Itinerant-Electron Ferromagnetism in a Titanium-Rich Magnesium

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Itinerant-Electron Ferromagnetism in a Titanium-Rich Magnesium Titanate Ilmenite Solid Solution Y. Fujioka,* J. Frantti, and R. M. Nieminen Department of Applied Physics, Aalto University School of Science and Technology, P.O. Box 14100, FI-00076 AALTO Espoo, Finland ABSTRACT: Magnetization hysteresis loops and magnetic susceptibility were measured from Mg0.9Ti1.1O3 and Mg0.88Ti1.12O3 samples. The hysteresis loops revealed that the ferromagnetic transition occurs at or below 260 K. The magnetization did not reach saturation up to 70 kOe at 5 K. In contrast, stoichiometric MgTiO3, consisting of closedshell ions, does not exhibit magnetic ordering. Combined magnetic susceptibility measurements, X-ray diffraction, X-ray photoelectron spectroscopy, and spin-polarized density-functional theory computations show that the ferromagnetism is due to the conduction electrons, which are responsible for the semimetallic nature of the titanium-rich magnesium titanate Mg1-xTi1þxO3 solid solution. Excess Ti at the Mg-O cation layer results in a partially occupied band at the conduction band edge. This in turn shows that the magnetic properties can be controlled by a transition metal element substitution in a cation layer, which is a technological advantage.

1. INTRODUCTION The ABO3 ilmenite structure covers three different structure variants: ilmenite, corundum, and lithium niobate structure. The cation coordination is the same in each case, but whereas in the corundum structure both the A and B sites are occupied by the same elements (sapphire, Al2O3, being a well-known example), the A and B cations alternate in planes perpendicular to the hexagonal c-axis in the case of the ilmenite structure. In the case of the lithium niobate structure, the A and B cations are distributed in the planes perpendicular to the c-axis in such a way that no cation is bridged through two oxygens to another like cation.5 Thus, the cation ordering is the distinctive feature between the three structure variants and can be distinguished by diffraction techniques. MgTiO3 has the ilmenite structure with space group R3 in which basal planes, consisting of triangular networks of Mg2þ and Ti4þ ions, alternate along the hexagonal c axis. The ilmenite structure is shared in ternary oxide systems M2þTiO3 (M = Mn, Fe, Co, Ni) and is isostructural to the corundum (Al2O3) oxide family with the space group R3c. Magnetic ordering in stoichiometric M2þTiO3 (M = Mn, Fe, Co, Ni) and Ti2O3 is reported to be antiferromagnetic, although the susceptibility of MnTiO3 shows anomalous temperature dependence6 suggesting that the true order is somewhat more complicated. A metal-insulator transition was reported to take place at around 250 K in Ti2O3.7 An early study of Ti2O38 indicates that the puckered sheets of Ti3þ, parallel to hexagonal (0001), are ferromagnetic with moments lying in the plane normal to the trigonal axis, and the adjacent cation sheets, separated by a layer of oxygen, have antiparallel moments. The magnitude of the moment is about 0.2μB per Ti3þ, and no evidence was found for a moment parallel to the hexagonal c-axis.8 This is in contrast to the many other antiferromagnetic ilmenites in which the magnetic moment was r 2011 American Chemical Society

reported to be parallel to the hexagonal c-axis.9 Because of the triangular cationic arrangement, magnetic ilmenite oxides are potentially spin-frustrated systems and indeed exhibit a variety of magnetic phenomena including metamagnetism10 and spin glass behavior.11 Magnesium titanate, MgTiO3, is a typical dielectric material with an optical band gap of 4 eV.1 MgTiO3 has been studied for microwave applications due to its high quality factor (Q-value).2 The stoichiometric MgTiO3 was reported to be paramagnetic in refs 3 and 4. MgTiO3 sintered in a reducing atmosphere becomes metallic.12 Interestingly, at low temperatures, below 30 K, the electrical resistivity was found to increase exponentially with decreasing temperature in the Ti-rich magnesium-titanate ilmenite. 13 This in turn suggests that it is worth checking the magnetic properties of nonstoichiometric MgTiO3. Varying the composition by introducing oxygen vacancies or by changing the Mg/Ti ratio could, in principle, affect the valence state of Ti. Further, understanding the origin of magnetism, notably whether it originates from localized states or from band magnetism, is crucial for applications. Here we show that, in contrast to the stoichiometric MgTiO3 possessing only closed shell (nonmagnetic) ions, solid solution Mg1-xTi1þxO3 exhibits itinerant-electron ferromagnetism.

