Ion-Exchange Reactions for Two-Dimensional Quantum Antiferromagnetism

1. Introduction

1.1. Insertion of metal halide array

Topotactic low-temperature reactions such as intercalation, deintercalation and ion-exchange reactions provide a rational design of new structures of non-molecular extended solids which are otherwise not accessible by conventional high-temperature solid-state reactions [1-4]. Among candidate oxide materials used as a precursor of such reactions, the most intensively studied system is the Dion-Jacobson (DJ) type layered perovskite (Figure 1). The chemical formula of the DJ phase is expressed as A´[A_n–1B_nO_3n+1], where A´ is an alkali metal (Na, Rb, …), A is an alkaline earth or rare earth metal (Ca, Sr, La, …), B is a d⁰ transition metal (Ti, Nb, Ta, …), and n is the number of perovskite layers (2, 3, 4, …) [5, 6]. Here, alkali metal ions at the A´ site are highly reactive because of ionic (i.e., weak) A´-O bonding, while the perovskite unit [A_n–1B_nO_3n+1] is strongly bonded and is chemically inert. By exploiting ion-exchange reactions with various reagents, a wide variety of new or improved chemical and physical functionalities including (photo)catalysis [7, 8], ionic conductivity [9] and superconductivity [10] have been developed. However, ion-exchange reactions are rarely employed for the purpose of materials design toward low-dimensional magnetism, because those who work in this filed (mostly physicists) are not familiar with such chemical processing. In addition, compounds obtained by soft-chemical approaches involve negative effects on the crystal structure, for example, poor crystallinity, non-stoichiometry and defects. In particular, it is known that a tiny defect can easily destroy or mask intrinsic magnetic properties of low-dimensional quantum systems.

In 1999, John B. Wiley et al. in the University of New Orleans reported a new type of ion-exchange reactions involving the simultaneous co-exchange of transition-metal cation and chloride anion [11]. As shown in Figure 1(a) and 1(b), the reactions of the n = 2 and 3 DJ phases using CuX₂ (X = Cl, Br) result in the Rb⁺-to-(CuX)⁺ exchange, yielding new metastable compounds (CuX)⁺[A_n–1B_nO_3n+1]^– [11, 12]. Here, the Cu²⁺ ions are octahedrally coordinated, bridging between two apical oxide ions from the perovskite blocks and also surrounded by four halogen ions. The CuO₂X₄ octahedra share edges to form a square lattice network in the ab plane. (CuX)A_n–1B_nO_3n+1 has two interesting features in terms of magnetic interactions. First, the chemical bonds between the transition-metal cations and halide anions are covalent, thereby providing sizable Cu-X-Cu superexchange interactions within the CuX layer. Second, the two-dimensional (2D) CuX layers are well-separated by the non-magnetic perovskite blocks A_n–1B_nO_3n+1 along the c-axis, with the interlayer distance of 12 Å (n = 2) and 16 Å (n = 3). Thus, (CuX)A_n–1B_nO_3n+1 is regarded as an ideal candidate of S = 1/2 2D square lattice systems (Figure 1(c)). What is also important is the fact that this ion-exchange reaction proceeds stoichiometrically, making it possible in principle to observe intrinsic quantum phenomena.

Figure 1.

Ion-exchange reaction involving the insertion of copper halide layer into the interlayer spaces of the Dion-Jacobson type layered perovskites A´[A_n–1B_nO_3n+1] for (a) n = 2 and (b) n = 3. (c) Local coordination environment around the copper atom. J₁ and J₂ denote nearest-neighbor and 2nd nearest-neighbor exchange constants, respectively.

1.2. A new family of two-dimensional quantum antiferromagets

A simple geometrical consideration reveals that the magnetism of (CuX)A_n–1B_nO_3n+1 is described by a square-lattice J₁-J₂ model, where J₁ and J₂ represent the nearest neighbor (NN) interaction and the 2nd NN interaction (Figure 1(c)). According to the Goodenough-Kanamori rule, J₁ and J₂ are expected to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively, giving a situation where geometrical frustration is present in the lattice. The J₁-J₂ model was originally proposed to explain the origin of high-T_c superconductivity in carrier-doped cuprates with S = 1/2 square lattice [13]. Although the detail of theoretical phase diagram is still controversial [14-18], regardless of the approaches employed, several interesting phases appear as a function of α = J₂/J₁ (see Figure 2). Let us define hereafter positive and negative J as AFM and FM interaction, respectively. The most interesting phase predicted is a spin liquid phase with a spin-singlet ground state, being located at around α ~ |0.5| (in the regions of both J₁ < 0, J₂ > 0 and J₁, J₂ > 0), where frustration effect is most prominent. So far, several prototypes of the J₁-J₂ model were reported, for example, Li₂VO(Si,Ge)O₄ [19] and Pb₂VO(PO₄)₂ [20]. Unfortunately, all of them undergo magnetic long-range ordering at low temperatures and the estimated α values are far from α ~ |0.5|. In contrast, the magnetic study for (CuCl)LaNb₂O₇ revealed that this material does not show long-range magnetic order down to low temperatures [21]. (CuCl)LaNb₂O₇ and related compounds obtained by ion-exchange process exhibit a rich variety of quantum phenomena due to geometrical frustration. Hereafter, we will overview recent studies of the ion-exchanged (CuX)A_n–1B_nO_3n+1 compounds, which allows a systematic understanding and tuning of magnetic properties.

Figure 2.

Phase diagram of the J₁-J₂ model on the square lattice where FM, NAF, CAF represent a (0 0) ferromagnetic state, a (π π) Néel antiferromagnetic state, and a (π 0) collinear antiferromagnetic state.

