortion during the magnetic phase transition inCuFe0.95Al0.05O2 is mitigated by the substitution of nonmagnetic Al3+, the application of p along theconjugate direction revives the “latent” spin–lattice coupling, causing the triangular lattice to distortduring magnetic phase transition. The application of a magnetic filed considerably reduces p-inducedferroelectric polarization, but does not affect lattice distortion. These results indicate that p-inducedferroelectric polarization is not a consequence of the piezoelectric effect. Instead, the sinusoidalmagnetic structure would contribute to the emergence of p-induced ferroelectric polarization throughspin-lattice coupling.I. INTRODUCTIONIn geometrically frustrated magnets, competing in-teractions often result in complex magnetic structures,such as spiral magnetic ordering, which break the in-version symmetry in the system1,2. Recent studies onmagnetoelectric effects have reported that such spiralmagnetic ordering can induce ferroelectric polarizationdriven by either spin–orbit interactions or the exchangestriction effect3–7. Additionally, these magnetic systemstend to strongly correlate lattice degrees of freedom andspins, lifting the large ground-state degeneracy causedby frustration8–11. Consequently, degrees of freedom ingeometrically frustrated magnet–namely charge, spin, or-bital, and lattice–are potentially interconnected. The in-terplay between these degrees of freedom often inducesexotic phenomena, such as piezomagnetoelectric effects,which can be controlled by external fields12–19. Delafos-site CuFeO2, which exhibits both spin-driven ferroelec-tricity and strong spin–lattice coupling, serves as an ex-ample of a system where multiple degrees of freedom areinterlinked.The crystal structure of CuFeO2 belongs to the R3̄mspace group at room temperature (a = b = 3.03 Å andc = 17.17 Å in the hexagonal notation)20. As shownin the inset of Fig. 1(a), Fe3+ in CuFeO2 (S = 5/2)form a triangular lattice with antiferromagnetic inter-actions, resulting in geometrical frustration. With de-creasing temperature (T ), CuFeO2 undergoes sequentialmagnetic phase transitions from the paramagnetic (PM)phase to a partially disordered (PD) phase at TN1 = 14 Kand subsequently to a four-sublattice (4SL) phase at TN2= 11 K21,22. Spin configurations in the PD phase and the4SL phase are sinusoidally amplitude-modulated almostalong the c axis (Fig. 1(b)) and collinear ↑↑↓↓ along thec axis (Fig. 1(c)), which are characterized by magneticpropagation wave vectors (q, q, 3/2; q = 0.196–0.220) (Tdependent) and (1/4, 1/4, 3/2), respectively21,22. Sub-stituting Fe3+ with a few percentage nonmagnetic Al3+or Ga3+ induces two additional magnetic phases: theferroelectric-incommensurate (FE-ICM) phase and theoblique-PD (OPD) phase23–26. A schematic of the x–T phase diagram for CuFe1−xAlxO2 is illustrated in Fig.1(a). In the FE-ICM phase, known as the spin-driven fer-roelectric phase, a screw helical magnetic structure witha wave vector (q, q, 3/2; q ∼ 0.207) breaks the spatial in-version symmetry of the system (Fig. 1(d)) and generatesferroelectric polarization P along the [110] direction27,28.The helicity of this magnetic structure, with its screwaxis along the [110] direction, directly determines the di-rection of P . This relationship is well explained by the Fe3d–O 2p hybridization mechanism29 and/or the extendedinverse Dzyaloshinskii–Moriya mechanism30,31. Similarto that in the PD phase, the magnetic structure in theOPD phase is the sinusoidal and inclined at ∼50◦ fromthe c axis toward the [1̄10] direction (Fig. 1(e))32. Unlikethat in the PD phase, the value of q = 0.195 in the OPDphase remains independent of T 25,33.24SL FE-ICMPDPMTN1TN2OPDCuFe1-xAlxO2T highN2T