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[Noriki Terada](https://orcid.org/0000-0002-8676-5586), Dmitry D. Khalyavin, Pascal Manuel, Shinichiro Asai, Takatsugu Masuda, Hiraku Saito, Taro Nakajima, Toyotaka Osakabe

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[Elastic and inelastic neutron scattering experiments under high pressure in the frustrated antiferromagnet <math>  <msub>    <mtext>CuFeO</mtext>    <mn>2</mn>  </msub></math>](https://mdr.nims.go.jp/datasets/e5a19788-0194-419f-a7f6-a89da6cf2038)

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Elastic and inelastic neutron scattering experiments under highpressure in frustrated antiferromagnet CuFeO2Noriki Terada1, Dmitry D. Kyalyavin2, Pascal Manuel2, Shinichiro Asai3,Takatsugu Masuda3, Hiraku Saito3, Taro Nakajima3,4, and Toyotaka Osakabe51National Institute for Materials Science,Sengen 1-2-1, Tsukuba, Ibaraki 305-0047, Japan2ISIS facility, STFC Rutherford Appleton Laboratory,Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom3Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan4RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan and5Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan(Dated: June 23, 2024)AbstractThe frustrated antiferromagnet CuFeO2 exhibits pressure-induced complex magnetic phase tran-sitions from the commensurate collinear (CM1) phase to several incommensurate noncollinearphases. To study the effect of high pressure on magnetic interactions, we performed neutrondiffraction and inelastic neutron scattering experiments under high-pressure conditions. With in-creasing pressure, the CM1 ground state becomes less stable against application of a magnetic fieldeven below the critical pressure (P ≤ 3 GPa), as proved by the significant reduction in the criticalmagnetic field from Hc1 =7.5 T to 4.5 T at 2.1 GPa. Additionally, the energy gap in the spin-wavedispersion relation is reduced from 1.0 to 0.88 meV by the application of a pressure of P = 2.1GPa. Comparing the experimental results with spin-wave calculations revealed that the change inthe spin-wave excitation can be explained by the reduction in either the uniaxial anisotropy termor the degree of separation in the nearest-neighbor exchange interactions.PACS numbers: 75.80.+q, 75.50.Ee, 75.25.+z, 77.80.-e1I. INTRODUCTIONIn frustrated magnets, as a consequence of competing exchange interactions caused bygeometric lattice patterns (triangular, Kagomé, pyrochlore lattices) and additional specialinteractions (Dzyaloshinskii–Moriya (DM), biquadratic exchange interactions), exotic mag-netic ground states often emerge, such as spiral-order1,2, spin ice3,4, skyrmions5,6, and spinliquids7,8. Furthermore, when frustrated spins are strongly coupled to the crystal latticethrough inverse effects, such as exchange striction9 and the inverse DM effect10,11, novelphysical phenomena can occur, such as magnetoelectric multiferroic properties12,13 and mag-netization plateaus14,15. Because the magnetic ground state in a frustrated magnetic systemis nearly degenerated by the others, it can be renewed by a small change in the spin Hamil-tonian parameters. High pressure (hydrostatic and uniaxial) and chemical substitution canbe used to modify these parameters, leading to significant changes in the magnetic groundstate by disturbing the delicate balance of competing interactions in frustrated magneticsystems.Recently, pressure-induced magnetic phase transitions have been reported in triangular-lattice antiferromagnetic CuFeO2 (CFO)16,17. CFO is a delafossite-family compound (ABO2,A =Cu, Ag, Pd, Pt, B = Fe, Cr)18–20 and has been extensively studied as a typical frustratedmagnet. At the ambient pressure, the commensurate (CM) collinear ↑↑↓↓magnetic structureis realized (magnetic propagation vector k = (0, 12, 12) in the monoclinic setting shown in Fig.1) as the magnetic ground state below T = 11 K in the CM1 phase21,22. In the intermediatetemperature range of 11 K ≤ T ≤ 14 K, a sinusoidally modulated magnetic structure withincommensurate (ICM) k = (0, q, 12) is stabilized in the ICM1 phase23. As indicated bythe temperature–pressure phase diagram in Fig. 2, application of pressure above P =2.5GPa