Journal of Science: Advanced Materials and Devices xxx (xxxx) xxx Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Magnetic interactions and spin-wave stiffness constant of In-substituted yttrium iron garnets Vu Thi Hoai Huong a, Dao Thi Thuy Nguyet a, *, Nguyen Phuc Duong a, To Thanh Loan a, Siriwat Soontaranon b, Le Duc Anh c a b c International Training Institute for Materials Science (ITIMS), Hanoi University of Science and Technology, Dai Co Viet Road, Hanoi, 10000, Viet Nam Synchrotron Light Research Institute, University Avenue 111, Nakhon Ratchasima, 30000, Thailand Department of Electronic Engineering and Information System, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan a r t i c l e i n f o a b s t r a c t Article history: Received 29 December 2019 Received in revised form 22 February 2020 Accepted 24 February 2020 Available online xxx Indium-substituted yttrium iron garnet samples, Y3Fe5ÀxInxO12 (x ¼ 0e0.7, step 0.1), were prepared using a citrate solgel method Synchrotron X-ray diffraction (SXRD) measurements combined with the Rietveld refinement technique were used to investigate the crystallization, structure parameters and lattice distortion in the samples Magnetization and Curie temperature of the samples were measured with the SQUID and VSM equipments The non-magnetic indium ions were found to reside at the octahedral sites, leading to an increase of the total magnetization and a decrease in the Curie temperature Molecular field coefficients Naa, Ndd and Nad were determined by fitting the experimental thermomagnetization curves in the framework of a two-sublattice ferrimagnetic model The stiffness constant of the spin waves, D, in these samples was calculated based on the exchange interaction constants, Jij, and its temperature dependence was derived for the sublattice magetizations The calculated results for D(T) are in good agreement with the experimentally measured data and are significantly large around room temperature © 2020 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Keywords: In-substituted yttrium iron garnets Magnetization Curie temperature Molecular field coefficients Spin-wave stiffness constant Introduction Yttrium iron garnet (YIG) belongs to a cubic ferrite family with the space group Oh10eIa3d [1] Considering one formula unit, Y3Fe5O12, three Y atoms occupy the 24c (dodecahedral) sites, two Fe atoms occupy the 16a (octahedral) sites and three Fe atoms occupy the 24d (tetragonal) sites which are formed by the surrounding O2À ions Since Y ions have no magnetic moment, there are only two magnetic sublattices formed by Fe ions at the 16a and 24d sites, which couple antiparallel to each other with the net magnetization, el model [1] With the Mtot ¼ Md À Ma, in accordance with the Ne existence of differently sized crystallographic sites, YIG can be used for substituting a wide variety of ionic radii and valence states, which provide a wide range of control of magnetization and Curie temperature At substitution of nonmagnetic ions for Fe in moderate concentrations, the decrease in the number of nearest magnetic iron neighbors leads to a canting of magnetic moments Hence, the pair exchange constants Jij (where i and j are a or d) * Corresponding author E-mail addresses: nguyet@itims.edu.vn, nguyet.daothithuy@hust.edu.vn (D.T Thuy Nguyet) Peer review under responsibility of Vietnam National University, Hanoi between an iron ion and its remaining surrounding magnetic ions also decrease [2] Our recent study on the magnetic properties of the co-substituted Y3À2xCa2xFe5ÀxVxO12 series, revealed that a severe local structure distortion, along with the magnetic dilution effect, can reduce the overlap between the 3d orbitals of Fe and the 2p orbitals of O, leading to another cause of reduction for Jij [3] Within a molecular field model, the temperature dependence of the spontaneous magnetization (Ms) and the Curie temperature (TC) can be calculated on the basis of molecular field coefficients, which characterize the interactions in each sublattice (Naa, Ndd) and those between sublattices (Nad) Studies on magnetically diluted YIG samples have shown that appropriate sets of coefficients can effectively reproduce the experimental MseT curves Studies on magnonics have been explored for YIG because it is a ferrimagnetic insulator with a low magnetization damping [4e8] and a long spin-wave propagation lifetime [9,10] Spin waves can be manipulated for various applications, including logic operations [6e8,11e13], data buffering elements [7], and magnon transistors [8] Hence, YIG shows the potential for application in computing technology This study discusses the magnetic properties of the solid solution systems of Y3Fe5ÀxInxO12, where In atoms favorably occupy the a sites that form the weak magnetization sublattice The solubility of these solid solutions has not fully been studied, and their magnetic https://doi.org/10.1016/j.jsamd.2020.02.007 2468-2179/© 2020 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Please cite this article as: V.T Hoai Huong et al., Magnetic interactions and