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[Hiroaki Mamiya](https://orcid.org/0000-0002-7840-3008), [Noriki Terada](https://orcid.org/0000-0002-8676-5586), [Kosuke Hiroi](https://orcid.org/0000-0002-1043-1969), [Takenao Shinohara](https://orcid.org/0000-0003-4432-7681), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897)

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Role of neutron Bragg-edge spectroscopy in development of practical magnetic materialsViewOnlineExportCitationRESEARCH ARTICLE |  OCTOBER 09 2025Role of neutron Bragg-edge spectroscopy in development ofpractical magnetic materials Hiroaki Mamiya   ; Noriki Terada  ; Kosuke Hiroi  ; Takenao Shinohara  ; Hossein Sepehri-Amin J. Appl. Phys. 138, 143904 (2025)https://doi.org/10.1063/5.0285904Articles You May Be Interested InAnalysis of 60 nm diam spin dependent tunneling memory cells with thermally assisted writingJ. Appl. Phys. (May 2006)Optical depth profiling of strontium titanate and electro-optic lanthanum-modified lead zirconium titanatemultilayer structures for active waveguide applicationsJ. Vac. Sci. Technol. A (December 2005)Characterization of atomic layer deposited semiconducting Co3O4J. Vac. Sci. Technol. A (January 2019) 14 October 2025 07:36:36https://pubs.aip.org/aip/jap/article/138/14/143904/3367196/Role-of-neutron-Bragg-edge-spectroscopy-inhttps://pubs.aip.org/aip/jap/article/138/14/143904/3367196/Role-of-neutron-Bragg-edge-spectroscopy-in?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0002-7840-3008javascript:;https://orcid.org/0000-0002-8676-5586javascript:;https://orcid.org/0000-0002-1043-1969javascript:;https://orcid.org/0000-0003-4432-7681javascript:;https://orcid.org/0000-0002-7856-7897https://crossmark.crossref.org/dialog/?doi=10.1063/5.0285904&domain=pdf&date_stamp=2025-10-09https://doi.org/10.1063/5.0285904https://pubs.aip.org/aip/jap/article/99/8/08N906/856970/Analysis-of-60nm-diam-spin-dependent-tunnelinghttps://pubs.aip.org/avs/jva/article/24/1/55/242670/Optical-depth-profiling-of-strontium-titanate-andhttps://pubs.aip.org/avs/jva/article/37/2/020903/247234/Characterization-of-atomic-layer-depositedhttps://e-11492.adzerk.net/r?e=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&s=hlQVlfPYiZWZK11WAskd-23Ko5cRole of neutron Bragg-edge spectroscopy indevelopment of practical magnetic materialsCite as: J. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904View Online Export Citation CrossMarkSubmitted: 18 June 2025 · Accepted: 19 September 2025 ·Published Online: 9 October 2025Hiroaki Mamiya,1,a) Noriki Terada,1 Kosuke Hiroi,2 Takenao Shinohara,2 and Hossein Sepehri-Amin1AFFILIATIONS1National Institute for Materials Science, Tsukuba 305-0047, Japan2Japan Atomic Energy Agency, Tokai 319-1195, Japana)Author to whom correspondence should be addressed: mamiya.hiroaki@nims.go.jpABSTRACTNeutron diffractometry plays a pivotal role in fundamental magnetism research, especially in determining magnetic structures. However, itsapplication in practical magnetics was historically sparse due to the simplicity of ferromagnetic materials in conventional devices.Recent increase in utilization of materials with complex magnetic structures has introduced new challenges that necessitate advancedneutron techniques in applied magnetics. This study investigates the applicability of neutron Bragg-edge spectroscopy for developingpractical magnetic materials, substantiating its effectiveness through experimental validations and theoretical analysis. We discuss theprinciples of Bragg-edge spectroscopy for magnetic materials and highlight enhanced experimental throughput using multisample trans-mission spectroscopy. The study provides insights into the in situ visualization of magnetic state distribution using Bragg-edge imaging,both post-assembly and during operational use. These results indicate that neutron Bragg-edge spectroscopy can address emerging needsin applied magnetics, offering significant advancements in the field.© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0285904I. INTRODUCTIONX-ray diffraction is indispensable for analyzing crystal struc-tures, while neutron scattering excels in examining magnetic struc-tures. Despite their critical roles, the application of these techniquesin applied magnetics, particularly for practical materials, is relativelylimited compared to their widespread use in the study of fundamen-tal magnetism concerning condensed matter. For example, approxi-mately one-quarter of the papers in Physical Review B that mention“magnetic” also reference “neutron.” In contrast, the ratio was onlyapproximately 1.7% of the papers in IEEE Transactions onMagnetics.1 This discrepancy arises from the significant focus on fer-romagnetic materials with uniformly aligned spins in practical appli-cations during the 20th century. On the other hand, research infundamental magnetism has progressively concentrated on morecomplex magnetic structures, primarily using neutron scattering.Consequently, the exploration of magnetic structures and excitationsforms a significant part of neutron applications in fundamental mag-netism. Highlighting this significance, at the 1994 InternationalConference on Neutron Scattering2—the year Professors BertramN. Brockhouse and Clifford G. Shull were honored with the NobelPrize for developing neutron scattering techniques—approximatelyone-third of the papers featured the term “magnetic” in their titlesor abstracts. As a result, neutron technology has continuouslyevolved to meet the sophisticated demands of fundamental magne-tism, which increasingly requires enhanced sensitivity and resolution.Today, neutron science stands at the forefront of large-scale scientificresearch, focusing on meticulously chosen samples to advance thefundamental understanding.Since the late 20th century, the application of knowledge fromfundamental magnetism has led to the increased use of materialswith non-ferromagnetic structures, such as antiferromagnets, inapplied magnetics. Notably, the