A Method for Analyzing the Domain Structure in Magnetic Powder Microparticles

A Method for Analyzing the Domain Structure in Magnetic Powder Microparticles | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Method for Analyzing the Domain Structure in Magnetic Powder Microparticles Shamil Minkailovich Aliev, Zhavrail Gadzhievich Ibaev, Minkail Shamilevich Aliev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4137227/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Oct, 2019 Read the published version in Technical Physics Letters → Version 1 posted You are reading this latest preprint version Abstract A method for analyzing the domain structure in magnetic powder microparticles based on the Mössbauer effect is proposed. This method has been experimentally verified for gadolinium ferrite-garnet (Gd 3 Fe 5 O 12 ) powder particles 40 ± 5 µm in diameter in the vicinity of the magnetic compensation point T cm =286 K. It is shown that ferrite particles are single-domain near T cm and pass to the multidomain state while moving away from T cm . domain structure single-domain particles ferrites magnetic compensation point Mössbauer effect Figures Figure 1 Figure 2 Figure 3 1. Introduction It is known that thorough grinding of a magnetic results in the occurrence of single-domain particles. The physical reason is that the magnetostatic energy of a particle (proportional to the particle volume) decreases with a decrease in the size with a higher rate, as compared to the domain wall energy (proportional to the particle surface area). At some critical size, the single-domain state becomes energetically favorable. The critical diameter, at which the particle passes from the multidomain state to the single-domain one, is determined by the expression [ 1 ]: $${d}_{сr}=\frac{9}{2\pi }\frac{\sigma }{{M}_{s}^{2}}$$ 1 , where σ is the domain wall energy density and M s is the spontaneous particle magnetization. Magnetic powders of single-domain particles have a wide range of technical application [ 2 , 3 ]. Magneto-optical methods based on the Kerra and Faraday effects are generally applied to observe domain structure in magnet microparticles [ 1 ]. A method for analyzing the domain structure in a singlecrystal ferrite sample with magnetic compensation point T cm was proposed in [ 4 ] based on the Mössbauer effect. In this study, we describe a method for analyzing the domain structure in magnetic powder microparticles based on the Mössbauer effect. Note that Mössbauer spectroscopy is successfully applied for investigating the structural and magnetic properties of magnetic materials containing particles or nanoclusters [ 5 , 6 ]. The interest in systems of magnetic particles or small clusters is primarily due to their wide range of application in modern nanotechnology [ 7 , 8 ]. 2. Experimental Methods Let us consider an ensemble of single-domain particles isotropically distributed in space. If this ensemble of particles is magnetized to saturation and then magnetizing field H is switched off, maximum angle θ m of deviation of the particle magnetization vectors from the field-application direction is equal to angle α between the hard and easy magnetization axes in this magnet. For magnets with cubic and uniaxial anisotropies, α = 55° and 90°, respectively. Thus, in the state of residual magnetization, the magnetization vectors of single-domain particles are isotropically distributed in solid angle Ω = 2θ m = 2α. If the particles have a domain structure, θ m > α because closure domains and domain walls, in which the magnetic moments make an angle with the easy magnetization axes, exist in the domain structure along with domains, the magnetization vectors of which are directed along the easy magnetization axes. It is known that the relative areas of the Zeeman splitting lines in a Mössbauer spectrum of 57 Fe nuclei in a homogeneously magnetized sample depend on angle θ between the γ-ray propagation direction and magnetization direction in the sample [ 9 ]: $${S}_{\text{1,6}}=3\left(1+{\text{cos}}^{2}\theta \right)$$ $${S}_{\text{2,5}}=4{\text{sin}}^{2}\theta$$ 2 $${S}_{\text{3,4}}=1+{\text{cos}}^{2}\theta$$ Let the geometry of the experiment be as follows the γ-ray propagation direction coincides with the H direction. Then, the following expression can be written for parameter k equal to the ratio of the second-to-first (or fifth-to-sixth) absorption line areas in the Mössbauer spectrum of 57 Fe nuclei in the sample: $$k=\frac{{S}_{\text{2,5}}}{{S}_{\text{1,6}}}=\frac{4(1-\stackrel{-}{{cos}^{2}}{\theta }_{i})}{3(1+\stackrel{-}{{cos}^{2}}{\theta }_{i})}$$ 