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Conical spin arrangement and spin reorientation process in Er2-xHoxFe14B observed with Mössbauer spectroscopy
Accepted Manuscript Conical spin arrangement and spin reorientation process in Er2-xHoxFe14B observed with Mössbauer spectroscopy Piotr M. Kurzydło, Antoni T. Pędziwiatr, Bogdan F. Bogacz, Janusz Przewoźnik, Dariusz Oleszak PII:
S0925-8388(16)31473-6
DOI:
10.1016/j.jallcom.2016.05.140
Reference:
JALCOM 37660
To appear in:
Journal of Alloys and Compounds
Received Date: 14 February 2016 Revised Date:
12 May 2016
Accepted Date: 14 May 2016
Please cite this article as: P.M. Kurzydło, A.T. Pędziwiatr, B.F. Bogacz, J. Przewoźnik, D. Oleszak, Conical spin arrangement and spin reorientation process in Er2-xHoxFe14B observed with Mössbauer spectroscopy, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.05.140. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Conical spin arrangement and spin reorientation process in Er2-xHoxFe14B observed with Mössbauer spectroscopy.
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Piotra M. Kurzydło ([email protected]), Antonia T. Pędziwiatr ([email protected]), Bogdana F. Bogacz ([email protected]), Januszb Przewoźnik ([email protected]), Dariusz Oleszakc ([email protected])
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Corresponding author: Piotra M. Kurzydło [email protected] Tel.: +48 12 664 45 80, Fax: +48 12 664 49 05
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M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, PL 30-348 Kraków, Poland b
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of Solid State Physics, Mickiewicza 30, PL 30-059 Kraków, Poland c
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Faculty of Materials Science and Engineering, Warsaw University of Technology, Wołoska 141, PL 02-507 Warszawa, Poland
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ACCEPTED MANUSCRIPT Abstract
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The series of Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) intermetallic compounds was studied in order to investigate different types of spin arrangements expected in this series. The variety of processes connected with spin reorientation, especially transition through conical spin arrangements was of special interest. The compounds have been measured with 57 Fe Mössbauer spectroscopy over the temperature range 5.2 – 320 K. Each compound was studied with precise Mössbauer scanning in the vicinity of the transition. A special fitting procedure of Mössbauer spectra, enabling to analyze up to ten spectra simultaneously, was developed to determine the arrangement of spins. The path of spin rotation was proposed. The results were verified and compared by applying computer simulations based on the Yamada-Kato model. The spin arrangement diagram was constructed. Obtained results are convincing enough to conclude that Mössbauer spectroscopy can be very helpful in studies of tilt angle in conical spin arrangements in the studied type compounds.
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permanent magnet materials, Mössbauer effect, spin reorientation, spin diagrams
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ACCEPTED MANUSCRIPT 1. Introduction Intermetallic compounds of general formula R2Fe14B (R – rare earth) exhibit many interesting properties [1], including spin reorientation phenomena [2, 3, 4]. The most studied is Nd2Fe14B as a material for high performance permanent magnets [5, 6, 7].
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The compounds based on Ho and Er also show interesting magnetic behaviour: with increasing temperature, around the spin reorientation temperature, TSR,, their magnetocrystalline anisotropy changes from planar (for Er2Fe14B) or conical (for Ho2Fe14B) to axial (along c-axis). For Ho2Fe14B the conical spin arrangement exists at temperature region 0 – 58 K and then changes into axial [8]. Er2Fe14B is planar up to TSR=323 K and becomes axial above TSR [9]. The series of Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) constitutes a transition combination of magnetic properties with intermediate TSR.
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The compounds crystallize in a tetragonal structure and belong to P42/mnm space group symmetry with six inequivalent crystal sites for Fe (16k1, 16k2, 8j1, 8j2, 4c, 4e) and two sites (4f, 4g) for R atom [1, 7, 10]. Single crystal neutron diffraction measurements report that crystal structure changes to orthorhombic below TSR for Er2Fe14B and starts to distort below 100 K for Ho2Fe14B [11].
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Studies of all above mentioned processes, especially spin reorientation phenomenon, are important to establish the spin structure which is crucial for high-performance permanent magnet applications [12]. So far, the literature data were obtained using mainly magnetometric measurements [10]. It was interesting to observe the spin reorientation process in this series with Mössbauer spectroscopy which enables a microscopic insight into magnetic properties.
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The main goal of our study was to determine the way of change of magnetic spin direction during the spin reorientation process in Er2-xHoxFe14B series caused by temperature. Mössbauer spectra obtained for this series suggested quite different course of the process than previously observed in similar series Er2-xGdxFe14B [13] so it was necessary to describe the spin reorientation process by introducing a more detailed, modified model which is presented below.
2. Experimental method For preparing samples of Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) materials, a standard procedure was used: high purity elements were melted in an electric arc furnace in a high purity argon atmosphere. Then the ingots were annealed at 900 °C for two weeks. After that, the samples were analyzed using XRD measurements at room temperature (Philips PANalytical Empyrean apparatus). These measurements were used to qualify each sample for further studies. X-ray data proved the existence of tetragonal Nd2Fe14B-type phase but also indicated the existence of small amounts of Fe. The existence of natural iron impurity can be expected because R2Fe14B are known to be difficult to synthesize in a pure single phase form 3
ACCEPTED MANUSCRIPT [3]. To prepare absorbers for Mössbauer measurements the samples were crushed into fine powder. The Mössbauer spectra of all samples were recorded in the temperature range 5.2 – 320.0 K, using a 57Co(Rh) source and a computer driven constant acceleration mode spectrometer. Velocity scale was calibrated using high purity natural iron foil. Isomer shifts were established with respect to the center of gravity of the room temperature iron Mössbauer spectrum.
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A majority of the spectra for each sample was recorded in the vicinity of TSR (with the step of 1 K). Additional spectra were recorded at temperatures well below and well above the TSR. In order to record Mössbauer spectra at low temperatures, a standard helium cryostat was used. Due to XRD analysis which indicated existence of natural iron impurity, the high purity iron foil was measured also in temperature range 80 – 300 K to enable the identification of natural iron impurity in the spectra.
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3. Data analysis 3.1. Spectra analysis
Before the main analysis was conducted all Mössbauer spectra were processed to eliminate the influence of small natural iron impurities evidenced in XRD studies. A subspectrum coming from Fe impurities was numerically subtracted from every spectrum. Such procedure was necessary to enable technically the application of further fitting procedure.