antiferromagnet HoCu2 has beenutilized as a heat storage material,3 enabling efficient cooling ofGifford–McMahon refrigerators to 4 K, which has ensured thewidespread adoption of liquid helium-free MRI systems. Similarly,using the antiferromagnetic material IrMn as the pinning layer inspin valves has substantially enhanced the storage capacity of harddisk drives,4 thereby contributing significantly to the IT revolution.These advancements using a non-uniform magnetic structureextend beyond microscale spin arrangements to mesoscale phases,Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-1© Author(s) 2025 14 October 2025 07:36:36https://doi.org/10.1063/5.0285904https://doi.org/10.1063/5.0285904https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0285904http://crossmark.crossref.org/dialog/?doi=10.1063/5.0285904&domain=pdf&date_stamp=2025-10-09https://orcid.org/0000-0002-7840-3008https://orcid.org/0000-0002-8676-5586https://orcid.org/0000-0002-1043-1969https://orcid.org/0000-0003-4432-7681https://orcid.org/0000-0002-7856-7897mailto:mamiya.hiroaki@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0285904https://pubs.aip.org/aip/japincluding the use of nanogranular recording media5 and nanocom-posite magnets.6 At the macroscale, functionally graded magneticmaterials7 and multi-material components8 are being developed,with magnetic properties engineered to vary within a single compo-nent. In the future, it is expected that practical magnetic materialswill increasingly feature complex internal magnetic structures,moving away from a uniform magnetic state.When leveraging complex internal magnetic structures, it isessential to assess these structures sequentially throughout every stageof material development, from optimization to assembly. To achievethis, the use of neutrons is indispensable at each stage. In the materialdevelopment stage, a critical need exists for high-throughputevaluation methods to enable the optimization of compositions,structures, and processing parameters. Comprehensive assessmentspost-assembly or during operation are essential in the next imple-mentation stage. Although current neutron diffraction facilities haveevolved significantly in advancing the understanding of fundamentalmagnetic phenomena through high-accuracy/high-resolution mea-surements, it is unclear whether they can meet these emergingrequirements. If challenges remain, alternative methodologies needto be explored.In this study, we initially investigated the application of theincreasingly recognized neutron transmission spectroscopy9,10 tovarious magnetic materials, incorporating findings from experi-mental validations and theoretical analysis to determine theinsights this method can provide. Subsequently, we determinedthe capacity of neutron transmission spectroscopy to address thenew demands in the development of practical magnetic materials,focusing on throughput and in situ imaging. Based on the identi-fied benefits and limitations of this spectroscopic method, wedemonstrate its important role in advancing the development ofnext-generation magnetic materials.II. EXPERIMENTALA single crystal of holmium, with a purity of 99.99%, was pro-cured from Accumet Materials Co. The crystal was fashioned intoplate-like shapes measuring approximately 1 × 1 × 0.5 mm3 andinstalled in a cryostat maintained at 4 K, devoid of any magneticfield. Ultra-fine-grained high-carbon steel containing 0.87 wt. %carbon was sourced from Tokushu Kinzoku Excel Co., Ltd. Twelvesheets of this steel were stacked and stored at room temperaturewithout a magnetic field influence (this sample was previouslyutilized in studies reporting transmission spectra under a mag-netic field of 0.4 MA/m11). A magnetic core made of non-orientedelectrical steel was manufactured by Nippon Cut Core Trans Co.,Ltd. This core was fabricated by winding sheets of Nippon Steel’sHi-Lite Core 35H360 (6 mm wide, 0.35 mm thick) to a totalthickness of 10 mm, followed by stress-relief annealing at 800 °C.Since neutrons were irradiated from the side, the thickness alongthe transmission direction tactual was 6 mm. A magnetomotiveforce within the core was generated using a permanent magnet(10 × 7 × 5 mm3) integrated into a gap at the core’s base, whichwas sourced from Niroku Seisakusho and exhibits a residual mag-netic flux density of 1.2 T.All transmission spectra were recorded as functions of thetime-of-flight (ToF) of neutrons at beamline 22 (BL22) RADEN12at J-PARC. The neutron beam was polarized vertically using a mag-netic mirror or antiparallelly through a spin flipper, as requiredprior to striking the sample. Detection of transmitted neutrons wasconducted using a boron-coated gas electron multiplier for roomtemperature experiments, or a μPIC-based neutron imaging detec-tor equipped with a boron converter for cryogenic temperatureexperiments.13III. RESULTS AND DISCUSSIONA. Neutron transmission spectroscopyIt has been well established that when neutrons encounter anarray of nuclei or magnetic moments with periodic structures,14denoted as Qτ and Q0τ , respectively, Bragg’s diffraction occurs ifthe scattering vector q is equal to Qτ or Q0τ . The differential crosssection, dσBragg/dΩ, for unpolarized neutrons can be described asdσBraggdΩ¼ N(2π)3v0XτjFN(q)j2δ(q� Qτ)þ jFM(q)j2δ(q� Q0τ)� �,(1)where N is the total number of unit cells; v0 denotes the unit cellvolume; and FN(q) and FM(q) are the crystal and magnetic struc-ture factors, respectively. This principle forms the basis for neutrondiffractometry for a crystal.14 When diffraction occurs, the intensityof the transmitted beam decreases at the corresponding wavelengthby a specific amount.15,16 Consequently, dips (referred to as mag-netic Bragg dips) are expected to appear in the transmission spec-trum Tr(λ) at λ, which satisfy the Laue condition q =Qτ.As expected, we observed this type of dip in the transmissionspectrum when measuring the wavelength dependence with aneutron detector positioned behind the sample,17 as shown inFig. 