3 , where θ i is the angle between the γ-ray propagation direction and the magnetization direction of the i - particle (0 ≤ θ i ≤ θ m ): $$\stackrel{-}{{cos}^{2}}{\theta }_{i}=\frac{\underset{0}{\overset{{\theta }_{m}}{\int }}\underset{0}{\overset{2\pi }{\int }}{cos}^{2}\theta \bullet sin\theta d\theta d\phi }{\underset{0}{\overset{{\theta }_{m}}{\int }}\underset{0}{\overset{2\pi }{\int }}sin\theta d\theta d\phi }=\frac{{cos}^{3}{\theta }_{m}-1}{3(cos{\theta }_{m}-1)}$$ 4 , For single-domain particles, we have \(\stackrel{-}{{cos}^{2}}{\theta }_{i}=\text{0,63}\) (cubic anisotropy) and \(\stackrel{-}{{cos}^{2}}{\theta }_{i}=\text{0,33}\) (uniaxial anisotropy). Substituting these values into (3), we arrive at the following criteria: if k + Δ k ≤0.30 (cubic anisotropy) and k + Δ k ≤0.67 (uniaxial anisotropy), the powder particles are single-domain (Δ k is the experimental error in determining parameter k ). If k –Δ k > 0.30 (cubic anisotropy) and k – Δ k > 0.67 (uniaxial anisotropy), the powder particles have a domain structure; the relative number of domains in the particles can be estimated from the k value. Rare-earth ferrite garnets (REFG) having the magnetic compensation point T cm are the most favorable magnets for the organization of the experiment. Indeed, fairly large REFG particles may become single-domain near T cm due to the small value of spontaneous magnetization [ 10 ]. In addition, the particles that are single-domain near T cm pass to the multidomain state while moving away from T cm . Therefore, one can experimentally validate the found criteria gradually increasing the difference in temperature from T cm . Note that the interest in REFG is related to the prospects of formation of materials based on the domain structure of these ferrimagnets for the element base of magnetic microelectronic devices [ 11 – 13 ]. The method was verified on particles of a Gd 3 Fe 5 O 12 ferrite single crystal with cubic anisotropy prepared according to the standard technology from pure initial oxides Gd 2 O 3 and Fe 2 O 3 [ 14 ]. The magnetization was measured in the temperature range of 150–400 K on a VM2-A vibrational magnetometer. It was established that the ferrite compensation point is T cm = 286 K (Fig. 1 ). The Mössbauer spectra of 57 Fe nuclei were recorded on a YGRS-4M spectrometer with a 57 Co(Cr) γ-radiation source. A ferrite single crystal powdered in an agate mortar was filtered through a set of hair sieves to obtain spherical particles with a diameter d = 40 ± 5 µm. These particles were used to make a sample (absorbent for Mössbauer measurements) by depositing the powder in a glue mixture on a thin mica disk. The absorbent thickness with respect to natural iron was 20 mg/cm 2 . For temperature measurements, the sample was placed in a temperature chamber combined with a cryostat with a fine temperature control in the range of 120–500 K. Automatic temperature control system maintained a specified temperature with an error of ± 0.5 K. Before measuring the Mössbauer sample, the spectrum was brought into the residual-magnetization state at a specified temperature. The sample temperature was brought to the desired value, and then the magnetic field applied perpendicular to the sample plane was increased from zero to the value H S = 2 kOe, which is sufficient for magnetic saturation of the sample, after which it was reduced to zero. Before each measurement, the sample was preliminarily demagnetized in an alternating magnetic field with amplitude decreasing to zero. Typical spectra measured in the vicinity of T cm are shown in Fig. 2 . They are a superposition of two Zeeman sextets caused by iron ions in the a and d ferrite \(\left\{{Gd}_{3}^{3+}{\}}_{c}\right[{Fe}_{2}^{3+}{]}_{a}({Fe}_{3}^{3+}{)}_{d}{O}_{12}^{2-}\) sublattices. Note that the Mössbauer spectrum does not distinguish symmetric and antisymmetric magnetic-moment orientations of ions in the ferrite microparticle sublattices with respect to the γ-ray propagation direction (Fig. 3 ), because (sin(180° + α) = –sinα) the relative areas of the absorption lines of the Mössbauer spectrum of 57 Fe nuclei are determined by squared trigonometric functions (2). Taking into account this fact, parameter k can be determined as a ratio of the integral areas of the Mössbauer spectrum absorption lines corresponding to the a and d ferrite sublattices. In view of the aforesaid, particles may have either ferromagnetic or ferrimagnetic ordering in the method of analyzing the domain structure in magnetic powder microparticles based on Mössbauer spectroscopy. In both cases, the Mössbauer spectroscopy data