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[Taro Nakajima](https://orcid.org/0000-0001-6557-5508), Masao Watanabe, Yasuhiro Inamura, Kazuki Matsui, [Tomoki Kanda](https://orcid.org/0000-0003-4626-387X), [Tetsuya Nomoto](https://orcid.org/0000-0002-5367-2965), [Kazuki Ohishi](https://orcid.org/0000-0003-1494-6502), [Yukihiko Kawamura](https://orcid.org/0000-0002-6768-9389), Hiraku Saito, Hiromu Tamatsukuri, [Noriki Terada](https://orcid.org/0000-0002-8676-5586), [Yoshimitsu Kohama](https://orcid.org/0000-0003-0149-704X)

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[Stroboscopic time-of-flight neutron diffraction in long pulsed magnetic fields](https://mdr.nims.go.jp/datasets/c2aa50a9-265c-4a14-8f1b-54be71062530)

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Stroboscopic time-of-flight neutron diffraction in long pulsed magnetic fieldsPHYSICAL REVIEW RESEARCH 6, 023109 (2024)Stroboscopic time-of-flight neutron diffraction in long pulsed magnetic fieldsTaro Nakajima ,1,2,* Masao Watanabe,3 Yasuhiro Inamura,1,3 Kazuki Matsui,1 Tomoki Kanda ,1 Tetsuya Nomoto ,1Kazuki Ohishi ,4 Yukihiko Kawamura ,4 Hiraku Saito,1 Hiromu Tamatsukuri,3 Noriki Terada,5 and Yoshimitsu Kohama 11The Institute for Solid State Physics, the University of Tokyo, Kashiwa, Chiba, 277-8581, Japan2RIKEN Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan3J-PARC Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan4Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society (CROSS),Tokai, Ibaraki 319-1106, Japan5National Institute for Materials Science, Sengen 1-2-1, Tsukuba, Ibaraki 305-0047, Japan(Received 18 August 2023; revised 27 February 2024; accepted 27 March 2024; published 1 May 2024)We present proof-of-principle experiments of stroboscopic time-of-flight (TOF) neutron diffraction in longpulsed magnetic fields. By utilizing electric double-layer capacitors, we developed a long pulsed magnet forneutron diffraction measurements, which generates pulsed magnetic fields with the full widths at half maximumof >102 ms. The field variation is slow enough to be approximated as a steady field within the time scale of apolychromatic neutron pulse passing through a sample placed in a distance of the order of 101 m from the neutronsource. This enables us to efficiently explore the reciprocal space using a wide range of neutron wavelength inhigh magnetic fields. We applied this technique to investigate field-induced magnetic phases in the triangularlattice antiferromagnets CuFe1−xGaxO2 (x = 0, 0.035).DOI: 10.1103/PhysRevResearch.6.023109I. INTRODUCTIONExploring quantum states of matter in extreme conditions,such as low temperatures, high magnetic fields, and highpressures, is one of the central topics in condensed mat-ter physics. Among them, field-induced phases have beenextensively investigated, for example, spin-lattice-coupledmagnetization plateaus in frustrated spin systems [1–4],field-induced flop of the spin-driven electric polarization inmultiferroics [5,6], and spin-nematic states in quantum spinsystems [7,8]. Neutron scattering is one of the most power-ful techniques to study these exotic phenomena because itcan probe Fourier-transformed time-space correlation func-tions of atomic positions and magnetic moments; specificallycrystal and magnetic structures are determined by the elasticscattering, and phonons and magnons are measured by theinelastic scatterings. However, the highest magnetic field forneutron scattering instruments is limited to ∼15 T even forstate-of-the-art superconducting magnets. Although there wasa superconducting and nonsuperconducting hybrid magnet forneutron scattering with the highest magnetic field of 26 Tin the Helmholtz Zentrum Berlin (HZB) [9], it is no longeravailable since the research reactor in HZB was shut down in2019.