1(a). For instance, Fig. 1(b) displays the transmission spectrumfor neutrons incident on the c-plane of a 0.5 mm thick pureholmium single crystal. At a temperature of 150 K, which is in theparamagnetic state, a pronounced dip appears at a wavelength corre-sponding to twice the (002) plane spacing of holmium in its hexago-nal close-packed structure. This dip is due to backscatter diffractionfrom the (002) plane of the holmium crystal. Conversely, at a tem-perature of 30 K, below the Néel temperature of holmium at 132 K,18two additional dips, termed satellite dips, flank the original dip.These satellite dips suggest the formation of a magnetic structurecharacterized by a long periodicity that matches the distance betweenthese satellites. Thus, similar to the conventional use of magnetic dif-fraction for determining magnetic structures, the observation of such“magnetic Bragg dips” provides significant insights into spin configu-rations in a single crystal.17In the case of polycrystalline materials, these dips are uniqueto individual crystals within the sample. It is important to notethat for any orientation of microcrystals, diffraction does notoccur if the wavelength λ exceeds twice the interplanar spacing dτdue to the Bragg condition: 2dτsin θ = nλ, where θ is the diffrac-tion angle and n is an integer representing the order of diffrac-tion. Consequently, several edge-like features, known as magneticBragg edges, manifest at λ = 2d in the spectrum of a polycrystal-line material. Figure 2(a) schematically depicts this relationship.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-2© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japAs diffraction varies from backscattering to forward scatteringdepending on the orientation distribution of microcrystals, theanalysis of such spectra often employs the Rietveld method.19At this point, let us fully express the spectra using the followingequation:15Tr(λ) ¼ exp �XiσBraggi þ σTDSi þ σ absi� �nitih i, (2)where i denotes the ith phase of the multiphase material in multi-component devices. The decay of neutron transmission is influ-enced by three critical cross sections: the elastic coherent Braggdiffraction cross section σBraggi , thermal diffuse scattering crosssection σTDSi , and absorption cross section σabsi . Additionally, niand ti represent the total number of unit cells in the unit volumeand the effective thickness of the ith phase, respectively. Amongthese terms, σBraggi is of particular interest and can be written asfollows:14,19σBraggi ¼ λ22v0XjFN qð Þj2δ(q� Qτ)þ jFM(q)j2δ(q� Q0τ)� �dτPτEτ ,(3)where v0 is the unit cell volume, Pτ is the preferred orientationfactor, and Eτ is the extinction factor. Figure 2(b) displays thespectrum for the high-carbon steel plate, a typical example of apractical polycrystalline magnetic material, in a zero magneticfield. As anticipated, the transmission of unpolarized neutronsexhibits a significant decrease in the wavelength range below thebackscattering wavelength for each set of lattice planes {hkl}.Upon closer inspection, the attenuation due to {200} diffraction isnotably pronounced near θ = π/2, while the attenuation due to{110} diffraction is most apparent around θ = π/3. These patternsindicate that the (110) planes of most microcrystals were inclinedaway from the rolling surface, whereas the (200) planes tended toFIG. 1. Principle and typical results ofneutron transmission spectroscopy fora single crystal. (a) Schematic demon-strating the principle of decreasingtransmission at wavelengths where dif-fraction occurs and (b) transmissionspectra for the Ho single crystal whenunpolarized neutrons are incident onthe c-plane. At 30 K, below the Néeltemperature, two satellite dips causedby magnetic diffraction are evident inthe spectra.FIG. 2. Neutron transmission spectroscopy principles and typical results for polycrystalline materials. (a) Schematic showing diffraction and transmission through microcrys-tals with varying orientations of diffraction planes and (b) transmission spectra of a carbon steel plate for neutrons incident on the rolling face, displayed for both unpolar-ized and vertically polarized neutrons (data in the magnetic field were retrieved from Ref. 11). For context, the spectrum under the zero magnetic field is compared withresults obtained in a magnetic field. The bars in the figure denote the wavelengths at which backward and oblique scattering occur for each diffraction plane.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-3© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japalign parallel to it. Further discussion of the incline has beencarried out by applying a model function11 for Pτ.Let us now consider the details of the magnetic state thatholds our interest. In ferromagnetic materials such as steel, whereQτ ¼ Q0τ , no separate magnetic Bragg edge exists distinct fromthe edge due to nuclear scattering. For iron atoms, which possessmagnetic moments of 2.2 bohr magnetons (μB), the magnitudeof jFM(q)j2 is typically no more than 10% of jFN(q)j2 aroundQτ = 3 Å−1 (dτ = 2 Å). This makes it challenging to discern themagnetic scattering cross section from spectra obtained usingunpolarized neutrons. Consequently, neutron diffractometry oftenrelies on polarized neutrons to reveal the magnetic structure offerromagnetic materials. For neutrons polarized either upward ordownward along the z-axis, the part inside the brackets in Eq. (1)can be reformulated as [(FN(Qτ)δ(q�Qτ)+ FnsfM (Q0τ)δ(q�Q0τ))2þ(FsfM(Q0τ)δ(q�Q0τ))2] using magnetic structure factors fornon-spin-flip and spin-flip scatterings,20FnsfM Q0τð Þ ¼Xjoj rmmz?j2μBfj� �exp irj � Q0τ�  , (4a)FsfM Q0τð Þ ¼Xjoj �rmmx?j � imy?j2μBfj !exp irj � Q0τ�  , (4b)where rm is the magnitude factor (5.39 fm); oj is the site occu-pancy; m⊥j = (m⊥xj, m⊥yj, m⊥zj ); fj represents the site occupancy; andthe vector projection of the magnetic moment mj of the jth atomon the plane perpendicular to q and the magnetic form factor ofthe jth atom, respectively. By employing polarized neutrons, wecan detect relatively subtle changes in FM(Qτ) by analyzing themore substantial cross terms of FM(Qτ)⋅FMnsf(Qτ0).Figure 2(b) also depicts the previously reported transmissionspectra obtained for the same sample in the presence of a magneticfield (H = 0.4 MA/m) applied along the vertical axis. The spectra inFig. 