lowN2(a)(b) PD(c) 4SL(d) FE-ICM(e) OPD[110][001][1-10]isosceles trianglescalene trianglescalene triangletriangle~50°abFe3+ bmam [1-10][110]FIG. 1. Schematic x-T magnetic phase diagram ofCuFe1−xAlxO2. Illustrations of the magnetic structure andFe3+ triangular lattice in the (b) PD, (c) 4SL, (d) FE-ICM,and (e) OPD phases.Magnetic phase transitions in this system, except forthe transition from the PM phase to the OPD phase, areaccompanied by spontaneous lattice distortions that par-tially relieve geometrical frustration20,34–36. During thetransition from the PM phase to the PD phase at TN1,the crystal symmetry changes from hexagonal R3̄m tomonoclinic C2/m20,35 and further changes into the lowermonoclinic symmetry in the 4SL and FE-ICM phase34,37.As shown in Figs. 1(b)–1(e), previous synchrotron ra-diation x–ray diffraction studies have well establishedtriangular lattices in each of the aforementioned mag-netic phases36,38. During lattice distortion, the hexago-nal [110] (monoclinic bm) axis elongates while the hexag-onal [11̄0] (monoclinic am) axis contracts. Thus, uniaxialpressure p along the [11̄0] direction acts as a conjugatefield to lattice distortion in this system.Based on this relationship, the effects of p on mag-netic phase transitions39,40, lattice distortions40,41, andspin-driven ferroelectricity42,43 in CuFe1−xMxO2 (M =Ga and Al) have been extensively investigated. In par-ticular, applying p ∥ [11̄0] ≥ 200 MPa, with the valueof p varying with x, generates a new ferroelectric phasedifferent from the FE-ICM phase19,33. Hereafter, thisp-induced ferroelectric phase is referred to as the FE2phase. Ferroelectric polarization in the FE2 phase isaligned along the [110] direction, similar to that in theFE-ICM phase, and its value is comparable with or largerthan that in the FE-ICM phase19,33. Previous studieshave reported that under applied p, PD or OPD phasesbecome ferroelectric, with the magnetic structure of thep-induced FE2 phase apparently retaining a collinear si-nusoidal configuration19,33. These results suggest thata collinear sinusoidal magnetic structure is essential forthe emergence of the FE2 phase, irrespective of the tiltof the sinusoidal plane. However, as will be discussedin Sec. III B, using a two-axis diffractometer prevents adefinitive distinction between sinusoidal and screw helicalorderings. Consequently, the magnetic structure of theFE2 phase remains largely unclear. Meanwhile, the tri-angular lattice distorts into an isosceles shape in the PDphase even at ambient pressure, while it remains equilat-eral in the OPD phase, as mentioned earlier. Elucidatingthe deformation of the triangular lattice during transitionfrom the OPD phase to the FE2 phase under applied pand its relationship with the ferroelectricity of the FE2phase is critical.In this study, to shed light on the origin of P[110] in theFE2 phase, we reinvestigate the magnetic structure inthe FE2 phase using a four-circle neutron diffractometer,and examine how applied p distorts the triangular latticeduring the transition from the OPD to the FE2 phase.CuFe0.95Al0.05O2, indicated by an orange arrow in Fig.1(a), is chosen as the target material because its latticedistortion during the PM-to-OPD phase transition wassuppressed by the substitution of nonmagnetic Al3+. Themagnetic structure of the FE2 phase is identified as thecollinear sinusoidal type. As such a collinear sinusoidalmagnetic structure does not break the inversion symme-try, we reconfirm our previous conclusion that P[110] inthe FE2 phase is not purely spin-driven, unlike in the FE-ICM phase. The T dependence of bm in CuFe0.95Al0.05O2exhibits variations under applied p even in the PM phaseand certain anomalies around TN1 and the OPD-to-FE2transition