Magnetic interactions and spin-wave stiffness constant of In-substituted yttrium iron garnets

iff ye nce 00, T o, 7- 22 February 2020 Accepted 24 February 2020 to a c 3 5 12 netic iron neighbors leads to a canting of magnetic moments. Hence, the pair exchange constants Jij (where i and j are a or d) duction for Jij [3]. dependence of the temperature (TC) coefficients, which aa, Ndd) and those ically diluted YIG f coefficients can rves. YIG because it is a n damping [4e8] 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 Y3Fe5
xInxO12, 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 * Corresponding author. E-mail addresses: nguyet@itims.edu.vn, nguyet.daothithuy@hust.edu.vn (D.T. Thuy Nguyet). Contents lists availab Journal of Science: Advanc journal homepage: www.el Journal of Science: Advanced Materials and Devices 5 (2020) 270e277Peer review under responsibility of Vietnam National University, Hanoi.erate concentrations, the decrease in the number of nearest mag- and a long spin-wave propagation lifetime [9,10]. Spin waves can beatoms occupy the 16a (octahedral) sites and three Fe atoms occupy the 24d (tetragonal) sites which are formed by the surrounding O2
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, Mtot ¼ Md
Ma, in accordance with the N
eel model [1]. With the 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 mod- 2p orbitals of O, leading to another cause of re Within amolecular fieldmodel, the temperature spontaneous magnetization (Ms) and the Curie can be calculated on the basis of molecular field characterize the interactions in each sublattice (N between sublattices (Nad). Studies on magnet samples have shown that appropriate sets o effectively reproduce the experimental MseT cu Studies on magnonics have been explored for ferrimagnetic insulator with a low magnetizatiothe space group Oh10eIa3d [1]. Considering one formula unit, Y Fe O , three Yatoms occupy the 24c (dodecahedral) sites, two Fe vere local structure distortion, along with the magnetic dilution effect, can reduce the overlap between the 3d orbitals of Fe and theAvailable online 29 February 2020 Keywords: In-substituted yttrium iron garnets Magnetization Curie temperature Molecular field coefficients Spin-wave stiffness constant 1. Introduction Yttrium iron garnet (YIG) belongshttps://doi.org/10.1016/j.jsamd.2020.02.007 2468-2179/© 2020 The Authors. Publishing services b ( 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 ( ubic ferrite family with between an iron ion and its remaining surrounding magnetic ions also decrease [2]. Our recent study on the magnetic properties of the co-substituted Y3
2xCa2xFe5
xVxO12 series, revealed that a se-Received 29 December 2019 Received in revised form refinement technique were used to investigate the crystallization, structure parameters and latticeArticle history: Indium-substituted yttrium iron garnet samples, Y3Fe5
xInxO12 (x ¼ 0e0.7, step 0.1), were prepared using a citrate solgel method. Synchrotron X-ray diffraction (SXRD) measurements combined with the RietveldOriginal Article Magnetic interactions and spin-wave st In-substituted yttrium iron garnets Vu Thi Hoai Huong a, Dao Thi Thuy Nguyet a, *, Ngu Siriwat Soontaranon b, Le Duc Anh c a International Training Institute for Materials Science (ITIMS), Hanoi University of Scie b Synchrotron Light Research Institute, University Avenue 111, Nakhon Ratchasima, 300 c Department of Electronic Engineering and Information System, The University of Toky a r t i c l e i n f o a b s t r a c ty Elsevier B.V. on behalf of Vietnamness constant of n Phuc Duong a, To Thanh Loan a, and Technology, 1 Dai Co Viet Road, Hanoi, 10000, Viet Nam hailand 3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan le at ScienceDirect ed Materials and Devices sevier .com/locate/ jsamdNational University, Hanoi. This is an open access article under the CC BY license Fig. 1. SXRD patterns of the Y3Fe5
xInxO12 samples (x ¼ 0, 0.3 Table 1 Structural parameters of the YFe5
xInxO12 series estimated from Rietveld refine- ment: lattice constant (A), average interatomic distances (ddeO, daeO, dceO) and microstrain (ε). x A (Å) ddeO (Å) daeO (Å) dceO (Å) (Å) ε (%) 0 12.369 1.8568 1.9814 2.3804 20 0.345 0.1 12.397 1.8610 1.9859 2.3858 21 0.376 0.2 12.412 1.8639 1.9882 2.3886 25 0.388 0.3 12.414 1.8634 1.9884 2.3840 21 0.413 0.4 12.416 1.8639 1.9889 2.3894 22 0.420 0.5 12.429 1.8658 1.9910 2.3919 21 0.430 0.6 12.433 1.8664 1.9916 2.3927 21 0.448 0.7 12.466 1.8714 1.9969 2.3990 20 0.455 Fig. 2. SXRD pattern and Rietveld refinement data of the sample Y3Fe4.7In0.3O12. The difference between the experimental and calculated data is also indicated. V.T. Hoai Huong et al. / Journal of Science: Advancproperties 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 anti- ferromagnetically ordered in case the number ofmagnetic neighbors at the a sites surrounding amagnetic ion in the d sublattice exceeds a , 0.6). The inset shows the highest intensity peaks (420). ed Materials and Devices 5 (2020) 270e277 271concentration 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 ¼ Sc3þ, Zr3þ, and In3þ at the a sublattice with the following general formula: Y3[Fe2