2(b) reveal a notable difference in transmission depending onthe direction of neutron polarization when a magnetic field(H = 0.4 MA/m) is applied vertically. In contrast, no such differenceis observed in the current result obtained in a zero magnetic field.This phenomenon suggests that the application of H aligns themagnetic moment m⊥j of each iron atom parallel to H, resultingin significant changes in transmission as σBraggi either decreases orincreases due to the interaction 2FM(Qτ)⋅FMnsf(Qτ0). More detailedmagnetic information can be derived from these powder spectrausing full pattern fitting with the model described by Eqs. (3)and (4).19As discussed thus far, it is feasible, in principle, to conductstructural analysis using neutron transmission spectroscopy, similarto neutron diffractometry. However, each method has its ownadvantages and disadvantages. For example, in a randomly orientedpowder composed of atoms with a magnetic moment of 1 μBarranged on a face-centered cubic lattice with a lattice constant of0.35 nm, the magnetic backscattering cross section from the (111)plane can be calculated to be approximately 30 fm2 per atom. For asample thickness of 1 cm, this corresponds to about 3% of theincident neutrons being scattered. If 10 000 neutrons are incident ona 1 cm2 sample surface, 9700 neutrons will be transmitted anddetected by a zero-dimensional counter with a 1 cm2 aperture, result-ing in a signal-to-noise (S/N) ratio of approximately 300ffiffiffiffiffiffiffi9700p � 3.In contrast, assuming a large area detector (103–104 cm2) with solidangle coverage of 30% in a diffractometer, 100 neutrons would bedetected, corresponding to an S/N ratio of approximately 100ffiffiffiffiffi100p � 10.Thus, when the magnetic moment is relatively small, the signal-to-noise ratio is, in principle, more favorable for diffractometry thanfor transmission spectroscopy. Conversely, in cases where thebackground level per unit detection area is high, transmissionspectroscopy may demonstrate superiority with respect to thesignal-to-background ratio. In any case, the relative merits ofthese methods depend on the specific sample and experimentalsetup. Therefore, in Sec. III B, we further investigate the potentialof transmission spectroscopy through specific measurement exam-ples and assess its suitability for the development of practical mag-netic materials, focusing on measurement throughput andcomprehensive in situ imaging, as outlined in the Introduction.B. Potential of neutron transmission spectroscopy1. Multi-sample spectroscopyDuring the material optimization stage, numerous samples areproduced to refine their composition and processing conditions.High throughput is essential for efficiently evaluating these materi-als. In diffractometry, intensity measurements for each scatteringangle are typically conducted on a single sample centered withinthe detector array. The measurement time per sample can bereduced by increasing either the intensity of the incident neutronbeam or the area of the detectors. Furthermore, if sample exchangesare conducted swiftly, measurement throughput can be significantlyimproved, even though each sample is measured individually.21–23However, under specialized conditions tailored to practical environ-ments, sample auto-changers are sometimes not usable. In suchcases, the entire process—including installing a sample, preparingthe experimental environment, conducting measurements, waitingfor the sample’s residual radioactivity to diminish and, subsequently,exchanging the sample—may require up to a full day for a singlespecimen. This duration is independent of the neutron source inten-sity. Consequently, studies involving the comparison of a largenumber of samples—such as investigations into the compositionaldependence of multi-element doped systems or the effects of subtleprocess conditions—demand significant and valuable beamline time,making their implementation difficult.How does neutron transmission spectroscopy perform in com-parison? In this section, we consider the case in which a neutronbeam with a small divergence angle is divided into multiple parallelbeams by means of a mask with numerous apertures. These parallelbeams travel rectilinearly and reach the detector directly withoutintersecting one another. By aligning the samples and detectorsalong parallel paths, it is possible to obtain their spectra separately.Figure 3 illustrates a conceptual diagram of an experiment conductedwith holmium alloys, alongside the representative results obtained.While detailed descriptions are provided in the original publication,24this experiment successfully captured the spectra of 25 differentJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-4© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japsamples simultaneously. Moreover, it effectively extracted magneticstructural information from these spectra. For example, the analysisof the heights of the satellite Bragg edges, marked by arrows in thefigure, revealed variations in the magnitude of the magneticmoments organized into a helical structure. In this paper, we shallexplore the advantages and challenges of simultaneous multi-samplemeasurements, drawing on the referenced success.24Considering the capabilities of multi-sample transmissionspectroscopy, it is crucial to assess the number of samples that canbe measured simultaneously. Theoretically, the array size can beunlimited if only transmitted neutrons are captured by the detectorarray. However, one must be cautious about the potential of widedetectors to inadvertently capture diffracted neutrons. To reducethis risk, employing a chopper to filter out short-wavelength