drives the magnetic phase transition to the ICM noncollinear spiral state (ICM2)with k = (0, q, 12; q ∼ 0.4)16,17. Spiral magnetic ordering—called proper screw—in theICM2 phase is identical to that observed in the ground state of the magnetic-field-inducedphase or chemical-substitution-induced phase24,25. When the pressure is further increasedfrom the ICM2 phase above P =4.0 GPa, another ICM noncollinear phase (ICM3) withk = (qa, qb, qc; qa ∼ 0, qb ∼ 0.34, qc ∼ 0.42) is induced, which is called a general spiral16,17.For the intermediate temperature range between these ground states and the paramagneticphase, the ICM spin-density-wave ordering (ICM1) for lower pressures changes to another2noncollinear state (ICM4) above P ∼3 GPa17.In previous studies on the ambient pressure conditions in CFO, magnetic interactionparameters, including exchange constants and anisotropies, were determined via inelasticneutron scattering (INS) and electron spin resonance (ESR) experiments26–28. However, theeffect of pressure on the magnetic interactions in CFO has not been investigated. Therefore,the origin of pressure-induced phase transitions is not yet understood. In the present study,to investigate the pressure-induced phase transitions in CFO, we examined the stability ofthe pressure-induced ICM states against an external magnetic field and the pressure changein spin-wave excitation spectra through elastic and INS experiments.II. EXPERIMENTAL DETAILSA single-crystal crystal sample was grown using the optical floating-zone method. Neu-tron diffraction (ND) experiments were performed using the cold neutron time-of-flightdiffractometer WISH29 at the ISIS Facility in the U.K. To apply a hydrostatic pressurelower than P = 2.5 GPa, we used a clamp cell with a diameter of ϕ20 mm and a length of55 mm, which was made of NiCrAl and CuBe alloys with thicknesses of 3.0 and 4.5 mm,respectively (ElectroLAB). A single crystal with a volume of approximately 20 mm3 wasmounted in a Teflon capsule with a ϕ4.0-mm inner diameter, and the sample was filledwith a glycerin pressure transmitting medium. The pressure was calibrated by the NH4Fstructure phase transition points at room temperature. The hexagonal c axis (c∗ axis in themonoclinic setting) was parallel to the external magnetic field generated by the vertical-fieldcryomagnet (up to 13.4 T).For ND experiments in the upper pressure range, i.e., P = 3.0 to 4.1 GPa, we useda hybrid anvil-type high-pressure cell30–32. The sample was cut into a plate-like shapewith dimensions of approximately 0.6 × 0.5 × 0.2 mm3. We used a sapphire crystal andWC alloy for the pair of anvils and an aluminum alloy (Al2017) for the gasket. We alsoused glycerin as the pressure transmitting medium. Pressure values were determined usingthe ruby fluorescence method at room temperature. The pressure cell was inserted intoa vertical-field superconducting magnet (up to 10 T) such that the hexagonal c axis wasvertical.For the INS experiment, we used the triple-axis neutron spectrometers HER and PONTA3at the reactor source neutron facility JRR-3 in Tokai, Japan. In these experiments, we usedthe same clamp cell that was employed for the ND experiments and a 38-mm3-volume CFOsingle crystal. A deuterated glycerin pressure transmitting medium was used for the INSexperiments. The pressure cell was set up and calibrated using the same procedures em-ployed in the ND experiments. To measure the spin-wave excitation spectra in the hexagonal(H,H,L) zone (monoclinic (0, K, L) zone), the sample was mounted such that the hexago-nal [11̄0] axis (monoclinic a axis) was vertical. A closed-cycle refrigerator was used to coolthe samples. We employed the constant-Ef mode (Ef represents the energy of scatteredneutrons) with the fixed Ef=2.5 meV and Ef=3.64 meV for the cold neutron experimentwith HER and Ef=14.7 meV for the thermal neutron experiment with PONTA. The in-strumental E resolutions were 0.08 meV for Ef=2.5 meV (0.12 meV for Ef=3.64 meV) forHER and 0.94 meV for PONTA at the elastic position.III. EXPERIMENTAL RESULTSA. Elastic neutron scatteringAs shown in the phase diagram as a function of the magnetic field (along the hexagonalc axis) at the ambient pressure in