2. EXPERIMENTAL SECTION Polycrystalline stoichiometric MgTiO3 was first prepared through the solid-state technique from MgO and TiO2 powders Received: August 14, 2010 Revised: November 22, 2010 Published: January 5, 2011 1457

dx.doi.org/10.1021/jp107698j | J. Phys. Chem. C 2011, 115, 1457–1463

The Journal of Physical Chemistry C

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Table 1. Structural Data, Reliability Factors, and Goodnessof-Fit Indicator for the Tested Modelsa sample

a

Mg0.9Ti1.1O3

a (Å)

5.05923(3)

c (Å) z(A)

13.9081(2) 0.35355(14)

Mg0.88Ti1.12O3 5.06209(5) 13.9102(3) 0.3511(2)

z(B)

0.1400

0.1400

x(O)

0.3085(4)

0.3088(7)

y(O)

0.0118(5)

0.0039(9)

z(O)

0.2435(2)

0.2465(4)

U(A)

0.0119(5)

0.015

U(B)

0.0131(3)

0.015

U(O) Rwp

0.0043(6) 21.77

0.015 19.83

Rp

15.98

15.43

χ2

3.392

3.609

In the case of the space groups symmetry R3, the A and B cations are at the position 6c (0, 0, z), and the oxygen was at the Wyckoff position 18f (x, y, z). In the case of Mg0.9Ti1.1O3 and Mg0.88Ti1.12O3, the minor MgO and brookite phase, respectively, was modeled, and the refined value for the mass fraction of the ilmenite phase was found to be 0.9746(9) (Mg0.9Ti1.1O3) and 0.9456(2) (Mg0.88Ti1.12O3). In the case of the Mg0.9Ti1.1O3 sample, individual isotropic atomic displacement parameters (ADPs) were refined for the ilmenite phase. In the case of the Mg0.88Ti1.12O3 sample, no reasonable ADP values could be refined and were fixed. During the refinements, the B cation position z(B) was fixed. Also, preferred orientation was tested but not found.

Figure 1. XRD pattern measured from the (a) Mg0.9Ti1.1O3 and (b) Mg0.88Ti1.12O3. Structural data were extracted by the Rietveld refinement. In panel (a), the upper and lower tick marks indicate MgO and R3 phases, respectively. In panel (b), the MgTi2O5 phase is indicated by upper tick marks. Pink line indicates the difference between the calculated and measured intensities. Only data between 15 and 70 2θ degrees are shown, though data collected up to 120 2θ degrees were used for the refinement. In panel (b), the hump of the background in the small 2θ region is from the glass sample holder.

in the molar ratio 1:1 sintered in air. MgO powder absorbs water, which was taken into account by weighing excess 10 wt % of the powder. Two Ti-rich magnesium-titanate samples were synthesized by a different route. One sample was obtained from further annealing of stoichiometric MgTiO3 in a sealed quartz tube with a titanium foil. The other sample was prepared from sintering in a sealed quartz tube the mixture of MgTiO3 and Ti2O3 (Aldrich, 99.9%) in the molar ratio 9:1. Composition analysis was carried out by energy dispersive spectroscopy of X-rays (EDS) using a W-cathode LEO 1450 SEM (Department of Materials Science and Engineering) and a JEOL JSM-7500FA Analytical FieldEmission Scanning Electron Microscope (Nanomicroscopy center), which indicated that the amount of titanium was larger than the amount of magnesium in both cases. Hereafter, the former and the latter samples are referred to as Mg0.9Ti1.1O3 and Mg0.88Ti1.12O3, respectively. Compositions refer to the values determined by EDS. Both samples were gray in color. For comparison, the two end members, stoichiometric MgTiO 3 (white in color) and Ti2O3 powders, were studied. Also a slightly