*taro.nakajima@issp.u-tokyo.ac.jpPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.An alternative is a pulsed magnetic field [10–13]. For in-stance, Nojiri et al. [11] successfully observed a magneticBragg peak in a field-induced phase of multiferroic MnWO4by time-of-flight (TOF) pulsed neutron diffraction measure-ments with pulsed magnetic fields up to 30 T. However, thewidths of the pulsed magnetic fields are often limited to sev-eral milliseconds, which are shorter than a time spread ofa polychromatic neutron pulse after flying a typical source-to-sample distance in existing TOF neutron diffractometers,as we explain later. In this case, the high magnetic field isachieved only for a limited wavelength range of the neutrons,and this situation makes explorations of magnetic peaks in thereciprocal space difficult.To overcome this problem, in this paper, we have devel-oped a long pulsed magnet for neutron scattering experiments.By utilizing electric double-layer capacitors (EDLCs) [14],we successfully generated pulsed magnetic fields whose fullwidths at half maximum exceed 100 ms. We establishedthe low-temperature neutron scattering environment with thislong pulsed magnet and performed stroboscopic TOF neutrondiffraction measurements on triangular lattice antiferromagnetCuFe1−xGaxO2 (x = 0, 0.035). By virtue of the extended timescale of the magnetic field, we can use a wide wavelengthrange of the incident neutron beam, which enables us to mapout the neutron diffraction intensities in the reciprocal spacein high magnetic fields.CuFeO2 has been extensively investigated as a geometri-cally frustrated system [15,16]. The crystal structure of thiscompound belongs to the space group of R3̄m and consistsof triangular lattice layers of magnetic Fe3+ ions, which arerhombohedrally stacked along the c axis. In zero magneticfield, this compound exhibits a collinear four-sublattice (4SL)2643-1564/2024/6(2)/023109(9) 023109-1 Published by the American Physical Societyhttps://orcid.org/0000-0001-6557-5508https://orcid.org/0000-0003-4626-387Xhttps://orcid.org/0000-0002-5367-2965https://orcid.org/0000-0003-1494-6502https://orcid.org/0000-0002-6768-9389https://orcid.org/0000-0003-0149-704Xhttps://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevResearch.6.023109&domain=pdf&date_stamp=2024-05-01https://doi.org/10.1103/PhysRevResearch.6.023109https://creativecommons.org/licenses/by/4.0/TARO NAKAJIMA et al. PHYSICAL REVIEW RESEARCH 6, 023109 (2024)antiferromagnetic order, in which the spins are arranged toform an up-up-down-down sequence running along the [110]direction, <11 K. The spins in the adjacent layers are anti-ferromagnetically aligned, and thus, the magnetic modulationwave vector (q vector) is described as q = ( 14 , 14 , 32 ). The4SL antiferromagnetic order breaks the threefold rotationalsymmetry about the c axis of the crystal and thus results inthree magnetic domains corresponding to the q vectors ofq = ( 14 , 14 , 32 ), (− 12 , 14 , 32 ), and ( 14 ,− 12 , 32 ), which are inter-converted to each other by the threefold rotation operation.Previous x-ray diffraction studies revealed that each magneticdomain exhibits a monoclinic lattice distortion associated withthe q vector [17,18]. For convenience, we employ the hexag-onal basis when referring to q vectors and positions in thereciprocal space in the rest of this paper, although they couldbe properly indexed using the monoclinic basis.By applying a magnetic field along the c axis at lowtemperatures, CuFeO2 exhibits field-induced successive phasetransitions [19–21]. The first field-induced phase is knownto have an incommensurate q vector and spin-driven ferro-electricity (FE) [22]. The second field-induced phase exhibitsa 15 -magnetization plateau. In this paper, we refer to thesephases as FE incommensurate-magnetic (FE-ICM) and 15 -plateau phases, respectively.The FE-ICM phase has been of particular interest in termsof multiferroicity, which has been one of the main top-ics in condensed matter physics since the discovery of thefield-induce polarization flop in TbMnO3 [22]. The magneticstructures of the FE phases in TbMnO3 were determined tobe cycloidal magnetic structures [23–26], which agree wellwith the theoretical models describing directions of the lo-cal magnetic moments and induced electric dipole moments[27–29]. However, it was pointed out that the