neu-trons that cause forward scattering prior to their incidence is aneffective strategy. For instance, setting a cutoff wavelength at 1/5 ofthe longest interplanar spacing would preclude diffraction at anglescharacterized by 2 sin θ < 1/5. Therefore, if the detector array ispositioned 300 mm behind the sample array (l = 300 mm), main-taining the sample array width (w) (equal to the detector arraywidth) at 60 mm would effectively prevent contamination from dif-fraction lines. However, given the presence of certain magneticstructures with exceptionally long periods, a meticulous evaluationis necessary when configuring the actual experimental setup.Subsequently, it is essential to investigate the lower limit of theindividual sample size. The most significant factor in this context isthe signal-to-noise (S/N) ratio of the spectrum, which is inherentlydependent on the experimental objectives and the intensity of theincident beam at the utilized facility. As a result, it is challenging toestablish definitive values for the sample size. However, the success-ful analysis using 6 mm diameter polycrystalline samples atJ-PARC (0.7 MW)24 serves as a practical benchmark for polycrys-talline magnetic materials with large magnetic moments, providingvaluable guidelines for future applications. Conversely, for single-crystal samples, as illustrated in Fig. 1, a sufficient signal has beenobtained from a relatively small specimen (with dimensions of1 mm). However, densely packing and aligning numerous smallsamples presents challenges. The angular dispersion Δw of the inci-dent neutrons significantly impacts the parallelism of the neutronbeam’s path. For example, neutrons passing through an aperture ofdiameter da and traveling a distance L0 to the sample will exhibitan angular spread defined by sin Δw = da/L. This dispersion causesa broadening of l sin Δw = l da/L in a detector located at a distance lbehind the sample. To avoid overlap of transmitted neutrons fromadjacent samples, it is necessary to maintain a gap equivalent tol da/L between the samples. If Δw equals 0.3° (da/L = 1/180), thiscorresponds to a width of approximately 2 mm when l is 300 mm.Reducing this value by placing the detector closer to the samplecan lead to interference from diffracted neutrons, as previously dis-cussed. Therefore, selecting conditions that meet the experimentalobjectives is crucial. For example, given the parameters mentioned(w = 60 mm and the gap between the samples = 2 mm), it is theo-retically feasible to simultaneously measure up to 400 single-crystalsamples, each measuring 1 × 1mm2, under these experimental condi-tions. When utilizing polycrystalline samples measuring 6 × 6mm2,it is feasible to measure up to 49 samples simultaneously. The capac-ity to measure 49 or 400 at the same time is considered sufficient forthe optimization of material composition and processing. Therefore,FIG. 3. Principle and typical results of multi-sample neutron transmission spectroscopy for polycrystalline samples with appropriate thicknesses (data were retrieved fromRef. 24). (a) Schematic illustrating the experimental setup and representative results for unpolarized neutrons and (b) and (c) examples of typical spectra.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-5© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japmulti-sample spectroscopy is expected to be useful when a largenumber of samples need to be measured, especially when an auto-matic sample changer is not available in special environments.Before concluding this section, it is crucial to address the signif-icant limitations inherent to multi-sample transmission spectroscopy.A primary constraint is the necessity to conduct measurementsunder uniformly identical conditions for all samples simultaneously.In conventional neutron diffractometry, which focuses on individualsamples, it is possible to precisely adjust the measurement tempera-ture to suit the unique characteristic temperature of each sample andextend the measurement duration as needed to ensure experimentalaccuracy. On the other hand, such flexibility in adjusting experimen-tal conditions is challenging when measuring multiple samples con-currently. In other words, conventional diffractometry is more suitedfor detailed investigations. It is important to note that the field ofmagnetic materials is currently experiencing a shift towards data-driven optimization, a trend that is promising but still in its nascentstages. However, for data-driven material optimization, precise physi-cal details as features are not always necessary. Given these consider-ations, the high-throughput capabilities of multi-sample transmissionspectroscopy hold significant promise.2. Spectroscopic imagingAs highlighted in the Introduction, during the final imple-mentation stage, a comprehensive evaluation of magnetic materialsfollowing assembly or operational use is desirable. This necessityarises because magnetic energies are much smaller than chemicalbond energies of several electron volts (eV). For instance, theZeeman energy of a magnetic moment of 10 μB in a 1 T magneticfield is less than 1 meV. Consequently, the magnetic state of materi-als is highly susceptible to subtle changes in the local environment,such as magnetic anisotropy during formation and minor varia-tions in heat and stress during operation. This sensitivity extends tostrain and magnetic poles on the surface, highlighting the need formethodologies that can nondestructively observe the microstruc-tural and magnetic states within a material’s interior.Neutrons, recognized for their high penetration depth, havebeen conventionally used in this type of nondestructive analysis,known as neutron radiography.25 The internal structures of objectshave been imaged by exploiting the differences in neutron attenua-tion cross sections of various materials. Figure 4(b) shows the distri-bution of the ratio of the effective thickness, teff, derived from theneutron transmission measured in the 5–6 Å