Fig. 2, the spin-flop phase transition occurs from CM1 tothe ICM noncollinear spiral state (ICM2) at Hc1 = 7.5 T. Another CM collinear state, i.e.,↑↑↑↓↓ (CM2), was induced at Hc2 = 12.5 T33–35. Because the critical phase transitions Hc1and Hc2 are sensitive to changes in exchange interactions and anisotropies in the CFO, weinvestigated the effect of pressure on the phase transitions via ND experiments. Althoughfurther high-field phases exist, such as the ↑↑↓ phase (20 T ≤ H||c ≤ 34 T) and the canted↑↑↓ phase (34 T ≤ H||c ≤ 53 T)28,36, we could not investigate the pressure effect on thesephases in the present study, because of experimental limitations.As shown in Fig. 3(a), the magnetic neutron Bragg peaks were observed on Q =(1,−0.5,−0.5) in the monoclinic setting (Q = (−0.25,−0.5,−0.5) in the hexagonal set-ting), at T = 2 K and H||c = 0 T. Hereafter, we use a monoclinic setting unlessspecified otherwise. The reciprocal lattice maps with the magnetic Bragg positions forthe monoclinic bases are presented in Supplementary Fig. 1.37 The Bragg peak posi-tion can be expressed as the satellite reflection from the reciprocal lattice position at4τ = (1,−1,−1) using the CM kCM1 = (0, 0.5, 0.5) characteristic of the CM1 phase, i.e.,Q = τ + k. In addition, two low-intensity signals were observed at the two ICM positionsQ = (1,−0.6,−0.5) and (1,−0.4,−0.5) even without a magnetic field, which can be ex-pressed as Q = (1,−1,−1) + kICM2 and Q = (1, 0, 0) − kICM2 with kICM2 = (0, q, 0.5)having the q ∼ 0.4 characteristic of the ICM2 spiral phase. The crystal lattice in the CM1and ICM2 phases is distorted from the parent rhombohedral space group R3̄m to a mono-clinic symmetry because of the exchange-striction mechanism described in previous X-raydiffraction studies38–41.With increasing H||c at T = 1.5 K and P = 2.1 GPa, the CM peak disappeared, andthe intensities of the ICM peaks were increased at H||c = 4.5 T, as shown in Figs. 3(b),3(c), and 3(e). This result corresponds to the transition from the CM1 phase to the ICM2phase at Hc1. The critical field is significantly reduced by the application of a 2.1 GPapressure from the ambient pressure of 7.5 T. The k vector component q depends on H||c inthe ICM2 phase, which changes from 0.405 at 5 T to 0.390 at 12 T for P = 2.1 GPa. Theq value at P = 2.1 GPa is slightly different from that at ambient-pressure values of 0.415at 7.5 T and 0.402 at 12.5 T. With a further increase H||c, the magnetic Bragg reflectionscorresponding to the ICM2 phase disappeared at 13 T, and the intensity at the other CMposition of Q = (1,−0.6,−0.5) onsets at this field. The CM position is consistent with thatobserved for the CM2 phase at the ambient pressure. Hc2 =12.5 T at P = 2.1 GPa, whichis almost the same as the critical field at the ambient pressure. Consequently, we found thatthe first critical field Hc1 was significantly weakened by the application of pressure, whereasthe second critical field Hc2 was almost independent of the pressure in the CFO.To investigate the stabilities of the pressure-induced phases of ICM2 and ICM3 againstthe application of H||c, we performed ND experiments with a hybrid anvil-cell for P = 3.1GPa and 4.0 GPa. At P = 3.1 GPa, a magnetic Bragg reflection at Q = (−1, 0.6, 0.5)corresponding to ICM2 ordering was observed, as shown in Fig. 4(a). Another satellitepeak for the ICM2 phase was observed at Q = (−1, 0.4, 0.5) (not shown). In addition,two Bragg spots were observed at Q = (−1, 0.66, 0.41) and Q = (−1, 0.66, 0.59), whichoriginated from the ICM3 ordering with kICM3 = (qa, qb, qc) with qa ∼ 0, qb ∼ 0.34, andqc ∼ 0.41. The coexistence of the ICM2 and ICM3 phases around P ∼ 3 GPa was alsoobserved in previous ND experiments16,17. When H||c of up to 10 T is applied, the magneticBragg intensities are not changed within the experimental accuracy, as shown in Figs. 4(b)5and 4(e).The temperature dependences of the magnetic reflections corresponding to the ICM2and ICM3 phases are shown in Figs. 4(f) and 4(g), respectively. The intensity of the Braggreflection for the ICM2 phase is constant below T =8 K and is increased in the intermediatetemperature range of 8–12 K (Fig. 4(f)). This intensity enhancement is