Cr-Doped TiSe 2 − A Layered Dichalcogenide Spin Glass

Article pubs.acs.org/cm Cr-Doped TiSe2 − A Layered Dichalcogenide Spin Glass Huixia Luo,*,† Jason W. Krizan,† Elizabeth M. Seibel,† Weiwei Xie,† Girija S. Sahasrabudhe,† Susanna L. Bergman,† Brendan F. Phelan,† Jing Tao,‡ Zhen Wang,§ Jiandi Zhang,§ and R. J. Cava*,† † Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973, United States § Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, United States ‡ ABSTRACT: We report the magnetic characterization of the Cr-doped layered dichalcogenide TiSe2. The temperature dependent magnetic susceptibilities are typical of those seen in geometrically frustrated insulating antiferromagnets. The Cr moment is close to the spin-only value, and the Curie−Weiss temperatures (θcw) are between −90 and −230 K. Freezing of the spin system, which is glassy, characterized by peaks in the ac and dc susceptibility and specific heat, does not occur until below T/θcw = 0.05. The CDW transition seen in the resistivity for pure TiSe2 is still present for 3% Cr substitution but is absent by 10% substitution, above which the materials are metallic and p-type. Structural refinements, magnetic characterization, and chemical considerations indicate that the materials are of the type Ti1−xCrxSe2‑x/2 for 0 ≤ x ≤ 0.6. occupy the interstitial octahedral sites in the van der Waals layers, but at higher concentrations they occupy both the octahedral interstitial sites and sites in the Ti layers; when they do that they then displace some Ti into the interstitial positions and the system becomes quite disordered. (The materials system is complex: previous studies25,26 of Cr-intercalated TiSe2 yielded magnetic properties that are significantly different from those that are observed here, implying that the magnetic behavior of the system may be dependent on synthetic conditions.) Cr ions most frequently are ionic and have the oxidation state Cr3+ in solids due to their very strong Hundsrule coupling.27 In a material like TiSe2, which is a small band gap semiconductor with a conduction band made from empty Ti d states and a valence band made from filled Se p states (i.e., consisting of Ti4+ and Se2−), the presence of Cr3+ along with Ti4+ and Se2− requires a decrease in the Se to metal ratio to below 2:1 and a formula Ti1−xCrxSe2‑x/2 to maintain charge neutrality. Our XPS analysis supports these formal oxidation state assignments. This picture for Cr-doped TiSe2 is further supported by the materials synthesis, the diffraction data, the magnetic data, and the presence of two types of magnetic spins clearly seen in the ac susceptibility for higher x materials. The DC magnetic susceptibilities confirm that the Cr moments in Ti1−xCrxSe2‑x/2 are within experimental error of the expected Cr3+ spin-only value.28 The antiferromagnetic Curie−Weiss temperatures are large, between −90 and −230 K. The freezing INTRODUCTION Frustration of magnetic ordering arises in both atomically disordered systems and systems where the magnetic interactions are not compatible with the underlying structural symmetry.1−5 Classical spin glasses and systems with magnetic ions on triangular or tetrahedral lattices display such frustration. The most-often-studied materials with strong geometric magnetic frustration are electrically insulating or at best strongly semiconducting,5−16 and classical spin glass systems can be either metallic or semiconducting.17 Typically, frustrated magnetic materials are characterized by a Curie−Weiss theta θcw that is significantly greater than the spin freezing temperature Tf. The frustration index f = θcw/Tf is often taken as a general characterization of the degree of frustration. The MX2 layered transition-metal dichalcogenides (TMDCs, M = Mo, W, V, Nb, Ta, Ti, Zr, Hf, and Re, and X = Se, S, or Te) are a large family of solids with