temperature. These results suggest that ap-plying p along the conjugate direction activated “latent”spin–lattice coupling, leading to triangular lattice dis-tortion during magnetic phase transition. Such latticedistortion into at least an isosceles triangular lattice aswell as the sinusoidal magnetic structure would be essen-tial for generating the FE2 phase. These findings formthe basis for discussing the origin of “spin-associated”ferroelectricity.II. EXPERIMENTSA single crystal of CuFe0.95Al0.05O2 with the nomi-nal composition was prepared using the floating zonetechnique44. The crystal was cut into a rectangular shapewith typical dimensions of 1.12× 1.98× 2.60 mm3, inwhich three axes are along [110], [11̄0], and [001] direc-3tions.Uniaxial pressure p was applied along the [11̄0] direc-tion using a custom-built uniaxial pressure device andpressure cell. Details regarding this equipment can befound elsewhere [39, 41, and 45]. The maximum force ofour uniaxial pressure device is 2000 N. Since the pres-surized area of the sample is 1.12× 2.60 ≃ 2.91 mm2,we can apply p up to 600 MPa to the sample. Exceptfor the neutron diffraction experiment described below,p was applied at 25 K in all measurements.The T dependence of magnetic susceptibility (χ) undera 1000 Oe magnetic field applied along the [11̄0] directionwas measured using a superconducting quantum inter-ference device magnetometer (Quantum Design). Thereal and imaginary parts of dielectric constant, ϵ′r/ϵ′′r ,were obtained at 10 kHz using an LCR meter (Agilent4980A) with silver paste electrodes applied to the [110]surfaces. Ferroelectric polarization using [110] electrodes,P[110], was determined by integrating the polarizationcurrent measured using an electrometer over time (Keith-ley 6517A). Before polarization current measurements, apoling electric field Ep (typically 240 kV/m) was appliedduring the cooling process, and then removed. For P[110]measurements under an applied magnetic filed (H) par-allel to the [11̄0] direction, H was generated using a 15-Tsuperconducting magnet installed at the Tsukuba Mag-net Laboratory of the National Institute for MaterialsScience (NIMS).Neutron-diffraction measurements under applied pwere performed using the four-circle neutron diffractome-ter (FONDER) installed at the JRR-3 in the JapanAtomic Energy Agency, Tokai, Japan. The incidentneutron wavelength was 1.24 Å. The sample with thecramped-type pressure cell (see Sec. III B) was mountedonto a closed-cycle He-gas refrigerator, and cooled downto 3 K.The synchrotron radiation x-ray diffraction measure-ments under applied p andH were performed at beamlineBL-3A of the Photon Factory, High Energy AcceleratorResearch Organization, Tsukuba, Japan. A supercon-ducting cryomagnet generated an H field of up to 7 T,parallel to the [11̄0]. The energy of the incident x-raywas set to 14 keV unless otherwise specified. Since p ∥[11̄0] was applied vertically, the scattering plane was the(H,H,L) plane.III. RESULTSA. Emergence of ferroelectricity under applied p inCuFe0.95Al0.05O2Figure 2(a) shows the T dependence of χ under appliedp. TN1 increases with increasing p. This TN1(p) agreeswell with previously reported results including neutrondiffraction measurements33,40.The application of p induces P[110], accompanied by asignificant increase in ϵ′r/ϵ′′r and large thermal hysteresis15 MPa150 MPa300 MPa450 MPa550 MPa15 MPa150 MPa300 MPa550 MPa(a)(b)μ0H = 0.1 T02004006000 200 400 600p (MPa)P[110] (μC/m2)@2 KTN1TN1TN1TN1TFE25 10 15 20 25T (K)(c) f = 10 kHz15 MPa150 MPa300 MPa550 MPa1.00.50ε’’ r10 15 205T (K)TFE22004006000.0320.0330.034P[110] (μC/m2)χ (emu/mol)202428ε’ r0FIG. 2. Temperature dependence of (a) χ, (b) P[110], and (c)ϵ′r under specific applied p. The insets