spontaneouselectric polarization can appear not only in the cycloidal orderbut also in a screw-type magnetic order. Specifically, Arima[30] proposed that the FE in the FE-ICM phase of CuFeO2can be explained by assuming a screw-type magnetic modu-lation running on the triangular lattice planes. To confirm thisscenario, neutron diffraction measurements in high fields wereneeded.In previous neutron diffraction studies, the FE-ICM and15 -plateau phases were studied by using vertical-field su-perconducting magnets [20,21]. However, the accessiblescattering plane was limited to the (h, k, 0) plane, wherethe fundamental magnetic reflections were not observed dueto the finite l component of the q vectors. Instead, themagnetic structure of the FE-ICM phase was studied us-ing CuFe1−xAxO2 (A = Al, Ga). This is because a smallamount of nonmagnetic substitution for Fe3+ strikingly affectsthe critical fields of CuFeO2, and the phase boundaries onthe x-T -H phase diagram suggest that the FE-ICM phasein pure CuFeO2 is equivalent to the substitution-inducedzero-field incommensurate magnetic phase [31,32]. Thus,neutron diffraction measurements on CuFe1−xAxO2 (A =Al, Ga) were carried out, revealing that the 4SL groundstate is replaced by a screw-type magnetic structure bythe substitution [33,34]. Although the substitution-inducedphase was considered the same as the field-induced FE-ICMphase in pure CuFeO2, the direct evidence was still lack-ing because the fundamental magnetic Bragg reflections inthe field-induced phase of pure CuFeO2 were not directlyobserved.Field-induced magnetic phase transitions inCuFe1−xGaxO2 were also studied by means of magnetization,electric polarization, electron spin resonance, and heatcapacity measurements [35–37]. At x = 0.035, where theground state is already replaced with the FE-ICM phase, thefirst field-induced phase is considered to be the 15 -plateauphase. However, the plateau in magnetization is smeared withincreasing x, and therefore, the direct observation of the qvectors by neutron diffraction is necessary to unambiguouslydetermine the spin arrangements in the field-induced phase ofthe x = 0.035 sample.To address these unsolved issues regarding the multifer-roicity and field-induced phase transitions in CuFeO2, it isnecessary to explore the three-dimensional reciprocal spaceby neutron diffraction measurements in high magnetic fields.II. EXPERIMENTAL DETAILSA. Sample, cryostat, and magnetA single crystal of CuFeO2 was grown by the floating zonemethod [38] and cut into a cylinder shape with the diameterand length of 5 and 6 mm, respectively. The sample was gluedon a sapphire sample holder, which was connected to the coldhead of a 4He closed-cycle refrigerator (CCR).We prepared a pulsed magnet consisting of an inner9-layered solenoid with 11 turns per layer and an outer 10-layered solenoid with 16 turns per layer; both were woundwith a copper wire having a rectangular cross-section of2.4 × 1.0 mm2. To prevent the permanent deformation of thecoil, the coil was inserted into the 304 stainless-steel ring.This structural reinforcement allows us to repeatedly use thecoil without any noticeable deformation <15 T. The magnetproduces a horizontal magnetic field and has two conicalwindows with a reasonably large opening angle of 60◦, asshown in Fig. 1. We note here that the large opening angle isindispensable for exploring the three-dimensional reciprocalspace by neutron diffraction, though the highest field wouldbe limited as the opening angle is increased. The inner boreof the magnet is 20 mm in diameter. The magnet was cooledby liquid N2 and was thermally isolated from the sample byvacuum. We measured the temperature of the sapphire sampleholder near the sample using a Cernox sensor and found noapparent heating during the pulsed field applications. The coilinductance, coil resistance, and the field factor at 77 K are3.9 mH, 57.5 m�, and 7.85 T/kA, respectively. The samplewas set at the field center. The direction of the magneticfield was parallel to the c axis, namely, perpendicular to thetriangular lattice plane. The [110] direction was selected to bethe horizontal direction perpendicular to the field direction.The magnet and sample were put in an Al chamber, whichwas also pumped to high vacuum. Note that the Al chamberand CCR were originally designed for the short pulsed magnetsystem in the Materials and Life-science experimental Facility(MLF) of J-PARC [39] and are also compatible with the longpulsed magnet.A single crystal of CuFe1−xGaxO2 (x = 0.035) was alsogrown by the floating zone method [38] and cut into a023109-2STROBOSCOPIC TIME-OF-FLIGHT NEUTRON … PHYSICAL REVIEW RESEARCH 6, 023109 (2024)FIG. 1. Schematic illustration of the side view of the long pulsedmagnet and closed-cycle refrigerator (CCR) in the Al vacuumchamber.rectangular shape with the dimensions of 4.9 × 2.9 ×3.5 mm3. The sample environments and the alignment of thecrystal were the same as those for the x = 0 sample.B. Time structure of a neutron pulseThe neutron diffraction experiments were carried out atthe small-angle and wide-angle neutron TOF diffractometerTAIKAN in MLF of J-PARC [40]. Figure 2 shows a typicalTOF diagram for TAIKAN. Since neutron velocity is inverselyproportional to its wavelength, a sharp polychromatic neutronpulse created at the neutron source has a wavelength spread af-ter flying the source-to-sample distance (L1), which is 14.35 mat TAIKAN. Considering that the interval between two ad-jacent neutron pulses is 40 ms in MLF, TAIKAN normallyuses the wavelength range from 0.7 to 7.7 Å. In this paper,we focus on the wavelength range from 1 to 3 Å to measuremagnetic Bragg reflections of CuFe1−xGaxO2, as we show inFIG. 2. The time-of-flight (TOF) diagram of TAIKAN in MLF.The color map shows the wavelengths of the incident neutrons.FIG. 3. (a) Circuit diagram of the electric double-layer capaci-tors (EDLC)-based pulse power supply for the generation of longpulsed magnetic fields. (b) Comparisons among the time-of-flight(TOF) diagram, the temporal profile of the long pulsed magnetic fieldgenerated with a charging voltage of 270 V, and the kicker signalsfor neutron pulse generation. The neutron pulses are triggered by therising edges of the kicker signals.the following sections. This wavelength range corresponds tothe time spread of 7.25 ms at the sample position, as shown inFig. 2. If the width of the pulsed magnetic field is much largerthan this time spread, we can fully utilize the wavelengthrange to map out the neutron diffraction intensities in thereciprocal space.C. Generation of long pulsed magnetic fieldsWe have constructed an electrical circuit for generatinglong pulsed magnetic fields which consists of an EDLC bank,a DC power supply, a trigger circuit, two thyristors (Th1and Th2), a discharge resistance (Rdis), and a pulsed mag-net, as shown in Fig. 3(a). The EDLC bank consists of aseries connection of 120 EDLC cells (Nippon Chemi-Con)and has a total capacitance of 30 F and an internal resistanceof 37 m� with a maximum charged voltage of 300 V. The DCpower supply (TDK-Lambda Americas) was used to chargethe EDLC bank. The trigger circuit controls the timing ofclosing Th1 and Th2. The current flow through the pulsed023109-3TARO NAKAJIMA et al. PHYSICAL REVIEW RESEARCH 6, 023109 (2024)magnet, which is proportional to the field strength, starts atthe timing of closing Th1.In Fig. 3(b), we show a temporal profile of the long pulsedmagnetic field generated by a charging voltage of Vc = 270 V.The width of the field pulse is >1 order of magnitude largerthan the time spread corresponding to the wavelength rangefrom 1 to 3 Å which is indicated by the light-blue rectanglesin Fig. 3(b). This means that the long pulsed magnetic fieldcan be approximated as a steady field within the time scale ofthe neutron pulses. We note here that there is a sudden drop ofthe magnetic field upon the field decreasing process. At thispoint, Th2 is intentionally closed so that the electric currentflows not only to the main circuit but also to the subcircuit fordischarge. While the intentional reduction of the field strengthslightly reduces the width of the pulsed field, this suppressesunnecessary