Competition between the Direct Exchange Interaction and

Jul 11, 2016 - Synopsis. Magnetic properties of new compounds LiCrSe2, LiCrTe2, and NaCrTe2 were systematically investigated in comparison with those ...
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Competition between the Direct Exchange Interaction and Superexchange Interaction in Layered Compounds LiCrSe2, LiCrTe2, and NaCrTe2 with a Triangular Lattice Shintaro Kobayashi,*,† Hiroaki Ueda,† Chishiro Michioka,† and Kazuyoshi Yoshimura†,‡ †

Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Research Center for Low Temperature and Materials Sciences, Kyoto University, Kyoto 606-8501, Japan

‡

S Supporting Information *

ABSTRACT: Physical properties of new S = 3/2 triangular-lattice compounds LiCrSe2, LiCrTe2, and NaCrTe2 have been investigated by X-ray diffraction and magnetic measurements. These compounds crystallize in the ordered NiAs-type structure, where alkali metal ions and Cr atoms stack alternately. Despite their isomorphic structures, magnetic properties of these three compounds are different; NaCrTe2 has an A-type spin structure with ferromagnetic layers, LiCrTe2 is likely to exhibit a helical spin structure, and LiCrSe2 shows a first-order-like phase transition from the paramagnetic trigonal phase to the antiferromagnetic monoclinic phase. In these compounds and the other chromium chalcogenides with a triangular lattice, we found a general relationship between the Curie−Weiss temperature and magnetic structures. This relation indicates that the competition between the antiferromagnetic direct d-d exchange interaction and the ferromagnetic superexchange interaction plays an important role in determining the ground state of chromium chalcogenides.

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reports on alkali chromium selenides and tellurides,15,20 which is probably due to the difficulty of synthesis. In this paper, we report on magnetic properties of three new compounds: LiCrSe2, LiCrTe2, and NaCrTe2. Their magnetic properties are different in low-temperature regions. Among them, LiCrSe2 exhibits a magnetic transition accompanied by a structural transition from a trigonal phase to a monoclinic phase. We conclude that the variety of magnetic properties originates in the competition between the antiferromagnetic direct d-d exchange interactions and the ferromagnetic superexchange interactions.

INTRODUCTION

Exotic ground states and physical properties are expected in two-dimensional triangular-lattice compounds. Among them, triangular-lattice compounds with the chemical formula AMX2 (A = monovalent ions, M = transition metals, X = O, S, Se, or Te) exhibit various interesting physical properties, such as a spin and orbital liquid-like behavior in LiNiO2,1,2 orbital orderings in NaTiO2, LiVO2, and LiVS2,3−7 multiferroic properties in CuFeO2 and AgFeO2,8,9 and superconductivity in the water intercalated sodium cobalt oxide NaxCoO2· yH2O.10 Chromium compounds ACrX2 with a triangular lattice are widely studied as a geometrically frustrated Heisenberg spin system with S = 3/2. Most chromium oxides ACrO2 exhibit a 120° spin structure, which is the classical ground state of Heisenberg triangular-lattice antiferromagnets.11−13 In these oxides, the antiferromagnetic direct d-d exchange interaction between adjacent Cr atoms is much larger than the ferromagnetic Cr-anion-Cr superexchange interaction. In contrast, chromium sulfides ACrS2 exhibit various magnetic structures, originating from the competition between these two interactions.14 For example, LiCrS2 exhibits a 120° spin structure, NaCrS2 exhibits an incommensurate helical spin structure, and KCrS2 exhibits an A-type antiferromagnetic structure.15,16 In addition, AuCrS2, AgCrS2, and CuCrS2 have strong magnetoelastic coupling and exhibit complex spin structures in their ground states.17−19 In contrast, chromium selenides ACrSe2 and tellurides ACrTe2 are less studied in comparison with sulfides ACrS2. Specifically, there are a few © XXXX American Chemical Society