in (b) and (c) depictthe value of the P[110] at 2 K as a function of p and the Tdependence of ϵ′′r , respectively. For clarity, the χ data for p= 150, 300, and 550 MPa are vertically offset .at the emergence temperature, as shown in Figs. 2(b)and 2(c). Around TFE2 where P[110] appears or disap-pears, ϵ′r exhibits a peak. Notably, the ϵ′r peak temper-ature during cooling is apparently closer to TFE2 thanthat during heating, although P[110] are measured on theheating run. The ferroelectricity of P[110] is evidenced bythe polarity reversal with dependence on the sign of Ep(see Fig. 4(b)). We add that TN1 can be determined alsoby deviation from the linear T dependence of ϵ′(T ) inthe PM phase. The above results are summarized in thep–T phase diagram in Fig. 3, which align well with pre-viously reported results33. The slight differences, suchas the smaller TFE2 and the smaller threshold pressureof the emergence of the FE2 phase, would be due to theslight difference in the Al concentration. The thresholdregion of the emergence of the FE2 phase are describedin the Sec. VIA.405101520250 100 200 300 400 500 600T(K)p (MPa)OPDPMFE2OPDTN1TFE2χ (T)ε’r(T)ε’r(T)P[110] (T)bm(T)FIG. 3. Temperature (T ) vs. uniaxial pressure (p ∥ [11̄0])magnetic–electric phase diagram of CuFe0.95Al0.05O2. Openand closed symbols represent data obtained under conditionsof increasing and decreasing T , respectively.B. Magnetic structure in the FE2 phaseNext, we investigate the magnetic structure of the FE2phase, which is crucial for determining whether P[110] inthis phase results from spin-driven ferroelectricity. Pre-liminary magnetic structure analysis conducted in ourprevious study revealed that the magnetic structure ofthe FE2 phase was not of the cycloidal type, which iswidely observed in spin-driven ferroelectrics, but resem-bled or was nearly identical to the PD or OPD mag-netic structures33. However, this study was restricted tomagnetic reflections in the (H,H,L) zone of the recip-rocal lattice space33. Within the (H,H,L) zone, “thespin orientation factor” (SOF) described below is sym-metric with respect to L for both the FE-ICM and thePD(OPD) models27,32. Consequently, it remains unclearwhether the magnetic structure of the FE2 phase defini-tively differs from the screw helical structure seen in theFE-ICM phase27,32. To address this limitation, we em-ploy a four-circle neutron diffractometer and a cramped-type uniaxial pressure cell, as shown in Fig. 4(a). Thispressure cell is required to pressurize the sample at roomtemperature, and the effective pressure applied to thesample becomes uncertain after cooling. Hence, beforethe neutron diffraction measurements, we confirm theemergence of P[110] (Fig. 4(b)) and estimate the effec-tive magnitude of applied p based on the results of P[110]and ϵ′r measurements. Judging from TFE2, the value ofP[110], and enhancement in ϵ′r (Fig. 4(c)), the magnitudeof applied p is estimated to be ∼200 MPa. Note thatthe absolute value of ϵ′r differs from the data presented inFig. 2(c). This difference likely originate from variationsin electrode conditions. However, the relative enhance-Disc springCramped-type pressure cell-200-1000100200P[110] (μC/m2)6064685 10 15T (K)(a)SampleZrO2 piston0501000 0.5 1 1.53 K20 K (deg)ωIntensity (cps)(b)(c)Ep > 0Ep < 0ε’ r(d)00.51-10 -5 0 5 10|Fobs|2 / f 2(κ)L(e)(1-q, -1+q, L)(-1+q, q, L)[110][001][1-10]φθf = 10 kHzFIG. 4. (a) Schematic drawing of the cramped-type uniax-ial pressure cell. Using CuBe disk springs, p was applied atroom temperature and maintained throughout the entire ex-periments. T dependence of (b) P[110] and (c) ϵ′r under appliedp determined using the cramped-type uniaxial pressure cell.