heating of the coil and thus reduces a waitingtime for applying the next magnetic field pulse, which was∼9 min at maximum in the present experiment.D. Stroboscopic TOF neutron diffractionDespite the extended time scale of the pulsed magneticfields, the intensity of one neutron pulse is still not strongenough to precisely measure the reflections from the sample.We thus repeated the application of a magnetic field pulseto accumulate the data. The application of a field pulse wastriggered by one of the kicker signals for the neutron pulsegeneration. The data measured by each neutron pulse werenumbered starting from this trigger, as shown in Fig. 3. Inthe following, we refer to these numbers as frame numbers.We also introduced a delay time td to adjust the peak positionof the magnetic field with respect to the neutron pulses. Afterrepeating the field applications, we extracted and accumulatedthe data having the same frame number by UTSUSEMI software[41]. Finally, we obtained stroboscopic neutron diffractionpatterns in the long pulsed magnetic fields.Figure 4(a) shows the experimental configuration. The an-gle between the incident neutron beam and the magnetic fieldwas set to be 23◦. We mainly used the high-angle detectorbank of TAIKAN, which has a horizontal coverage of the scat-tering angle from 24◦ to 48◦. Note that we can also measurereflections out of the horizontal plane owing to the verticalcoverage of the high-angle detector bank. Figure 4(b) is thecolor map of the neutron wavelengths for measuring inten-sities on the (h, k, 12 ) plane in the configuration mentionedabove. Specifically, the scattering vector Q(= ki − k f ), whereki and k f are wave vectors of the incident and scattered neu-trons, respectively, for an elastic scattering event is determinedby the wavelength and the direction of the scattered neutron.When the scattering vector is in the colored region in Fig. 4(b),the elastic scattering condition is satisfied with the wavelengthindicated by the color, and the direction of the scattered neu-tron is covered by the high-angle detector bank. In this region,we can observe satellite reflections with q vectors indexed as(q,−2q, 32 ), which is equivalent to (q, q, 32 ) under the three-fold rotation about the c axis, from the reciprocal lattice pointof (0, 1,−1). The wavelength range to cover this region isfrom 1 to 3 Å.FIG. 4. (a) A schematic illustration of the top view of the instru-ment layout in the present experiment. (b) A color map showing theneutron wavelengths for measuring intensities on the (h, k, 12 ) planein the scattering geometry shown in (a).III. RESULTS AND DISCUSSIONSA. CuFeO2We performed the stroboscopic neutron diffraction in longpulsed magnetic fields on CuFeO2 at 4 K, at which the lowercritical fields of the FE-ICM and 15 -plateau phases, namely,Hc1 and Hc2, are 7 and 13 T, respectively. We repeated theapplication of the long pulsed magnetic field with the chargingvoltage of 270 V 122 times and then extracted the diffractionpatterns of #3–#5 frames, which correspond to the 15 -plateau,FE-ICM, and 4SL phases, respectively, as shown in Fig. 3.The intensities are normalized to the incident neutron fluxconsidering its wavelength dependence and mapped onto the(h, k, 12 ) plane after integrating them with respect to l . Theintegration range for l is from 0.45 to 0.55.Figure 5(a) shows the intensity map of the 4SL phase.We observed a magnetic Bragg reflection at ( 14 , 12 , 12 ), whichis assigned as a satellite reflection having the q vector of( 14 ,− 12 , 32 ) from the reciprocal lattice point of (0, 1,−1). Wealso observed several magnetic reflections having the samedistance from the c∗ axis. They are magnetic Bragg peaksarising from multiply twinned crystal domains in which thedirections of the c∗ axes are common to each other, indicatingthat the sample is not an ideal single crystal. In Fig. 5(d), weshow a line profile along the (δ, 1 − 2δ, 12 ) direction in the4SL phase [42]. A sharp peak at the commensurate positionof δ = 14 is consistent with the 4SL antiferromagnetic order.In the FE-ICM