magnesium-deficient MgTiO3 pellet, gray in color, was studied. Rietveld refinements of XRD data were carried out using the GSAS14 and FP-Rietan Rietveld refinement program package.15 The profile function was a modified split pseudo-Voigt function, and the background was modeled by a 10th order polynomial. X-ray photoelectron spectroscopy (XPS) and time-of-flightsecondary-ion-mass-spectroscopy (ToF-SIMS) studies were carried out for Mg0.88Ti1.12O3 at Tascon GmbH. The purpose of the XPS experiments was to probe the impurity ion content and to address the issues related to cation valences. The detection limit of the XPS is of the order of 10-4. Since the issue of possible impurities is critical, also ToF-SIMS experiments, with a detection limit of 10-6, were carried out. The ToF-SIMS experiments were conducted to determine the spatial distribution of cations. Depth profiling was performed by removing the sample surface, layer by layer, by sputtering by Ceþ ions (sputter beam) and measuring the surface composition simultaneously by injecting Bi-cluster ions (analysis beam). Magnetization measurements were performed by a superconducting quantum interference device (SQUID) magnetometer (Quantum Design XL7). Zero-field-cooled (ZFC) and field-cooled (FC) runs were carried out over the temperature range from 10 to 300 K under various magnetic fields between 1 and 1000 Oe. Field-dependent magnetization data as a function of applied field up to 70 kOe were collected at various temperatures. It is crucial to estimate the residual magnetic field prior to and after each ZFC/FC susceptibility measurement. For this purpose, a small-field magnetization versus magnetic field curve of a paramagnetic material was measured, and the field value where M(H) = 0 was taken as the negative of the residual field value. Electronic-structure computations based on the density-functional theory within a generalized gradient approximation were 1458

dx.doi.org/10.1021/jp107698j |J. Phys. Chem. C 2011, 115, 1457–1463


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Figure 2. (a) Survey spectrum collected on the surface of the slightly magnesium-deficient MgTiO3 pellet. (b) A survey spectrum of the freshly broken slightly magnesium-deficient MgTiO3 pellet. (c) Mg0.88Ti1.12O3 powder. (d) MgTiO3 powder. Fresh surface, panel (b), shows only signals from Mg, Ti, and O and a hardly detectable amount of carbon (peak below 300 eV).

carried out using the VASP (Vienna Ab-initio Simulation Package)16 code employing the projected-augmented-wave (PAW) method.17,18 The valence states included 2s2p3s, 3p4s3d, and 2s2p for Mg, Ti, and O, respectively. The orthorhombic supercell corresponds to the two hexagonal unit cells doubled along the b-axis direction, with one Mg ion being replaced by Ti ion so that the chemical formula of the supercell was Mg11Ti13O36. The k-point mesh was 8 5 3. The energy cutoff value was 600 eV.

3. RESULTS AND DISCUSSION 3.1. Structural Model. The powder X-ray diffraction patterns, Figure 1, were typical to ilmenite structure (R3), though a trace amount of the MgO phase was revealed in the case of the Mg0.9Ti1.1O3 and a trace amount of brookite phase (MgTi2O5) was identified in the Mg0.88Ti1.12O3. Backscattering electron images observed by a scanning electron microscope confirmed this. Although the X-ray scattering cross sections of Mg and Ti cations are different and in principle allow one to find out the site occupancies, after trying a model in which the cation occupancies were refined, we decided to model the observed X-ray diffraction pattern by fixing the Mg and Ti cation content to the values found in the composition analysis. Consequently, the Mg/Ti ratio of the whole sample (consisting of the main ilmenite phase and a minor impurity phase) was constrained. Since there was an excess amount of Ti, we used a structural model where Ti cations were allowed to enter the Mg-O layer. The next point is to consider the valence of the Ti ions, which in the simplest model would be Ti2þ. However, in terms of the bond-valence model,19 this would require unrealistically long Ti-O bond lengths,