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The shape of recorded Mössbauer spectra suggested existence of conical spin arrangement during spin reorientation process in the whole series. Similar spectra shapes occurrence was observed in Mössbauer spectra of conical Er2-xTbxFe14B series [14]. During the main analysis, an attempt was made to find temperature dependence of angle between and principal axis of EFG (electric field gradient) tensor (Vxx, Vyy, Vzz). magnetic moment
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A special procedure was constructed to allow a simultaneous fitting of several spectra obtained for a given composition at different temperatures [15]. Recently, the procedure of simultaneous fitting was extended to enable fitting angular dependences. The aim was to establish a consistent description of hyperfine interactions as well as angle dependence and hence determine the character of spin reorientation. The shape of the spectra was described using transmission integral. The spectra of all samples were treated as convolution of six Zeeman subspectra with relative intensities according to iron occupation of crystallographic sublattices (4:4:2:2:1:1). Each subspectrum was characterized by the following hyperfine interaction parameters: magnetic field - B, isomer shift - IS, quadruple splitting – QS. The description of the spectra is correlated with the phenomenon of spin reorientation using some simplifying assumptions which are discussed below. The direction of total magnetization vector changes from the initial planar (within a-b crystallographic plane) arrangement below the temperature of the transition region to the final 4
ACCEPTED MANUSCRIPT axial (along crystallographic c-axis) arrangement above the temperature of transition region. The model assumes that this, induced by temperature process of changing direction (called takes place in an established plane, called the rotation plane. rotation) of magnetic moment This rotation plane of the magnetic moment is indicated in Fig. 1. It is the plane containing the c-crystallographic axis, so it is perpendicular to ab plane. The magnetic moment can form vector is in ab plane, ψ = 0˚), conical arrangement a planar arrangement (
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(0˚<ψ<90˚) or axial arrangement (ψ = 90˚). The rotation takes place in the transition temperature range and its rotation plane is fixed for every sublattice.
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Additionally, two sets of Zeeman sextets exist in the transition temperature region. One of them is connected with low temperature spectrum – before reorientation, second with high temperature spectrum – after reorientation. In the model, at every temperature in the reorientation temperature range, a contribution of high temperature Zeeman sextet refers to the quantity of spins that go into conical position. Also a high temperature Zeeman sextet determines the angle dependences at every temperature, while low temperature Zeeman sextet gives the initial value of angle. It is also assumed that the quadrupole splitting observed during the reorientation and process is due only to the change of angle θ (Fig. 1) between the magnetic moment principal axis Vzz of EFG tensor [16]. According to the perturbation theory the dependence of arrangement can be written in a following way [17]: = quadrupole splitting QS on
+ sin ∙ cos 2 , where is azimuth angle determining the orientation
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of magnetic moment in the coordinate system of the EFG tensor axes, is the EFG asymmetry parameter. In our model an asymmetry term was neglected. While constructing the model only a weak change of IS with increasing temperature caused by second order Doppler shift and smooth changes of magnetic fields described by second order polynomial were taken into account in the whole temperature range.
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The angle θ can be expressed by the angle , describing position of magnetic moment vector on the rotation plane, which is changing with temperature and by the angle , describing relation between principal axis Vzz of EFG tensor and the rotation plane (Fig. 2) which does not depend on temperature: "#$ = "#$ ∙ $%& ; is the angle between projection of principal axis Vzz of EFG tensor to the rotation plane and the magnetic moment . The angle between principal axis Vzz of EFG tensor and perpendicular to the rotation plane
is called . This angle is different for each crystallographic sublattice but it does not change with the position of magnetic moment on the rotation plane. The position of magnetic moment on the rotation plane is determined either with respect to ab plane by ψ angle or with respect to the projection of EFG axis on that plane by β angle (Fig 1, 2). The change of the angle is given by ( angle and describes the reorientation process. It is clear that the change in Mössbauer spectrum shape depends not only on the position of the magnetic moment during the reorientation process (indicated by the change of angle β) but also on the position of the rotation plane relative to EFG tensor axis. The strongest changes in the spectrum occur for EFG axis residing in the rotation plane (α = 90˚).
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Extended simultaneous fitting procedure was introduced to the analysis to check the possibility of obtaining distinct and coherent values of and angles. In order to determine these angles it is essential to process simultaneously a set of Mössbauer spectra for at least three different positions of magnetic moment for the given sample in specified temperatures from the transition region. It was also important to check if the adopted model describes behaviour (changes with temperature) of all six Zeeman subspectra in a correct way, i.e. if such simplified model constitutes a good description of the spin reorientation process in the studied materials.
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The result of application of the above described procedure is presented for the Er1Ho1Fe14B (x = 1) compound. This composition was chosen for discussion because all observed processes are clearly visible here. For selected temperatures the experimentally obtained Mössbauer spectra and fits from the procedure are shown in Fig. 3. The rest of the samples exhibit qualitatively similar behaviour. Generally, the procedure allows to obtain a good representation of spectra shapes. Series of fits also represent changes in spectra shapes for specified sample in the transition temperature region. The reorientation process of magnetic moments in the studied type compounds can be easily observed owing to the separation of the sixth line of 8j2 sextet from the remaining part of the spectrum during the reorientation process. On the Figure 3 not only a change of the amplitude of the sixth line of 8j2 sextet with temperature is observed but also a shift in its position. This suggests the existence of different angles between magnetic moment and EFG axis at different temperatures. All these processes have a reflection in the fits. The spectra analysis, based on the proposed model, indicated existence of the conical spin arrangements in studied samples. Our analysis confirms spin reorientation process from planar or initial-conical arrangement to final axial arrangement. The samples for x > 1.0 exhibit canted spin arrangement, even at the lowest temperatures. The samples with x < 1.0 have planar spin arrangement at low temperatures. As the temperature approaches the TSR, the angle describing conical arrangement increases to reach ψ = 90° for temperature above transition region. Additionally, behaviour of spectra shape, especially of 8j2 emerging sixth line suggests that spins do not rotate collectively. When the transition begins, shape of the spectrum starts to evolve in a way that is characteristic for conical spin arrangement i.e. arrangement between initial and final state. When this path of transition ends – the shape of the spectrum is characteristic for axial spin arrangement – the evolution characteristic for two state model begins. The process ends when all spins reach a final arrangement. The two-phase process vs. collective rotation, described by Mössbauer spectra fits is presented in Fig. 4. It was impossible to obtain good results for established collective rotation – the misfits always occur in this case. The shape of the first line in the spectrum as well as the amplitude of 8j2 line could not be described properly. The problem was solved by setting up the rotating phase at about 70% and leaving 30% of spins in non rotating, flipping phase. Such division of phases is maximal and is suitable for x = 1.0. With x→0 and x→2.0 the amount of not rotating, flipping phase decreases. For Ho2Fe14B we found that contribution of non rotating, flipping phase is insignificant and can be neglected.