are identical. The areas of the absorption lines of the Mössbauer spectra were determined using the UnivemMS program. The following values were obtained for the parameter k : k = 0.26 ± 0.04 at T = T cm + 2 K, k = 0.45 ± 0.04 at T = T cm +33 K, and k = 0.64 ± 0.04 at T = T cm + 45 K. It can be seen that ferrite particles are single-domain near T cm . While moving away from T cm , particles pass to the multidomain state and the number of domains in the particles increases. A similar situation was observed at temperatures below T cm . In the domain structure, domains occupy much larger volume in comparison with domain walls; therefore, the increase in parameter k while moving away from T cm is mainly due to the increase in the number of closure domains, which are magnetized at an angle with respect to the easy magnetization axes. Note that ferrite particles near T cm are weak magnetic; therefore, particles were not attached to each other during the preparation of the sample at room temperature and sample isotropy was provided automatically. In practice, strong magnetic materials are more often applied. Their single-domain particles may stick to each other as elementary magnets forming chains and lumps, which may violate the sample isotropy underlying the method proposed. Therefore, samples should be fabricated at temperatures above Curie temperature T c with a specially chosen adhesive material hardening near T c . 3. Conclusions In this paper, we propose a method for analyzing the domain structure in microparticles of magnetic powders based on the Mössbauer effect. Based on the relative areas of the absorption lines of the Mössbauer spectrum of 57 Fe nuclei in the sample in the state of residual magnetization, critical parameters were obtained that can be used to determine the absence of a domain structure in microparticles of ferro- and ferrimagnetic ordering. The critical parameters are determined for single-domain particles with cubic and uniaxial anisotropy. The method was experimentally tested on particles of gadolinium ferrite-garnet Gd 3 Fe 5 O 12 with a diameter of 40±5 µm in the region of the magnetic compensation point T cm =286 K. It is shown that, near T cm , ferrite particles are single-domain, with distance from T cm , the particles pass into a multidomain state, as they move away from T cm , the number of domains in the particles increases. Declarations Author Contribution Sh.M. Aliev - Writing an article and managementZh.G. Ibaev - mathematical processing and plottingM.Sh. Aliev - experimental studies References Krupichka S Physics of Ferrites and Magnetic Oxides, Izdatel'stvo Mir, Moskow, 1976, P.504. Sergeev VV, Bulygina TI (1980) Magnetically Hard Materials, Izdatel'stvo Energia, Moscow, P. 224 Preobrazhenski AA, Bishard EG (1986) Magnetic Materials and Elements, Izdatel'stvo. Vysshay Shckola, Moscow, p 532 Sh M, Aliev IK, Kamilov M, Ibaev ZG (2016) Tech Phys Lett 42:11 Chuev MA (2013) JETP Lett 98:523 Chuev MA (2014) JETP Lett 99:319 Urusov AE, Petrakova AV, Zherdev AV, Dzantiev BB (2017) Nanotechnol Russ 12:5 Kozlovskiy AL, Korolkov IV, Ibragimova MA, Zdorovets MV, Kutuzau MD, Nikolaevich LN, Shumskaya EE (2018) E. Yu. Kaniukov, Nanotechnol. Russ. 13, 118 Irkaev SM, Kuz’min RN, Opalenko AA (1970) Nuclear Gamma Reson Izdatel'stvo Moskow Univ, P. 207 Bar’yakhtar VG, Yablonski DA (1974) Phys Solid State 16:3511 Logginov AS, Meshkov GA, Nikolaev AV, Pyatakov AP (2007) JETP Lett 86:124 Logginov AS, Meshkov GA, Nikolaev AV, Nikolaeva EP, Pyatakov AP, Zvezdin AK (2008) Appl Phys Lett 93:182510 Zvezdin AK, Pyatakov AP (2009) Phys scien success 179:897 Rabkin LI, Soskin SA (1968) B. Sh. Epshtein, Ferrites, Izdatel'stvo Energia, Leningrad, P. 384 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 01 Oct, 2019 Read the published version in Technical Physics Letters → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4137227","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":284688576,"identity":"9bb5fdf2-c5a8-4ccf-9b44-9317fedda740","order_by":0,"name":"Shamil Minkailovich Aliev","email":"","orcid":"","institution":"Dagestan Federal Research Center of the Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Shamil","middleName":"Minkailovich","lastName":"Aliev","suffix":""},{"id":284688577,"identity":"5143f313-ee9c-4ce3-ba1e-8bfb00973429","order_by":1,"name":"Zhavrail Gadzhievich Ibaev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYBACNgkgwfjvvxyQbDxAvBYGNmZjoJYG4rQwQLUkNgAp4rTwSTc/fMzDw5a+tv1wwwHGPYeJcJjMMWNjHgme3G1nEoEOe0aMFokEM8kZBhK52w6AtBwgSkv6958zEgzSzc4/JFpLjhnDhwMJCWY3iLZF5kyxxMeGA4bbbgBtSTiQTliL/Oz2jR+A5subnU9/+ODDAWvCWlBBAqkaRsEoGAWjYBRgBwAAOj8rpsTTtwAAAABJRU5ErkJggg==","orcid":"","institution":"Dagestan