layered triangular metal lattices and have long been of interest due to the rich electronic properties that arise from their low dimensionality (see, e.g. refs 18−22). Within the TMDCs, 1T-TiSe2 has attracted special attention due to the presence of a Charge Density Wave (CDW) that onsets at 200 K.22,23 The material has trigonal symmetry,24 with TiSe6 octahedra sharing edges in triangular geometry TiSe2 layers that are bonded to each other by Se−Se van der Waals forces (Figure 1a). Here we study the effect of Cr substitution for Ti in 1T-TiSe2. We find that as Cr atoms are substituted for Ti, they induce metal occupancy in the van der Waals gap between the TiSe2 layers (Figure 1a). We interpret our data to indicate that at concentrations less than about 20%, the Cr ions primarily ■ © 2015 American Chemical Society Received: August 11, 2015 Revised: September 16, 2015 Published: September 17, 2015 6810 DOI: 10.1021/acs.chemmater.5b03091 Chem. Mater. 2015, 27, 6810−6817 Chemistry of Materials Article Figure 1. Structural and spectroscopic characterization of 1T-Ti1‑xCrxSe2‑x/2. (a and b) The overall crystal structure of 1T-TiSe2 (a), (b) Composition dependence of the room temperature lattice parameters a and c for Ti1−xCrxSe2‑x/2 (0 ≤ x ≤ 0.6), (c) and (d) refined powder Xray diffraction data for the two structural models for Ti0.4Cr0.6Se1.7. The superioriy of the model for metal interstitials (Model 2) over selenium vacancies (Model 1) is seen through comparison of the difference plots. Regions of interest are marked by circles. (e-h) XPS spectra of the Ti 2p, Cr 2p, and Se 3d regions of selected Ti1−xCrxSe2‑x/2 (x = 0.07, 0.6) materials. Vertical red lines indicate the positions for the Ti4+, Se2−, and Cr3+ species in the bulk material. For comparison, the Se 3d spectrum for single crystal Bi2Te2Se is included in (h). and heated in sealed evacuated quartz glass tubes at 700 °C for 72 h. Subsequently, the as-prepared powders were reground, repelletized, and sintered again at 700 °C for 48 h. Powder X-ray diffraction (PXRD, Bruker D8 Advance ECO, Cu Kα radiation) was initially used to structurally characterize the samples. Excess elemental selenium was present in all the synthesis tubes and easily separated from the sample pellets by sublimation. The presence of the excess Se in the system indicated that the Se:M ratio of the obtained products was less than 2:1, as described further below. Single phase powder samples (after the excess Se was distilled away) were studied by synchrotron X-ray diffraction at the Advanced Photon Source at Argonne National Laboratory on beamline 11-BM. All diffraction patterns were refined using the Rietveld method in the Fullprof software suite.29 The DC magnetization (M) as a function of applied magnetic field (H) was linear for all samples up to applied fields of μ0H = 1 T above the spin glass ordering temperature, and thus the magnetic susceptibility χ was defined as χ = M/μ0H at 1 T. Zero-field cooled of the spin system, characterized by peaks in the ac and dc susceptibility, occurs between about 2 and 12 K. Resistivity and hall effect measurements on polycrystalline pellets show the suppression of the CDW state in TiSe2 for low values of Cr substitution and metallic, p-type conductivity at higher levels of substitution. The complexity of the material system precludes the determination of a detailed model for the magnetism at this stage, but the general features are well described by a picture of magnetic disorder on a triangular lattice. ■ EXPERIMENTAL SECTION Polycrystalline samples of target composition Ti1−xCrxSe2 were synthesized by solid state reaction. Mixtures of high-purity fine powders of Ti (99.9%), Cr (99.95%), and Se (99.999%) in the appropriate stoichiometric ratios were thoroughly ground, pelletized, 6811 DOI: 10.1021/acs.chemmater.5b03091 Chem. Mater. 