(d) Typical neutron diffraction profiles recorded at (−0.804,0.196, 0.5) under applied p at 3 K and 20 K. (e) Index Ldependence of |Fobs|2/f2(κ) for the (1 − q,−1 + q, L) and(−1 + q, q, L) magnetic Bragg points, where q = 0.196. Solidcurves represent the fitting results for the oblique sinusoidalmodel (OPD model). The inset shows a schematic of themagnetic moment direction (red arrow) in the OPD model.ments in ϵ′r are consistent across measurements.Figure 4(d) shows the typical neutron diffraction pro-files at (−1 + q, q, 0.5; q = 0.196) under applied p at 3K and 20 K. Fourteen magnetic reflections outside the(H,H,L) plane were successfully observed. The mag-netic structure factor |F |2HKL is described as|F |2HKL = γ20f(κ)2µ2 · SOF, (1)where γ0 = −0.54× 10−12 cm and µ, κ, and f(κ) denotethe amplitude of the magnetic moment, a magnitude ofthe scattering vector, and a magnetic form factor of Fe3+,respectively27,32,46. Thus, |F |2obs/f(κ)2 is proportional tothe SOF. Here, |F |obs represents the observed magneticstructure factor. Following Refs. [27] and [32], we com-pare |F |2obs/f(κ)2 with the calculated SOF.Figure 4(e) shows the estimated L dependence of|F |2obs/f(κ)2, which is clearly asymmetric. For proper5TABLE I. Estimated angle parameters for the oblique sinu-soidal model.T (K) θ (deg.) ϕ (deg.) µ (µB)FE2 4.5 28 ± 5 -4 ± 5 4 (fixed)OPD [32] 9 51 ± 11 -2 ± 14 1.52 ± 0.13screw helical ordering in the FE-ICM phase, these curvesremain symmetric with respect to L even outside the(H,H,L) plane27,32. This asymmetry explicitly indicatesthat the magnetic structure and the associated mecha-nism of spin-related ferroelectricity in the FE2 phase dif-fer from those in the FE-ICM phase. Because the FE2phase was previously suggested to have a sinusoidal mag-netic structure, we employ an oblique sinusoidal model asour least-squares fitting function. Owing to the limitednumber and low intensity of magnetic reflections arisingfrom the small sample size, we fixed the moment size at4 µB27 and estimate the angle parameters in the obliquesinusoidal model. These parameters are summarized inTable I. For a constant moment size, the fit is acceptablewithin an accuracy and uncertainty range comparable tothat in prior analyses. Considering the large error mar-gins, there exists almost no difference in ϕ between thetwo phases. In contrast, θ is markedly reduced in theFE2 phase, indicating that the original OPD magneticstructure moves closer to the PD magnetic structure.This inclined sinusoidal magnetic structure does notbreak inversion symmetry in this system, because of theremaining mirror plane perpendicular to the [110] axis.Here, we emphasize that the values of the p-induced P[110]are comparable to those in other spin-driven ferroelec-tric materials3–7. Given the significant uncertainty of themagnetic structure analysis in this study, minor modifi-cations from the PD(OPD) ordering could, in principle,break inversion symmetry. However, it seems unlikelythat such minute alterations would yield a P[110] compa-rable to those in other spin-driven ferroelectric materials.We therefore reaffirm our previous conclusion that P[110]in the FE2 phase is not purely spin–driven as in the FE-ICM phase.C. Lattice distortion induced by applied p inCuFe0.95Al0.05O2Figure 5(a) shows the T dependence of bm under ap-plied p, which is estimated from the 040m Bragg reflectionusing the method used in a previous study40,41. Sincewe define am = a − b and bm = a + b (see the inset ofFig. 