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All Mössbauer spectra recorded for the studied series were analysed using model which includes rotation of spins via conical arrangements. It is worth to note that for this series of compounds it was impossible to use a two-state model which was applied successfully for other compounds of R2Fe14B (e.g. Er2-xGdxFe14B) [13]. Two-state model assumes spins flipping from initial to final position without intermediate conical arrangements. The contribution of spins in initial and final position changed with increasing temperature. The necessity of implementation of the model assuming spin rotation, not just simple “two state flipping”, seems to indicate a different course of spin reorientation process in the studied series. This may be attributed to different Stevens coefficients, ) , of Gd ( ) = 0) and Ho ( ) < 0 ).
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3.2. Theoretical model
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The obtained experimental results were compared with the results of the computer simulations of reorientation process. The computer program based on simplified phenomenological Yamada-Kato model [4, 18] was used. For each sample, using literature data [6, 19, 20], it was possible to obtain theoretical values of spin arrangement angle in a specific temperature. The simulation procedure assumed collective behaviour of spins. The two-phase model was not regarded in this case. To determine values of angle, the free energy calculations were used. Finding the angle dependence is achieved by minimizing the free energy of the system, F(T), which is assumed to be a sum of contributions derived from two coupled sublattices – rare earth (R) sublattice and iron (Fe) sublattice. F(T) = FR(T) + FFe(T). The R-sublattice is treated as an assembly of isolated atoms in crystal electric field, CEF, and exchange field. In this case R-R interaction is neglected. The magnetic free energy can be calculated from the energy levels corresponding to the particular set of CEF parameters. +,-. (%) = ∑3,4 234 (%) 534 , where 234 (%) are the crystal field parameters of the R atom at site * i and 534 are the Stevens operators. The contributions from different R ions are assumed to be linear. On the other hand, the iron (Fe) sublattice is treated in a different way – the experimental data were used. Experimentally obtained values of K1(T) – the anisotropy constant was scaled up to the Curie temperature and used to evaluate the free energy of 3d sublattice as E = K1(T)sin2θc [21], where θc is the angle between the magnetization direction and the crystal c-axis. In this simulation the entropy term was recognized as negligible. The magnetization of the 3d-sublattice acts on magnetization of the R-sublattice and thus exchange energy of the molecular magnetic field couples the two magnetic sublattices. The following formula, expressing the dependence of the total free energy as a function of temperature T and angle θc, was used: 6(7, θ9 ) = −;7 ∑@AB ln =(%) + 28? (7) sin (, ), where Z(i) is the partition function =(%) = ∑)I JB C
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and Ej(i) are the energy levels of R-
ion in i = 4f, 4g lattice sites. In case of these simulations, we assume that values for 4f and 4g sites are equal. The described above procedure was applied to obtain theoretical curves of spin arrangement angle in specific temperature for each sample of studied series. The simulation 7
ACCEPTED MANUSCRIPT procedure gave approximate image of the process, presenting collective behaviour of all spins in just one phase. The obtained results are presented in Fig. 5, where theoretical curves are presented together with experimental data. Experimental data refer only to rotating phase.
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These simulations confirm the existence of conical spin arrangement in measured samples in the temperature range indicated by Mössbauer spectra analysis.
4. Results and discussion
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The character of Mössbauer spectra obtained for the series Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) required to go beyond the two-state model used so far to describe the behavior of R2Fe14B compounds [13, 14]. Applied procedure allowed us to successfully perform operation of simultaneous fitting series of spectra for each sample and obtain angle dependence of spin arrangement. These results were compared with computer simulation of spin arrangements, based on Yamada-Kato model (Fig. 5). We found that theoretical simulations confirm the existence of conical spin arrangements in the measured samples in temperature region indicated by the spectra analysis. For samples for which the conical arrangements exist from the lowest temperatures, also the initial angle was confirmed. Strong changes observed with changing x may be caused by competition between Er and Ho.
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The experimental data do not follow theoretical curves ideally. Theoretical and experimental data are almost equal in initial and final states but do not overlap in intermediate position. A surprising compatibility between experimental and theoretical data was obtained for Ho content x = 0.5 where experimental data almost ideally reproduce theoretical predictions. For Ho2Fe14B our theoretical and experimental Mössbauer results were compared with literature data acquired by magnetometric [22] and neutron diffraction [11] measurements (Fig. 5).
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Finally, collected data were used to construct a spin arrangement diagram for studied series Er2-xHoxFe14B (Fig. 6). The existence of conical spin arrangement from the lowest temperatures was found for Ho content up to x ≥ 1.0. For Ho content x = 2.0 the arrangement corresponding to crystal c-axis is achieved at about 58 K and remains almost unchanged up to x ≈ 1.25. For lower Ho content these spin arrangements are also achieved at higher temperatures and strongly depend on composition. A disagreement about 30 K is visible for x = 1.0 which may be interpreted by a “two phase rotation” process. The results were compared also with literature data, where the series of Er2-xHoxFe14B was studied with magnetometric methods [10] (Fig. 6). Generally, the results on temperature ranges of conical arrangements are coherent with the literature data. The spin arrangement diagram based on Mössbauer spectra analysis and the one based on magnetometric studies are consistent. The temperature ranges for the existence of conical spin arrangements were confirmed.
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The process of spin reorientation in the series of Er2-xHoxFe14B can be observed by Mössbauer spectroscopy. The determination of spin reorientation temperature as well as tilt angle dependences on composition and temperature need very careful simultaneous fitting of the appropriate set of Mössbauer spectra. Temperature regions of spin reorientation process and the spin phase diagram are determined with good precision and they are verified by computer simulation based on Yamada-Kato model as well as literature reports.
6. Acknowledgment
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The research was funded by Polish Ministry of Science and Higher Education Grant no. 7150/E-338/M/2015 and was carried out with the equipment purchased thanks to the financial support of the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/08).
References
[1]
Herbst I. F. (1991). R2Fe14B materials: Intrinsic properties and technological aspects.
[2]
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Reviews of Modern Physics, 63, 819.
Buschow K. H. J. (1991). New developments in hard magnetic-materials, Reports on Progress in Physics, 54 (9), 1123 – 1213, DOI: 10.1088/0034-4885/54/9/001. R. C. O’Handley. (2000). Modern Magnetic Materials: Principles and Applications.
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[3]
New York: John Willey & Sons, Inc. Yamada M., Kato H., Yamamoto H., Nakagawa Y. (1988). Crystal-field analysis of
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[4]
the magnetization process in a series of Nd2Fe14B-type compounds. Physical Review
B, 38, 620 – 633. DOI: 10.1103/PhysRevB.38.620.
[5]
Pankratov N. Yu., Nikitin A. A., Iwasieczko W., et al. (2006). Spin-reorientation transition in Nd2(Fe,Co)14B compounds and their hydrides. Journal of Magnetism and Magnetic Materials, 300, 465 – 468. DOI: 10.1016/j.jmmm.2005.10.195.