inconsistent with the experimental observations. The estimated lattice parameters are within 0.2% difference from the ones of stoichiometric MgTiO3 (a = 5.054 Å, c = 13.898 Å20). In ilmenites, Ti can appear both as a three-valent (possessing a magnetic moment) and four-valent (no local magnetic moment) ion. Figure 1 shows the XRD patterns together with the model summarized in Table 1. The B layer can have Ti in 3þ and 4þ states. The form factors of titanium ions at different valence states are slightly different at a small 2θ region. We tested models where the B layer was assumed to contain only Ti4þ cations and oxygen and then a model where the site was allowed to have Ti in both valence states. However, there was no discernible difference between the modeled intensities. In practice, there is no way of distinguishing the valence state of Ti from X-ray diffraction data. To determine the amount of impurities and to estimate the cation oxidation states, XPS experiments were conducted. 3.2. XPS Experiments. The spectra shown in Figure 2 revealed no signal from magnetic impurities. Weak carbon, potassium, phosphorus, and silicon signals were observed on the asprepared surface. They were not observed in the sputtered and not in the broken pellet, except for the hardly detectable amount of carbon, and thus they were assigned to be surface contamination. Also, a signal from Ar-ions was seen, which was due to the neutralization performed by injecting low-energy electrons and Ar-ions on the sample surface. This was confirmed by ToF-SIMS experiments.21 The magnesium photoemission peak was fit by two peaks (see Figure 3). The strongest feature was centered at 50.0 eV, whereas the weaker one was centered at 51.2 eV. Both features are typical 1459



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Figure 3. (a) Magnesium, (b) titanium, and (c) oxygen XPS spectra collected on the Mg0.88Ti1.12O3. Magnesium and oxygen spectra revealed two (at 50.0 and 51.2 eV) and three different bonding states (at 530.2, 531.5, and 532.6 eV), respectively, whereas Ti showed a single doublet (2p1/2 and 2p3/2 transitions at 464.4 and 458.7 eV, respectively), characteristically to compounds in which Ti is in the 4þ state.

for elemental Mg and Mg compounds.22 The oxygen spectrum revealed three peaks, located between 530 and 533 eV. The titanium spectrum revealed only a 2p1/2 and 2p3/2 doublet, where the latter peak was at 458.7 eV. This is a quite usual value for the titanium compounds in which the titanium oxidation state is 4þ (standard example being TiO2). The presence of Ti3þ ions would result in lower-energy peaks, 456.8 and 456.9 eV, being reported for Ti2O3. This is important for the forthcoming discussion. 3.3. Magnetic Measurements. First, the magnetic data of the end members of the solid solution, MgTiO3 and Ti2O3, are shown. Consistently with the earlier report,3 MgTiO3 behaved as a paramagnet down to the lowest measurement temperature (see Figure 4 (a)). Similarly, no sign of magnetic hysteresis was observed in Ti2O3, as Figure 4 (b) shows. This agrees with the earlier observations.8 Figures 4 (a) and 4 (b) also show that there is a very weak magnetization component, identified to be due to the sample holder, which saturates at around 1000 Oe. Figure 5 shows the mass magnetization versus field at temperatures between 5 and 300 K for Mg0.9Ti1.1O3. The inset (b) in Figure 5 shows that the hysteresis loop is slightly opened at 260 K, which indicates reversible magnetization consistent with the idea that the sample is ferromagnetic. The magnetization, however, did not show a saturation with external fields of up to 70 kOe at the lowest measurement temperature. Similar behavior was also found in Mg0.88Ti1.12O3 (see Figure 6), but transition temperature was somewhat lower than in the case of Mg0.9Ti1.1O3. Figure 7 shows the zero-field-cooled (ZFC) and field-cooled (FC) susceptibilities of the Mg0.88Ti1.12O3 and Mg0.9Ti1.1O3 samples. We note that the aforementioned secondary MgO (Mg0.9Ti1.1O3) and MgTi2O5 (Mg0.88Ti1.12O3) phases contribute to the paramagnetic background. To confirm that the observed hysteresis is a real phenomenon, we carried out a test measurement at 10 K with a sample holder alone to determine the background signal. The difference between the magnetization before applying the 5 T field and the magnetization after applying the -5 T field was 5 10-7 emu. For comparison, the corresponding difference for the Mg0.9Ti1.1O3 (mass 62 mg) was 1.7 10-3 emu. Thus, the ratio between the magnetization values is roughly 3000, and the hysteresis observed in samples Mg0.88Ti1.12O3 and Mg0.9Ti1.1O3 indeed originates from the samples themselves.