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EXPERIMENTAL SECTION

Synthesis. Polycrystalline samples of LiCrSe2 and LiCrTe2 were synthesized by direct reaction of elements. Appropriate amounts of elements Li, Cr, and Se (or Te) were put into an alumina crucible, sealed in a silica tube under an Ar atmosphere, gradually heated to 700 °C at a heating rate of 10−30 °C/h, and then kept at 700 °C for 24 h. Polycrystalline samples of NaCrTe2 were synthesized using the conventional solid state reaction. The mixture of stoichiometric amounts of Na2Te and Cr2Te3 was sealed in a silica tube under an N2 atmosphere and heated at 500 °C for 24 h. All samples are sensitive to moisture. Therefore, these samples were kept in a N2-filled glovebox. Powder X-ray Diffraction. X-ray diffraction (XRD) measurements were conducted with Cu Kα radiation using a powder X-ray diffractometer (Mac Science M18X or RIGAKU Miniflex-600). During XRD measurements at room temperature, the samples covered with a polyimide film were exposed to air, and small signals derived from hydrate were sometimes observed in XRD profiles. We used a closed Received: March 10, 2016

A

DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry cycle He refrigerator for low-temperature XRD measurements. The signals from Cu Kα2 were numerically subtracted from the raw data of low-temperature XRD measurements. Lattice parameters were determined by refining the diffraction patterns through the Rietveld method. Magnetization Measurement. DC magnetization measurements were conducted using a superconducting quantum interference device magnetometer (Quantum Design MPMS) at the Research Center for Low Temperature and Materials Sciences, Kyoto University. To prevent exposure to air, samples were packed into a gelatin capsule in the N2-filled glovebox. Then, N2 gas in the capsule was substituted with He gas in the measurement system.

of LiCrTe2 contains small signals from Li2Te, LiTe3, and hydrated LiCrTe2, diffraction peaks from magnetic impurities are not observed. The XRD patterns of LiCrSe2, LiCrTe2, and NaCrTe2 are well-indexed with the trigonal space group P3m1. The obtained lattice constants are summarized in Table 1. We determined the crystal structure of these compounds by comparing the space group with those of the other ACrX2 compounds (A = monovalent ions, X = chalcogen atoms). All ACrX2 compounds have CdI2-type layers and can be roughly classified into three structure types: (1) the ordered rock-salttype structure observed in NaCrSe2 and KCrSe2,15,20,21 (2) the delafossite-like structure in AgCrSe 2 , CuCrSe 2 , and TlCrSe2,15,21−23 and (3) the ordered NiAs-type structure in LiCrS2 and TlCrTe2.24,25 The former two structures have a rhombohedral lattice R, and the last structure has a primitive lattice P. Thus, the P3m1 space group of LiCrSe2, LiCrTe2, and NaCrTe2 strongly suggests that these compounds crystallize in the ordered NiAs-type structure, where A and Cr atoms stack alternately along the c-axis in the Ni site, as shown in the inset of Figure 1. However, the peak intensities of the 00l indices of their powder patterns are larger than those of simulated profiles with the P3m1 space group. This is due to preferred orientation, specifically the two-dimensionality of the crystal structures. Then, we performed the Rietveld analysis with preferred-orientation parameters to ensure the correctness of our structural model. Although the precise atomic positions and isotropic displacement parameters could not be determined using preferred orientated samples, the relatively small reliability factors (RP = 7−10%, S = 0.8−1.7) indicate the suitability of the structural model (see the Supporting Information). Magnetic Properties. In high-temperature regions, the Curie−Weiss-like temperature dependence is observed in magnetic susceptibility χ = M/H of LiCrSe2, LiCrTe2, and NaCrTe2, where M is the magnetization and H is the external field. Figure 2 shows inverse magnetic susceptibility H/M under 1 and 7 T of these compounds. These magnetic measurements are conducted under high magnetic fields to reduce the contribution of tiny amounts of ferromagnetic impurities. Specifically, LiCrTe2 exhibits significant field dependence of H/ M even in the high-temperature region, which originates from ferromagnetic impurities. The details are discussed later. The obtained parameters are summarized in Table 1. The peff values are in good agreement with the spin-only value of 3.87 for S = 3/2, similar to that in the case of NaCrSe2.21 In layered ACrX2 compounds, it is expected that the Curie− Weiss temperature Θ mainly reflects the magnitude of in-plane magnetic interactions. The in-plane magnetic interactions are