1(a)), b∗m lies on the a∗–b∗ plane; namely, the elon-gation of the hexagonal [110] axis by applied p ∥ [11̄0]corresponds to the change in bm (b∗m), as shown in Fig.5(b). At near-zero pressure (15 MPa), no anomaliesin bm(T ) are apparent at TN1 = 14 K, indicating thatthe triangular lattice does not distort during the tran-3.0223.0243.0263.0283.0303.0325 10 15 20 2515 MPa75 MPa150 MPa300 MPa450 MPa550 MPabm(Å)T (K)3.0223.0243.0260 300 600p (MPa)bm(Å)T = 25 Ka*b*bm*am*⊥c*220040m(a)(b)FIG. 5. (a) T dependence of bm under applied p. Error barsare within the size of the symbols. All data were recordedunder conditions of decreasing T . The inset presents the bmvalues at 25 K as a function of p. Anomalies around TFE2 (in-dicated by open triangles) were identified by deviations fromthe linear bm(T ) dependence in the OPD phase (see the insetof Fig.6), although these anomalies are difficult to discern atthe vertical scale used in this figure. (b) Reciprocal latticemap of CuFe0.95Al0.05O2 showing the relationship betweenthe 040m and 220 Bragg reflections. In the absence of thelattice distortion, the 040m and 220 reciprocal lattice pointscoincide. The horizontal dashed arrow denotes the scan di-rection. a∗m⊥ denotes the c-plane projection of a∗m, whichcorresponds to the pressure direction.sition into the OPD phase36. As shown in the inset ofFig. 5, the value of bm at 25 K increases linearly withp, consistent with observations in other CuFe1−xMxO2compositions40,41. This result implies that the triangu-lar lattice of CuFe0.95Al0.05O2 is distorted by p even inthe PM phase. Note that the magnitude of this distor-tion induced by applied p at 25 K is comparable to thatof the spontaneous lattice distortion occurring duringthe PM-to-4SL phase transition in CuFeO2 at ambientpressure34,40. Because the 030m superlattice reflection,an indicator of scalene triangular distortion37,40, is not6P[110] (μC/m2 )3.0263.0283.0303.032bm (Å)(a) p = 550 MPa(b) p = 550 MPa02004006005 10 15 20 250 T3 T5 T7 T9 TT (K)TFE2 TN10 T,T decrease0 T,T increase3 T,T decrease7 T,T decrease5 10 15T (K)3.0303.0283.026d(bm )/dT (a.u.)FIG. 6. Magnetic-field-induced variations in (a) bm and (b)P[110] under applied p = 550 MPa as a function of T . Openand closed symbols represent data measured with increasingand decreasing T , respectively. The magnetic filed is ap-plied parallel to the [11̄0] direction (∥ p). The inset in (a)shows a magnified view of bm(T ) (0 T, T decrease) and itsT–derivative.observed down to the lowest temperature, the triangularlattice in the FE2 phase is inferred to remain isosceles.With decreasing T , bm(T ) under applied p, particu-larly below 300 MPa, exhibits anomalies near both TN1and TFE2. These temperatures are plotted in the p–T phase diagram shown in Fig. 3. The upward kinksat TN1 resemble those observed in other CuFe1−xMxO2compositions40,41. Although spin–lattice coupling is sup-pressed by the substitution of nonmagnetic Al3+, the ap-plication of p along the conjugate direction appears toactivate “latent” spin–lattice coupling, causing the trian-gular lattice to distort during magnetic phase transitionin CuFe0.95Al0.05O2. Additionally, the anomaly in bm(T )near TFE2 corresponds to the peak structure in ϵ′(T ),even within the ambiguous emergence region around p= 75 MPa. These results suggest that lattice distortioninto at least an isosceles triangular lattice is essential forthe emergence of the FE2 phase, alongside the sinusoidalmagnetic structure. As can be seen in the inset of Fig.6, the anomalies in bm(T ) at TFE2 in bm(T ) under p of450 and 550 MPa are detectable but rather small. Thisobservation further supports the conclusion that p actsas a “conjugate” field to lattice distortion in this system,similar to the T dependence of magnetization under anapplied magnetic field.Figure 6 shows the T dependence of bm and P[110] un-der applied p = 550 MPa and a magnetic field. In ad-051015Intensity (a.u.)7.05 7.10 7.15 7.20Energy (keV)25 K4.5 Kp = 550 MPaOn (1,1,0) Bragg pointFIG. 