Figure 4. Temperature dependence of the susceptibility per mass [M/(Hm) where m is the sample mass] measured at ZFC (blue marks) and FC (red marks) cycles between 2 and 300 K measured from (a) the preannealed stoichiometric MgTiO3 and (b) Ti2O3 powders. The samples are paramagnetic down to the lowest measurement temperature. Insets illustrate the field dependence of the magnetization at 5 K.

3.3.1. Testing the Localized Magnetic Moment Model. In addition to the structural model specified in Table 1, a model in which the excess titanium ions (with valence þ3) were in the Mg-layer (A-cation layer) was tested by the FP-Rietan Rietveld 1460



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Figure 5. Hysteresis loops measured at 5, 10, and 300 K temperatures from Mg0.9Ti1.1O3. Data show that the sample behaves as a paramagnetic material at 300 K and possesses reversible net magnetization at lower temperatures. Inset (a) shows that at 5 K the magnetization is not saturated at 70 kOe. The inset (b) shows the evolution of magnetization in the vicinity of the phase transition, showing that a small magnetization has already developed at 260 K.

Figure 6. Hysteresis loops measured at 100, 200, and 300 K temperatures from the Mg0.88Ti1.12O3 sample. The behavior is similar to the data shown in Figure 5.

refinement program. We allowed vacancy forming at the A-cation layer and also refined the magnesium and titanium contents. The refinement resulted in a composition of (Mg0.772þTi0.113þ)Ti4þO3 for the Mg0.9Ti1.1O3 sample. The measured magnetization values can now be compared to the values based on the localized magnetic moment model. Taking the refined structural parameters (not shown) and assuming that the orbital angular momentum is quenched, we could estimate that the saturated net magnetic moment due to the localized spin moments of Ti3þ ions (S = 1/2) per mass would be roughly 30 times the measured value. There are now two routes to take to explain the observed

Figure 7. Temperature dependence of the susceptibility per mass [M/(Hm) where m is the sample mass] of the Mg0.9Ti1.1O3 (red marks) and Mg0.88Ti1.12O3 (blue marks) in ZFC (solid line) and FC (dashed line) runs. The data on the Mg0.9Ti1.1O3 and Mg0.88Ti1.12O3 samples were measured with the field of 6 and 10 Oe, respectively.

phenomenon. The first is to assume that only a fraction of the sample is ferromagnetic, for instance, due to the segregation of magnetic impurities on pore walls (ferromagnetic regions in a paramagnetic matrix). The second is to look for an entirely different explanation for the phenomenon yet still assuming that the ferromagnetism is spatially homogeneous. The first picture would keep the localized spin moment picture, whereas the other 1461



Figure 8. Orthorhombic supercell used for the electronic energy band structure computations. The cell corresponds to doubling of the cell along the hexagonal b-axis direction. In the second half of the supercell, one Mg was replaced by a Ti ion. Though it is customary and illustrative to use the hexagonal cell in crystallographical context, an orthorhombic cell was used for computational convenience.