2. Crystal structures and magnetic properties

2.1. Double layered system

2.1.1. (CuCl)LaNb₂O₇

A polycrystalline sample of (CuCl)LaNb₂O₇ is typically synthesized by heating a mixture of RbLaNb₂O₇ and anhydrous CuCl₂ at 320 °C for 1 weak. The white specimen becomes light green after the ion-exchange reaction. This color change is due to insertion of Cu²⁺. The crystal structure of (CuCl)LaNb₂O₇ was originally assigned as tetragonal (space group P4/mmm), with one copper ion at (1/2, 1/2, 1/2) and one chlorine ion at (0, 0, 1/2) per unit cell, forming the ideal S = 1/2 square lattice. Shortly later, the neutron powder diffraction suggested the same space group but a random distribution of chlorine atoms at more general site (x, 0, 1/2) [22]. The tetragonal lattice constants are a = 3.88 Å, c = 11.73 Å. Compared with RbLaNb₂O₇ (a = 3.90 Å, c = 11.03 Å), the c-axis of the ion-exchanged product significantly increases by ~ 0.7 Å, while the a-axis remains almost unchanged. This is consistent with cupper occupation between two terminal apical oxide ions from NbO₆ octahedra.

The absence of long-range magnetic order in (CuCl)LaNb₂O₇ down to low temperatures was demonstrated first by means of magnetic susceptibility and inelastic neutron scattering (INS) experiments [21]. On cooling, the magnetic susceptibility χ (= M/T) (Figure 3) exhibits a Curie-Weiss (CW) behavior followed by a broad peak at around 16.5 K, which is characteristic of low-dimensional AFM system. The χ decreases rapidly with decreasing temperature further. The Weiss temperature θ estimated from the CW fitting is –9.6 K. The magnitude of θ is smaller than the temperature at the broad maximum, indicating the presence of competing FM and AFM interactions. The obtained value of C (= 0.385 emu K/mol) agrees well with that expected theoretically for 1 mol of Cu²⁺, ensuring (almost) completion of the ion-exchange reaction. The upturn at 3.5 K in the raw data is ascribed to a tiny amount of Cu-containing impurities or defects in the CuCl layers. When the impurity contribution was subtracted, the intrinsic susceptibility approaches to zero for T 0. As shown in Figure 4(a), the INS measurements (constant-Q scan in zero field), carried out at JRR-3, Tokai, Japan, provide direct evidence for the spin-singlet ground state with a one-triplet excitation gap of Δ = 2.3 meV. The full widths at half maximum (FWHM) for the 2.3 meV excitation is 1.3 meV, being close to the instrumental resolution. The scattering intensity of the one-triplet excitation decreases with increasing T and levels off above approximately 20 K, a temperature comparable to the spin gap. There is another excitation centered at 5.0 meV, whose T-dependence shows the same tendency as that of the one-triplet transition. Accordingly, the second mode is the collective bound state excitations of several elementary triplets.

In general, magnetic excitations in 2D systems with a spin-singlet ground state are highly dispersive along the magnetic plane. However, the spectrum shape in constant Q scans for the one-triplet mode in powder (CuCl)LaNb₂O₇ specimen is completely symmetric and almost independent of Q (ΔE ~ 0.2 meV), indicating an extremely localized nature of the excited triplets. Such a flat dispersion is characteristic of isolated spin dimer systems such as CaCuGe₂O₆ [23]. Since the Cu spins in (CuCl)LaNb₂O₇ are not isolated, the observation of the dispersionless spin spectrum is a consequence of geometrical frustration. The same behavior has been observed in the 2D Shastry-Sutherland system SrCu₂(BO₃)₂, where compared to in-plane exchange constants (5 – 8 meV) the dispersion of the single-triplet excitation is much suppressed (~ 0.02 meV) [24]. As shown in Figure 4(b), the Q dependence of the scattering intensity of the singlet-triplet excitation, I(1.7 K) – I(20 K), exhibits a fast oscillation. The geometrical frustration in (CuCl)LaNb₂O₇ gives a situation that the spin-singlet pairs are effectively isolated, which may allow us to use the isolated dimer model:

$$I\left(Q\right)\propto F^2\left(Q\right)\left(1-\frac{\sin QR}{QR}\right)$$E1

where the second term sinQR/(QR) is the interference term reflecting the intradimer distance R. Unexpectedly, the estimated value of R is 8.8 Å, which is far longer than the NN Cu-Cu distance (~ 3.9 Å), and is rather close to the 4th NN distance (8.67 Å). This result contradicts the J₁-J₂ model, where the NN bonds are responsible for the spin-singlet formation.

Figure 3.

Temperature dependence of the magnetic susceptibility in (CuX)LaNb₂O₇ (X = Cl, Br) [21, 37].

Figure 4.

a) Constant-Q scan at 0.8 Å^–1 in (CuCl)LaNb₂O₇. The solid circles are the difference, I(1.7 K) – I(20 K) [21]. (b) The Q dependence of the transition at 2.3 meV. The solid line indicates the fit according to eq. (1), which resulted in R = 8.8 Å [21].

Figure 5 shows the field dependence of magnetization M-H and the differential magnetization dM/dH at 1.3 K [25], demonstrating field-induced phase transitions at H_c1 = 10.3 T and H_c2 = 30.1 T. Reflecting the spin-singlet ground state with a finite energy gap, the initial magnetization slope is very small. Note that the small increase for H < H_c1 comes from a tiny amount of impurities or defects as also seen in the magnetic susceptibility for T < 5 K. The intrinsic magnetization curve is obtained by subtracting the extrinsic component (2.0% of free magnetic ions of S = 1/2) from the raw magnetization. The field-induced transition at H_c1 should be caused by the level crossing of the singlet and one of triplet states, following the relation H_c1 = Δ/gμ_B, where Δ is the gap in zero field. However, the observed value of H_c1 is much smaller than 18.5 T calculated from the neutron data (Δ = 2.3 meV). This observation indicates that some other states like a two-triplet bound state causes the level crossing at H_c1.