wavelength range, tothe actual thickness, tactual, for a non-oriented electromagnetic steelcore with tactual of 6mm along the transmission direction, as shownin Fig. 4(a). In this image, the effective thickness, which correlateswith the bulk density, appears relatively greater outside the curvedsection. The insights obtained from neutron attenuation imaging areinstrumental for evaluating processing methods. However, thisconventional technique does not allow for the visualization of thedispersion of magnetic anisotropy, which influences the magneticproperties or affects the flow of magnetic flux.FIG. 4. Principle of Bragg edgeimaging and typical results. (a)Experimental setup and transmissionspectra from different regions of a non-oriented electrical steel wound core.The light blue and yellow areas in thespectra represent contributions fromBragg diffraction and absorption,respectively, for incident neutrons. (b)Distribution of the ratio of the effectivethickness, teff, derived from the neutrontransmission measured for unpolarizedneutrons in the 5–6 Å wavelengthrange, to the actual thickness, tactual,for a non-oriented electromagneticsteel core with tactual of 6 mm along thetransmission direction. (c) Differencesin transmission between upward anddownward polarized neutrons. (d)Maps showing the height ratio of the{110} to {211} edges for unpolarizedneutrons. (e) Ratio maps comparingthe contributions of {110} backscatter-ing (θ = π/2) with oblique diffraction(θ = π/3) for unpolarized neutrons.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-6© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japConversely, as discussed in Sec. II, Bragg edges manifest in thewavelength region below a specific threshold (4.04 Å for iron). Asin the multi-sample spectroscopy described above, the distributionof crystal structures can be visualized by analyzing the Bragg edgesat different positions. This method has been utilized to analyze theinternal microstructure of valuable cultural heritage items andartifacts without inflicting damage, thereby aiding in the determi-nation of their archaeological origins.10 More recently, suchneutron imaging technique has been extended26 to practical mag-netic materials,11,20,27 as well as other types of neutron imagingtechniques, such as analysis of Larmor precession in magneticflux,28 differential neutron phase contrast,29 and mapping of thedepolarization coefficient.30 In the case of the non-oriented ironcore presented here, the shapes of the edges vary depending ontheir location, as depicted in Fig. 4(a). Figure 4(d) highlightsthese variations by focusing on the ratios of the heights of the{110} to {211} edges. The edge heights in the neutron transmis-sion spectra are proportional to the diffraction intensity of thebackscattered neutrons, and the intensity ratio of the {110} to{211} edges should be approximately 3 for random orientationswhen considering multiplicity factors, interplanar spacing, andminor differences in magnetic scattering. Consequently, the 〈211〉axis appears relatively aligned with the incident neutron directionacross the entire core, although this alignment diminishes on theinner side of the curved section. Conversely, Fig. 4(e) contraststhe contribution of {110} backscattering diffraction at the edge[4.04 Å = 2d110 sin(π/2)] with that of oblique diffraction observedat a shorter wavelength [3.5 Å = 2d110 sin(π/3)]. Given that thisratio approximates 0.75 for random orientations, the 〈110〉 axisexhibits a tilt relative to the incident direction, with this inclina-tion intensifying within the curved sections. These observationssuggest that, after stress-relief annealing above recrystallizationtemperature,31 the forming process continues to influence thecrystal structure. Therefore, by analyzing the features of the trans-mission spectrum of neutrons, a preliminary visualization ofcrystal texture information is achievable.For a more detailed examination of this crystal texture, it isnecessary to apply methods such as Rietveld refinement to thecollected spectra. However, as discussed above, the transmissionspectroscopy technique is less sensitive than diffractometry fordetecting weak reflections required for such analyses. At thisstage, it is crucial to recognize that the precise data demanded infundamental science may not always be necessary for enhancingmanufacturing processes. In practical scenarios, where the focusis on improving processing or assembly procedures and prevent-ing degradation during use, it is often sufficient to correlatedescriptors related to microstructural changes and magnetic prop-erties through machine learning from numerous examples. Insuch contexts, the straightforward spectral mapping demonstratedhere can be effectively utilized. Let us now consider the imagingof magnetic structures, a critical factor influencing magnetic proper-ties. As we have observed, the treatment of magnetic scattering variessignificantly between antiferromagnets and ferromagnets; in antifer-romagnets, magnetic scattering occurs at different wavelengths fromnuclear scattering, whereas in ferromagnets, these scatterings alwaysoverlap. While we have previously discussed multi-sample transmis-sion spectroscopy for antiferromagnets, our focus here will be onferromagnets. The use of polarized neutrons is particularly valuablefor imaging these materials.Let us consider how the flow of magnetic flux, the arrange-ment of magnetic domains across micrometer-to-millimeter-scalegrains, and magnetic structures within nanometer-scale compositesmanifest when examined with polarized neutrons. Equations (4a)and (4b) demonstrates that when neutrons polarized along the Zdirection are incident from the X direction, the polarization depen-dence of the backscattering intensity in a microcrystal correlateswith the Z component of the magnetization direction. By analogywith the derivation of Eq. (3), the height of the Bragg edge similarlycorrelates with the Z component of the magnetization direction.Although