7. Energy dependence of scattering intensities at the(1, 1, 0) Bragg point near the Fe K edge. Data are recoded at25 K and 4.5 K under applied p = 550 MPa and normalizedby the value at 7.05 keV. Error bars are within the size ofsymbols.dition to the absence of thermal hysteresis, bm(T ) underthis applied pressure remains unaffected by the magneticfield. Conversely, the magnetic field significantly reducesthe magnitude of P[110] in the FE2 phase. These resultsindicate that P[110] in the FE2 phase is not caused bythe piezoelectric effect. Instead, the sinusoidal magneticstructure likely contributes to the emergence of P[110] inthe FE2 phase through spin–lattice coupling.IV. DISCUSSIONHaving established that p-induced P[110] in the FE2phase is neither a consequence of purely spin-driven ferro-electricity nor the piezoelectric effect, we now discuss itsorigin. Given that our magnetic structure analyses haverevealed that the magnetic structure of the FE2 phase isneither cycloidal nor helical, mechanisms requiring spi-ral magnetic ordering, such as the spin current modeland the extended inverse Dzyaloshinskii–Moriya model,would be excluded as potential explanations for the ori-gin of P[110] in the FE2 phase. Thus, the most plausi-ble mechanism would be the exchange striction model,which involves the induction of ferroelectric polarizationin collinear magnetic structures7. However, in CuFeO2,analyses of the magnetoelectric coupling coefficients inthe generalized bilinear function of spin components haverevealed that collinear magnetic structures (4SL and PDphases) do not induce P[110]31. Furthermore, this modeloriginally requires the spin modulation to be commensu-rate with the lattice structure7,29. Therefore, in the con-text of the exchange striction model, it is somewhat puz-zling that the PD and OPD phases become ferroelectricunder applied p whereas the 4SL phase does not19,33,40.To investigate whether the application of p affects7charge transfer from Fe3+ to O2− depending on the mag-netic structure, we tentatively examine the energy depen-dence of x-ray scattering intensities. Resonant x-ray scat-tering (RXS) spectra are proportional to the square of theatomic scattering factor, given by f0(Q)+f ′(E)+if ′′(E),where f0(Q), f ′(E), and f ′′(E) denote the Thomsonscattering factor, real part of the anomalous scatteringfactor, and imaginary part of the anomalous scatter-ing factor, respectively. The anomalous scattering fac-tor changes significantly near the absorption edge energy,reflecting electronic state changes during the absorptionprocess. Also, the absorption edge energy is sensitive tothe valence state of ions. Figure 7 illustrates the RXSspectra at the (1, 1, 0) Bragg point near the Fe K edgeunder applied p = 550 MPa. Although these data corre-spond to the Fe K edge (1s → 4p), significant changesin the 3d states would be expected to slightly affect the4p states. However, the RXS spectra of the PM (25 K)and FE2 (4.5 K) phases show almost no changes nearthe absorption edge energy. Moreover, no signals are ob-served in the so-called pre-edge region (1s → 3d) on thelower energy side. These results suggest that the appli-cation of p does not significantly modify the electronicconfiguration of the FE2 phase.Even in pure CuFeO2, the PD phase becomes theFE2 phase upon the application of p19. However, inthis system, the induction of P[110] requires the com-bined application of p and a magnetic field H19. Basedon this observation, we have proposed that the induc-tion of P[110] through the combined application of p andH can be regarded as a nonlinear piezomagnetoelectriceffect19. In this study, we have argued that the appli-cation of H introduces a site-dependent modulation ofthe magnetic moment magnitudes, specifically