Figure 5.

Magnetization curve measured at T = 1.3 K and its derivative [25]. Arrows point to the transition fields.

For H_c1 < H, the magnetization gradually increases up to the saturated magnetization. This intermediate state is stable over a wide field range (H_c2 – H_c1 = 19.8 T), which is due to substantial interdimer interactions. No magnetization plateaus are observed, unlike SrCu₂(BO₃)₂ with 1/8, 1/4, and 1/3 plateaus [26, 27] and NH₄CuCl₃ with 1/4 and 3/4 plateaus [28]. Such a difference is understood in terms of competition between localization and delocalization among excited triplets. The magnetization is correlated with the total number of magnons N through the relation M = gμ_BN. The chemical potential of the S^z = +1 magnons is described as μ = gμ_B(H – H_c1). The transverse components of the exchange interactions generate hopping of the magnons, while the longitudinal components generate repulsion of the magnons. When the delocalization term is dominant as in the present material, the Bose-Einstein condensation (BEC) of excited triplets, or magnons, occurs. On the other hand, when the localization term is dominant, magnons are crystallized in an ordered fashion to minimize the repulsive interactions, leading to a plateau in the magnetization curve.

Figure 6(a) shows the temperature dependence of total specific heat C_p (in the inset) and C_p/T under applied magnetic fields ranging from 0 to 14 T [29]. The zero field data reveal no anomaly associated with a long-range magnetic ordering, in consistent with magnetic susceptibility and INS experiments. The Schottky anomaly is seen at around 7 K. After subtracting the lattice contribution βT³ (β = 0.717 mJ/K⁴ mol), the magnetic contribution C_m is obtained, and the subsequent T-integration of C_m/T gives the magnetic entropy S_m of 1.1 J/mol K, which is 13% smaller than the total magnetic entropy (Rln2) for 1mol of S = 1/2.

Figure 6.

a) C_p/T for (CuCl)LaNb₂O₇ collected under several fields. The dotted curve represents the phonon contribution βT³. The inset shows the C_p vs T plots. Arrows denote the transition temperature [29]. (b) Low-temperature magnetizations measured at various external magnetic fields up to 14 T [29].

When the magnetic field is increased up to 7 T, the broad maximum of C_p/T shifts gradually to lower temperature, indicating reduction of the spin gap owing to Zeeman splitting of the excited triplet states (Figure 6(a)). The broad maximum in C_p(T)/T changes into a cusp at and above 11 T (H_c1), corresponding to the field-induced transition to the BEC state. When the magnetic field is further increased, the peak associated with the phase transition develops and shifts systematically to higher temperatures. The transition temperatures T_N at 11 T and 14 T are 2.3 K and 3.3 K, respectively. The growth of the peak area at T_N is consistent with the BEC scenario. Figure 6(b) shows the temperature dependence of magnetization at various constant magnetic fields. A cusp-like anomaly above 10 T shows the occurrence of the BEC transition. The increase in magnetization with decreasing temperature below T_N corresponds to the increased magnon density on the basis of the BEC scenario. Shown in Figure 7 is a T vs H phase diagram. All C_p(T), M(T) and M(H) data agree well with one another. A theoretical curve based on the Hartree-Fock approximation gives the power low behavior [H_c(T) – H_c(0)] T^ϕ with the critical exponent ϕ = 3/2 [30].

Figure 7.

Phase boundary between spin-singlet state and the BEC state in (CuCl)LaNb₂O₇ determined from the results of M(T), M(H), and C_p(T). The solid line represents a theoretical curve described in the text [29].

Nuclear magnetic resonance (NMR) is a useful tool to clarify the local symmetry. It is revealed that none of the Cu, Cl, and La sites have the tetragonal symmetry [31], which is incompatible with the initially reported tetragonal structure with P4/mmm [11]. For example, the Cu- and Cl-NMR spectra could not be accounted for by C₄ symmetry along the c direction. Furthermore, transmission electron microscopy (TEM) measurements demonstrated superlattice reflections indicating the doubling along a- and b-axes (2a 2b). From the obtained spectra, a single-site occupation without site disorder is indicated for both Cu and Cl, in contradiction to the early neutron diffraction study [22]. In addition, the Nb hyperfine coupling constant for H ||c is as large as 2.84(8) T/μ_B, suggesting a strong Cu-O-Nb hybridization. Thus, the in-plane magnetic interactions come not only by the Cu-Cl-Cl superexchange pathways but also by the Cu-O-O-Cu super-superexchange pathways. Figure 8 shows two possible superstructures of the CuCl layer, proposed on the basis of the NMR and TEM results [31].

A single crystal X-ray diffraction is essential to determine the real crystal structure. However, the difficulty is that one cannot directly obtain the single crystal of (CuCl)LaNb₂O₇ by a conventional high-temperature flux method, because it is a metastable phase. Nevertheless, the (CuCl)LaNb₂O₇ single crystals could be obtained topochemically through the ion-exchange reaction of the CsLaNb₂O₇ single crystals [32, 33]. The CsLaNb₂O₇ crystal was grown by a self-flux method [34]. As shown in Figure 9, transparent, plate-shaped crystals with a typical size of 0.5 0.5 0.1 mm³ are obtained. The crystals of CsLaNb₂O₇ were embedded in CuCl₂ powder, for the ion exchange at 340 °C for 1 week. This yielded dark-green single crystals of (CuCl)LaNb₂O₇. Energy dispersive spectroscopy (EDS) shows the absence of Cs in the crystal after the reaction. The time-dependent study revealed that, despite the use of large single crystal and low temperature for reaction, the diffusion occurs surprisingly fast, at a rate of 20 μm h^–1.