2015, 27, 6810−6817 Chemistry of Materials Article (ZFC) dc magnetization measurements to obtain χ were performed on heating from 1.8 to 300 K in a magnetic field of 1 T in a Quantum Design superconducting quantum interference device (SQUID) equipped Magnetometer (MPMS-XL-5). Temperature dependent magnetizations for selected high Cr content samples were also measured in the MPMS with an applied field of 200 Oe to allow the observation of the bifurcation of the zero field cooled and field cooled magnetizations at the spin freezing transition. Measurements of the temperature dependence of the electrical resistivity, ac magnetic susceptibility, and heat capacity were performed in a Quantum Design Physical Property Measurement System (PPMS). Resistivities and heat capacities below 2 K for selected compositions were measured in the PPMS equipped with a 3He cryostat. The nonmagnetic analogue TiSe2 was synthesized and used for the subtraction of the phonon contribution to estimate the magnetic contribution to specific to the specific heat for the Cr-doped TiSe2 materials. X-ray Photoelectron Spectroscopy (XPS) characterization was performed with a VG ESCA Lab Mk.II instrument. All spectra were obtained using Mg Kα radiation (1284 eV) and 20 eV pass energy. The sample powder was placed on carbon tape attached to the metal sample holder. To avoid charging effects during XPS, a positive bias of 10 V was applied to the holder during spectral acquisition.30,31 Spectra were taken for polycrystals of Ti0.93Cr0.07Se1.965, Ti0.75Cr0.25Se1.875, Ti0.4Cr0.6Se1.7, and single crystal Bi2Te2Se (BTS). The Se 3d XPS for single crystal BTS was used for calibration purposes. All scans were taken with a 0.05 eV step size and 0.5 s dwell time. The obtained scans were fit with the Casa XPS software using a Shirley background; area and positions were constrained using standard values. Specimens for transmission electron microscopy (TEM) were obtained from synthesized samples crushed in a drybox and transported to the microscope in ultrahigh vacuum. Scanning TEM (STEM) in high-angle annular dark-field (HAADF) mode, energydispersive X-ray spectroscopy (EDXS), electron energy-loss spectroscopy (EELS), selected area electron diffraction (SAED), and highresolution TEM (HRTEM) were conducted in a JEOL 2100F microscope equipped with a liquid-helium cooled sample holder at Brookhaven National Laboratory. intercalation corresponds to the value appropriate to the material composition. The superiority of this model for describing the structures of the Ti1−xCrxSe2‑x/2 materials is clearly seen by comparison of Figures 1c and 1d. The fits to the synchrotron X-ray pattern for Ti0.6Cr0.4Se1.8 for the interstitial occupancy model (full metal site occupancy in the Ti layer by both Ti and Cr, interstitial ions, and no selenium vacancies) and the alternative Se vacancy model model (full metal site occupancy in the Ti layer by both Ti and Cr, no interstitial ions, and selenium vacancies) are compared. At higher Cr contents than those studied here, the related compound Cr4TiSe8 has been reported to have two magnetic transitions, at Tf = 50 K and TN = 120 K.34 In our magnetic measurements, we did not see those transitions in any samples (see Figure 3) indicating that this compound is not present as an impurity in our materials. The diffraction data analysis, the requirements of charge neutrality, and the presence of excess Se in the synthetic system indicate that the best way to represent the composition of the fabricated compounds is Ti1−xCrxSe2‑x/2, which we use here. (An equivalent, though more complex formula reflecting the observed crystal structure, which shows the presence of both interstitial metal atoms and full Se site occupancy, would be Cry/3(Ti1−yCry)Se2, where the leading Cr is intercalated and the metal atoms in parentheses are