phase, we observed two peaks as indicatedby the two blue arrows in Fig. 5(b). From the line profile023109-4STROBOSCOPIC TIME-OF-FLIGHT NEUTRON … PHYSICAL REVIEW RESEARCH 6, 023109 (2024)FIG. 5. Stroboscopic neutron diffraction results on CuFeO2. Intensity maps on the (h, k, 12 ) plane in the (a) 4SL, (b) FE-ICM, and (c) 15 -plateau phases. These data are obtained from the #5, #4, and #3 frames, respectively, measured with the long pulsed magnetic field generatedwith the charging voltage of 270 V, as shown in Fig. 3. The application of the magnetic field was repeated 122 times. Solid arrows indicatethe positions of the magnetic Bragg peaks in each phase. Line profiles along the (δ, 1 − 2δ, 12 ) direction in the (d) 4SL, (e) FE-ICM, and (f)15 -plateau phases. Inset of (f) shows the spin arrangement of the 15 -plateau phase cited from Ref. [20].shown in Fig. 5(e), the peak positions are determined to beδ = 0.203 and 0.297. The former is assigned as a satellitereflection from the reciprocal lattice point of (0, 1,−1) us-ing the q vector of (qICM,−2qICM, 32 ) where qICM = 0.203.The latter peak can also be assigned as a satellite reflectionfrom ( 12 , 0, 2), which becomes a crystallographic zone cen-ter due to the lattice distortion associated with the magneticorder [43,44], using the same q vector. The two peaks atδ = qICM and 12 − qICM and their intensity distributions arequite similar to those in CuFe1−xGaxO2 with x = 0.035 inzero magnetic field [45], confirming that the nonmagneticsubstitution-induced FE-ICM phase is equivalent to the field-induced FE-ICM phase in pure CuFeO2.In the 15 -plateau phase, a sharp magnetic Bragg reflectionwas observed at ( 15 , 35 , 12 ), which corresponds to the commen-surate q vector of ( 15 ,− 25 , 32 ), as shown in Figs. 5(c) and 5(f).This means that there are commensurate three-up-two-downmodulations running along the [110] and its equivalent di-rections on the triangular lattice plane. The strong magneticBragg peak on the (h, k, 12 ) plane indicates that the majorityof the spins maintain the antiferromagnetic coupling along thec axis. This is consistent with the magnetic structure modelproposed in the previous study by Mitsuda et al. [20], whichis shown in the inset of Fig. 5(f).The slopes of the long pulsed magnetic fields can be tunedby changing the charging voltage. Figure 6(a) shows a profileof a long pulsed magnetic field generated by a charging volt-age of 142 V. Though the maximum of the field is reduced to9 T, the field variation becomes slower, so that we can measurethe diffraction patterns upon the phase transition between theFE-ICM and 4SL phases in detail. We repeated the field appli-cation with Vc = 142 V 40 times and extracted the diffractionprofiles of #3–#5 frames, as shown in Figs. 6(b)–6(d), respec-tively. Among them, frame #4 clearly shows the coexistenceof the magnetic Bragg peaks of the FE-ICM and 4SL phases,as shown in Fig. 6(c). The field variation within this frame is∼0.2 T, which is small enough to capture the phase coexis-tence during the first-order phase transition between the twophases.We also performed the measurements with different charg-ing voltages and obtained the positions of the magnetic peakson the (δ, 1 − 2δ, 12 ) line as functions of the magnetic field,as shown in Fig. 6(e). Here, we refer to the in-plane mag-netic modulation wave number as q. The q values of the 4SLand 15 -plateau phases coincide with the commensurate values,while that of the FE-ICM phase continuously changes withmagnetic field. This is consistent with the results obtainedby the previous neutron diffraction measurements with steadymagnetic field, in which the q values were deduced from thehigher harmonic magnetic reflections on the (h, k, 0) plane[20,21]. The present results also demonstrate that the strobo-scopic neutron diffraction with long pulsed fields is suitable023109-5TARO NAKAJIMA et al. PHYSICAL REVIEW RESEARCH 6, 023109 (2024)FIG. 6. (a) Comparisons among the time-of-flight (TOF) diagram, the temporal profile of the long pulsed magnetic field generated witha charging voltage of 142 