Federal Research Center of the Russian Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Zhavrail","middleName":"Gadzhievich","lastName":"Ibaev","suffix":""},{"id":284688578,"identity":"2bf926f8-e997-446f-90f3-5961c55a028b","order_by":2,"name":"Minkail Shamilevich Aliev","email":"","orcid":"","institution":"Dagestan Federal Research Center of the Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Minkail","middleName":"Shamilevich","lastName":"Aliev","suffix":""}],"badges":[],"createdAt":"2024-03-20 12:45:58","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4137227/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4137227/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1134/S106378501910002X","type":"published","date":"2019-10-01T13:44:43+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":53864468,"identity":"22292cbe-b438-4697-b6f2-aac6deb36aad","added_by":"auto","created_at":"2024-04-01 13:43:52","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":53063,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature dependence of the saturation magnetization of Gd\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e5\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e ferrite.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4137227/v1/1bdd9e53ca5d303e44ef8646.jpeg"},{"id":53864469,"identity":"7a1e4d84-4be9-47d7-a43b-275e0b86d80b","added_by":"auto","created_at":"2024-04-01 13:43:52","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":149035,"visible":true,"origin":"","legend":"\u003cp\u003eMössbauer spectra of the sample made of particles (\u003cem\u003ed \u003c/em\u003e= 40 ± 5 mm) of a powdered Gd\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e5\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e ferrite single crystal. The sample was brought into the residual-magnetization state in the direction perpendicular to the sample plane at: \u003cem\u003eT\u003c/em\u003e= (\u003cem\u003e1\u003c/em\u003e) \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e+ 2, (\u003cem\u003e2\u003c/em\u003e) \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e+ 33, and (\u003cem\u003e3\u003c/em\u003e) \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e+ 45K.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4137227/v1/0c4fa561019001bea2dd81a5.jpeg"},{"id":53864470,"identity":"feeb947d-337c-4236-8bc0-ab343e819769","added_by":"auto","created_at":"2024-04-01 13:43:52","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":45479,"visible":true,"origin":"","legend":"\u003cp\u003eSpacial distribution of the magnetic moments of ions in the \u003cem\u003ea\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e, and \u003cem\u003ec \u003c/em\u003esublattices of the sample made of Gd\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e5\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e ferrite microparticles in the residual-magnetization state near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4137227/v1/203f3e143865288fcb1acf63.jpeg"},{"id":53865098,"identity":"38f78c90-c407-4778-b3b9-e9aec436ebb4","added_by":"auto","created_at":"2024-04-01 13:51:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":305536,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4137227/v1/fb6fe2ae-c89b-4832-add4-5f036b49a65f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Method for Analyzing the Domain Structure in Magnetic Powder Microparticles","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIt is known that thorough grinding of a magnetic results in the occurrence of single-domain particles. The physical reason is that the magnetostatic energy of a particle (proportional to the particle volume) decreases with a decrease in the size with a higher rate, as compared to the domain wall energy (proportional to the particle surface area). At some critical size, the single-domain state becomes energetically favorable. The critical diameter, at which the particle passes from the multidomain state to the single-domain one, is determined by the expression [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${d}_{сr}=\\frac{9}{2\\pi }\\frac{\\sigma }{{M}_{s}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere σ is the domain wall energy density and \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the spontaneous particle magnetization. Magnetic powders of single-domain particles have a wide range of technical application [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMagneto-optical methods based on the Kerra