those in the normal dichalcogenide layers; the relation between this and the simpler formula employed here is [y + y/3]/[1+y/3] = x.) X-ray photoelectron spectroscopy (XPS) was performed on Ti1−xCrxSe2‑x/2 (x = 0.07, 0.25, and 0.6) to compare the effects of Cr doping on the oxidation state of Ti and Cr. The XPS of Ti 2p (Figure 1e) shows the presence of two Ti species. The Ti 2p3/2 peak at 458.7 eV, corresponding to TiO235,36 is an indication of the oxidation of the surface of the polycrystals from exposure to ambient conditions, while the Ti 2p3/2 peak at 455.5 eV originates from the bulk material.36,37 The remaining two peaks (Ti 2p1/2), at 464.9 and 461.7 eV, are the result of spin orbit coupling. Similarly, the XPS of Cr 2p (Figure 1f) shows two Cr 2p3/2 peaks: The peak at 576.0 eV corresponds to Cr2O3 formed due to air oxidation,38,39 while the second peak at 573.7 eV is representative of the bulk material.40 The 2p1/2 peaks are located at 586.2 and 584.0 eV. The Se 3d XPS (Figure 1g), when deconvoluted using standard restriction parameters, indicates the presence of two major Se species. The Se 3d peak at 53.2 eV originates from the bulk material, while the peak at 54.3 eV is the result of surface oxidation in air. The binding energies of Ti, Cr, and Se for the bulk material were calibrated using the Se XPS of single crystal BTS (Figure 1h). Due to the layered structure of single crystal BTS,35 the Se is never exposed to air which prevents oxidation. As the XPS of single crystal BTS exhibits only one Se species with a well-defined Se 3d peak (fwhm =1.6 eV) at 53.2 eV, it makes a reliable calibration standard. We find that the binding energies of Ti and Cr in the bulk do not change with the chromium doping level. This observation corroborates well with other measurements. Thus, the XPS characterization of the Ti1−xCrxSe2‑x/2 materials over a wide range of x spectroscopically confirms the formal Cr3+, Ti4+, and Se2− oxidation state assignments. For more detailed structural characterization, in order to check for possible Cr clustering, deviation from random subsititution, short-range Cr−Ti ordering, or nanoscale precipitates in Cr doped TiSe2, which would impact the magnetism of the system, high-resolution transmission electron microscopy (HRTEM) was used to examine one of the high Cr content materials, Ti0.6Cr0.4Se1.8. Figure 2a shows the crystal RESULTS AND DISCUSSION Figure 1b shows the composition dependence of the room temperature lattice parameters for Ti1−xCrxSe2‑x/2 (0 ≤ x ≤ 0.6). x = 0.6 is the high Cr composition limit of the intercalated TiSe2-like solid solution. Surprisingly, for 0 ≤ x ≤ 0.2, a decreases slightly and c decreases slightly. For x ≥ 0.2, in contrast, the unit cell parameter a increases with Cr content, and c decreases more quickly. Thus, for Cr-doped TiSe2, the composition-dependent unit cell parameters do not follow Vegard’s law. This is the fundamental characteristic showing that there is a change in the structure of the system near x = 0.2. The complexity is due to the way that the Cr atoms are accommodated in the structure−on Cr substitution extra metal atoms are found in the van der Waals gap between in the layers, as described below. At low Cr doping levels, the powder diffraction data were not very sensitive to the presence of intercalated metals,32 but for the higher Cr doping levels, quantitative tests of different structural models were possible. In these tests we observed clearly that the Se sites are fully occupied. This is consistent with what has been found for all layered dichalcogenides of the type MxMX2 where the X:M ratio is less than 2:1; on doping, metal interstitials are found in the van der Waals gap rather than vacancies in the close packed chalcogen planes.33 Further, free refinement of the occupancy of the interstitial metal sites led to occupancies that were within the standard error of expectations for the nominal compositions. Thus, we conclude that Se sites are fully occupied and that the level of metal ■ 6812 DOI: 10.1021/acs.chemmater.5b03091 Chem. Mater. 