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ACCEPTED MANUSCRIPT [6]
Burzo E. (1998). Permanent magnets based on R–Fe–B and R–Fe–C alloys. Reports on Progress in Physics, 60(9), 1099 – 1266. DOI: 10.1088/0034-4885/61/9/001.
[7]
Lim J. T., Kim H. K., Kim C. S., An S. Y., Choi K. R. (2015). Investigation of the Magnetic Properties of Dy doped Nd-Fe-B Permanent Magnet by Using Mössbauer
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Spectroscopy. Journal of the Korean Physical Society, 66(12), 1913-1917. DOI: 10.3938/jkps.66.1913. [8]
Rillo C., et al. (1988). Dynamical susceptibility of Ho2Fe14B single crystal: Spin
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rotation and domain wall motions, Journal of Applied Physics, 64, 5534 – 5536. DOI: 10.1063/1.342327.
Basso V., et al. (2011). Er2Fe14B single crystal as magnetic refrigerant at the spin
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[9]
reorientation transition. Journal of Applied Physics, 109, 083910. DOI: 10.1063/1.3567925.
[10] Ibarra M. R., et al. (1993). Magnetic anisotropy in (ErxHo1-x)2Fel4B pseudoternary
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intermetallic compounds, Journal of Physics: Condensed Matter, 5 (1993), 56375648. DOI: 10.1088/0953-8984/5/31/025. [11] Wolfers P., Bacmann M., Fruchart D. (2001). Single crystal neutron diffraction
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investigations of the crystal and magnetic structures of R2Fe14B (R=Y, Nd, Ho, Er). Journal of Alloys and Compounds, 317 – 318, 39 – 43. DOI: 10.1016/S0925-
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8388(00)01353-0.
[12] Batancourt R. J. I. (2002). Nanocrystalline hard magnetic alloys. Revista Mexicana de Fisica. 48(4), 283 -289.
[13] Wojciechowska A., Pędziwiatr A. T, Bogacz B. F., Wróbel S. (2007). Spin reorientation phenomena in Er2-xRxFe14B (R = Gd, Th) – Mössbauer and calorimetric study. Nukleonika, 52(1), 77 – 79.
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ACCEPTED MANUSCRIPT [14] Kurzydło P. M., Bogacz B. F., Pędziwiatr A. T., Oleszak D., Przewoźnik J. (2015). Search for Canted Spin Arrangement in Er2-xTbxFe14B with Mössbauer Spectroscopy. Nukleonika, 60(1), 93 – 96. DOI: 10.1515/nuka-2015-0019. [15] Pędziwiatr A. T., Bogacz B. F., Gargula R., Wróbel S., (2002). Mössbauer and DSC
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studies of spin reorientations in Er2−xYxFe14B. Journal of Alloys and Compounds, 336, 5 – 10. DOI: 10.1016/S0925-8388(01)01872-2.
[16] Susilo R. A., Munoz Perez S., Cobas R., Cadogan J. M., Avdeev M. (2012). Magnetic
012071. DOI: 10.1088/1742-6596/340/1/012071.
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order and spin-reorientation in HoGa. Journal of Physics: Conference Series, 340,
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[17] Delyagin N. N., Krylov V. I., Rozantsev I. N. (2007). The magnetic spin-reorientation transitions in the RGa (R = rare earth) intermetallic compounds studied by measurements of the hyperfine interactions of the 119Sn probe atoms. Journal of Magnetism and Magnetic Materials, 308, 74 – 79. DOI:
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10.1016/j.jmmm.2006.05.004.
[18] Piqué C., Burriel R., Bartolomé J. (1996). Spin reorientation phase transitions in R2Fel4B (R = Y, Nd, Ho, Er, Tm) investigated by heat capacity measurements. Journal
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of Magnetism and Magnetic Materials, 154, 71 – 82. DOI: 10.1016/03048853(95)00571-4.
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[19] Liu Y., Sellmyer D. J., Shindo D. (2006). Handbook of advanced magnetic materials, Volume I, New York: Springer.
[20] Coey J. M. D. (1996). Rare-earth iron permanent magnet. Oxford: Clarendon Press. [21] Andreev A. V., Bartashevich M. I., Goto T., Zadvorkin S. M. (1997). Magnetic properties of (Y1-xThx)2Fe14B. Journal of Alloys and Compounds, 262/263, 467 – 470, DOI: 10.1016/S0925-8388(97)00356-3.
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ACCEPTED MANUSCRIPT [22] Hirosawa S., Yutaka M., Hitoshi Y., Setsuo F., Masato S., Hiroshi Y. (1986). Magnetization and magnetic anisotropy of R2Fe14B measured on single crystals.
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Journal of Applied Physics, 59, 873. DOI: 10.1063/1.336611.
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ACCEPTED MANUSCRIPT Fig. 1.
ሬሬԦ and a, b, crystallographic axes. ψ angle The rotation plane of the magnetic moment ܯ determines the direction of the magnetic moment relative to ab plane.
Fig. 2.
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The position of EFG axis relative to the rotation plane of magnetic moment. Angle α is between EFG axis and a normal to the rotation plane. Angle β is between the magnetic moment and the projection of EFG axis on the rotation plane, θ angle is between the magnetic moment and EFG axis.
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Fig. 3.
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The set of diagrams constructed for Er1Ho1Fe14B compound in selected temperatures. The 57Fe Mössbauer transmission spectra (crosses) and fits from the model (solid lines) presenting evolution of lines position and amplitude. The long vertical line visualizes move of the sextet 8j2 6th line from the initial position. The angle ψ describing the rotation of magnetic moment and temperaturę were also indicated in the graph.
Fig. 4.
Fig. 5.
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Two Mössbauer spectra for Er1Ho1Fe14B selected from the set processed by the fitting program. The comparison presents misfit appearing for assumed „collective rotation”. The misfit was canceled by introducing „two-phase rotation”.
Fig. 6.
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Temperature dependance of spin reorientatin angle ψ presented for measured samples of Er2xHoxFe14B series. Black squares present values determined by fitting program (only rotating phase was presented) while solid lines are data from computer simulations. For Ho2Fe14B also literature data was presented: (black circles) - neutron diffraction experiments [11], (black triangles) – magnetometric measurements [22].
Spin arrangement diagram for Er2−xHoxFe14B compounds. TC − Curie temperature, TSR (black squares) − spin reorientaAon temperatures limits from Mössbauer measurement and fiCng procedure, TSR (solid lines) − limits of spin reorientaAon temperature determined by the computer simulaAons. The area between lines – space of conical spin arrangement. There was also literaturę data presented [10]. TSR (black triangle) – limits of the spin rotating, TSR (white and black diamonds) – respectively AC and DC susceptibility measurements.
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ACCEPTED MANUSCRIPT Highlights
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Spin reorientation process has been studied in a new series of Er2-xHoxFe14B. Unique method of simultaneous spectra analysis is presented. Computer simulation of spin reorientation process is performed. Temperature dependence of tilt angle is presented Spin arrangement diagram is constructed.