The crystal structure of (CuCl)LaNb₂O₇ was refined using single crystal X-ray diffraction and high- resolution powder neutron diffraction data, and Figure 9(b) shows the determined structure [32]. (CuCl)LaNb₂O₇ adopts the orthorhombic 2a 2b c superstructure with the Pbam space group. The lattice constants at 2 K are a = 7.7556 Å, b = 7.7507(5) Å, and c = 11.7142(4) Å. The closeness of the in-plane constants is the reason why earlier low-resolution X-ray/neutron studies gave a tetragonal cell. In the new structure, the NbO₆ octahedra are strongly tilted around the a-axis in a staggered manner. The tilting pattern of the NbO₆ is correlated with the positions of both the Cu and Cl atoms. In particular, the Cl atoms move significantly along the b direction and slightly along a direction from their tetragonal position. The Cu ions occupy the 4h site are displaced along the a- and b-axis, yielding different Cu-Cu distances of 3.626 Å and 4.129 Å along the b-axis and 3.885 Å along the a-axis. The Cu ions take octahedral coordination against two oxide ions with a distance of 1.865 Å and against four chlorine ions with two shorter bonds (2.386 Å and 2.389 Å) and two longer bonds (3.136 Å and 3.188 Å). When the local z and x axes for each Cu²⁺ are taken along the Cu-O and the short Cu-Cl bonds, respectively, the overall symmetry of the magnetic orbital including the ligand p orbitals has the z²–x² character, making the exchange interactions in the CuCl layer highly anisotropic.

Figure 8.

a, b) Superstructures and (c, d) their corresponding exchange paths for the CuCl layer, suggested by NMR/NQR and TEM experiments. The yellow/orange and blue circles represent the Cl and Cu ions, respectively [31]. The dashed lines in (a) and (b) indicate the unit cell for the superstructure. In the structure (a), the yellow and orange circles represent Cl atoms above and below the Cu layer, respectively.

The first principles calculations based on the new structure [32] yielded the superexchange interactions (see Figure 10(a) and Table 1). Interestingly, the 4th NN interaction, J₄, of the Cu-Cl-Cl-Cu exchange path is the strongest and is AFM. The other 4th NN interaction, J₄′ is also AFM, but is much weaker than J₄ (J₄′/ J₄ = 0.18). This is understood as J₄ has a larger Cu-Cl-Cl angle and a shorter Cl-Cl distance than J₄′ (164.9 and 3.835 Å for J₄ vs 156.0 and 4.231 Å for J₄′). The other major J′s are FM. The relative strength of the six exchange interactions is J₄ > J_1a > J_2a > J₄′ > J_2b > J_1b.

Figure 9.

a) Photos of single crystals of CsLaNb₂O₇ (top) and ion-exchanged (CuCl)LaNb₂O₇ (bottom) [33]. (b) Projection of the crystal structure for [100] (left) and for [010] (right) [32].

Figure 10.

a) Exchange interactions in the CuCl layer in (CuCl)LaNb₂O₇ based on the revised structural model. The lines connecting Cu atoms represent exchange interactions: J_1a (light blue), J_2a (pink), J_2b (gray), J₄ (red), and J₄′ (black). J_1b is not plotted for clarity [32]. (b) Shastry-Sutherland model where spin dimers form the orthogonal array [35].

Js	path	d (Å)	angle (º)	Js/J4
J1a	Cu-Cl-Cu	3.88548	108.9, 75.8	–0.39
J1b	Cu-Cl-Cu	3.88548	80.9	–0.04
J2a	Cu-Cl-Cu	5.46148	156.7	–0.38
J2b	Cu-Cl-Cu	5.5053	170.2	–0.14
J4	Cu-Cl-Cl-Cu	8.81262	164.9	1
J4ʹ	Cu-Cl-Cl-Cu	8.53250	150.0	0.18

Table 1.

Exchange paths for up to the fourth NN interactions in (CuCl)LaNb₂O₇ and the corresponding coupling constants relative to the strongest AFM interaction J₄ [32].

The strongest AFM J₄ gives the spin-singlet dimers in (CuCl)LaNb₂O₇. The distance of Cu-Cl-Cl-Cu (J₄ bond) is 8.533 Å, which is in good agreement with the intradimer distance obtained from the INS analysis (Figure 4b). Using the set of J values, the INS data was analyzed again and the better agreement was obtained [32]. Most remarkably, the 4th NN Cu ions form spin singlet arranged in a staggered manner in the ab plane (Figure 10a) and the coupling between them is primarily ferromagnetic. Therefore, the spin lattice is best described as ferromagnetically coupled Shastry-Sutherland quantum spin singlet [32, 35]. In otehr words, (CuCl)LaNb₂O₇ is a ferromagnetic counterpart of SrCu₂(BO₃)₂.

2.1.2. (CuBr)LaNb₂O₇

(CuBr)LaNb₂O₇ is synthesized in a way similar to (CuCl)LaNb₂O₇, but using CuBr₂ [11]. The color of the cupric bromide is brown. The structure of (CuBr)LaNb₂O₇ has the tetragonal P4/mmm space group (a = 3.90 Å and c = 11.70 Å), without any superstructure. When this structure is assumed when refined, the Br atoms exhibits an extraordinarily large displacement parameter U_iso = 0.087 Ų. As in the case of (CuCl)LaNb₂O₇, a deviation from the tetragonal P4/mmm structure is inferred from the NMR/NQR experiments [36]. The Cl-to-Br replacement resulted in the magnetic order. Figure 3 shows χ(T) of this material [37]. The CW fitting gives θ = –5.1 K. The χ(T) shows a round maximum at T_max = 36 K, which is much larger than θ in magnitude, suggesting competing AFM and FM interactions. A tiny kink is seen at 30 K, right below T_max, which is ascribed to magnetic order. Consistently, the specific heat measurements show a peak at 32 K. The neutron diffraction experiments demonstrated a collinear antiferromagnetic (CAF) order with a modulation vector of (1/2 0 1/2). The estimated magnetic moment is 0.60(11) μ_B. The reduced magnetic moment probably results from quantum fluctuations. Figure 11 shows the high-field magnetization M(H) measured at 1.3 K. For 0 < H < 30 T, M(H) increases linearly with magnetic fields, which is followed by non-linear growth. The upward curvature should be caused by the gradual suppression of zero-point oscillations by the external field and is expected to be observed in the framework of spin-wave theory. On the assumption of the J₁-J₂ model [17], J₁/k_B and J₂/k_B are estimated as –35.6 K and 41.3 K, giving α = |J₂/J₁| = 1.10, which is located within the range of the CAF phase in the J₁-J₂ model (Figure 2).