2015, 27, 6810−6817 Chemistry of Materials Article Figure 2. High-resolution transmission electron microscopy (HETEM) characterization of 1T-Ti0.6Cr0.4Se1.8 showing the random Ti−Cr Solid Solution (a) crystal model in the [100] zone; (b) and (c) HAADF-STEM image in the [100] zone at different magnifications; (d) HAADF-STEM image in the [001] zone; (e)-(i) Electron energy loss spectroscopy (EELS) spectra (g-i) obtained at each pixel during scanning in the boxed area (e,f). Intensities of the core-loss edge of each element were integrated and mapped in the scanning area to show the elemental distribution at the atomic level. No segregation or short-range ordering of Cr was found. Ti0.6Cr0.4Se1.8, even at the atomic level. Therefore, there is a homogeneous random distribution of Cr within the structure. Figure 3a shows the zero-field cooled temperature (T) dependence, from 1.8 to 300 K, of the dc magnetic susceptibility (χ) for the Ti1−xCrxSe2‑x/2 polycrystalline samples. The plot of χ versus T in Figure 3a shows increasing χ with decreasing T for all samples, and the inset shows that the magnetic susceptibility increases linearly with Cr concentration at a fixed temperature; this is a qualitative indication of the fact that the Cr has a constant magnetic moment across the series. Figure 3b shows the character of the AFM transition under the relatively low applied field of 200 Oe. The antiferromagnetic (AFM) transition temperature increases with increasing Cr content for x ≤ 0.4. For higher Cr doping, however, the AFM transition, while still seen, becomes broad and poorly defined. Figure 4a shows the temperature dependent inverse susceptibilities, 1/(χ − χ0) vs T, constructed from the data shown in Figure 3a. In the high temperature region, above 200 K, all magnetic susceptibilities (χ) can be fit to χ − χ0 = C/(T − structure model for the [100] zone for this material, where the Ti/Cr atoms (gray balls) are in octahedral coordination with Se (yellow balls). Figures 2b and 2c show the HAADF-STEM image for the [100] zone at different magnifications, and the inset of Figure 2b, top, is the selected area electron diffraction (SEAD) pattern along a [100] zone axis. Figure 2d shows the HAADF-STEM image for the [001] zone, and the inset of Figure 2d on top is the SAED pattern in the [001] zone. The STEM-HAADF micrographs in Figure 2b-d as well as the SAED patterns reveal a homogeneous Cr distribution in Ti0.6Cr0.4Se1.8 at the atomic level; no clusters, short-range order, or nanoscale Cr-precipitates were observed. Figures 2d-i show the EELS spectra obtained at each pixel during scanning in the boxed area. Intensities of the core-loss edge of each element were integrated and mapped in the scanning area to show the Ti, Cr, and Se elemental distribution at the atomic level. The element maps images further confirm that there is no segregation, short-range ordering, or clustering of Cr in 6813 DOI: 10.1021/acs.chemmater.5b03091 Chem. Mater. 2015, 27, 6810−6817 Chemistry of Materials Article Figure 3. General magnetic characterization of Ti1‑xCrxSe2‑x/2 (a) Magnetic susceptibility (χ) versus temperature for Ti1−xCrxSe2‑x/2 (x = 0, 0.07, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6). Inset χ at 200 K vs x for Ti1−xCrxSe2‑x/2. (b) Normalized χ/χmax versus temperature in a 200 Oe field for Ti1−xCrxSe2‑x/2 (x = 0.25, 0.3, 0.4, 0.5, 0.6). Figure 4. Curie−Weiss plots for Ti1‑xCrxSe2‑x/2. (a) Inverse susceptibility (1/χ−χ0) versus temperature in a 1 T field for Ti1−xCrxSe2‑x/2. Inset: effective moment and Curie−Weiss temperatures. (b) Plot of C/|θcw|(χ−χ0) versus T/|θcw| for Ti1−xCrxSe2‑x/2 (x = 