and Faraday effects are generally applied to observe domain structure in magnet microparticles [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. A method for analyzing the domain structure in a singlecrystal ferrite sample with magnetic compensation point \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e was proposed in [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] based on the M\u0026ouml;ssbauer effect. In this study, we describe a method for analyzing the domain structure in magnetic powder microparticles based on the M\u0026ouml;ssbauer effect. Note that M\u0026ouml;ssbauer spectroscopy is successfully applied for investigating the structural and magnetic properties of magnetic materials containing particles or nanoclusters [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The interest in systems of magnetic particles or small clusters is primarily due to their wide range of application in modern nanotechnology [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Experimental Methods","content":"\u003cp\u003eLet us consider an ensemble of single-domain particles isotropically distributed in space. If this ensemble of particles is magnetized to saturation and then magnetizing field \u003cem\u003eH\u003c/em\u003e is switched off, maximum angle θ\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e of deviation of the particle magnetization vectors from the field-application direction is equal to angle α between the hard and easy magnetization axes in this magnet. For magnets with cubic and uniaxial anisotropies, α\u0026thinsp;=\u0026thinsp;55\u0026deg; and 90\u0026deg;, respectively. Thus, in the state of residual magnetization, the magnetization vectors of single-domain particles are isotropically distributed in solid angle Ω\u0026thinsp;=\u0026thinsp;2θ\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2α.\u003c/p\u003e \u003cp\u003eIf the particles have a domain structure, θ\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;α because closure domains and domain walls, in which the magnetic moments make an angle with the easy magnetization axes, exist in the domain structure along with domains, the magnetization vectors of which are directed along the easy magnetization axes.\u003c/p\u003e \u003cp\u003eIt is known that the relative areas of the Zeeman splitting lines in a M\u0026ouml;ssbauer spectrum of \u003csup\u003e57\u003c/sup\u003eFe nuclei in a homogeneously magnetized sample depend on angle θ between the γ-ray propagation direction and magnetization direction in the sample [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${S}_{\\text{1,6}}=3\\left(1+{\\text{cos}}^{2}\\theta \\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${S}_{\\text{2,5}}=4{\\text{sin}}^{2}\\theta$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${S}_{\\text{3,4}}=1+{\\text{cos}}^{2}\\theta$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLet the geometry of the experiment be as follows the γ-ray propagation direction coincides with the \u003cem\u003eH\u003c/em\u003e direction. Then, the following expression can be written for parameter \u003cem\u003ek\u003c/em\u003e equal to the ratio of the second-to-first (or fifth-to-sixth) absorption line areas in the M\u0026ouml;ssbauer spectrum of \u003csup\u003e57\u003c/sup\u003eFe nuclei in the sample:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$k=\\frac{{S}_{\\text{2,5}}}{{S}_{\\text{1,6}}}=\\frac{4(1-\\stackrel{-}{{cos}^{2}}{\\theta }_{i})}{3(1+\\stackrel{-}{{cos}^{2}}{\\theta }_{i})}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere θ\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the angle between the γ-ray propagation direction and the magnetization direction of the \u003cem\u003ei\u003c/em\u003e - particle (0 \u0026le; θ\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e \u0026le; θ\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e):\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\stackrel{-}{{cos}^{2}}{\\theta }_{i}=\\frac{\\underset{0}{\\overset{{\\theta }_{m}}{\\int }}\\underset{0}{\\overset{2\\pi }{\\int }}{cos}^{2}\\theta \\bullet sin\\theta d\\theta d\\phi }{\\underset{0}{\\overset{{\\theta }_{m}}{\\int }}\\underset{0}{\\overset{2\\pi }{\\int }}sin\\theta d\\theta d\\phi }=\\frac{{cos}^{3}{\\theta }_{m}-1}{3(cos{\\theta }_{m}-1)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003eFor single-domain particles, we have \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{{cos}^{2}}{\\theta }_{i}=\\text{0,63}\\)\u003c/span\u003e\u003c/span\u003e (cubic anisotropy) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{{cos}^{2}}{\\theta }_{i}=\\text{0,33}\\)\u003c/span\u003e\u003c/span\u003e (uniaxial anisotropy).