xRx]Fe3O12. The results show that the samples are ordered ferrimagnetically in the con- centration region 0  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 the collinear N
eel configuration because of the spin canting in the d sublattice. As the concentration increases beyond ~0.7, the degree of canting abruptly changes and, consequently, the antiferromag- netic phase dominates with the net moment decreasing to zero at x¼ 1. Thiswork focuses on the ferrimagnetic phases of Y3Fe3
xInxO12 with 0  x  0.7. The saturation magnetizations in a wide temper- ature range (minimum value of 5 K) and the Curie temperatures of these compositions are collected. Their spinwave stiffness constants are evaluated on the basis of exchange constants and sublattice magnetizations derived from the molecular field theory. 2. Experimental 2.1. Sample preparation Y3Fe5
xInxO12 particle samples (x ¼ 0e0.7, step 0.1) were pre- paredusing the solegelmethod in accordancewith 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 1 M HNO3 to form nitrate solutions. The vibrating sample magnetometer (ADE Technology-DMS 5000) at 80e600 K. In both facilities, the maximum applied magnetic field was 10 kOe. 3. Results and discussion 3.1. Crystal structure and morphological characteristics 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. 1. 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 pa- rameters, including the lattice constant A and the average bond V.T. Hoai Huong et al. / Journal of Science: Advanced Materials and Devices 5 (2020) 270e277272metal nitrate solutions were mixed with the required amount of metal ions at a stoichiometric ratio of [Y]:[Fe]:[In] ¼ 3:(5
x):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 2 h and annealed at Tan ¼ 900 C for 5 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. Datawere analyzed using the Rietveldmethod 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 JSM- Fig. 3. FESEM images of the Y3Fe5-xInxO12 samples with x ¼ 0, 0.1, 0.3, and 0.7.7600 F) was adopted to examine particle sizes and morphological characteristics. Magnetization curves in the temperature range from 5 K to room temperature were measured using a superconducting quan- tum interference device (Quantum Design) with magnetic fields of up to 10 kOe. The magnetic characteristics were also studied with a Fig. 4. Magnetization curves measured at 5 K and 2lengths between cations in d, a, and c sites and oxygen (ddeO, daeO, and dceO), were determined via the Rietveld refinement. The in- crease in lattice constant can be ascribed to the larger atomic radius of In compared to Fe. In the octahedral a sites, the radius of Fe3þ (rFe3þ ¼ 0.785 Å) is smaller than that of In3þ (rIn3þ ¼ 0.94 Å) [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 Rietveldmethod 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 1. Themean crystallite sizes are in the range of 20e25 nm. The increase in the average microstrain with increasing x can be un- derstood 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. 3. 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.90 K of the Y3Fe5
xInxO12 samples (x ¼ 0e0.7). 3.2. Magnetic properties The magnetization curves MeH of the investigated samples were measured at different temperatures. For demonstration, the MeH curves recorded at T ¼ 5 K and 290 K are displayed in Fig. 4. 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 suscepti- bility. Themagnetization 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 momentsmexp were calculated in Bohr magneton per formula unit. The saturation magnetic moments of the samples at 5 K as a function of indium concentration are presented in Fig. 5, and the values are listed in Table 2. The saturation magnetization monot- onously increases as the substitution level increases, indicating that In atoms mostly reside in a sites, which belong to the weak magnetization sublattice. Fig. 5 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 (Sc3þ, Zr3þ, In3þ) reported by Geller [14] and Gilleo [15]. m(x) versus x dependence follows the expression m(x) ¼ 5 þ 4.05*x. (1) m(x) in Eq. (1) is lower than that in the collinear N
eel configuration, i.e., m(x) ¼ 5 þ 5*x, because of the spin canting in the d sublattice. Fig. 5. Magnetic moment, mexp, at 5 K of the samples as a function of the In concen- tration, x. The solid line represents the calculated values according to Eq. (1). Table 2 Curie temperature (TC), experimental magnetic moment at 5 K (m(5)exp) and calculatedmagnetic moment at 0 K (m(0)cal), and estimated indium contents at the a sites and d sites of the Y3Fe5