0.03, 0.07, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5). This plot shows that these compounds exhibit consistent Curie behavior at high temperatures. θCW), where C is the Curie constant, θCW is the Curie−Weiss temperature, and χ0 is the temperature independent contribution to the susceptibility. The fits were performed in the temperature range between 200 and 300 K (as is commonly done for frustrated magnetic materials, the fits are best performed for temperatures above θCW); linear relationships (shown as solid lines in Figure 4a) were found for all Ti1−xCrxSe2‑x/2 compounds above 200 K. χ0 is negligibly small and set to 0 for all samples with the exception of the sample with the lowest Cr content studied, x = 0.03, where it is 0.00005. The effective magnetic moment (Peff) per Cr ion can be obtained by using Peff = (8C)1/2. The Curie−Weiss temperature is an estimate of the net magnetic interaction strength; the θcws are larger in magnitude than −90 K for all materials. In Ti0.75Cr0.25Se1.875, for example, θcw is −174 K, and no magnetic transition is apparent until approximately 2.5 K, giving this material a frustration index f of ∼70, indicating that Ti0.75Cr0.25Se1.875 is strongly frustrated. The effective moment per Cr, Peff, is ∼4 μB and is observed to be only weakly dependent on Cr concentration. The θCW values, however, increase in magnitude with increasing Cr content (see the inset of Figure 4a, top). To better compare the magnetic characteristics of all members of the Ti1−xCrxSe2‑x/2 (0.03 ≤ x ≤ 0.6) family, we rearrange the Curie−Weiss Law to the normalized form C/ (χ|θcw|) = T/|θcw|−1. Plots of the magnetic data in this form are especially useful in comparing the general behavior of geometrically frustrated magnets.1,2,41 The result is a dimensionless plot of the normalized inverse susceptibility against normalized temperature for all samples - the susceptibility is scaled by the magnitude of the moments (C) and the temperature is normalized by the strengths of the magnetic interactions (|θcw|).33 Ideal antiferromagnets would have a slope of 1 and intercept of the y axis at 1 in this representation (shown as a solid green line y = x − 1 in Figure 4b), with indications of magnetic ordering on the order of T/ θcw in the range of 0.5 to 1. Antiferromagnetic or ferromagnetic correlations at lower temperatures in excess of those expected for simple Curie−Weiss behavior are manifested as positive or negative deviations respectively from the green solid line y = x − 1, respectively. This allows differences in the nature of correlations above TN to be identified and easily compared among different materials. It can be seen in the figure that the Ti1−xCrxSe2‑x/2 system maintains nearly ideal Curie−Weiss behavior to normalized temperatures near 1.2 T/θcw before exhibiting increased ferromagnetic fluctuations just before its spin freezing transition, which occurs well below a T/θcw of 0.05. The plot shows that the higher Cr doping compositions show larger relative ferromagnetic deviations from the green line. The ferromagnetic deviations from the antiferromagnetic 6814 DOI: 10.1021/acs.chemmater.5b03091 Chem. Mater. 2015, 27, 6810−6817 Chemistry of Materials Article Figure 5. Spin glass characterization of Ti1‑xCrxSe2‑x/2. (a) Temperature dependence of the dc susceptibility in an applied field of 200 Oe for Ti0.5Cr0.5Se1.75. (b) Temperature dependence of the ac susceptibility in an applied field of 20 Oe for Ti0.5Cr0.5Se1.75 as a function of frequency. (c) MH curve for Ti0.5Cr0.5Se1.75 at 2 and 20 K. (d) The behavior parametrized in a fit to the Volger-Fulcher law. ideal glass temperature”.43,44 After rearranging the VolgerFulcher law, a simple relation between Tf and f with the presentation of Tf = T0 − (Ea/kb)(1/(ln(τ0 f))) can be used. Figure 5d shows the resulting fits. The intrinsic