\u003c/p\u003e \u003cp\u003eSubstituting these values into (3), we arrive at the following criteria: if \u003cem\u003ek\u003c/em\u003e\u0026thinsp;+\u0026thinsp; Δ\u003cem\u003ek\u003c/em\u003e\u0026le;0.30 (cubic anisotropy) and \u003cem\u003ek\u003c/em\u003e\u0026thinsp;+\u0026thinsp;Δ\u003cem\u003ek\u003c/em\u003e\u0026le;0.67 (uniaxial anisotropy), the powder particles are single-domain (Δ\u003cem\u003ek\u003c/em\u003e is the experimental error in determining parameter \u003cem\u003ek\u003c/em\u003e). If \u003cem\u003ek\u003c/em\u003e \u0026ndash;Δ\u003cem\u003ek\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.30 (cubic anisotropy) and \u003cem\u003ek\u003c/em\u003e \u0026ndash; Δ\u003cem\u003ek\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.67 (uniaxial anisotropy), the powder particles have a domain structure; the relative number of domains in the particles can be estimated from the \u003cem\u003ek\u003c/em\u003e value.\u003c/p\u003e \u003cp\u003eRare-earth ferrite garnets (REFG) having the magnetic compensation point \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e are the most favorable magnets for the organization of the experiment. Indeed, fairly large REFG particles may become single-domain near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e due to the small value of spontaneous magnetization [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In addition, the particles that are single-domain near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e pass to the multidomain state while moving away from \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e. Therefore, one can experimentally validate the found criteria gradually increasing the difference in temperature from \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e. Note that the interest in REFG is related to the prospects of formation of materials based on the domain structure of these ferrimagnets for the element base of magnetic microelectronic devices [\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe method was verified on particles of a Gd\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e5\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e ferrite single crystal with cubic anisotropy prepared according to the standard technology from pure initial oxides Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Fe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The magnetization was measured in the temperature range of 150\u0026ndash;400 K on a VM2-A vibrational magnetometer. It was established that the ferrite compensation point is \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e = 286 K (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The M\u0026ouml;ssbauer spectra of \u003csup\u003e57\u003c/sup\u003eFe nuclei were recorded on a YGRS-4M spectrometer with a \u003csup\u003e57\u003c/sup\u003eCo(Cr) γ-radiation source. A ferrite single crystal powdered in an agate mortar was filtered through a set of hair sieves to obtain spherical particles with a diameter \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;40\u0026thinsp;\u0026plusmn;\u0026thinsp;5 \u0026micro;m. These particles were used to make a sample (absorbent for M\u0026ouml;ssbauer measurements) by depositing the powder in a glue mixture on a thin mica disk. The absorbent thickness with respect to natural iron was 20 mg/cm\u003csup\u003e2\u003c/sup\u003e. For temperature measurements, the sample was placed in a temperature chamber combined with a cryostat with a fine temperature control in the range of 120\u0026ndash;500 K. Automatic temperature control system maintained a specified temperature with an error of \u0026plusmn;\u0026thinsp;0.5 K. Before measuring the M\u0026ouml;ssbauer sample, the spectrum was brought into the residual-magnetization state at a specified temperature. The sample temperature was brought to the desired value, and then the magnetic field applied perpendicular to the sample plane was increased from zero to the value \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e = 2 kOe, which is sufficient for magnetic saturation of the sample, after which it was reduced to zero.