Figure 11.

High-field magnetization for (CuBr)LaNb₂O₇ at 1.3 K [37].

2.1.3. Cu(Cl, Br)La(Nb, Ta)₂O₇

Two kinds of solid solutions have been investigated, against Br-for-Cl [38, 39] and Ta-for-Nb [39, 40] substitution. For (CuCl_1−xBr_x)LaNb₂O₇ (0 ≤ x ≤ 1), the a-axis linearly increases with x, while the c-axis decreases. The temperature dependence of the magnetic susceptibility (Figure 12(a)) shows the reduction of Néel temperature from T_N =32 K (x = 1), 25 K (x = 0.67), 21 K (x = 0.5), 17 K (x = 0.33) (Figure 12(b)). The magnetization curves for x ≥ 0.33 show a linear increase over a wide field range, and the saturation field decreases with decreasing the Br concentrations, implying a weaker superexchange constant for Cu-Cl-Cu than Cu-Br-Cu.

Figure 12.

a) Magnetic susceptibilities of (CuCl_1–xBr_x)LaNb₂O₇ [38]. (b) x dependence of T_N. S and CAF stand for the spin-singlet state and the collinear antiferromagnetic state [38].

Figure 13.

ZF-μSR time spectra in (CuCl_1−xBr_x)LaNb₂O₇ and (CuCl)La(Nb_1−yTa_y)₂O₇ [39].

Muon spin relaxation (μSR) offers a unique opportunity in detecting a static magnetic order at high sensitivity. Figure 13 shows the Zero-field (ZF) μSR spectra of (CuCl_1–xBr_x)LaNb₂O₇ [39]. The x = 1 spectrum exhibits a long-lived precession below T_N, indicating the existence of a well-defined local field at the muon site expected for homogeneous long-range order. With decreasing x, the internal field at ~ 2 K becomes increasingly inhomogeneous as shown by the damping of the oscillation. The x = 0.05 also exhibits a long-range magnetic order at 7 K, in spite of the spin−gapped behavior in magnetic susceptibility and magnetization. The inhomogeneous static local field was observed in the low x range, a characteristic behavior often seen in dilute alloy spin-glass systems [41]. The change in the initial damping rate between x = 0.33 and 0.05 indicates that the size and/or spatial uniformity of the ordered moment changes between these two Br concentrations. In fact, the neutron scattering experiments for x = 0.05 reveals the CAF ordered structure with a magnetic moment being significantly reduced to 0.2(1) μ_B. The long-range magnetic order induced by only 5%-Br doping and the significantly reduced ordered moment indicates that (CuCl)LaNb₂O₇ is located in the vicinity of the quantum phase boundary adjacent to the ordered state.

Contrasting behaviors are observed in the Nb-site substituted system, (CuCl)La(Nb_1–yTa_y)₂O₇ (0 ≤ y ≤ 1) [40]. Reflecting similar ionic radii between Nb⁵⁺ and Ta⁵⁺, the lattice parameters are almost constant with y. However, the magnetic ground state is affected significantly by the Nb-to-Ta substitution. The magnetic susceptibility of (CuCl)LaTa₂O₇ exhibits a broad maximum at T_max = 11.5 K, which is close to 16.5 K in (CuCl)LaNb₂O₇. However, it exhibits only a slight decrease below T_max, indicating a magnetic ground state. The neutron diffraction and μSR experiments (Figure 13(b)) evidence a magnetic order at 7 K, with the reduced magnetic moment of 0.69(1) μ_B and the propagation vector of (1/2 0 1/2). Unlike the (Cl, Br) solid solution, the spin-singlet state is quite robust against the Ta substitution. Substantial substitution up to y ~ 0.4 is necessary to induce the magnetic order. It is remarkable that the spin disordered phase persists up to y = 0.9. This indicates the occurrence of the phase separation. In this range, T_N remains almost unchanged against the Ta concentrations (Figure 14). The volume fraction of the spin-disordered phase increases with decreasing y. It should be noted that the observed phase separation is not caused by chemical inhomogeneity because of uniform distribution of the Nb and Ta atoms as revealed by TEM/EDS images.

Figure 14.

Magnetic phase diagram as a function of temperature and concentration. P, S and CAF stand for the paramagnetic state, the spin-singlet state, and the collinear type AFM state, respectively [40].

The difference in magnetic behaviors between A- and B-site solid solutions is accounted for by the chemical randomness; the superexchange interactions mediated by halogen atoms should be larger than those mediated the non-magnetic perovskite block. Some theories on 1D systems showed the staggered spin-spin correlations in the vicinity of spin vacancies, which results in the emergence of the ordered phase as observed in CuGeO₃ [42] and SrCu₂O₃ [43]. By analogy, the induced magnetic order by a small amount of Br substitution in (CuCl)LaNb₂O₇ may be associated with staggered correlations induced around Br ions.