transmission spectroscopy provides information averagedover the thickness of the sample, its unique capability enables thevisualization of the internal magnetization states of bulk devices—adetail that is typically unattainable using alternative methods.For instance, in a transformer equipped with a manganese zincferrite core wrapped in copper windings, when fully saturated,Bragg-edge spectroscopic imaging recently revealed that the mag-netization vector rotates along the circumferential direction of thetoroidal core.20 While this behavior aligns with expectations fromAmpère’s law, it had previously been inferred only indirectlythrough integrated values of magnetic flux captured by the elec-tromotive force induced in an external pick-up coil. This exampleclearly demonstrates that the deep penetration capability of neu-trons enables the direct observation of internal magnetizationstates that were previously unobservable. Meanwhile, under whatcircumstances can such imaging be performed? In this study, wefurther investigate the versatility of this method.While it is possible to visualize the internal magnetic states ofdevices in a saturated state as shown previously,20 it is important torecognize that magnetic cores do not operate in the fully saturatedregions. In practical magnetic materials, as the magnetic fieldincreases, magnetization initially rises easily due to the movementof magnetic domain walls and then gradually approaches saturationas the magnetization vector rotates away from the magnetic easyaxis. Typically, this process is inferred from observations made atthe surface of the device. However, can the changes in the internalmagnetization state at each location be directly observed duringthese processes?Figure 4(c) depicts the differences in the transmission ofupward and downward polarized neutron beams when a closedmagnetic circuit was formed by integrating a neodymium magnet(μ0Ms = 1.2 T) into the core of the non-oriented electrical steelsheet discussed previously. In this illustration, no difference intransmission is apparent. For non-oriented electrical steel sheets,the transition from magnetic wall movement to magnetization rota-tion is believed to occur around 1.6 T.32 Therefore, at 1.2 T, the mag-netization within each grain is likely still tilted from the averagemagnetization direction toward the magnetic easy axis. In such cases,the neutron spin undergoes Larmor precession around the tiltedmagnetic flux lines that are different for each grain. During this pre-cession, depolarization occurs, which can be described as follows:33P ¼ P0 1� 12ϒnmnhδBtλ� �2" #Dδ, (5)Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-7© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japwhere P and P0 are the polarizations of the neutrons and their initialvalues, respectively; γn denotes the gyromagnetic ratio; mndenotes the neutron mass; h is Planck’s constant; δ is the averagedomain size; D is the penetration depth; and Bt is the transversemagnetic field dispersion. Figure 5 depicts the change in polari-zation at a depth of 1 mm when Bt = 0.4 T. From this figure, it isevident that in non-oriented electrical steel, which features mag-netic domains on the scale of tens of micrometers,34 maintainingneutron polarization during deep penetration is challengingunless the material is fully saturated.This observation suggests that transmission spectroscopy maynot be ideal for evaluating conventional ferromagnetic materials.However, Fig. 5 depicts that depolarization does not occur when thescale of magnetization inhomogeneity is sufficiently small. Therefore,transmission spectroscopy can prove valuable for assessing nanocom-posite magnetic materials, which have recently emerged as promisingnext-generation materials. These materials, such as exchange springmagnets,35,36 exhibit magnetic states that vary with operating condi-tions, including the magnetization directions of the two nanophases.Evaluating these states in bulk components using existing technolo-gies is particularly challenging. The magnetic coupling and interfacialmagnetic anisotropy between the nanocomposite phases are likelysensitive to fabrication conditions and degradation, posing significantchallenges for the integration of such novel materials into devices.Neutron transmission spectroscopy allows for the analysis of mul-tiphase materials by differentiating phases with distinct crystallinestructures, as each phase’s Bragg edge appears at different wave-lengths. Furthermore, as illustrated in Fig. 5, the polarization ofneutrons at each edge is not disturbed by magnetic inhomogenei-ties on the nanoscale, enabling expectations of mapping magneti-zation orientation for each phase. In other words, leveraging thecapabilities of transmission spectroscopy may facilitate the simultane-ous mapping of nanoscale magnetic states and nanocrystalline texturesin multiphase nanocomposites during post-production, integration,and operational stages.IV. SUMMARY AND PROSPECTIVEThis study investigated the applicability of Bragg-edge trans-mission spectroscopy for analyzing complex magnetic structures inadvanced magnetic materials. The incorporation of multi-sampletransmission measurements significantly increased experimentalthroughput, enabling the generation of large datasets essential formaterials optimization. The non-destructive nature of the methodallowed for internal magnetic structure visualization under bothmanufacturing and operational conditions. These capabilities canimprove quality control and functional evaluation in technologiesreliant on magnetic materials, including those used in energy anddata storage. Furthermore, we can expect that this approach enablesmicrostructural and magnetic state mapping in multiphase nano-composite systems, supporting assessment after fabrication, duringintegration, and in-service operation. While polarized neutronBragg-edge analysis showed limitations in resolving micrometer-scale domains in conventional ferromagnetic