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• • • • •
S0925-8388(16)31473-6
DOI:
10.1016/j.jallcom.2016.05.140
Reference:
JALCOM 37660
To appear in:
Journal of Alloys and Compounds
Received Date: 14 February 2016 Revised Date:
12 May 2016
Accepted Date: 14 May 2016
Please cite this article as: P.M. Kurzydło, A.T. Pędziwiatr, B.F. Bogacz, J. Przewoźnik, D. Oleszak, Conical spin arrangement and spin reorientation process in Er2-xHoxFe14B observed with Mössbauer spectroscopy, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.05.140. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Conical spin arrangement and spin reorientation process in Er2-xHoxFe14B observed with Mössbauer spectroscopy.
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Piotra M. Kurzydło ([email protected]), Antonia T. Pędziwiatr ([email protected]), Bogdana F. Bogacz ([email protected]), Januszb Przewoźnik ([email protected]), Dariusz Oleszakc ([email protected])
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Corresponding author: Piotra M. Kurzydło [email protected] Tel.: +48 12 664 45 80, Fax: +48 12 664 49 05
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M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, PL 30-348 Kraków, Poland b
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of Solid State Physics, Mickiewicza 30, PL 30-059 Kraków, Poland c
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Faculty of Materials Science and Engineering, Warsaw University of Technology, Wołoska 141, PL 02-507 Warszawa, Poland
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ACCEPTED MANUSCRIPT Abstract
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The series of Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) intermetallic compounds was studied in order to investigate different types of spin arrangements expected in this series. The variety of processes connected with spin reorientation, especially transition through conical spin arrangements was of special interest. The compounds have been measured with 57 Fe Mössbauer spectroscopy over the temperature range 5.2 – 320 K. Each compound was studied with precise Mössbauer scanning in the vicinity of the transition. A special fitting procedure of Mössbauer spectra, enabling to analyze up to ten spectra simultaneously, was developed to determine the arrangement of spins. The path of spin rotation was proposed. The results were verified and compared by applying computer simulations based on the Yamada-Kato model. The spin arrangement diagram was constructed. Obtained results are convincing enough to conclude that Mössbauer spectroscopy can be very helpful in studies of tilt angle in conical spin arrangements in the studied type compounds.
Keywords
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permanent magnet materials, Mössbauer effect, spin reorientation, spin diagrams
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ACCEPTED MANUSCRIPT 1. Introduction Intermetallic compounds of general formula R2Fe14B (R – rare earth) exhibit many interesting properties [1], including spin reorientation phenomena [2, 3, 4]. The most studied is Nd2Fe14B as a material for high performance permanent magnets [5, 6, 7].
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The compounds based on Ho and Er also show interesting magnetic behaviour: with increasing temperature, around the spin reorientation temperature, TSR,, their magnetocrystalline anisotropy changes from planar (for Er2Fe14B) or conical (for Ho2Fe14B) to axial (along c-axis). For Ho2Fe14B the conical spin arrangement exists at temperature region 0 – 58 K and then changes into axial [8]. Er2Fe14B is planar up to TSR=323 K and becomes axial above TSR [9]. The series of Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) constitutes a transition combination of magnetic properties with intermediate TSR.
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The compounds crystallize in a tetragonal structure and belong to P42/mnm space group symmetry with six inequivalent crystal sites for Fe (16k1, 16k2, 8j1, 8j2, 4c, 4e) and two sites (4f, 4g) for R atom [1, 7, 10]. Single crystal neutron diffraction measurements report that crystal structure changes to orthorhombic below TSR for Er2Fe14B and starts to distort below 100 K for Ho2Fe14B [11].
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Studies of all above mentioned processes, especially spin reorientation phenomenon, are important to establish the spin structure which is crucial for high-performance permanent magnet applications [12]. So far, the literature data were obtained using mainly magnetometric measurements [10]. It was interesting to observe the spin reorientation process in this series with Mössbauer spectroscopy which enables a microscopic insight into magnetic properties.
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The main goal of our study was to determine the way of change of magnetic spin direction during the spin reorientation process in Er2-xHoxFe14B series caused by temperature. Mössbauer spectra obtained for this series suggested quite different course of the process than previously observed in similar series Er2-xGdxFe14B [13] so it was necessary to describe the spin reorientation process by introducing a more detailed, modified model which is presented below.
2. Experimental method For preparing samples of Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) materials, a standard procedure was used: high purity elements were melted in an electric arc furnace in a high purity argon atmosphere. Then the ingots were annealed at 900 °C for two weeks. After that, the samples were analyzed using XRD measurements at room temperature (Philips PANalytical Empyrean apparatus). These measurements were used to qualify each sample for further studies. X-ray data proved the existence of tetragonal Nd2Fe14B-type phase but also indicated the existence of small amounts of Fe. The existence of natural iron impurity can be expected because R2Fe14B are known to be difficult to synthesize in a pure single phase form 3
ACCEPTED MANUSCRIPT [3]. To prepare absorbers for Mössbauer measurements the samples were crushed into fine powder. The Mössbauer spectra of all samples were recorded in the temperature range 5.2 – 320.0 K, using a 57Co(Rh) source and a computer driven constant acceleration mode spectrometer. Velocity scale was calibrated using high purity natural iron foil. Isomer shifts were established with respect to the center of gravity of the room temperature iron Mössbauer spectrum.
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A majority of the spectra for each sample was recorded in the vicinity of TSR (with the step of 1 K). Additional spectra were recorded at temperatures well below and well above the TSR. In order to record Mössbauer spectra at low temperatures, a standard helium cryostat was used. Due to XRD analysis which indicated existence of natural iron impurity, the high purity iron foil was measured also in temperature range 80 – 300 K to enable the identification of natural iron impurity in the spectra.
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3. Data analysis 3.1. Spectra analysis
Before the main analysis was conducted all Mössbauer spectra were processed to eliminate the influence of small natural iron impurities evidenced in XRD studies. A subspectrum coming from Fe impurities was numerically subtracted from every spectrum. Such procedure was necessary to enable technically the application of further fitting procedure.