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBefore each measurement, the sample was preliminarily demagnetized in an alternating magnetic field with amplitude decreasing to zero. Typical spectra measured in the vicinity of \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. They are a superposition of two Zeeman sextets caused by iron ions in the \u003cem\u003ea\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e ferrite \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left\\{{Gd}_{3}^{3+}{\\}}_{c}\\right[{Fe}_{2}^{3+}{]}_{a}({Fe}_{3}^{3+}{)}_{d}{O}_{12}^{2-}\\)\u003c/span\u003e\u003c/span\u003e sublattices. Note that the M\u0026ouml;ssbauer spectrum does not distinguish symmetric and antisymmetric magnetic-moment orientations of ions in the ferrite microparticle sublattices with respect to the γ-ray propagation direction (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), because (sin(180\u0026deg; + α) = \u0026ndash;sinα) the relative areas of the absorption lines of the M\u0026ouml;ssbauer spectrum of \u003csup\u003e57\u003c/sup\u003eFe nuclei are determined by squared trigonometric functions (2).\u003c/p\u003e \u003cp\u003eTaking into account this fact, parameter \u003cem\u003ek\u003c/em\u003e can be determined as a ratio of the integral areas of the M\u0026ouml;ssbauer spectrum absorption lines corresponding to the \u003cem\u003ea\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e ferrite sublattices. In view of the aforesaid, particles may have either ferromagnetic or ferrimagnetic ordering in the method of analyzing the domain structure in magnetic powder microparticles based on M\u0026ouml;ssbauer spectroscopy. In both cases, the M\u0026ouml;ssbauer spectroscopy data are identical. The areas of the absorption lines of the M\u0026ouml;ssbauer spectra were determined using the UnivemMS program. The following values were obtained for the parameter \u003cem\u003ek\u003c/em\u003e: \u003cem\u003ek\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.26\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04 at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e + 2 K, k\u0026thinsp;=\u0026thinsp;0.45\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04 at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e +33 K, and k\u0026thinsp;=\u0026thinsp;0.64\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04 at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e + 45 K. It can be seen that ferrite particles are single-domain near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e. While moving away from \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e, particles pass to the multidomain state and the number of domains in the particles increases. A similar situation was observed at temperatures below \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e. In the domain structure, domains occupy much larger volume in comparison with domain walls; therefore, the increase in parameter \u003cem\u003ek\u003c/em\u003e while moving away from \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e is mainly due to the increase in the number of closure domains, which are magnetized at an angle with respect to the easy magnetization axes.\u003c/p\u003e \u003cp\u003eNote that ferrite particles near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e are weak magnetic; therefore, particles were not attached to each other during the preparation of the sample at room temperature and sample isotropy was provided automatically. In practice, strong magnetic materials are more often applied. Their single-domain particles may stick to each other as elementary magnets forming chains and lumps, which may violate the sample isotropy underlying the method proposed. Therefore, samples should be fabricated at temperatures above Curie temperature \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e with a specially chosen adhesive material hardening near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e"},{"header":"3. Conclusions","content":"\u003cp\u003eIn this paper, we propose a method for analyzing the domain structure in microparticles of magnetic powders based on the M\u0026ouml;ssbauer effect. Based on the relative areas of the absorption lines of the M\u0026ouml;ssbauer spectrum of \u003csup\u003e57\u003c/sup\u003eFe nuclei in the sample in the state of residual magnetization, critical parameters were obtained that can be used to determine the absence of a domain structure in microparticles of ferro- and ferrimagnetic ordering. The critical parameters are determined for single-domain particles with cubic and uniaxial anisotropy. The method was experimentally tested on particles of gadolinium ferrite-garnet Gd\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e5\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e with a diameter of 40\u0026plusmn;5 \u0026micro;m in the region of the magnetic compensation point T\u003csub\u003ecm\u003c/sub\u003e=286 K. It is shown that, near T\u003csub\u003ecm\u003c/sub\u003e, ferrite particles are single-domain, with distance from T\u003csub\u003ecm\u003c/sub\u003e, the particles pass into a multidomain state, as they move away from T\u003csub\u003ecm\u003c/sub\u003e, the number of domains in the particles increases.