devices, it showed sig-nificant potential for characterizing future nanostructured magneticmaterials with complex internal order.Before concluding this paper, we would like to briefly refer thepotential of transmission spectroscopy to make neutron diffractionmore accessible. In the field of x-ray diffraction, alongside large-scale synchrotron facilities, small-scale laboratory x-ray diffractioninstruments (lab-XRD) are commonly installed in universities andcompanies, providing ample opportunities for the rapid testing ofnew ideas. In contrast, lab-scale neutron diffraction instruments arerarely available, and this lack is frequently cited as the criticalbarrier to the utilization of neutrons in magnetic materials develop-ment.37,38 It is worth considering whether the distinct characteris-tics of neutron transmission spectroscopy could help to addressthis challenge.First, it should be noted that even with future advancements insmall neutron source technology, the number of neutrons that canbe generated in a laboratory setting will remain significantly lowerthan that available at large-scale neutron facilities. When using suchlow-intensity sources, focusing optics becomes crucial to deliverthe required neutron flux to the sample. However, as depicted inFig. 6(a), in diffractometry, the convergence angle Δw of the incidentbeam significantly affects the resolution of the diffraction angle.For instance, achieving a resolution of 0.1° necessitates that the con-vergence angle not exceed 0.1°. Without the ability to focus, onealternative would be to increase the sample size to enhance the totalFIG. 5. Depolarization due to various scales of inhomogeneity. Variation in thepolarization of neutrons at a wavelength of 4 Å and a depth of 1 mm, character-ized by a typical heterogeneity size δ and a transverse magnetic field dispersionBt of 0.4 T.FIG. 6. Focusing optics and the sample size in neutron diffractometry and spec-troscopy. (a) Diagram depicting the resolution of a focused neutron beam acrossa range of incident angle sizes (Δθ) striking a sample of size (ΔL) and (b) illus-tration of a spectrometer using a pulsed neutron generator with a time-resolveddetector located at the foci of a rotating elliptical neutron mirror.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 143904 (2025); doi: 10.1063/5.0285904 138, 143904-8© Author(s) 2025 14 October 2025 07:36:36https://pubs.aip.org/aip/japincidence. However, in this scenario, as the neutron path lengthvaries with the sample size, it results in degraded time-of-flight(ToF) resolution, thereby reducing the wavelength resolution. Forthis reason, it is not easy to perform effective diffraction measure-ments using low-intensity neutron sources.In the transmission spectroscopy of polycrystalline materials,the positions of Bragg edges in the spectra are independent of theangle of the incident beam, with the resolution being solely deter-mined by the flight distance from the source to the detector and thepulse width. A theoretical setup involves placing a point neutronsource and a zero-dimensional time-resolutive detector at the focalpoints of a rotating elliptical neutron mirror. This configurationensures constant flight distances, irrespective of the sample’s position,size, or the angle of the incident beam, as depicted in Fig. 6(b).In theory, this arrangement allows for the measurement of Braggedges by exposing all of the generated neutrons to a large samplevolume. In practice, current neutron mirrors are limited to reflec-tions of up to approximately 3°;39 nevertheless, under such condi-tions, the collected neutron flux is 1000 times greater than that at0.1°. Although this concept remains theoretical at present, it maynonetheless merit further exploration.ACKNOWLEDGMENTSExperiments at BL22 of J-PARC were performed using userprograms (Grant Nos. 2017A0042, 2018A0062, and 2021B0189).A part of this work was supported by “Advanced ResearchInfrastructure for Materials and Nanotechnology in Japan (ARIM)”of the Ministry of Education, Culture, Sports, Science andTechnology (MEXT) (Grant No. 24NM5119). This work was par-tially supported by JSPS KAKENHI (Grant No. 19H04400);MEXT-Program for Creation of Innovative Core Technology forPower Electronics (Grant No. JPJ009777); and JST-Mirai Program,Japan (Grant No. JPMJMI18A3). During the preparation of thiswork, the author used the NIMS Azure Chat to refine English. Afterusing this tool or service, the author(s) reviewed and edited thecontent as needed and took (s) full responsibility for the content ofthe publication.AUTHOR DECLARATIONSConflict of interest statementThe authors have no conflicts to disclose.Author ContributionsHiroaki Mamiya: Conceptualization (equal); Data curation (equal);Methodology (equal); Writing – original draft (equal); Writing –review & editing (equal). Noriki Terada: Conceptualization(equal); Methodology (equal); Writing – original draft (equal);Writing – review & editing (equal). Kosuke Hiroi:Conceptualization (equal); Data curation (equal); Writing – review& editing (equal). Takenao Shinohara: Conceptualization (equal);Data curation (equal); Writing – review & editing (equal). HosseinSepehri-Amin: Conceptualization (equal); Methodology (equal);Writing – review & editing (equal).DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1Survey using Scopus, Elsevier B.V. (2025). See https://www.scopus.com/.2S. Funahashi, S. Katano, and R. A. Robinson, Phys. B: Condens. Matter213–214, 1–1052 (1995), available at https://www.sciencedirect.com/journal/physica-b-condensed-matter/vol/213/suppl/C.3Y. Ohtani, H. Hatakeyama, H. Nakagome, T. Usami, T. Okamura, andS. Kabashima, Cryocoolers 10, 581 (1999).4H. Iwasaki, A. T. Saito, A. Tsutai, and M. Sahashi, IEEE Trans. Magn. 33, 2875(1997).5S. Iwasaki and K. Ouchi, IEEE Trans. Magn. 14, 849 (1978).6R. Coehoorn, D. B. Demooij, J. P. W. B. Duchateau, and K. H. J. Buschow,J. Phys 49, 669 (1988).7S. Kasai, M. Namikawa, and T. 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