2.2. Triple layered system

2.2.1. (CuBr)Sr₂Nb₃O₁₀

(CuBr)Sr₂Nb₃O₁₀ is a triple-layered compound, prepared by the ion-exchange reaction of RbSr₂Nb₃O₁₀ with CuBr₂ at 350 °C for 1 week. The crystal structure of (CuBr)Sr₂Nb₃O₁₀ at room temperature is tetragonal (a = 3.91069(4) Å, c = 16.0207(3) Å) with the space group P4/mmm [44, 45]. As in the double layer compounds, a random displacement of the Br atoms from the ideal site is pointed out. In comparison with the double-layered system, the c axis is expanded by ~ 4 Å corresponding to the one-perovskite unit. Thus, the enhanced two-dimensionality is expected in magnetism.

Figure 15.

a) Temperature dependence of the (inverse) magnetic susceptibility for (CuBr)Sr₂Nb₃O₁₀ measured at 0.1 T [44]. (b) C_p vs T measured at 0, 2, 3, and 5 T [44].

Figure 15(a) shows the temperature dependence of the magnetic susceptibility for (CuBr)Sr₂Nb₃O₁₀ measured at H = 0.1 T. The CW fitting gives θ = 20.9(3) K. The positive θ implies that FM interactions are dominant over the AFM ones, which is in contrast to the negative θ for the double layered compounds: –9.6 K for (CuCl)LaNb₂O₇ [21] and –5.1 K for (CuBr)LaNb₂O₇ [37]. Instead of a broad maximum in χ(T) typically seen for low-dimensional spin systems, χ(T) increases with reducing T until it flattens out below 5 K. A noticeable anomaly associated with a long-range magnetic order is not seen. However, specific heat measurements in Figure 15(b) show successive phase transitions at 9.3 K (T_c1) and 7.5 K (T_c2). Non-discontinuous character and the absence of T hysteresis in C_p(T) as well as χ(T) indicate the 2nd-order phase transitions. Successive phase transitions are characteristic phenomena observed in spin frustrated systems such as CsNiCl₃ and CsCoCl₃ [46]. Application of magnetic fields finally merges two transitions together at around 3 T. At higher field, the transition temperature has a dome-shaped boundary peaking at 5 T, as shown in Figure 16. Zero-field μSR spectra demonstrate a long-range magnetic order below T_c2, but a paramagnetic state for T_c2 < T < T_c1 [45]. Thus, the transitions at T_c1 and T_c2 are, respectively, structural and magnetic.

The most prominent observation in (CuBr)Sr₂Nb₃O₁₀ is a 1/3 magnetization plateau in the magnetization curve (see Figure 17). The plateau becomes obscured with increasing T and vanishes at 9 K, in agreement with the phase boundary determined by heat capacity measurements. Since the magnetization curves at 4.2 K and 1.3 K are nearly identical, non-flat plateau is not due to thermal effects. Dzyaloshinskii-Moriya interactions and/or staggered g tensors are a possible origin as discussed in SrCu₂(BO₃)₂ [47].

Figure 16.

T-H phase diagram for (CuBr)Sr₂Nb₃O₁₀, determined by C_p(T) and M(H) [44].

Figure 17.

a) High-field magnetization curves for (CuBr)Sr₂Nb₃O₁₀ [44]. (b, c) Originally proposed magnetic structures in the 1/3 plateau state. Only Cu ions are depicted. Magnetic unit cells are represented in yellow.

The 1/3 magnetization plateau has been theoretically predicted for various triangle-based lattices. Experimentally, triangular- and diamond-lattice antiferromagnets such as Cs₂CuBr₄ [48] and Cu₃(CO₃)₂(OH)₂ [49] exhibit the 1/3 plateau. However, for commensurability reasons, 1/2 and 1/4 plateaus are naturally expected for the square-based systems [50]. The exception is found in SrCu₂(BO₃)₂ with the Shastry-Sutherland lattice, which is due to the stronger 2nd NN interdimer interaction than the NN interdimer one [27]. Oshikawa et al. formulated the quantization condition [51]; p(S − m) = integer, where p and m are the period of the spin state, the magnetization per site, respectively. For S = 1/2, the minimal necessary condition of the 1/3 plateau (m = 1/6) is p = 3. Since (CuBr)Sr₂Nb₃O₁₀ has one Cu²⁺ ion in its chemical unit cell (p = 1), the breaking of translational symmetry is needed to satisfy the quantization conditions. Based on these considerations, we initially proposed two possible in-plane magnetic structures with a propagation vector of (1/3 0) and (1/3 1/6) as shown in Figure 17(b) and 17(c), respectively [44].

In order to observe the magnetic structure at zero field and at the 1/3 plateau, the neutron powder diffraction experiments were carried out at ILL in Grenoble [52]. Figure 18 shows the magnetic diffraction patterns without magnetic field at 8 K and 2 K after subtraction of the 26 K nuclear data. The magnetic Bragg reflections were discernible below T_c2, while no magnetic reflections were detected above T_c2. The magnetic peaks can be indexed with the propagation vector of (0 3/8 1/2), and the magnetic structure is shown in Figure 19. The Cu moments rotate around the c-axis within the ab plane, and the helix propagates along the b-axis with a rotation of 135° between adjacent moments. The helical chains are coupled ferromagnetically along the a-axis. The ordered moment at 2 K is 0.79(7) μ_B/Cu²⁺.

Figure 18.

The low angle region of the magnetic diffraction patterns for (CuBr)Sr₂Nb₃O₁₀ at 8 and 2 K after subtraction of the 26 K nuclear pattern [52].