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eSh.M. Aliev - Writing an article and managementZh.G. Ibaev - mathematical processing and plottingM.Sh. Aliev - experimental studies\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKrupichka S \u003cem\u003ePhysics of Ferrites and Magnetic Oxides, Izdatel'stvo Mir, Moskow, 1976, P.504.\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSergeev VV, Bulygina TI (1980) \u003cem\u003eMagnetically Hard Materials, Izdatel'stvo\u003c/em\u003e Energia, Moscow, P. 224\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePreobrazhenski AA, Bishard EG (1986) Magnetic Materials and Elements, Izdatel'stvo. Vysshay Shckola, Moscow, p 532\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSh M, Aliev IK, Kamilov M, Ibaev ZG (2016) Tech Phys Lett 42:11\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChuev MA (2013) JETP Lett 98:523\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChuev MA (2014) JETP Lett 99:319\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUrusov AE, Petrakova AV, Zherdev AV, Dzantiev BB (2017) Nanotechnol Russ 12:5\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKozlovskiy AL, Korolkov IV, Ibragimova MA, Zdorovets MV, Kutuzau MD, Nikolaevich LN, Shumskaya EE (2018) E. Yu. Kaniukov, Nanotechnol. Russ. 13, 118\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIrkaev SM, Kuz\u0026rsquo;min RN, Opalenko AA (1970) Nuclear Gamma Reson Izdatel'stvo Moskow Univ, P. 207\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBar\u0026rsquo;yakhtar VG, Yablonski DA (1974) Phys Solid State 16:3511\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLogginov AS, Meshkov GA, Nikolaev AV, Pyatakov AP (2007) JETP Lett 86:124\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLogginov AS, Meshkov GA, Nikolaev AV, Nikolaeva EP, Pyatakov AP, Zvezdin AK (2008) Appl Phys Lett 93:182510\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZvezdin AK, Pyatakov AP (2009) Phys scien success 179:897\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRabkin LI, Soskin SA (1968) B. Sh. Epshtein, \u003cem\u003eFerrites, Izdatel'stvo\u003c/em\u003e Energia, Leningrad, P. 384\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"domain structure, single-domain particles, ferrites, magnetic compensation point, Mössbauer effect","lastPublishedDoi":"10.21203/rs.3.rs-4137227/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4137227/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA method for analyzing the domain structure in magnetic powder microparticles based on the M\u0026ouml;ssbauer effect is proposed. This method has been experimentally verified for gadolinium ferrite-garnet (Gd\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e5\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e) powder particles 40\u0026thinsp;\u0026plusmn;\u0026thinsp;5 \u0026micro;m in diameter in the vicinity of the magnetic compensation point \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e =286 K. It is shown that ferrite particles are single-domain near \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e and pass to the multidomain state while moving away from \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ecm\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e","manuscriptTitle":"A Method for Analyzing the Domain Structure in Magnetic Powder Microparticles","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-01 13:43:47","doi":"10.21203/rs.3.rs-4137227/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"83f5ae6d-e4c5-4561-9722-6cb08bb37178","owner":[],"postedDate":"April 1st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-04-01T13:44:43+00:00","versionOfRecord":{"articleIdentity":"rs-4137227","link":"https://doi.org/10.1134/S106378501910002X","journal":{"identity":"technical-physics-letters","isVorOnly":true,"title":"Technical Physics Letters"},"publishedOn":"2019-10-01 13:44:43","publishedOnDateReadable":"October 1st, 2019"},"versionCreatedAt":"2024-04-01 13:43:47","video":"","vorDoi":"10.1134/S106378501910002X","vorDoiUrl":"https://doi.org/10.1134/S106378501910002X","workflowStages":[]},"version":"v1","identity":"rs-4137227","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4137227","identity":"rs-4137227","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}