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The shape of recorded Mössbauer spectra suggested existence of conical spin arrangement during spin reorientation process in the whole series. Similar spectra shapes occurrence was observed in Mössbauer spectra of conical Er2-xTbxFe14B series [14]. During the main analysis, an attempt was made to find temperature dependence of angle between and principal axis of EFG (electric field gradient) tensor (Vxx, Vyy, Vzz). magnetic moment
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A special procedure was constructed to allow a simultaneous fitting of several spectra obtained for a given composition at different temperatures [15]. Recently, the procedure of simultaneous fitting was extended to enable fitting angular dependences. The aim was to establish a consistent description of hyperfine interactions as well as angle dependence and hence determine the character of spin reorientation. The shape of the spectra was described using transmission integral. The spectra of all samples were treated as convolution of six Zeeman subspectra with relative intensities according to iron occupation of crystallographic sublattices (4:4:2:2:1:1). Each subspectrum was characterized by the following hyperfine interaction parameters: magnetic field - B, isomer shift - IS, quadruple splitting – QS. The description of the spectra is correlated with the phenomenon of spin reorientation using some simplifying assumptions which are discussed below. The direction of total magnetization vector changes from the initial planar (within a-b crystallographic plane) arrangement below the temperature of the transition region to the final 4
ACCEPTED MANUSCRIPT axial (along crystallographic c-axis) arrangement above the temperature of transition region. The model assumes that this, induced by temperature process of changing direction (called takes place in an established plane, called the rotation plane. rotation) of magnetic moment This rotation plane of the magnetic moment is indicated in Fig. 1. It is the plane containing the c-crystallographic axis, so it is perpendicular to ab plane. The magnetic moment can form vector is in ab plane, ψ = 0˚), conical arrangement a planar arrangement (
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(0˚<ψ<90˚) or axial arrangement (ψ = 90˚). The rotation takes place in the transition temperature range and its rotation plane is fixed for every sublattice.
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Additionally, two sets of Zeeman sextets exist in the transition temperature region. One of them is connected with low temperature spectrum – before reorientation, second with high temperature spectrum – after reorientation. In the model, at every temperature in the reorientation temperature range, a contribution of high temperature Zeeman sextet refers to the quantity of spins that go into conical position. Also a high temperature Zeeman sextet determines the angle dependences at every temperature, while low temperature Zeeman sextet gives the initial value of angle. It is also assumed that the quadrupole splitting observed during the reorientation and process is due only to the change of angle θ (Fig. 1) between the magnetic moment principal axis Vzz of EFG tensor [16]. According to the perturbation theory the dependence of arrangement can be written in a following way [17]: = quadrupole splitting QS on
+ sin ∙ cos 2 , where is azimuth angle determining the orientation
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of magnetic moment in the coordinate system of the EFG tensor axes, is the EFG asymmetry parameter. In our model an asymmetry term was neglected. While constructing the model only a weak change of IS with increasing temperature caused by second order Doppler shift and smooth changes of magnetic fields described by second order polynomial were taken into account in the whole temperature range.
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The angle θ can be expressed by the angle , describing position of magnetic moment vector on the rotation plane, which is changing with temperature and by the angle , describing relation between principal axis Vzz of EFG tensor and the rotation plane (Fig. 2) which does not depend on temperature: "#$ = "#$ ∙ $%& ; is the angle between projection of principal axis Vzz of EFG tensor to the rotation plane and the magnetic moment . The angle between principal axis Vzz of EFG tensor and perpendicular to the rotation plane
is called . This angle is different for each crystallographic sublattice but it does not change with the position of magnetic moment on the rotation plane. The position of magnetic moment on the rotation plane is determined either with respect to ab plane by ψ angle or with respect to the projection of EFG axis on that plane by β angle (Fig 1, 2). The change of the angle is given by ( angle and describes the reorientation process. It is clear that the change in Mössbauer spectrum shape depends not only on the position of the magnetic moment during the reorientation process (indicated by the change of angle β) but also on the position of the rotation plane relative to EFG tensor axis. The strongest changes in the spectrum occur for EFG axis residing in the rotation plane (α = 90˚).
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Extended simultaneous fitting procedure was introduced to the analysis to check the possibility of obtaining distinct and coherent values of and angles. In order to determine these angles it is essential to process simultaneously a set of Mössbauer spectra for at least three different positions of magnetic moment for the given sample in specified temperatures from the transition region. It was also important to check if the adopted model describes behaviour (changes with temperature) of all six Zeeman subspectra in a correct way, i.e. if such simplified model constitutes a good description of the spin reorientation process in the studied materials.
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The result of application of the above described procedure is presented for the Er1Ho1Fe14B (x = 1) compound. This composition was chosen for discussion because all observed processes are clearly visible here. For selected temperatures the experimentally obtained Mössbauer spectra and fits from the procedure are shown in Fig. 3. The rest of the samples exhibit qualitatively similar behaviour. Generally, the procedure allows to obtain a good representation of spectra shapes. Series of fits also represent changes in spectra shapes for specified sample in the transition temperature region. The reorientation process of magnetic moments in the studied type compounds can be easily observed owing to the separation of the sixth line of 8j2 sextet from the remaining part of the spectrum during the reorientation process. On the Figure 3 not only a change of the amplitude of the sixth line of 8j2 sextet with temperature is observed but also a shift in its position. This suggests the existence of different angles between magnetic moment and EFG axis at different temperatures. All these processes have a reflection in the fits. The spectra analysis, based on the proposed model, indicated existence of the conical spin arrangements in studied samples. Our analysis confirms spin reorientation process from planar or initial-conical arrangement to final axial arrangement. The samples for x > 1.0 exhibit canted spin arrangement, even at the lowest temperatures. The samples with x < 1.0 have planar spin arrangement at low temperatures. As the temperature approaches the TSR, the angle describing conical arrangement increases to reach ψ = 90° for temperature above transition region. Additionally, behaviour of spectra shape, especially of 8j2 emerging sixth line suggests that spins do not rotate collectively. When the transition begins, shape of the spectrum starts to evolve in a way that is characteristic for conical spin arrangement i.e. arrangement between initial and final state. When this path of transition ends – the shape of the spectrum is characteristic for axial spin arrangement – the evolution characteristic for two state model begins. The process ends when all spins reach a final arrangement. The two-phase process vs. collective rotation, described by Mössbauer spectra fits is presented in Fig. 4. It was impossible to obtain good results for established collective rotation – the misfits always occur in this case. The shape of the first line in the spectrum as well as the amplitude of 8j2 line could not be described properly. The problem was solved by setting up the rotating phase at about 70% and leaving 30% of spins in non rotating, flipping phase. Such division of phases is maximal and is suitable for x = 1.0. With x→0 and x→2.0 the amount of not rotating, flipping phase decreases. For Ho2Fe14B we found that contribution of non rotating, flipping phase is insignificant and can be neglected.
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All Mössbauer spectra recorded for the studied series were analysed using model which includes rotation of spins via conical arrangements. It is worth to note that for this series of compounds it was impossible to use a two-state model which was applied successfully for other compounds of R2Fe14B (e.g. Er2-xGdxFe14B) [13]. Two-state model assumes spins flipping from initial to final position without intermediate conical arrangements. The contribution of spins in initial and final position changed with increasing temperature. The necessity of implementation of the model assuming spin rotation, not just simple “two state flipping”, seems to indicate a different course of spin reorientation process in the studied series. This may be attributed to different Stevens coefficients, ) , of Gd ( ) = 0) and Ho ( ) < 0 ).