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RESULTS AND DISCUSSION Synthesis and Crystal Structure. We successfully synthesized polycrystalline samples of LiCrSe2, LiCrTe2, and NaCrTe2, which were black in color. To our knowledge, these compounds have not been reported yet. XRD profiles of polycrystalline samples of LiCrSe2, LiCrTe2, and NaCrTe2 are shown in Figure 1. Although the XRD profile

Figure 1. X-ray diffraction patterns of polycrystalline samples of LiCrSe2, LiCrTe2, and NaCrTe2 measured using Cu Kα radiation. Simulated profiles are also shown in the graph, and the numbers above the simulated profiles exhibit indices of diffraction peaks. Signals from impurities are indicated by markers: open triangles (Li2Te), solid triangles (LiTe3), and asterisks (hydrate of LiCrTe2). The inset exhibits the crystal structure of ACrX2 with the P3m1 space group. The structure is drawn to emphasize the octahedral coordination. Atoms of A (alkali metal), Cr, and X (chalcogen) are represented by green, blue, and red balls, respectively. Solid lines in the inset indicate the unit cell.

Table 1. Space Groups, Lattice Constants (a and c), Effective Bohr Magneton Numbers (peff), Curie−Weiss Temperatures (Θ), and Néel Temperatures (TN) of LiCrSe2, NaCrSe2, LiCrTe2, and NaCrTe2a space group

a (Å)

c (Å)

peff

Θ (K)

Hext (T)

TN (K)

reference

LiCrSe2

P3m1

3.654

6.291

33

this work

R3m P3m1

3.729 3.960

20.48 6.699

40 71

ref 21 this work

NaCrTe2

P3m1

4.019

7.395

−28 −14 108 58 101 140 133

7 1

NaCrSe2 LiCrTe2

4.06 3.96 3.84 3.66 3.59 4.11 4.33

101

this work

7 1 7 1

a peff and Θ are estimated from the inverse magnetic susceptibility under the external fields Hext of 1 and 7 T. The data for NaCrSe2 were obtained from a previous report.21

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DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Θ.15,20,25−27 In fact, the isomorphic layered telluride TlCrTe2 with a large Θ is an A-type antiferromagnet.25 In contrast to the large in-plane interaction, the interplane interaction is small owing to the two-dimensionality of the crystal structure. One feature of the weak interlayer coupling is that the metamagnetic transition to a ferromagnetic state occurs at a low magnetic field. The inset of Figure 3 exhibits magnetization curves of NaCrTe2 at 2, 100, and 300 K. At 2 K, M increases linearly with increasing H and jumps approximately at 3 T. Then, M increases gradually and approaches 3 μB, which is the saturation magnetization of S = 3/2. In addition, the ferromagnetic temperature dependence of M/H is observed under 7 T, indicating that the interplane antiferromagnetic interaction is small. The mean-field approximation also suggests the weak interlayer coupling. The ferromagnetic in-plane interaction J1 and the antiferromagnetic interplane exchange interaction J2 can be estimated from the Curie−Weiss temperature Θ and χ(TN) using

Figure 2. Inverse magnetic susceptibility of LiCrSe2, LiCrTe2, and NaCrTe2 under 1 (dotted curves) and 7 T (solid curves). The dashed lines indicate results of the Curie−Weiss fit to the inverse magnetic susceptibility under 1 (gray) and 7 T (black) in the temperature regions between 240 and 300 K.