attributed to theadditional contribution of either the ICM1 phase (sinusoidal spin state) or the ICM4 phase(canted proper screw), owing to the same propagation vector of k = (0, q, 12; q ∼ 0.4) inboth the ICM2 and ICM1 (or ICM4) phases. In contrast, the intensity of the ICM3 phasedecreases monotonically as the temperature increases from 1.5 K, and the peak disappearsat T = 8 K (Fig. 4(g)). This indicates a phase transition from ICM3 to ICM4.At 4.0 GPa, only the reflection of the ICM3 phase was observed (Fig. 4(c)). The intensityof the ICM3 reflection was constant up to 10 T, within the experimental accuracy. The peakposition of the ICM3 phase, corresponding to the ICM3 k vector components, did not changewith an increase in H||c to 10 T. Consequently, the pressure-induced ICM3 phase is robustagainst H||c up to 10 T.The ND experimental results are presented as functions of H||c and the pressure at thelowest temperature in the phase diagram of Fig. 1. The H||c-induced phase transition fromCM1 to ICM2 at Hc1 was significantly suppressed by the application of pressure, whereasthat from ICM2 to CM2 at Hc2 was robust against the application of pressure, at least upto P = 2.1 GPa. We also observed that the magnetic ordering of the ICM3 phase was notaffected by H||c up to 10 T.B. Inelastic neutron scatteringTo directly study the changes in the magnetic interactions in CFO caused by the ap-plication of pressure, we investigated the spin-wave dispersion relation at 2.1 GPa via INSexperiments. At the ambient pressure, CFO exhibits a spin-wave dispersion relation withdouble minima at Q = (0, q, 0.5) and Q = (0, 1 − q, 0.5) in the CM1 phase. The energygap is 1.0 meV at the ambient pressure26,27. The INS intensity in the present high-pressureexperiment with a clamp cell having a 15-mm thickness (CuBe and NiCrAl alloys) windowwas approximately 20 times lower than that without the pressure cell, which was normal-ized to the sample mass. Thus, we focused on measuring the spin-wave spectra at typical6Q positions in the (0, K, L) scattering plane.A comparison of the INS spectra measured by the HER between the ambient pressure andP =2.1 GPa at T =2.5 K is presented in Fig. 5(a). The energy gap for the energy minimumat the ICM position Q = (0, 0.42, 0.5) is reduced from 1.0 meV at the ambient pressureto 0.88 meV at P =2.1 GPa. The excitation signals above 1.0 meV (double arrows) origi-nate from another magnetic domain contribution that depends on the domain population.Furthermore, the energy around the zone boundary at Q = (0, 0, 0.5) is slightly reducedfrom 2.51 meV at the ambient pressure to 2.45 meV at P = 2.1 GPa. (Figs. 5(b)) We alsoperformed a constant-Q scan at Q = (0, 0, 2.4) at the ambient pressure and P = 2.1 GPausing the PONTA spectrometer. No clear differences were observed between the spectra(Supplementary Fig. 237).IV. DISCUSSIONConsidering the ND and INS experimental results, we discuss the effect of pressure onthe magnetic interactions in CFO. The spin Hamiltonian for CFO can be expressed asH = −12∑i,jJnSi · Sj −∑iD(Szi )2, (1)where Jn and D denote the exchange interaction and uniaxial anisotropy constant, respec-tively. The crystal structure of CFO is distorted from an equilateral triangular lattice to ascalene triangular lattice in the CM1 phase because of exchange restriction38–41. In previousINS and ESR studies at the ambient pressure, inequivalent exchange interactions due tolattice distortion were essential for explaining the spin-wave dispersion relation of CFO27,28.Additionally, in other theoretical studies, researchers considered the separation of exchangeinteractions due to lattice distortion in CFO43,44. The exchange paths considered in thepresent study for the scalene triangular lattice are illustrated in Fig. 6(a). The nearest-neighbor interaction J1 in the equeary triangular lattice is separated into one weak (J11)and two strong (J12 and J13) exchange interactions. However, for the second neighbor J2,third neighbor J3, and interplane bond Jz, the lattice distortion effect is negligible. In thisstudy, we considered the exchange separation due to lattice distortion only for the nearest-neighbor interaction J1. Thus, we considered seven