spin-wave stiffness constant of In-substituted yttrium iron garnets, Journal of Science: Advanced Materials and Devices, https://doi.org/10.1016/j.jsamd.2020.02.007 V.T Hoai Huong et al / Journal of Science: Advanced Materials and Devices xxx (xxxx) xxx Fig SXRD patterns of the Y3Fe5ÀxInxO12 samples (x ¼ 0, 0.3, 0.6) The inset shows the highest intensity peaks (420) Fig SXRD pattern and Rietveld refinement data of the sample Y3Fe4.7In0.3O12 The difference between the experimental and calculated data is also indicated Table Structural parameters of the YFe5ÀxInxO12 series estimated from Rietveld refinement: lattice constant (A), average interatomic distances (ddeO, daeO, dceO) and microstrain (ε) x A (Å) ddeO (Å) daeO (Å) dceO (Å) (Å) ε (%) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 12.369 12.397 12.412 12.414 12.416 12.429 12.433 12.466 1.8568 1.8610 1.8639 1.8634 1.8639 1.8658 1.8664 1.8714 1.9814 1.9859 1.9882 1.9884 1.9889 1.9910 1.9916 1.9969 2.3804 2.3858 2.3886 2.3840 2.3894 2.3919 2.3927 2.3990 20 21 25 21 22 21 21 20 0.345 0.376 0.388 0.413 0.420 0.430 0.448 0.455 properties have not been comprehensively investigated Previous studies showed that the total magnetization is enhanced in a certain concentration range of nonmagnetic elements, although magnetic dilution in the a sublattice causes spin canting in the oppositely magnetized d sublattice However, the d sublattice becomes antiferromagnetically ordered in case the number of magnetic neighbors at the a sites surrounding a magnetic ion in the d sublattice exceeds a concentration threshold value close to zero, at which the total magnetization drastically decreases [2] Gilleo and Geller [14,15] investigated the magnetic moments of YIG samples substituted with nonmagnetic ions, i.e., R ẳ Sc3ỵ, Zr3ỵ, and In3ỵ at the a sublattice with the following general formula: Y3[Fe2ÀxRx]Fe3O12 The results show that the samples are ordered ferrimagnetically in the concentration region x ~0.7, and that their net magnetic moment increases proportionally with x The increase rate is similar to that of the series of the samples substituted with different R species Nevertheless, the increase rate is lower than the expected value of el configuration because of the spin canting in the the collinear Ne d sublattice As the concentration increases beyond ~0.7, the degree of canting abruptly changes and, consequently, the antiferromagnetic phase dominates with the net moment decreasing to zero at x ¼ This work focuses on the ferrimagnetic phases of Y3Fe3ÀxInxO12 with x 0.7 The saturation magnetizations in a wide temperature range (minimum value of K) and the Curie temperatures of these compositions are collected Their spin wave stiffness constants are evaluated on the basis of exchange constants and sublattice magnetizations derived from the molecular field theory Experimental 2.1 Sample preparation Y3Fe5ÀxInxO12 particle samples (x ¼ 0e0.7, step 0.1) were prepared using the solegel method in accordance with a previous study [3] The starting materials for the preparation of the samples were high-purity Fe(NO3)3, Y2O3, and In2O3 (99.99%, Sigma-Aldrich) The oxides were dissolved in M HNO3 to form nitrate solutions The Please cite this article as: V.T Hoai Huong et al., Magnetic interactions and spin-wave stiffness constant of In-substituted yttrium iron garnets, Journal of Science: Advanced Materials and Devices, https://doi.org/10.1016/j.jsamd.2020.02.007 V.T Hoai Huong et al / Journal of Science: Advanced Materials and Devices xxx (xxxx) xxx vibrating sample magnetometer (ADE Technology-DMS 5000) at 80e600 K In both facilities, the maximum applied magnetic field was 10 kOe Results and discussion 3.1 Crystal structure and morphological characteristics Fig FESEM images of the samples x ¼ 0, 0.1, 0.3, 0.7 metal nitrate solutions were mixed with the required amount of metal ions at a stoichiometric ratio of [Y]:[Fe]:[In] ¼ 3:(5Àx):x An aqueous citric acid solution was added to the solution with a total cation/citric acid molar ratio of 1/3 The mixtures were stirred at 400 rpm and slowly evaporated at 80 C to form gels The gels were dried at 95 C for more than 12 h to form xerogels Particle samples were obtained after the xerogels were burned at 400 C for h and annealed at Tan ¼ 900 C for h 2.2 Characterization Synchrotron X-ray powder diffraction (SXRD) experiments were carried out at the beamline SAXS of the Synchrotron Light Research Institute in Thailand (l ¼ 1.54 Å) to identify the crystal structure of the samples Data were analyzed using the Rietveld method and the FullProf program [16] Diffraction peaks were modeled using a pseudo-Voigt function LaB6 was used as the standard to determine the instrumental broadening Field emission scanning electron microscopy (FESEM; JEOL JSM7600 F) was adopted to examine particle sizes and morphological characteristics Magnetization curves in the temperature range from K to room temperature were measured using a superconducting quantum interference device (Quantum Design) with magnetic fields of up to 10 kOe The magnetic characteristics were also