The observed helical AFM structure is incompatible with those expected from the simple J₁-J₂ model in the absence of magnetic field. It can only be explained when an additional magnetic interaction J₃ is introduced. In the J₁-J₂-J₃ model, several magnetically ordered states appear depending on J₁, J₂, J₃ [53-55]: (0 0) FM phase, (π π) NAF phase, (π 0) CAF phase, (0 q) spiral phase with q = cos^–1[–(J₁ + 2J₂)/4J₃], (q q) spiral phase with q = cos^–1[–J₁/(2J₂ + 4J₃)]. The propagation vector of (0 3/8) in (CuBr)Sr₂Nb₃O₁₀ corresponds to the third case. The magnetic Bragg reflections at 4.5 T (in the 1/3 plateaus region) can be indexed with an incommensurate propagation vector (0 1/3 0.446), which corresponds to the magnetic structure in Figure 17(c). Recently, Furukawa et al. have found theoretically helical AFM ordered states in the ferromagnetically coupled Shastry-Sutherland model [56]. Whether this model can explain the 1/3 plateau or not is interesting to check.

Figure 19.

The magnetic structure of (CuBr)Sr₂Nb₃O₁₀ in zero field [52].

2.2.2. (CuBr)A₂B₃O₁₀ (A = Ca, Sr, Ba, Pb; B = Nb, Ta)

A series of triple layered copper bromides, (CuBr)A₂B₃O₁₀, was synthesized [45]. Since the Rb compounds could not be formed for A = Pb and Ba, CsA₂B₃O₁₀ was prepared as a precursor. A′Pb₂Ta₃O₁₀ (A′ = Rb, Cs) could not be isolated because of formation of Pb₃Ta₄O₁₃ as a main phase. The ion-exchange reaction using CuBr₂ successfully proceeded at 320 – 350 °C. From the XRD patterns at room temperature, all the (CuBr)A₂B₃O₁₀ compounds are found to be isostructural with (CuBr)Sr₂Nb₃O₁₀. Both a- and c- axes show a linear increase with the ionic radius of A²⁺, except Pb. A deviation from the linear relation for A = Pb is due to the steric effect of the 6s² lone pair in Pb [57]. There is no B-site dependence because of the similar ionic radii.

The χ-T curves of (CuBr)Ca₂B₃O₁₀ exhibit a broad maximum. T_max, is 15 K for Nb and 22 K for Ta. The Weiss temperature θ is positive for all the compounds. (CuBr)Ba₂Nb₃O₁₀ shows a drastic drop at 5 K, suggesting an antiferromagnetic transition, while its Ta counterpart shows a monotonous temperature dependence, which is similar to that of (CuBr)Sr₂Nb₃O₁₀. Figure 20 shows the magnetizations normalized by the saturation magnetizations. The 1/3 plateau state is remarkably robust against the chemical substitution. As seen in Figure 20(c), (CuBr)Pb₂Nb₃O₁₀ exhibits a 1/3 plateau between H_c1 = 1.7 T and H_c2 = 5.8 T. The narrowed plateau region of the plateau (4.1 T) indicates that the A-site replacement by the larger cation destabilizes the plateau phase. Further increasing the size of the A-site cation leads to the disappearance of the plateau; no plateau was observed in (CuBr)Ba₂Nb₃O₁₀ (Figure 20(d)). Decreasing the size of the A-site (vs. Sr) produces the same results; no plateau was observed in (CuBr)Ca₂Nb₃O₁₀ (Figure 20(a)). As shown in Fig. 20(e), the H_c2 − H_c1 vs. r_A²⁺ plot clearly demonstrates an intimate correlation between r_A²⁺ and the stability of the plateau phase.

Figure 20.

a)-(d) Magnetization curves measured for (CuBr)A₂B₃O₁₀. (e) The compositional dependence of the plateau width H_c2 – H_c1 as a function of the ionic radius of the A site [45].

The 1/3 plateau phase can be tuned not only by the A site but also by the B site. In the case of B = Ta, only (CuBr)Ba₂Ta₃O₁₀ showed a 1/3 plateau with H_c1 = 1.0 T and H_c2 = 4.0 T. Although the data available are limited, it is anticipated, in analogy to the Nb case, that the plateau-stabilizing region is shifted to the right in Figure 20(e). Conditions for the appearance of the plateau would come from a subtle balance between the magnetic interactions mediated by Br and those mediated by BO₆−BO₆.

2.3. Quadruple layered system

2.3.1. (CuCl)Ca₂NaNb₄O₁₃

A quadruple layered compound, (CuCl)Ca₂NaNb₄O₁₃ [58], was prepared by the reaction of RbCa₂NaNb₄O₁₃ [59] and CuCl₂ at 320 °C for 1 week. Laboratory XRD patterns of both RbCa₂NaNb₄O₁₃ and (CuCl)Ca₂NaNb₄O₁₃ at room temperature could be indexed in the tetragonal cell with the lattice parameters a = 3.869 Å and c = 18.859 Å, and a = 3.866 Å and c = 19.608 Å, respectively. The TEM and synchrotron powder diffraction experiments revealed superlattice reflections that are correlated with the original cell by 2a 2a c (Figure 21). Such a structural deviation from the ideal structure is reasonable in light of the tolerance factor (t = [r_A + r_O]/√2[r_B + r_O]). Perovskite compounds with the ideal cubic structure such as SrTiO₃ have t = 1. When t is smaller than unity, coherent octahedral tilting takes place. Indeed, t = 0.955 for (CuCl)Ca₂NaNb₄O₁₃, implying the octahedral tilting in the perovskite blocks. However, the precursor exhibited very weak and diffuse superlattice reflections. The difference in the TEM patterns would be related to the difference in the bonding nature connecting adjacent perovskite blocks; in RbCa₂NaNb₄O₁₃, the adjacent Ca₂NaNb₄O₁₃ blocks are weakly bound via the Rb cations, while in (CuCl)Ca₂NaNb₄O₁₃, the adjacent perovskite blocks are connected covalently via the edge-shared CuCl₄O₂ octahedra, which results in a long-ranged coherent octahedral tilting. In order to find the most reasonable space group for (CuCl)Ca₂NaNb₄O₁₃, Aleksandrov’s analysis of symmetry reduction in response to octahedral tilting in layered perovskites was employed [60]. Among possible space groups, only I4/mmm with (++0) tilt met the extinction conditions derived from the TEM and XRD results. Here, + and 0 denote, respectively, in-phase tilt and no tilt in Glazer’s notation [61].