mainly mediated by two processes: an antiferromagnetic direct exchange process through t2g orbitals and a ferromagnetic Cranion-Cr superexchange process. The interlayer interactions are mediated by superexchange processes through two anions. Considering that the interlayer Cr−Cr distance (lattice constant c) is much larger than the in-plane Cr−Cr distance (lattice constant a), interplane magnetic interactions are expected to be negligibly small. In addition, the values of Θ are closely related to the in-plane Cr−Cr distance. As shown in Table 1, Θ and the lattice parameter a of LiCrSe2 are smaller than those of NaCrSe2.21 Similarly, Θ and a of LiCrTe2 are smaller than those of NaCrTe2. These relations are consistent with the expectation that the in-plane antiferromagnetic direct d-d exchange interaction increases with decreasing adjacent Cr−Cr distance. Please note that the ferromagnetic superexchange interaction between adjacent Cr atoms does not largely depend on the Cr−Cr distance. As described below, the variation in Θ has a significant influence on the spin structure in the ground state. Among the three compounds, NaCrTe2 has the largest value of Θ ≃ 140 K, indicating that the ferromagnetic superexchange interaction is dominant within a layer. In addition, M/H under 1 T exhibits a cusp at TN ≃ 101 K, as shown in Figure 3, which

Θ=

2S(S + 1) (6J1 + 2J2 ) 3kB

8J S(S + 1) C =− 2 χ (TN) 3kB

(1)

(2)

These types of calculations were conducted in refs 20 and 21, although the equation is slightly different owing to the different coordination number. The value obtained for 6J1/kB is 52 K, and that obtained for 2J2/kB is −2 K, where coefficients 6 and 2 correspond to the coordination numbers. In this sense, the interplane interaction between Cr atoms is weak as is the case in the general ACrX2 compounds.20,21 In the case of LiCrTe2, the effect of ferromagnetic impurities is considered to be relatively large, which makes it difficult to estimate the effective Bohr magneton number peff and Curie− Weiss temperature Θ correctly. As mentioned above, inverse magnetic susceptibility H/M exhibits field dependence even in the high-temperature region. We think this field dependence originates from a small amount of ferromagnetic tellurides such as CrTe (TC ≃ 340 K), Cr5Te6 (TC ≃ 303 K), Cr2Te3 (TC ≃ 170 K), and Cr5Te8 (TC ≃ 220 K).28−31 For example, the rapid increase of M/H under 0.1 T at approximately 160 K is due to the ferromagnetic transition of Cr2Te3, which is consistent with the occurrence of spontaneous magnetization at 10 K, as shown in the inset of Figure 4. Please note that the amount of magnetic impurities is too small to detect in the XRD patterns, as shown in Figure 1. LiCrTe2 has the second-largest value of Θ, and the magnetic properties are different from those of NaCrTe2. In the lowtemperature regions, M/H under 7 T exhibits a typical anomaly

Figure 3. Magnetic susceptibility of NaCrTe2 under 1 (blue) and 7 T (red). The dashed and solid curves represent the results of zero-fieldcooled (ZFC) and field-cooled (FC) measurements, respectively. The inset exhibits the magnetization process at 2, 100, and 300 K.

is a typical behavior for an antiferromagnetic transition. The splitting of zero-field-cooled (ZFC) and field-cooled (FC) curves below TN also indicates the occurrence of a magnetic ordering. The large ferromagnetic interaction and antiferromagnetic behavior indicate that NaCrTe2 consists of antiferromagnetically coupled ferromagnetic layers. This type of spin structure is known as an A-type structure, which is sometimes observed in layered antiferromagnets with positive

Figure 4. Magnetic susceptibility of LiCrTe2 under 0.1 (black) and 7 T (red). The inset exhibits the magnetization process at 10 (blue) and 300 K (red). C

DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry of antiferromagnetic ordering at TN ≃ 71 K, as shown in Figure 4. One important feature is that the value of TN is smaller than or very close to that of Θ, although its value depends on analyses. This result indicates that not only the nearest neighbor ferromagnetic interaction but also further neighbor antiferromagnetic interactions are likely to play significant roles in this compound. The situation is similar to those of NaCrS2 and AgCrSe2 with a spiral spin structure within a layer.15 Thus, the ground state of LiCrTe2 is likely to be helimagnetic if the further neighbor antiferromagnetic interactions are not small. LiCrSe2 has the smallest, negative value of Θ and exhibits a characteristic anomaly around 33 K. As shown in Figure 2, M/ H exhibits Curie−Weiss-like temperature dependence in hightemperature regions. With decreasing temperature, M/H drops drastically by approximately at 33 K, as shown in Figure 5,