studied with a The SXRD measurements of the sample series show that the diffraction peaks of all samples can be indexed within the standard diffraction pattern of YIG without any indication of foreign phases For demonstration, the SXRD patterns of three compositions (x ¼ 0, 0.3, and 0.6) are shown in Fig The inset shows a shift of the (420) lines toward small Bragg angles, indicating that the lattice constant increases as the indium concentration increases Structural parameters, including the lattice constant A and the average bond lengths between cations in d, a, and c sites and oxygen (ddeO, daeO, and dceO), were determined via the Rietveld refinement The increase in lattice constant can be ascribed to the larger atomic radius of In compared to Fe In the octahedral a sites, the radius of Fe3ỵ (rFe3ỵ ẳ 0.785 ) is smaller than that of In3ỵ (rIn3ỵ ẳ 0.94 ) [17] In accordance with the lattice expansion effect, ddeO, daeO, and dceO also increase with x The average size of the coherent scattering region and the average lattice microstrain ¼ DA/A were determined through the analysis of the peak that broadened after the Rietveld method application by using the FullProf program with the instrumental resolution function identified via the SXRD analysis of LaB6 All the obtained structure parameters are listed in Table The mean crystallite sizes are in the range of 20e25 nm The increase in the average microstrain with increasing x can be understood in terms of lattice unit cell distortion caused by the In substitution The microstructure of the samples was characterized through FESEM The micrographs of the samples are shown in Fig The grain sizes of the sample with the lowest In content at x ¼ 0.1 are considerably increased compared with those of the pure sample possibly because of the low melting point of the In component It has been shown that the melting temperature of indium oxide (In2O3) in powder form is as low as 850 C [18] For Tan ¼ 900 C, the indium component can be in a melting state and this molten part can draw the surrounding materials to form big grains The grain sizes reach the micron scale as the indium concentration further increases The micrographs of the substituted samples indicate that small grains melt and merge to form larger ones during crystallization The grain sizes are much larger than the crystallite sizes as determined via the SXRD line broadening Fig Magnetization curves measured at K and 290 K of the Y3Fe5ÀxInxO12 samples (x ¼ 0e0.7) Please cite this article as: V.T Hoai Huong et al., Magnetic interactions and spin-wave stiffness constant of In-substituted yttrium iron garnets, Journal of Science: Advanced Materials and Devices, https://doi.org/10.1016/j.jsamd.2020.02.007 V.T Hoai Huong et al / Journal of Science: Advanced Materials and Devices xxx (xxxx) xxx 3.2 Magnetic properties Fig Magnetic moment, mexp, at K of the samples as a function of the In concentration, x The solid line represents the calculated values according to Eq (1) Table Curie temperature (TC), experimental magnetic moment at K (m(5)exp) and calculated magnetic moment at K (m(0)cal), and estimated indium contents at the a sites and d sites of the Y3Fe5ÀxInxO12 series x TC (K) M (5 K)exp (mB/f.u.) In3ỵ at a sites In3ỵ at d sites 0.1 0.2 0.3 0.4 0.5 0.6 0.7 564 540 522 510 484 466 450 433 4.9 5.4 5.8 5.97 6.35 6.84 7.3 7.65 0.1 0.2 0.273 0.37 0.48 0.586 0.68 0 0.027 0.03 0.02 0.014 0.02 The magnetization curves MeH of the investigated samples were measured at different temperatures For demonstration, the MeH curves recorded at T ¼ K and 290 K are displayed in Fig A general behavior is that the magnetization approaches technical saturation above ~2.5 kOe As the magnetic field further increases, the saturation state is attained with negligible magnetic susceptibility The magnetization loops of the samples show small magnetic hysteresis behavior The coercivity for the pure YIG nanoparticle sample was discussed in detail in [19] The values of the saturation magnetization Ms were determined on the basis of the flat part of the curves in the high field region As such, the saturation magnetic moments mexp were calculated in Bohr magneton per formula unit The saturation magnetic moments of the samples at K as a function of indium concentration are presented in Fig 5, and the values are listed in Table The saturation magnetization monotonously increases as the substitution level increases, indicating that In atoms mostly reside in a sites, which belong to the weak magnetization sublattice Fig also shows the plot of the linear behavior of the saturation magnetic moment m(x) of the samples prepared via a solid-state reaction versus the concentration of nonmagnetic atoms (Sc3ỵ, Zr3ỵ, In3ỵ) reported by Geller [14] and Gilleo [15] m(x) versus x dependence follows the expression m(x) ẳ ỵ 4.05*x (1) el conguration, m(x) in Eq (1) is lower than that in the collinear Ne i.e., m(x) ẳ ỵ 5*x, because of the spin canting in the d sublattice The magnetic moments of the samples agree with those derived using Eq (1), although their values are slightly lower (