relaxation time (τ0) cannot be fitted for the current data, and thus selected values were used varying from 1 × 10−7 s (superparamagnets, cluster glasses)45 to 1 × 10−13 s (conventional spin glasses).46 When τ0 was set to a value of 1 × 10−7 s, we obtain Ea = 7.17 × 10−4 eV and T0 = 8.48 K, yielding Ea/kB = 2.14. Setting the intrinsic relaxation time τ0 to be the smallest value, 1 × 10−13 s, we obtain Ea = 4.57 × 10−3 eV, T0 = 7.10 K, and the value of Ea/kB = 53. Finally, if τ0 = 1 × 10−12 s, a midrange value, is assumed, we obtain Ea = 3.70 × 10−3 eV, T0 = 7.33 K. and the ratio Ea/kB = 43. Further characterization of the freezing of the spins was performed via heat capacity measurements. Figure 6 shows in the main panel the raw heat capacity data for Ti1−xCrxSe2‑x/2 (x = 0, 0.25, 0.5), presented as Cp/T vs T for T between 2 and 120 K. Estimates of the magnetic specific heat can be obtained by performing a subtraction of the TiSe2 data from that of the Cr doped materials after normalization by 2% such that the Cp/T values match at temperatues of 100 K and higher. This subtracted data is shown in the inset to Figure 6. A sharp ordering feature is not seen in the heat capacity, consistent with a picture where the spins freeze in a random configuration.47 Rough integration of the magnetic heat capacities indicates that the total integrated entropy values are low compared to those expected for two-state or S = 3/2 Heisenberg systems, (R ln(2) or R ln(2S+1)) and thus that the spin freezing observed in the magnetic susceptibility does involve all of the spins; there may be considerable residual magnetic entropy in the Ti1−xCrxSe2‑x/2 system below 2 K. Finally, the temperature dependence of the electrical resistivities, plotted as the ρ/ρ300 K ratios for polycrystalline Ti1−xCrxSe2‑x/2 (0.03 ≤ x ≤ 0.6) are shown in Figure 7. All the Cr-doped samples have resistivities below 6 mOhm cm at 300 Curie−Weiss law in the frustrated regime, at T/θcw = 0.1, are illustrated in the inset of Figure 4b. The low temperature dc and ac susceptibilities of Ti0.5Cr0.5Se1.75 near the magnetic freezing transition are presented in Figure 5. Figure 5a shows the dc susceptibility under an applied 200 Oe field, which indicates that the transition temperature is 8−9 K. Figure 5b presents the ac susceptibility under an applied field of 20 Oe at different frequencies. On this plot, we can see that the transition temperature Tf shifts to higher temperature as the frequency of the ac field increases (10 Hz data omitted for clarity), which is a characteristic trait of spin glasses. Small hysteresis is observed in the M(H) data at 2 K, but no hysteresis is observed at 20 K recorded during increasing and decreasing of magnetic field. In addition, it can be seen that the data shows slight curvature but is nowhere near saturation within the accessible field range. A broad peak is seen in the ac susceptibility data in the 7−12 K temperature range, characteristic of spin freezing. Figure 5c shows the field-dependent magnetization (as M vs μ0H) at 2 K. The ratio of the shift in transition temperature (ΔTf) to the transition temperature (Tf) times the log of the change in frequency (Δlogf) used in the expression of ΔTf/(TfΔlogf), which parametrizes the dependence Tf on f, can be used to characterize spin glasses and spin glass like materials.42 Based on the ac susceptibilities, taking the transition temperature as the maximum of χ′ in Figure 5b, we obtain p = ΔTf/(TfΔlogf) = 0.004, which is much smaller, for example, than that of insulating pyrochlore NaCaCo2F7 (where p = 0.029); however, it is very similar to what is seen for metallic alloy spin glasses such as MMn (M = Cu, Au, Ag, around 0.005).34 To further parametrize the spin glass behavior, the frequency (f) dependence of Tf can be fitted by the empirical Volger-Fulcher law with the following equation: τ = 1/f = τ0 exp(Ea/(kb(Tf − T0))), where Tf is the freezing temperature, f is the frequency, τ0 is the intrinsic relaxation time, Ea is the activation energy of the process, and T0 is “the 6815 DOI: 10.1021/acs.chemmater.5b03091 Chem. Mater. 