in the PDphase, which may be a critical factor for the nonlinearpiezomagnetoelectric effect. Additionally, we have notedthat because nonmagnetic impurities influence geometri-cally frustrated magnets by acting as an effective randomfield47–49, substituting Fe3+ with Al3+ introduces site-random effects that function analogously to a magneticfield to some extent. This creates conditions similar tothe site-dependent modulation of magnetic moments byH19. Therefore, the results of Al-doped CuFeO2 withoutH may be understood as a similar effect of the nonlinearpiezomagnetoelectric effect.However, the response of p-induced P[110] to H dif-fers between CuFe0.95Al0.05O2 and CuFeO2. Specifi-cally, H significantly reduces the magnitude of P[110] inCuFe0.95Al0.05O2 as described above, while in CuFeO2,H is essential for the emergence of the FE2 phase andfacilitates the induction of P[110]19. To fully understandthis phenomenon, further investigations, including theo-retical calculations, are necessary.V. SUMMARY AND CONCLUSIONWe reinvestigate the magnetic structure in the FE2phase in CuFe0.95Al0.05O2 using the four-circle neutrondiffractometer, and examine how the triangular lattice inthis system is distorted by applied p as the OPD phasetransitions into the FE2 phase. The magnetic structureof the FE2 phase is determined to be the collinear si-nusoidal type. The application of p along the conjugatedirection activates the “latent” spin–lattice coupling inCuFe0.95Al0.05O2, causing the triangular lattice to dis-tort during magnetic phase transition. This suggests thatlattice distortion into at least an isosceles triangular lat-tice, alongside the sinusoidal magnetic structure, is es-sential for the emergence of the FE2 phase. The T de-pendence of bm and P[110] under applied p and a magneticfiled indicates that the p-induced ferroelectric polariza-tion is not a consequence of the piezoelectric effect. In-stead, the sinusoidal magnetic structure would contributeto the emergence of p-induced ferroelectric polarizationthrough spin–lattice coupling. To elucidate the origin ofthis “spin-associated” ferroelectricity, further investiga-tions, including theoretical calculations, are necessary.ACKNOWLEDGMENTSH.T., T.U., and S.M. thank late Hiroyuki Kimura forhis support during the neutron diffraction experimentsperformed at JRR-3. The neutron diffraction experi-ments at JRR-3 and x-ray scattering experiments per-formed at the Photon Factory were conducted under Pro-posal Nos. NSL00001213 and 2021G093, respectively.This work was supported by JSPS KAKENHI (GrantNo. JP20K14421) and the NIMS Joint Research HubProgram.VI. APPENDIXA. Threshold pressure for the emergence of theFE2 phaseFigure 8(a) shows the T dependence of P[110] under ap-plied p near the emergence zone of the FE2 phase. Thesample used for the present P[110] measurements exhibitsrelatively low resistivity, causing leakage currents thatcomplicates the subtraction of the background signal.Combined with the small P[110] values at the emergencepoint of the FE2 phase, this contributes to deviationsin the TFE2 values determined from P[110](T ) relative tothose derived from other physical quantities.Figure 8(b) shows the p dependence of P[110] at 2 Kon a logarithmic scale. P[110](T ) appears to be graduallyinduced under the application of p, rather than resultingfrom an abrupt phase transition. As shown in Fig. 2(c),ϵ′(T ) displays a small hump in the temperature region80.111010010000 100 200 300 400 500 600p (MPa)P[110] (μC/m2)@2 K0510152 3 4 5 6 7 850 MPa62 MPa75 MPa100 MPa125 MPaT (K)P[110] (μC/m2)(a) (b)FIG. 8. (a) T dependence of P[110] under applied p near theemergence region of the FE2 phase. 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