xInxO12 series. x TC (K) M (5 K)exp (mB/f.u.) In3þ at a sites In3þ at d sites 0 564 4.9 0 0 0.1 540 5.4 0.1 0 0.2 522 5.8 0.2 0 0.3 510 5.97 0.273 0.027 0.4 484 6.35 0.37 0.03 0.5 466 6.84 0.48 0.02 0.6 450 7.3 0.586 0.014 0.7 433 7.65 0.68 0.02 Fig. 6. Spontaneous magnetization Ms as a function of temperature for the samp V.T. Hoai Huong et al. / Journal of Science: Advanced Materials and Devices 5 (2020) 270e277 273The magnetic moments of the samples agree with those derived using Eq. (1), although their values are slightly lower (<4%) than the expected values for some of the samples. This deviation can be attributed to a small amount of nonmagnetic impurity in these samples, or to a fraction of In atoms (<0.03 atoms per formula unit)les x ¼ 0, 0.2, 0.5, 0.7. The solid lines are the molecular field fitting results. Fig. 7. Temperature dependence of magnetization measured in an applied field, H ¼ 100 Oe, for the Y3Fe5
xInxO12 samples (x ¼ 0e0.7). Fig. 8. Curie temperatures TC of the Y3Fe5
xInxO12 samples (x ¼ 0e0.7). Solid square: experiment; line: calculated results (see text). vancthat occupy the a sites. Thus, the cation distribution in this sample series can be approximately expressed as {Y3}[Fe2
xInx](Fe3)O12. To justify this derivation, we reproduced the corresponding SXRD patterns by using the FullProf program. In the calculations, the cation distribution model was constructed with the following atomic coordinations: Y is in the dodecahedral site 24c (1/8,0,1/4), Fe/In in the octahedral 16a (0,0,0) and tetrahedral 24d (3/8,0,1/4) sites, and O in the 96h position (x, y, z). The O position parameters were fixed at the values determined on the basis of neutron diffraction data [1]. The calculated results agree with the experi- mental findings with a goodness of fit (c2) in the range of 1.13e1.68 and theweighted profile R-factor (Rwp) in the range of 8.43%e11.3%. For demonstration, the SXRD pattern and the Rietveld refinement of the sample x ¼ 0.3 are shown in Fig. 2. The Curie temperature was determined (Table 2) on the basis of Ms expressed in emu per gram as shown in Fig. 6 for the sam- ples x ¼ 0, 0.2, 0.5 and 0.7. The thermomagnetic measurements in the low field (H ¼ 100 Oe) were also determined (Fig. 7). TC extracted from the curves agrees with those determined using Ms versus T curves. Gilleo [15] predicted the evolution of the Curie temperature for magnetically diluted YIG series by using a simplified model based on the number of magnetic interactions pairs. A comparison between the experimental and calculated values is shown in Fig. 8. An agreement between the two sets of TC values is observed showing the dominance of the intersublattice magnetic interaction Jad over the intrasublattice interactions JaaV.T. Hoai Huong et al. / Journal of Science: Ad274and Jdd in establishing the magnitude of the magnetic ordering temperature. 3.3. Molecular field calculations Dionne [2] calculated the Ms versus T curve of YIG and its nonmagnetic substituted derivatives through a molecular field approximation. The intrasublattice and intersublattice interactions between the magnetic moments in the a and d sublattices are characterized by Naa, Ndd, and Nad, respectively. Dionne [2] exam- ined the magnetization curves of various compositions with the general formula Y3[Fe2
uRu](Fe3
wQw), where the results for nonmagnetic elements R and Q are Sc4þ, Sn4þ, Zr4þ, In3þ, Al3þ and Ga3þ; revealed linear relations of the exchange parameters with the nonmagnetic ion concentrations of the a and d sublattices for u  0.70 and w  1.95 (for further details, see [2]). In a random distribution assumption, the average microscopic exchange in- tegrals are related to the molecular field coefficient Nij as follows [20]:ed Materials and Devices 5 (2020) 270e277 ¼ 4pnjgigjm2B 2Zij 1 4p A3NA 8 ! Nij; (2) where nj and gj are the number of Fe ions and spectroscopic split- ting factor in the j sublattice, respectively; zij is the nearest neighbor; A is the lattice constant; and NA is Avogadro's number. Molecular field calculations were performed for the sample series to further investigate the influence of In substitution in the magnetic interactions. According to the derived cation distribution, the In concentration at the d sublattice is set to zero (w ¼ 0). In the calculations, the effect of spin canting in the d sublattice was Fig. 9. Intra- (a) and intersublattice (b) molecular field coefficients, Ndd and Nad, respectively, of the samples as a function of the In concentration x. The solid lines are the corresponding values calculated from the rules derived by Dionne [2]. considered. The sublattice magnetizations per mole at 0 K, Ma(0), and Md(0) are determined as Ma(0) ¼ SagmBNA(2
x), Md(0) ¼ Ma(0) þ (5 þ 4.05*x)NA, (3) where Md(0) is derived from Eq. (1), Sa is the spin number of the magnetic ions in the a sublattice (S ¼ 5/2 for Fe), g is the spectro- scopic splitting factor