Figure 6. X-ray diffraction patterns of the 002 and 201 signals of LiCrSe2 between 8 and 60 K. The signals from Cu Kα2 were numerically subtracted from the raw data. Numbers below the X-ray diffraction profiles are monoclinic indices.

subgroups). Hereafter, diffraction peaks above TN are indexed with the P3m1 space group, and peaks below TN are indexed with the C2/m space group. When the monoclinic lattice distortion is considered, the 201 signal above TN should be split into four peaks below TN: 401, 401, 221, and 221 peaks. In our experimental resolution, the positions of the 401 and 401 signals are almost the same and the positions of the 221 and 221 signals are almost the same, indicating that the monoclinic angle β is very close to 90°. Accompanied by the structural transition, the Cr−Cr distance changes drastically at TN. Figure 7 exhibits the Figure 5. Magnetic susceptibility of LiCrSe2 under 1 (blue) and 7 T (red) in the low-temperature regions. The upper left inset exhibits magnetic susceptibility under 0.1 T. The dashed and solid curves represent the results of ZFC and FC measurements, respectively. The lower right inset exhibits the magnetization process at 5 (solid squares) and 100 K (open circles).

indicating the first-order nature. Below this temperature, M/H becomes large by applying a magnetic field and exhibits small splitting of ZFC and FC curves under 0.1 T, as shown in the upper left inset of Figure 5. These behaviors indicate the occurrence of magnetic ordering below TN ≃ 33 K. In addition, the magnetization process at 5 K is convex downward, as shown in the lower right inset of Figure 5, which is probably due to the change in spin structure under high magnetic fields. These results are different from those of LiCrTe2 and NaCrTe2. Structural Transition in LiCrSe2. A first-order-like magnetic transition in LiCrSe2 indicates the occurrence of a structural change at TN. In fact, chromium sulfides AuCrS2, AgCrS2, and CuCrS2 exhibit a first-order magnetic transition with a monoclinic lattice distortion.17−19 To clarify the details of transition in LiCrSe2, we conducted low-temperature XRD measurements. As a result, we found a distinct structural change at TN as follows. The XRD patterns of LiCrSe2 change drastically at TN. As representative examples, temperature dependence of diffraction patterns of the 002 and 201 signals is shown in Figure 6. With decreasing temperature, the position of the 002 signals shifts to higher angles down to TN and drastically shifts to lower angles at approximately TN. This abrupt change results from the increase of the c-axis (interplane Cr−Cr distance). In addition, the 201 signal splits into at least two peaks below TN, indicating a structural transition from trigonal symmetry to monoclinic symmetry. On the basis of the space group relations, the space group below TN is a subgroup of P3m1 (C2/m or its

Figure 7. Temperature dependence of the interplane (top panel) and in-plane (bottom panel) Cr−Cr distances. The inset in the bottom panel exhibits schematic views of the arrangement of Cr atoms in a Cr3 triangle at 8 (left) and 300 K (right). Cr atoms are represented by blue balls.

temperature dependence of interplane and in-plane Cr−Cr distances. With decreasing temperature, the interplane Cr−Cr distance decreases down to TN and then increases below TN. In addition, two sides of the in-plane Cr−Cr distance within a Cr3 triangle slightly elongate and one side contracts below TN while three sides are equal to each other above TN. The schematic views of Cr arrangements in a Cr3 triangle are shown in the inset of Figure 7. The simultaneous occurrence of magnetic and structural transitions at TN is evidence of strong magnetoelastic coupling. It is considered that the structural transition of LiCrSe2 occurs to stabilize the magnetic ordered state. At TN, the magnitude of magnetic interactions changes owing to the monoclinic lattice distortion. This is because the direct D

DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry exchange interaction is closely related to the Cr−Cr distance, and the superexchange interaction is related to Cr−Se−Cr angles. Thus, the three nearest neighbor interactions in a Cr3 triangle are not equivalent below TN, indicating suppression of geometrical frustration. The above scenario is similar to those of chromium sulfides AuCrS2, AgCrS2, and CuCrS2.17−19 The structural transition and magnetic properties of LiCrSe2 are discussed in more detail below in comparison with those of magnetoelastic materials AuCrS2, AgCrS2, and CuCrS2.17−19 As well as these three compounds, LiCrSe2 exhibits monoclinic lattice distortions below the antiferromagnetic ordering temperature. However, the distortion in LiCrSe2 is qualitatively different from those of AuCrS2, AgCrS2, and CuCrS2.17−19 In the case of these compounds, one side of the Cr3 triangle elongates in the antiferromagnetically ordered phase. In contrast, one side of the Cr3 triangle contracts in LiCrSe2, as shown in the inset of Figure 7. The difference can be caused by the large further neighbor interactions in LiCrSe2. The effects of further neighbor interactions can be estimated from Θ and frustration index f ∼ |Θ|/TN. The values of Θ roughly reflect the magnitude of the nearest neighbor interaction. The absolute value of |Θ| of LiCrSe2 is much smaller than those of AuCrS2 (Θ ≃ −119 K),17 AgCrS2 (Θ ≃ −55 K),18 and CuCrS2 (Θ ≃ −90 K),19 indicating that the nearest neighbor interaction of LiCrSe2 is small. In addition, the frustration index f indicates the effect of further neighbor interactions because they often lift spin frustration. The value of f ≃ 1 of LiCrSe2 is smaller than those of AuCrS2 ( f ≃ 2.5),17 AgCrS2 ( f ≃ 1.3),18 and CuCrS2 (f ≃ 3.2).19 These results indicate that further neighbor interactions play an important role in LiCrSe2 in comparison with those in chromium sulfides. This is consistent with the expectation that superexchange interactions through two anions in selenides are larger than those in sulfides owing to the large orbital overlap. Due to the large effect of further neighbor exchange interactions, LiCrSe2 is likely to select the ground state, which is different from those of AuCrS2, AgCrS2, and CuCrS2. Thus, LiCrSe2 can form unusual magnetic structures at low temperatures and can be an interesting candidate for clarifying the spin−lattice effects in the chromium triangular-lattice compounds. Relationship between the Curie−Weiss Temperature and Cr−Cr Distance. We summarize the magnetic properties of LiCrSe2, LiCrTe2, and NaCrTe2 in comparison with those of the other ACrX2 compounds.15−25 As described above, all ACrX2 compounds consist of the CdI2-type CrX2 layer, although there are several types of stacking sequences in the layer. In this system, magnetic properties are well-classified with respect to Θ and the in-plane Cr−Cr distance. In Figure 8, the values of Θ of the ACrX2 compounds are plotted with respect to the nearest neighbor in-plane Cr−Cr distance. As mentioned in other reports,14,32 Θ of chromium sulfides increases monotonically as the Cr−Cr distance increases. This is because the antiferromagnetic direct exchange interaction decreases with increasing Cr−Cr distance. The monotonic increase of Θ with the Cr−Cr distance is also observed in selenides and tellurides. These relations are typical in trivalent chromium chalcogenides such as in the chromium spinel systems.33,34 In addition, we found that magnetic properties of ACrX2 compounds can be systematically categorized with respect to the value of Θ. Spin structures of ACrX2 compounds are divided into four types: ferromagnetic or A-type spin structures

Figure 8. Relationship between the Curie−Weiss temperature and inplane Cr−Cr distance for LiCrSe2, LiCrTe2, NaCrTe2, and the other ACrX2 compounds. The plotted data of the other ACrX2 compounds were obtained from previous reports.15−25 The green, black, and brown markers indicate data of sulfides, selenides, and tellurides, respectively. The solid lines represent the guide lines. Magnetic properties of ACrX2 compounds are indicated by markers: circles with crosses (ferromagnet), open circles (A-type), diamonds (helical), squares (magnetoelastic coupling), and triangles (120°). The solid and open diamonds of the Curie−Weiss temperature of LiCrTe2 indicate the data estimated from 1 and 7 T, respectively.