magnetic interaction parameters: J11,J12, J13, J2, J3, Jz, and the uniaxial anisotropy parameter D. (Weak in-plane anisotropy7TABLE I: Spin Hamiltonian parameters (in meV). The exchange parameters at 0 GPa were takenfrom Ref.27.J11S J12S J13S J2S J3S JzS DS Eg Ezb0 GPa −0.150 −0.455 −0.422 −0.10 −0.33 −0.19 0.20 1.01 2.40(a) −0.150 −0.455 −0.422 −0.10 −0.33 −0.19 0.16 0.89 2.34(b) −0.150 −0.420 −0.401 −0.10 −0.33 −0.19 0.20 0.89 2.34(c) −0.150 −0.455 −0.422 −0.12 −0.33 −0.19 0.20 0.90 2.41(d) −0.150 −0.455 −0.422 −0.10 −0.39 −0.19 0.20 0.90 2.49(e) −0.150 −0.455 −0.422 −0.10 −0.33 −0.17 0.20 1.04 2.31(f) −0.200 −0.455 −0.422 −0.10 −0.33 −0.19 0.20 1.01 2.40interactions were ignored.)Owing to the limited number of experimental results for the present INS under high-pressure conditions, it was not possible to determine all magnetic interactions under high-pressure conditions simultaneously. Therefore, we discuss the influence of pressure on themagnetic interactions by comparing the calculated spin-wave dispersion relations based onthe modified individual magnetic interaction parameters with the experimental results. Spin-wave calculations were conducted using the Holstein–Primakoff transformation method de-scribed in a previous report27.We calculated the spin-wave dispersion relation using the spin Hamiltonian parameters atthe ambient pressure based on a previous study27. These parameters are presented in Table1. As mentioned previously, the dispersion relation has two minima with an energy gap of1 meV, as indicated by the solid lines in Figs. 6(b). In the experiment, the energy gap (Eg)at Q = (0, 0.42, 0.5) was reduced to 0.88 meV. There are many possibilities for reproducingthe reduction in the energy gap, as summarized in Table 1. For case (a) in Table 1, whenwe change the anisotropy parameter D from -0.20 to -0.16 meV, the calculated energy gapis reduced to the experimental value at P = 2.1 GPa. In addition, by changing the ratiobetween the nearest-neighbor antiferromagnetic exchange interactions for case (b), i.e., theweak J11 and strong J12 (J13) interactions, we can reproduce the energy gap at P = 2.1GPa. In both cases (a) and (b), the energy at the zone boundary (Ezb) Q = (0, 0, 0.5)is slightly lower, which is consistent with the experimental results. However, when the8other parameters are changed, the second-nearest neighbor J2, the third neighbor J3, Egis reduced, but Ezb is not reduced, as shown in Table 1 and Supplementary Fig. 3(a)37.Changing the interplane interaction Jz and J11 does not reproduce the reduction in Eg asin cases (e) and (f), respectively (Supplementary Fig. 3(b)37). Therefore, we found that themost probable magnetic interaction parameters to be changed by the application of pressurewere either the anisotropy parameter D or the nearest-neighbor exchange interactions J12and J13.Let us discuss the effect of pressure on the phase stability against H||c and magnetic-field-induced phase transitions in CFO. In the ND experiment, we observed a significant changein the critical field Hc1 between the collinear CM1 phase and the proper screw ICM2 phase,as illustrated in Figs. 7(a) and 7(b). The energy values per spin for the collinear state forthe CM1 and ICM2 phases at zero temperature are given as follows:ECM1 = −S2(J11 − (J12 + J13) + A)−DS2zEICM2 = −S2(αJ11 + β(J12 + J13) +B)− 12DS2z ,where A and B are the exchange energy terms associated with J2, J3, and Jz, α is close to1 because of the phase shift δ in Fig. 7(b) nearly equal to πq24,25, and β is cos(2πq) withq ∼ 0.42. When either the anisotropy parameter D or (J12 + J13) is reduced, as expectedfrom the INS experiment, the degree of energy increase in ECM1 exceeds that in EICM2.This implies that the CM1 magnetic state becomes more unstable than the ICM2 statewith a reduction in D or (J12 + J13), which is consistent with the significant decrease inthe critical field of the phase transition from CM1 to ICM2 observed in the present NDexperiment. Similar findings for the stability of the ICM2 phase have been reported in thecase of chemical substitution in Ga-doped CuFe1−xGaxO245. We did not understand thestability of the higher-pressure phase ICM3, owing to the lack of