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3.2. Theoretical model
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The obtained experimental results were compared with the results of the computer simulations of reorientation process. The computer program based on simplified phenomenological Yamada-Kato model [4, 18] was used. For each sample, using literature data [6, 19, 20], it was possible to obtain theoretical values of spin arrangement angle in a specific temperature. The simulation procedure assumed collective behaviour of spins. The two-phase model was not regarded in this case. To determine values of angle, the free energy calculations were used. Finding the angle dependence is achieved by minimizing the free energy of the system, F(T), which is assumed to be a sum of contributions derived from two coupled sublattices – rare earth (R) sublattice and iron (Fe) sublattice. F(T) = FR(T) + FFe(T). The R-sublattice is treated as an assembly of isolated atoms in crystal electric field, CEF, and exchange field. In this case R-R interaction is neglected. The magnetic free energy can be calculated from the energy levels corresponding to the particular set of CEF parameters. +,-. (%) = ∑3,4 234 (%) 534 , where 234 (%) are the crystal field parameters of the R atom at site * i and 534 are the Stevens operators. The contributions from different R ions are assumed to be linear. On the other hand, the iron (Fe) sublattice is treated in a different way – the experimental data were used. Experimentally obtained values of K1(T) – the anisotropy constant was scaled up to the Curie temperature and used to evaluate the free energy of 3d sublattice as E = K1(T)sin2θc [21], where θc is the angle between the magnetization direction and the crystal c-axis. In this simulation the entropy term was recognized as negligible. The magnetization of the 3d-sublattice acts on magnetization of the R-sublattice and thus exchange energy of the molecular magnetic field couples the two magnetic sublattices. The following formula, expressing the dependence of the total free energy as a function of temperature T and angle θc, was used: 6(7, θ9 ) = −;7 ∑@AB ln =(%) + 28? (7) sin (, ), where Z(i) is the partition function =(%) = ∑)I JB C
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and Ej(i) are the energy levels of R-
ion in i = 4f, 4g lattice sites. In case of these simulations, we assume that values for 4f and 4g sites are equal. The described above procedure was applied to obtain theoretical curves of spin arrangement angle in specific temperature for each sample of studied series. The simulation 7
ACCEPTED MANUSCRIPT procedure gave approximate image of the process, presenting collective behaviour of all spins in just one phase. The obtained results are presented in Fig. 5, where theoretical curves are presented together with experimental data. Experimental data refer only to rotating phase.
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These simulations confirm the existence of conical spin arrangement in measured samples in the temperature range indicated by Mössbauer spectra analysis.
4. Results and discussion
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The character of Mössbauer spectra obtained for the series Er2-xHoxFe14B (x=0.5, 1.0, 1.5, 2.0) required to go beyond the two-state model used so far to describe the behavior of R2Fe14B compounds [13, 14]. Applied procedure allowed us to successfully perform operation of simultaneous fitting series of spectra for each sample and obtain angle dependence of spin arrangement. These results were compared with computer simulation of spin arrangements, based on Yamada-Kato model (Fig. 5). We found that theoretical simulations confirm the existence of conical spin arrangements in the measured samples in temperature region indicated by the spectra analysis. For samples for which the conical arrangements exist from the lowest temperatures, also the initial angle was confirmed. Strong changes observed with changing x may be caused by competition between Er and Ho.
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The experimental data do not follow theoretical curves ideally. Theoretical and experimental data are almost equal in initial and final states but do not overlap in intermediate position. A surprising compatibility between experimental and theoretical data was obtained for Ho content x = 0.5 where experimental data almost ideally reproduce theoretical predictions. For Ho2Fe14B our theoretical and experimental Mössbauer results were compared with literature data acquired by magnetometric [22] and neutron diffraction [11] measurements (Fig. 5).
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Finally, collected data were used to construct a spin arrangement diagram for studied series Er2-xHoxFe14B (Fig. 6). The existence of conical spin arrangement from the lowest temperatures was found for Ho content up to x ≥ 1.0. For Ho content x = 2.0 the arrangement corresponding to crystal c-axis is achieved at about 58 K and remains almost unchanged up to x ≈ 1.25. For lower Ho content these spin arrangements are also achieved at higher temperatures and strongly depend on composition. A disagreement about 30 K is visible for x = 1.0 which may be interpreted by a “two phase rotation” process. The results were compared also with literature data, where the series of Er2-xHoxFe14B was studied with magnetometric methods [10] (Fig. 6). Generally, the results on temperature ranges of conical arrangements are coherent with the literature data. The spin arrangement diagram based on Mössbauer spectra analysis and the one based on magnetometric studies are consistent. The temperature ranges for the existence of conical spin arrangements were confirmed.
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ACCEPTED MANUSCRIPT 5. Conclusion
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The process of spin reorientation in the series of Er2-xHoxFe14B can be observed by Mössbauer spectroscopy. The determination of spin reorientation temperature as well as tilt angle dependences on composition and temperature need very careful simultaneous fitting of the appropriate set of Mössbauer spectra. Temperature regions of spin reorientation process and the spin phase diagram are determined with good precision and they are verified by computer simulation based on Yamada-Kato model as well as literature reports.
6. Acknowledgment
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The research was funded by Polish Ministry of Science and Higher Education Grant no. 7150/E-338/M/2015 and was carried out with the equipment purchased thanks to the financial support of the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/08).
References
[1]
Herbst I. F. (1991). R2Fe14B materials: Intrinsic properties and technological aspects.
[2]
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Reviews of Modern Physics, 63, 819.
Buschow K. H. J. (1991). New developments in hard magnetic-materials, Reports on Progress in Physics, 54 (9), 1123 – 1213, DOI: 10.1088/0034-4885/54/9/001. R. C. O’Handley. (2000). Modern Magnetic Materials: Principles and Applications.
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[3]
New York: John Willey & Sons, Inc. Yamada M., Kato H., Yamamoto H., Nakagawa Y. (1988). Crystal-field analysis of
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[4]
the magnetization process in a series of Nd2Fe14B-type compounds. Physical Review
B, 38, 620 – 633. DOI: 10.1103/PhysRevB.38.620.
[5]
Pankratov N. Yu., Nikitin A. A., Iwasieczko W., et al. (2006). Spin-reorientation transition in Nd2(Fe,Co)14B compounds and their hydrides. Journal of Magnetism and Magnetic Materials, 300, 465 – 468. DOI: 10.1016/j.jmmm.2005.10.195.
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ACCEPTED MANUSCRIPT [6]
Burzo E. (1998). Permanent magnets based on R–Fe–B and R–Fe–C alloys. Reports on Progress in Physics, 60(9), 1099 – 1266. DOI: 10.1088/0034-4885/61/9/001.