V, and the kicker signals for neutron pulse generation. Line profiles along the (δ, 1 − 2δ, 12 ) direction in CuFeO2measured by the frame (b) #3, (c) #4, and (d) #5, shown in (a). (e) Field dependence of the magnetic modulation wave number q in CuFeO2,which was determined from the peak position of the line profile along (δ, 1 − 2δ, 12 ).for investigating field-dependent incommensurate magneticmodulations, such as spin-density-wave states of frustratedquantum spin systems in high magnetic fields [46].B. CuFe1−xGaxO2 (x = 0.035)The field-induced phase transition in the x = 0.035 samplewas also investigated in the same manner. We applied pulsedmagnetic fields generated by the charging voltage of 254 V at4 K and repeated the field application 80 times. In addition,we also carried out the same set of the measurements with adifferent delay time to increase the number of data points withdifferent magnetic fields.Like the results of the x = 0 sample, we observed a pair ofmagnetic Bragg reflections on the (h, k, 12 ) plane in the FE-ICM phase, as shown in Fig. 7(a). We note here that the x =0.035 sample did not contain any crystal twinning, in contrastto the x = 0 sample. Therefore, the signal-to-noise ratio wasmuch improved in both the intensity map and the line profilealong the (δ, 1 − 2δ, 12 ) direction shown in Fig. 7(c).The critical field of the FE-ICM phase in the x = 0.035sample (H ′c2) is ∼10 T, above which we found that the peak atδ = 12 − q disappeared, as shown in Figs. 7(b) and 7(d). Weobtained integrated intensities of the magnetic Bragg peaksat δ = q and 12 − q as functions of magnetic field, as shownin Figs. 7(e) and 7(f), respectively, confirming that the in-tensity at δ = 12 − q drops to zero at H ′c2. The diffractionpattern above H ′c2 is quite similar to that in the 15 -plateauphase in pure CuFeO2; in fact, the phase diagram establishedby previous bulk measurements suggested that the 15 -plateauphase appears as the first field-induced phase in the x = 0.035sample [35–37]. However, the present results show that thewave number q was not exactly on the commensurate positionof 15 , as shown in Fig. 7(g).One possible explanation for the incommensurate na-ture would be the effects of magnetic domain walls, whichmay shift the phase of the magnetic modulations. A simi-lar peak-shift effect was reported in a commensurate Isingantiferromagnet [47] and became more significant when thesystem was divided into small magnetic domains. The halfwidth at half maximum (HWHM) of the peak at δ = qslightly increases in the field-induced phase, as shown inFig. 7(h), which implies the magnetic correlation length be-comes shorter upon the field-induced phase transition.IV. CONCLUSIONS AND OUTLOOKWe have established the stroboscopic TOF neutron diffrac-tion measurements with long pulsed magnetic fields at lowtemperatures. The widths of the magnetic fields are >1 orderof magnitude larger than the time scale of a polychromaticneutron pulse passing through the sample. As a result, wecan utilize a wide range of neutron wavelength to measurediffraction patterns in high magnetic fields. We applied thistechnique to study the field-induced magnetic phase tran-sitions of triangular lattice antiferromagnet CuFe1−xGaxO2(x = 0, 0.035) and successfully observed the field evolutionsof the magnetic Bragg reflections up to 14 T. As for the x = 0sample, we directly observed the magnetic Bragg reflectionsin the field-induced FE-ICM phase, confirming that the peakpositions and intensity distribution are the same as those in thenonmagnetic substitution-induced FE-ICM phase [33,34]. Wealso observed the diffraction patterns of the first field-inducedphase of the x = 0.035 sample, which were found to be quitesimilar to that in the 15 -plateau phase of the x = 0 sample. Thetiny peak shift might be explained by the phase shift of themagnetic modulations at the magnetic domain walls, which isinferred from the broadening of the peak profile.One of the biggest advantages of this technique is that onecan analyze the neutron diffraction data in the same man-ner as the analysis