Figure 21.

Electron diffraction patterns of (CuCl)Ca₂NaNb₄O₁₃ at room temperature obtained along the [001]- and [010]-zone axes [58].

The temperature dependence of magnetic susceptibility for (CuCl)Ca₂NaNb₄O₁₃ did not show an anomaly associated with magnetic ordering, which is also supported by μSR and specific heat measurements. FM interactions are dominant over AFM interactions, similar to the triple-layered CuBr compounds [45]. Figure 22 shows the magnetization curve measured at 1.3 K. The M(H) does not show either a fractional magnetization plateau or other field-induced phase transitions, but a rather slow increase. The M(H) does not saturate even at 57 T, implying that the in-plane interaction is fairly strong and that there is a strong competition between FM and AFM interactions.

Figure 22.

Magnetization curve of (CuCl)Ca₂NaNb₄O₁₃ at 1.3 K [58].

n	compounds	space; group	magnetic features	TN (K)	Δ/kB (K)	θ (K)	Ref.
2	(CuCl)LaNb2O7	Pbam; (2a2bc)	Spin-singlet state		26.7	–9.6	32
		P4/mmm					11
	(CuCl1–xBrx)LaNb2O7(0.05 ≤ x ≤ 1.0)	P4/mmm	CAF order	7 (x = 0.05) 17 (x = 0.33) 21 (x = 0.50) 25 (x = 0.67) 32 (x = 1.0)		−	38, 39
	(CuCl)La(Nb1–yTay)2O7(0.2 ≤ y ≤ 1.0)	P4/mmm	Coexistence of spin ordered and disordered states	7; (0.2 ≤ y ≤ 0.9)	23.2; (y = 0.2)	–5.6 (x = 0.20) –3.8 (x = 0.40) –3.1 (x = 0.60) –2.5 (x = 0.80)	39, 40
	(CuCl)LaTa2O7	P4/mmm	CAF order	7		–1.2	39, 40
3	(CuBr)(Ca1–xSrx)2Nb3O10(0 ≤ x ≤ 0.50)	P4/mmm	AFM order	13 (x = 0)		4.6 (x = 0)	45
	(CuBr)(Ca1–xSrx)2Nb3O10( x = 0.75, 1.0)	P4/mmm	Helical AFM order,; 1/3 magnetization plateau	7.5 (x = 1.0)		20.9 (x = 1.0)	44, 45
	(CuBr)Pb2Nb3O10	P4/mmm	AFM order,; 1/3 magnetization plateau	~ 6		17.4	45
	(CuBr)Ba2Nb3O10	P4/mmm	AFM order	5		14.9	45
	(CuBr)Ca2Ta3O10	P4/mmm	AFM order	16.6		3.2	45
	(CuBr)Sr2Ta3O10	P4/mmm	AFM order	11		13.2	45
	(CuBr)Ba2Ta3O10	P4/mmm	AFM order,; 1/3 magnetization plateau	5		14.7	45
4	(CuCl)Ca2NaNb4O13	I4/mmm; (2a2ac)	Paramagnetic state	−		22.4	58

Table 2.

Space group, magnetic features, Neel temperature, T_N, spin-gap energy, Δ/k_B and Weiss temperature, θ for (CuX)A_n−1B_nO_3n+1 (X = Cl, Br; A = Na, La, Ca, Sr, Ba, Pb; B = Nb, Ta; n = 2, 3, and 4 ).

3. Conclusion

We have demonstrated that the ion-exchange reaction using the DJ phase that involves the simultaneous co-exchange of metal cations and halide anions is effective approach to design a new class of two-dimensional quantum spin antiferromagnets, with tuned in-plane magnetic interactions and a variety of quantum phases. A series of (CuX)A_n–1B_nO_3n+1 with the S = 1/2 square lattice exhibits novel quantum spin phenomena such as spin-liquid state, quantized magnetization plateau, quantum phase separation, and field-induced BEC state. They are caused by the strong competition between FM and AFM interactions. Table 2 summarizes the structural and magnetic properties in (CuX)A_n–1B_nO_3n+1. Note that most studies on spin frustrated magnetism has been focused so far on the systems composed of only AFM interactions. It is only recently that attentions have been paid to frustrated systems including FM interactions from both experimentally and theoretically points of view. We hope that the (CuX)A_n–1B_nO_3n+1 system will continue to contribute to the development of new physics of the frustrated spin systems in the future. The ion-exchange reaction can be extended to other compounds with transition metals with different spin quantum number, for example, (MCl)LaNb₂O₇ (M = Mn²⁺, Fe²⁺, etc.) [62−65] and (NiCl)Sr₂Ta₃O₁₀ [66]. Reflecting the classical nature of magnetic moment, (MCl)LaNb₂O₇ (M = Co, Fe, Mn) exhibit antiferromagnetic order, but several anomalous behaviors have been still observed due to geometrical frustration. The nickelic chloride with S = 1 undergoes the successive magnetic phase transitions with an intermediate phase characterized by a partial magnetic order. The advantage of the ion-exchange reactions is that, once one finds an appropriate precursor or hosts, any desired spin lattices can be constructed in principle. Using this topochemical strategy, various magnetic lattices (triangle, kagomé, pyrochlore, etc.) might be prepared.