[7]
Lim J. T., Kim H. K., Kim C. S., An S. Y., Choi K. R. (2015). Investigation of the Magnetic Properties of Dy doped Nd-Fe-B Permanent Magnet by Using Mössbauer
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Spectroscopy. Journal of the Korean Physical Society, 66(12), 1913-1917. DOI: 10.3938/jkps.66.1913. [8]
Rillo C., et al. (1988). Dynamical susceptibility of Ho2Fe14B single crystal: Spin
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rotation and domain wall motions, Journal of Applied Physics, 64, 5534 – 5536. DOI: 10.1063/1.342327.
Basso V., et al. (2011). Er2Fe14B single crystal as magnetic refrigerant at the spin
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[9]
reorientation transition. Journal of Applied Physics, 109, 083910. DOI: 10.1063/1.3567925.
[10] Ibarra M. R., et al. (1993). Magnetic anisotropy in (ErxHo1-x)2Fel4B pseudoternary
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intermetallic compounds, Journal of Physics: Condensed Matter, 5 (1993), 56375648. DOI: 10.1088/0953-8984/5/31/025. [11] Wolfers P., Bacmann M., Fruchart D. (2001). Single crystal neutron diffraction
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investigations of the crystal and magnetic structures of R2Fe14B (R=Y, Nd, Ho, Er). Journal of Alloys and Compounds, 317 – 318, 39 – 43. DOI: 10.1016/S0925-
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8388(00)01353-0.
[12] Batancourt R. J. I. (2002). Nanocrystalline hard magnetic alloys. Revista Mexicana de Fisica. 48(4), 283 -289.
[13] Wojciechowska A., Pędziwiatr A. T, Bogacz B. F., Wróbel S. (2007). Spin reorientation phenomena in Er2-xRxFe14B (R = Gd, Th) – Mössbauer and calorimetric study. Nukleonika, 52(1), 77 – 79.
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ACCEPTED MANUSCRIPT [14] Kurzydło P. M., Bogacz B. F., Pędziwiatr A. T., Oleszak D., Przewoźnik J. (2015). Search for Canted Spin Arrangement in Er2-xTbxFe14B with Mössbauer Spectroscopy. Nukleonika, 60(1), 93 – 96. DOI: 10.1515/nuka-2015-0019. [15] Pędziwiatr A. T., Bogacz B. F., Gargula R., Wróbel S., (2002). Mössbauer and DSC
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studies of spin reorientations in Er2−xYxFe14B. Journal of Alloys and Compounds, 336, 5 – 10. DOI: 10.1016/S0925-8388(01)01872-2.
[16] Susilo R. A., Munoz Perez S., Cobas R., Cadogan J. M., Avdeev M. (2012). Magnetic
012071. DOI: 10.1088/1742-6596/340/1/012071.
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order and spin-reorientation in HoGa. Journal of Physics: Conference Series, 340,
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[17] Delyagin N. N., Krylov V. I., Rozantsev I. N. (2007). The magnetic spin-reorientation transitions in the RGa (R = rare earth) intermetallic compounds studied by measurements of the hyperfine interactions of the 119Sn probe atoms. Journal of Magnetism and Magnetic Materials, 308, 74 – 79. DOI:
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10.1016/j.jmmm.2006.05.004.
[18] Piqué C., Burriel R., Bartolomé J. (1996). Spin reorientation phase transitions in R2Fel4B (R = Y, Nd, Ho, Er, Tm) investigated by heat capacity measurements. Journal
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of Magnetism and Magnetic Materials, 154, 71 – 82. DOI: 10.1016/03048853(95)00571-4.
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[19] Liu Y., Sellmyer D. J., Shindo D. (2006). Handbook of advanced magnetic materials, Volume I, New York: Springer.
[20] Coey J. M. D. (1996). Rare-earth iron permanent magnet. Oxford: Clarendon Press. [21] Andreev A. V., Bartashevich M. I., Goto T., Zadvorkin S. M. (1997). Magnetic properties of (Y1-xThx)2Fe14B. Journal of Alloys and Compounds, 262/263, 467 – 470, DOI: 10.1016/S0925-8388(97)00356-3.
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ACCEPTED MANUSCRIPT [22] Hirosawa S., Yutaka M., Hitoshi Y., Setsuo F., Masato S., Hiroshi Y. (1986). Magnetization and magnetic anisotropy of R2Fe14B measured on single crystals.
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Journal of Applied Physics, 59, 873. DOI: 10.1063/1.336611.
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ACCEPTED MANUSCRIPT Fig. 1.
ሬሬԦ and a, b, crystallographic axes. ψ angle The rotation plane of the magnetic moment ܯ determines the direction of the magnetic moment relative to ab plane.
Fig. 2.
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The position of EFG axis relative to the rotation plane of magnetic moment. Angle α is between EFG axis and a normal to the rotation plane. Angle β is between the magnetic moment and the projection of EFG axis on the rotation plane, θ angle is between the magnetic moment and EFG axis.
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Fig. 3.
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The set of diagrams constructed for Er1Ho1Fe14B compound in selected temperatures. The 57Fe Mössbauer transmission spectra (crosses) and fits from the model (solid lines) presenting evolution of lines position and amplitude. The long vertical line visualizes move of the sextet 8j2 6th line from the initial position. The angle ψ describing the rotation of magnetic moment and temperaturę were also indicated in the graph.
Fig. 4.
Fig. 5.
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Two Mössbauer spectra for Er1Ho1Fe14B selected from the set processed by the fitting program. The comparison presents misfit appearing for assumed „collective rotation”. The misfit was canceled by introducing „two-phase rotation”.
Fig. 6.
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Temperature dependance of spin reorientatin angle ψ presented for measured samples of Er2xHoxFe14B series. Black squares present values determined by fitting program (only rotating phase was presented) while solid lines are data from computer simulations. For Ho2Fe14B also literature data was presented: (black circles) - neutron diffraction experiments [11], (black triangles) – magnetometric measurements [22].
Spin arrangement diagram for Er2−xHoxFe14B compounds. TC − Curie temperature, TSR (black squares) − spin reorientaAon temperatures limits from Mössbauer measurement and fiCng procedure, TSR (solid lines) − limits of spin reorientaAon temperature determined by the computer simulaAons. The area between lines – space of conical spin arrangement. There was also literaturę data presented [10]. TSR (black triangle) – limits of the spin rotating, TSR (white and black diamonds) – respectively AC and DC susceptibility measurements.
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Spin reorientation process has been studied in a new series of Er2-xHoxFe14B. Unique method of simultaneous spectra analysis is presented. Computer simulation of spin reorientation process is performed. Temperature dependence of tilt angle is presented Spin arrangement diagram is constructed.
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