for the steady-field measurements. Eachneutron data frame contains a wide range of wavelengths,which enables us to explore the three-dimensional reciprocalspace. This feature is essential to explore unknown magneticphases in high magnetic fields. It would also be possible toquantitatively investigate field variations of diffuse scattering023109-6STROBOSCOPIC TIME-OF-FLIGHT NEUTRON … PHYSICAL REVIEW RESEARCH 6, 023109 (2024)FIG. 7. Stroboscopic neutron diffraction results on CuFe1−xGaxO2 with x = 0.035. Intensity maps on the (h, k, 12 ) plane (a) above and(b) below the critical field H ′c2. These data are obtained by applying the long pulsed magnetic field generated with the charging voltage of270 V 80 times at 4 K. Solid arrows indicate the positions of the magnetic Bragg peaks in each phase. Line profiles along the (δ, 1 − 2δ, 12 )direction (c) above and (d) below the critical field H ′c2. Magnetic field dependence of the integrated intensities at (e) δ = q and (f) 12 − q, (g)the magnetic modulation wave number q, and (h) the half width at half maximum of the peak at δ = q. Open and closed symbols denote thedata measured field-increasing and decreasing process, respectively.patterns up to high magnetic fields. We note here that the timespreading of a polychromatic neutron pulse is determined bythe source-to-sample distance and the wavelength (λ)-velocity(v) relationship of neutrons, namely, λ = h/mv, where h andm are the Planck constant and neutron mass, respectively. Itdoes not primarily depend on the repetition rate of neutronpulse generation. Therefore, our long pulsed magnet is alsoapplicable for other TOF diffraction instruments in spallationneutron facilities other than the MLF of J-PARC.Another advantage is the portability of the experimentalsetup. As shown in Fig. 1, the cryostat and magnet are rela-tively small and can be moved from one beamline to another.The capacitor bank and voltage charger are also relativelysmall; they are ∼80 cm in width and <2 m in height. Inaddition, the stray field from the magnet is small; specifically,it is <3 Oe in a distance of 20 cm from the center of themagnet when the field reaches 14 T. Considering that thepulsed magnetic field is shielded by the Al radiation shield andAl vacuum chamber, it does not affect external instruments.These features provide opportunities of high-field experi-ments for a variety of instruments and their subject matter.In fact, high-field environments are necessary not only forphysics but also material science and its applications, suchas developments of ferromagnetic materials for industrial andmedical uses [48,49].The highest magnetic field of the present setup is 14 T.However, it was already demonstrated that long pulsed mag-netic fields with the height of 24.3 T and the width at thehalf maximum of >100 ms can be generated by using EDLCbanks [14]. Therefore, it is possible to develop a long pulsedmagnet for neutron scattering whose highest magnetic fieldexceeds that of existing superconducting magnets for scatter-ing experiments. Although a major drawback of the pulsedmagnetic field is the relatively long time interval for repeatingthe field applications, a recent study shows that the intervalcan be reduced by using a liquid-helium-cooled coil madeof high-purity copper wires, which remarkably reduces Jouleheating effect [50] and shortens the cooling period of themagnet with the improved thermal diffusivity at cryogenictemperatures [51]. These technological developments will ex-tend the high-field capability of neutron scattering.ACKNOWLEDGMENTSThe authors thank Y. Ihara for enlightening discussions.This paper was partly supported by Grants-in-Aid for Scien-tific Research (Grant No. 22H00104) from JSPS. The neutronscattering experiment at J-PARC MLF was carried out viaProposals No. 2021B0070 and No. 2022L0301. T.K. wassupported by a JSPS Research Fellowship and by JSPS KAK-ENHI Grant No. 23KJ0502. T.K. was also supported byQuantum Science and Technology Fellowship Program (Q-STEP).023109-7TARO NAKAJIMA et al. 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