model would assume a homogeneous distribution of magnetic moments over the phase responsible for the ferromagnetism and would not require one to invoke two phases; in other words, the first phase would possess the localized Ti3þ regions, whereas the other would not. Thus, it is important to check if either of the models is valid, and now the XPS and ToF-SIMS experiments have a determining role. Taking into account the XPS results, we discard the model explaining the magnetic properties by the localized spin moments of Ti3þ ions; no titanium in a 3þ valence state was observed, and thus we look for the model belonging to the second class. We note that in a metal or itinerant ferromagnetic material, the low-temperature (T f 0 K) magnetization keeps increasing above the saturation magnetization level (MS) so that the magnetization is of the form M(H) = MS þ χhfH, where χhf is the high-field susceptibility.23 The origin of the linear term is that with increasing field the number of electrons contributing to the net magnetization (difference between the number of spin up and down electrons) is increasing. Thus, the high-field behavior depends on the electronic energy band structure. It is also worth mentioning that no abrupt transition as a function of temperature was observed, which also is characteristic to the itinerant ferromagnetism; changes in the occupation of electronic states occur in a continuous manner. 3.4. Electronic Structure Calculations. To test the model based on itinerant electrons, electronic energy band structure calculations were carried out. To characterize the role of excess Ti, a supercell was constructed (see Figure 8). Both nonspinpolarized and spin-polarized computations were performed. For comparison, the calculations were also carried out for a stoichiometric compound. The nonspin-polarized computations revealed a large band gap of 3 eV and an excess Ti-generated state at the conduction band edge. These states were occupied, indicating that the material is a semimetal. To provide a more reliable estimation of magnetization, spin-polarized band structure was determined. The resulting density-of-states is shown in Figure 9 for both spin-up and spin-down states. As is seen, there are no states within the band gap; the band due to the Ti

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Figure 9. Density of states of Mg11Ti13O36 for a ferromagnetic structure. Fermi level, indicated by the dotted line, was put to zero. Positive (negative) DOS values correspond to the spin-up (spin-down) cases. Total DOS is indicated by the black line.

substitution for Mg in the Mg-O layer is located in the conduction band. The lowest part of the conduction band edge corresponds to the spin-up states and is partially occupied, which demonstrates that the reversible magnetization is due to the unpaired electrons. From density-functional-theory computations, the ground-state magnetic moment for the Mg11Ti13O36 compound was found to be 1.3μB per supercell. The calculations give a qualitative explanation for the magnetic properties of this system.

4. CONCLUSIONS We have shown that ilmenite magnesium titanates (Mg1-xTi1þxO3) possess reversible magnetization at or below 260 K. We tested a model in which the excess Ti enters the A-cation layer and found that it gave satisfying agreement with experimental results. Though a model where Ti has a 3þ valence adequately describes the X-ray diffraction data, the local magnetic moments alone do not explain the measured magnetization values nor XPS results showing that the valence state of Ti was 4þ, which suggests that the true origin of magnetization is related to the magnetization caused by conduction band edge electrons due to the excess Ti. The electronic-energy band structure calculations were in qualitative agreement with the experiments. Present results show that the cation substitution is a practical technological way to control magnetization in ilmenites. By selecting different 3d transition metal cations, the resulting band can be either kept within the band gap (corresponding to a localized magnetic moment) or pushed into a conduction band (itinerant electron case). The first challenge is to control the layer the substitute cation is to enter, and the second is to control the coupling between the magnetic moments. The present choice of cations shows that one can gradually switch the material from the paramagnetic MgTiO3 to a ferromagnetically ordered Mg1-xTi1þxO3 solid solution. This is particularly useful for making thin-film components, as the abrupt interfaces can be avoided. ’ AUTHOR INFORMATION Corresponding Author