2015, 27, 6810−6817 Chemistry of Materials Article clusters or Cr-rich particles in this system. XPS characterization supports oxidation state assignments of Cr3+, Ti4+, and Se2− for these materials. The X-ray diffraction refinements indicate that Cr goes into the van der Waals gap positions. Based on the partial substitution of Cr for Ti in Ti1−xCrxSe2‑x/2, Cr3+ on the triangular-planar geometry lattice leads to the frustration of the magnetic ordering: we have observed no long-range magnetic ordering at low temperatures. The Curie−Weiss temperatures θcw were much greater than the freezing temperatures Tfs, confirming that the system is highly frustrated. The system appears to be similar to systems such as Sr1−xEuxS,49 where both disorder-induced and geometry-induced frustration of the magnetic ordering are present, with the exception that the present system is metallic with low carrier concentration. More detailed studies of the charge transport and magnetism in this complex system would be of further interest. Figure 6. Heat capacity characterization of Ti1‑xCrxSe2‑x/2. Main panel: heat capacity of Ti1−xCrxSe2 (x = 0, 0.25, 0.5) in the form of Cp/T over a wide temperature range. The presence of extra entropy at low temperarture for the Cr-doped materials is clearly seen. Inset: The temperature dependence of the excess heat capacity of Ti1−xCrxSe2 (x = 0.25, 0.5), determined by the subtraction of the heat capacity of TiSe2. This heat capacity must be a reflection of the spin freezing in the system. ■ AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (R.J.C.). *E-mail: [email protected] (H.X.L.). Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The synthesis and magnetic characterization of the materials was supported by the DOE grant FG02-98ER45706. The DOE supported the powder diffraction work of J.K. through grant DE FG02-08ER46544. The electron diffraction study at Brookhaven National Laboratory was supported by the DOE BES, by the Materials Sciences and Engineering Division under contract DE-AC02-98CH10886, and through the use of the Center for Functional Nanomaterials. Z.W. was supported by U.S. DOE under Grant No. DOE DE-SC0002136. ■ ■ REFERENCES (1) Greedan, J. E. Geometrically frustrated magnetic materials. J. Mater. Chem. 2001, 11, 37−53. (2) Moessner, R.; Ramirez, A. R. Geometrical frustration. Phys. Today 2006, 59, 24−29. (3) Collins, M. F.; Petrenko, O. A. Triangular antiferromagnets. Can. J. Phys. 1997, 75, 605−655. (4) Gardner, J. S.; Gingras, M. J. P.; Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys. 2010, 82, 53−107. (5) Ramirez, A. P. Strongly Geometrically Frustrated Magnets. Annu. Rev. Mater. Sci. 1994, 24, 453−480. (6) Bramwell, S. T.; Gingras, M. J. P. Spin Ice State in Frustrated Magnetic Pyrochlore Materials. Science 2001, 294, 1495−1501. (7) Fennell, T.; Deen, P. P.; Wildes, A. 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Characterization of the resistivity of Ti1‑xCrxSe2‑x/2. The temperature dependence of the ratios (ρ/ρ300 K) for polycrystalline pellets of Ti1−xCrxSe2‑x/2 (0 ≤ x ≤ 0.6). K. The ratios (ρ/ρ300 K) for Ti1−xCrxSe2‑x/2 (0.03 ≤ x ≤ 0.6) were less than 1 (Figure 7a), except for the lowest doping (x = 0.03) case. For x = 0.03, an increase and then decrease in the resistivity is seen on cooling. This behavior is similar in character to what is observed for undoped TiSe2 (see Figure 7) but with the increase in resistivity on cooling from 300 K, which has been associated with the charge density wave in TiSe2,22 significantly depressed. 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