for Θ > 90 K, helical spin structures for 0 < Θ < 90 K, complex spin structures with monoclinic lattice distortions for −150 < Θ < 0 K, and 120° spin structures for Θ < −150 K. Here, we explain the origin of the variety of magnetic properties in ACrX2 compounds. Competition between the antiferromagnetic direct exchange interaction and ferromagnetic superexchange interaction is likely to play an important role, as discussed in the first principle study of ACrS2 compounds.14 In the case of compounds with large values of |Θ| (Θ > 90 K and Θ < −150 K), the nearest neighbor in-plane interaction is dominant, and further neighbor interactions are negligible. For compounds with Θ > 90 K, the ferromagnetic superexchange interaction is much larger than the antiferromagnetic direct exchange interaction owing to the large in-plane Cr−Cr distance. Therefore, these compounds are ferromagnets or Atype antiferromagnets with ferromagnetic layers.15,16,20,22,25 NaCrTe2 with Θ ≃ 140 K belongs to this class. For compounds with Θ < −150 K, the antiferromagnetic direct exchange interaction becomes much larger than the ferromagnetic superexchange interaction. As a result, these compounds have a 120° spin structure,15 which is the typical ground state for Heisenberg antiferromagnets with a triangular lattice. For compounds with relatively small values of |Θ| (0 < Θ < 90 K and −150 < Θ < 0 K), the nearest neighbor in-plane interaction becomes small as a result of the competition between the antiferromagnetic direct exchange interaction and ferromagnetic superexchange interaction. Thus, further neighbor interactions are not negligible. From the structural viewpoint, further neighbor in-plane interactions are antiferromagnetic, as discussed for some ACrX2 compounds14 because the superexchange angles between Cr atoms are much larger than 90°. In the case of compounds with 0 < Θ < 90 K, the nearest neighbor ferromagnetic interaction is relatively large, but further neighbor antiferromagnetic interactions are not negligible. As a result, helical spin structures are realized within a layer.15,23 LiCrTe2 is likely to belong to this class. The situation is more complex for ACrX2 compounds with −150 < Θ < 0 K owing to the competition between the nearest neighbor and further neighbor interactions in addition to E

DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

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geometrical frustration. They exhibit a magnetic transition with a monoclinic lattice distortion and relieve geometrical frustration.17−19 These compounds have been identified as magnetoelastic materials. LiCrSe2, with s small negative value of Θ, belongs to this class.

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CONCLUSION We synthesized three new compounds (LiCrSe2, LiCrTe2, and NaCrTe2) and investigated their magnetic properties. Competition between the antiferromagnetic direct d-d exchange interaction and ferromagnetic superexchange interaction plays an important role in these compounds. NaCrTe2, with the large value of Θ, is an A-type antiferromagnet with ferromagnetic layers because the ferromagnetic superexchange interaction is much larger than the antiferromagnetic direct exchange interaction. In the case of LiCrTe2 and LiCrSe2, the nearest neighbor in-plane interaction is small as a result of competition between these two interactions, and further neighbor superexchange interactions are not negligible. LiCrTe2, with small positive value of Θ, is considered to have a helical spin structure which originates in the nearest neighbor ferromagnetic superexchange interaction in addition to the further neighbor antiferromagnetic superexchange interactions. LiCrSe2, with the small negative value of Θ, exhibits a first-order-like antiferromagnetic transition with a monoclinic structural distortion. The magnetoelastic coupling is likely to originate from the competition between the nearest neighbor and further neighbor interactions in addition to geometrical frustration. We found that magnetic properties of ACrX2 compounds are wellclassified with respect to the Curie−Weiss temperature.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00610. Results of the Rietveld refinement of the crystal structures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

S.K.: Department of Applied Physics, Graduate School of Engineering, Nagoya University, Nagoya 464−8603, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially carried out using the facilities of the Research Center for Low Temperature and Materials Sciences, Kyoto University. This work was supported by JSPS KAKENHI Grants 26410089 and 261400 and a Grant-in-Aid for Science Research from the Graduate School of Science, Kyoto University. The figures of the crystal structure were created using VESTA.35 Rietveld analyses of powder XRD patterns were conducted using the RIETAN-FP program.36

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REFERENCES

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DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

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DOI: 10.1021/acs.inorgchem.6b00610 Inorg. Chem. XXXX, XXX, XXX−XXX