INS data for P < 4 GPa.Further INS experiments under high pressures are required.V. CONCLUSIONSWe investigated the magnetic interactions under high-pressure conditions for the frus-trated triangular-lattice antiferromagnet CFO through ND and INS experiments. In theND experiments, we found that the H||c-induced phase transition from CM1 to ICM2 at Hc19was significantly suppressed by the application of pressure. In contrast, the phase transitionfrom ICM2 to CM2 at Hc2 did not change with the application of pressure. We also observedthat the magnetic ordering of the ICM3 phase was not affected by H||c up to 10 T. In theINS experiment, we observed a change in the excitation energy at the energy minimum andthe zone boundary in the spin-wave dispersion relation. Comparing the experimental resultswith the spin-wave calculations revealed that the change in spin-wave excitation can be ex-plained by the reduction in either the uniaxial anisotropy term or the degree of separationin the nearest-neighbor exchange interactions.AcknowledgementsWe acknowledge the STFC for providing the neutron beamtime. Raw data were obtainedfrom https://doi.org/10.5286/ISIS.E.RB1610350. 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Fishman, Effect of interlayer interactions and lattice distortions onthe magnetic ground state and spin dynamics of a geometrically frustrated triangular-latticeantiferromagnet, Phys. Rev. B 82, 144441 (2010).45 J. T. Haraldsen, F. Ye, R. S. Fishman, J. A. Fernandez-Baca, Y. Yamaguchi, K. Kimura, andT. Kimura, Multiferroic phase of doped delafossite CuFeO2 identified using inelastic neutronscattering, Phys. Rev. B 82, 020404 (2010).14FIG. 1: (a)Crystal structure of CuFeO2. Dotted lines denote hexagonal and monoclinic unitcells. (b)The relationship between the hexagonal and monoclinic basis vectors (am = ah − bh,bm = ah + bh, ch = (−ah + bh + ch)/3, where Fe is at the origin).15FIG. 2: Schematic illustration of the magnetic phase diagram of CuFeO2 as functions of temper-ature, pressure and magnetic field along the hexagonal c axis. The temperature versus pressurephase diagram was taken from previous work17. The solid lines and the solid circles denote thephase boundaries and the points where the phase transitions were found in the present study. Thedotted line show the magnetic field that we have investigated in this study. The hatched areadenote the coexistence region of ICM2 and ICM3 phases.16FIG. 3: Neutron diffraction intensity images measured at typical magnetic fields along the hexago-nal c axis, (H||c) (a)H||c = 0 T, (b) H||c = 5.0 T, (c) H||c = 8.0 T and (d) H||c = 13.4 T for T = 1.5K and P=2.1 GPa. H||c dependence of (e)integrated intensity of the magnetic Bragg reflection atQ = (1, q,−12) and (f) magnetic propagation wave number q at T = 1.5 K and P=2.1 GPa.17FIG. 4: Neutron diffraction intensity images measured at typical magnetic fields along the hexago-nal c axis, (H||c) and pressures at T =1.5 K, (a)H||c = 0 T and (b)H||c = 10 T at P =3.1 GPa, and(c)H||c = 0 T and (b)H||c = 10 T at P =4.0 GPa. (e)H||c dependence of the integrated intensitiescorresponding to ICM2 and ICM3 phases at 3.1 GPa nad 4.0 GPa at T = 1.5 K. Temperature de-pendence of the integrated intensities corresponding to (f) ICM2 and (g) ICM3 phases at H||c = 4T and 8 T and P = 3.1 GPa.18FIG. 5: Energy dependence of neutron intensity for the constant-Q scans at (a) Q-position wherethe spin-wave dispersion shows the minimum (Q = (0, 0.42, 0.5)), and (b) the magnetic zoneboundary (Q = (0, 0, 0.5)). These data were measured with HER spectrometer. The data atambient pressure were measured without the pressure cell, which were taken from Ref.27.19FIG. 6: (a)The exchanged paths considered in the present study. (b)The calculated spin wavedispersion relation at ambient pressure (solid line)27. The dispersion curves denoted by dotted andbroken lines were calculated with the uniaxial anisotropy parameter, D, and J12 (and J13), whichare changed from the ambient pressure values, respectively. The details are described in the maintext.20FIG. 7: Schematic illustrations of magnetic structures for (a) collinear structure of CM1 and (b)proper screw structure of ICM2 phase.21