*E-mail:yukari.fujioka@hut.fi. 1462



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’ ACKNOWLEDGMENT We thank A. Savin (Aalto University, AU) for his help in operating the magnetometer and E. Heikinheimo of Department of Materials Science and Engineering (AU) for analyzing the sample composition. The XPS experiments were carried out together with B. Bock and H. Hebert at Tascon GmbH. We carried out the X-ray diffraction measurements at the Inorganic Chemistry laboratory (AU). The Finnish IT Center for Science provided the computation platform. Y.F. is grateful for the Finnish Cultural Foundation for financial support. This project was supported by the Academy of Finland (Project Nos 207071 and 207501) and the Centre of Excellence Program 2006-2011. ’ REFERENCES (1) Ferri, E. A. V.; Sczancoski, J. C.; Cavalcante, L. S.; Paris, E. C.; Espinosa, J. W. M.; de Figueiredo, A. T.; Pizani, P. S.; Mastelaro, V. R.; Varela, J. A.; Longo, E. Mater. Chem. Phys. 2009, 117, 192. (2) Ferreira, V. M.; Azough, F.; Baptista, J. L.; Freer, R. Ferroelectrics 1992, 133, 127. (3) Ishikawa, Y.; Akimoto, S. J. Phys. Soc. Jpn. 1958, 13, 1298. (4) Breitbarth, F. W.; Feltz, A.; Steinbr€uck, M. Phys. Status Solidi A 1991, 127, 253. (5) Navrotsky, A. Chem. Mater. 1998, 10, 2787. (6) Stickler, J. J.; Kern, S.; Wold, A.; Heller, G. S. Phys. Rev. 1967, 164, 765. (7) Morin, F. J. Phys. Rev. Lett. 1959, 3, 34. (8) Abrahams, S. C. Phys. Rev. 1963, 130, 2230. (9) Shirane, G.; Pickart, S. J.; Ishikawa, Y. J. Phys. Soc. Jpn. 1959, 14, 1352. (10) Kato, H.; Yamada, M.; Yamauchi, H.; Hiroyoshi, H.; Takei, H.; Watanabe, H. J. Phys. Soc. Jpn. 1982, 51, 1769. (11) Adachi, K. Magnetism of Compounds: Localised Spin System; Shokabo : Tokyo, 1996 (in Japanese). (12) Vigreux, C.; Deneuve, B.; El Fallah, J.; Haussonne, J. M. Electroceramics 2000, 21, 1681. (13) Sheikh, A. B.; Irvine, J. T. S. J. Solid State Chem. 1993, 103, 30. (14) Larson, A. C.; Von Dreele, R. B. General Structure Analysis System. LANSCE MS-H805; Los Alamos National Laboratory: Los Alamos, NM, 2000. (15) Izumi, F.; Momma, K. Solid State Phenom. 2007, 130, 15. (16) Kresse, G.; Furthm€uller, J. Comput. Mater. Sci. 1996, 6, 15. (17) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953. (18) Kresse, G.; Joubert, J. Phys. Rev. B 1999, 59, 1758. (19) Brown, I. D. The Chemical Bond in Inorganic Chemistry: The Bond Valence Model; Oxford University Press: Oxford, 2002. (20) Rohrer, G. S. Structure and Bonding in Crystalline Materials; Cambridge University Press: Cambridge, 2001. (21) ToF-SIMS experiments were carried out to study the homogeneity of the samples. Notably, we wanted to confirm that there is no segregation of cations at grain boundaries or pores. The depth profiling revealed that the composition was homogeneous. The experiments also confirmed that the observed magnetization cannot be due to the impurities. (22) Moulder, J. F.; Stickle, W. F.; Sobol, P. E.; Bomben, K. D. Handbook of X-ray Photoelectron Spectroscopy; Perkin-Elmer Corporation, MN, 1992. (23) Adachi, K. Magnetism of Compounds: Itinerant Electron System; Shokabo: Tokyo, 1996 (in Japanese).

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Itinerant-Electron Ferromagnetism in a Titanium-Rich Magnesium

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