Site-Selective d10/d0 Substitution in an S = 1/2 Spin Ladder Ba2CuTe1-xWxO6 (0 ≤ x ≤ 0.3).

Isovalent nonmagnetic d10 and d0 B″ cations have proven to be a powerful tool for tuning the magnetic interactions between magnetic B' cations in A2B'B″O6 double perovskites. Tuning is facilitated by the changes in orbital hybridization that favor different superexchange pathways. This can produce alternative magnetic structures when B″ is d10 or d0. Furthermore, the competition generated by introducing mixtures of d10 and d0 cations can drive the material into the realms of exotic quantum magnetism. Here, Te6+ d10 was substituted by W6+ d0 in the hexagonal perovskite Ba2CuTeO6, which possesses a spin ladder geometry of Cu2+ cations, creating a Ba2CuTe1-xWxO6 solid solution (x = 0-0.3). We find W6+ is almost exclusively substituted for Te6+ on the corner-sharing site within the spin ladder, in preference to the face-sharing site between ladders. The site-selective doping directly tunes the intraladder, Jrung and Jleg, interactions. Modeling the magnetic susceptibility data shows the d0 orbitals modify the relative intraladder interaction strength (Jrung/Jleg) so the system changes from a spin ladder to isolated spin chains as W6+ increases. This further demonstrates the utility of d10 and d0 dopants as a tool for tuning magnetic interactions in a wide range of perovskites and perovskite-derived structures.

Introduction

Chemical doping is widely used to tune, control, and influence the properties of materials. The periodic table offers a plethora of dopants from which to choose on the basis of differences in charge and ionic radii. By careful selection, it is possible to desirably modify the structural, electronic, and magnetic properties and, in some cases, to generate behaviors entirely different from those of the parent compound. The classic example is Sr2+ doping of the antiferromagnetic layered perovskite-type La2CuO4 that leads to high TC superconductivity in La2–SrCuO4 (x = 0.06–0.25).[1−3] This discovery has fascinated scientists for decades and led to a cascade of studies investigating low-dimensional copper systems.

Dopants have such dramatic effects because they intrinsically modify the interactions within the parent material. In magnetic oxides, these interactions are typically superexchange interactions mediated by oxygen anions. These interactions are generally well understood when the magnetic cations are connected by a single oxygen anion.[4] However, the situation is more complicated when the magnetic cations are farther away and the interactions occur by extended superexchange. Recently, a new method for directly tuning these extended superexchange interactions has been developed.[5,6] This method is based on doping diamagnetic d10 and d0 cations into extended superexchange pathways that link magnetic cations. This d10/d0 effect can be used in A2B′B″O6 double perovskites, where B′ is a magnetic cation and B″ is a diamagnetic d10 or d0 cation.[7,8] The double perovskite structure consists of corner-sharing B′O6 and B″O6 octahedra alternating in a rock salt-type order (Figure a).[9] The superexchange between the magnetic B′ cations is extended via orbital overlap with the linking B″ cations and O 2p orbitals (i.e., B′–O–B″–O–B′).

Figure 1

Magnetic interactions in B″ = W6+ (d0) and/or Te6+ (d10) perovskite structures. (a) Simple fcc Heisenberg J1 and J2 interactions in the cubic double perovskites Ba2Mn(Te/W)O6. (b) Heisenberg square lattice interactions in the Sr2Cu(Te/W)O6, Ba2CuWO6, and Ba2CuTeO6 high-pressure tetragonal perovskites. (c) Spin ladder interactions in the hexagonal perovskite Ba2CuTeO6. (d) (i) Structural motif present in the Sr2Cu(Te/W)O6 and Ba2CuTeO6 structures. The structural motif consists of four corner Cu2+ cations interacting via Cu–O–B″–O–Cu superexchange. (d) (ii) Illustration of the Cu2+ spin ladders running along the b-axis within the Ba2CuTeO6 structure when viewed along the a–b plane. The intraladder (Jleg and Jrung) and interladder (Jinter) interactions are shown by the red and blue arrows, respectively. The corner-sharing B″(c) and face-sharing B″(f) Te6+ sites in hexagonal Ba2CuTeO6 are indicated by the black arrows.

We have recently shown that diamagnetic d10 and d0 cations on the linking B″ site have a significant effect on the magnetic interactions and ground states in double perovskites.[7,10] We investigated this d10/d0 effect in the cubic double perovskites Ba2MnTeO6 and Ba2MnWO6, in which the magnetic Mn2+ cations are linked by either 4d10 Te6+ or 5d0 W6+ B″ cations. In these isostructural materials, Mn2+S = 5/2 magnetism is described using a simple face-centered cubic (fcc) Heisenberg model consisting of a 90° [nearest neighbor (NN), J1] and 180° [next-nearest neighbor (NNN), J2] Mn–O–(Te/W)–O–Mn interaction (Figure a). Neutron scattering experiments demonstrated the dominant interaction strongly depends on the nonmagnetic B″ cation, with a stronger J1 when B″ = Te6+ (4d10) and a stronger J2 when B″ = W6+ (5d0). The contrasting J1 and J2 interactions produce entirely different magnetic structures for Ba2MnTeO6 (type I AFM) and Ba2MnWO6 (type II AFM).

The d10/d0 effect is caused by differences in orbital hybridization in the B′–O–B″–O–B′ superexchange pathways. When B″ = Te6+, there is no d-orbital contribution to superexchange as the 4d10 orbitals lie far below the Fermi level.[11] Therefore, the majority of superexchange occurs via a NN B′–O–O–B′ interaction.[12,13] Conversely, when B″ = W6+, the 5d0 orbitals strongly hybridize with O 2p allowing W6+ to directly contribute to extended superexchange via NNN B′–O–W6+–O–B′.[14] This effect limits the NNN J2 exchange in Te6+ compounds, as this superexchange pathway requires a d-orbital contribution from the B″ cation. We also highlight the fact that the d10/d0 effect extends beyond simple cubic structures to a large range of 3d transition metal B′ = Co,[15,16] Ni,[17−19] and Cu[11,14,20,21] double perovskites, all of which follow the same principle based on the nonmagnetic B″ site: d0 with strong J2 (type II) or d10 with strong J1 (type I/Néel order).

The most striking examples of the d10/d0 effect in 3d double perovskites are the Cu2+S = 1/2 compounds Sr2CuTeO6 and Sr2CuWO6 and their solid solution Sr2CuTe1–WO6, where the d10/d0 doping stabilizes a novel quantum disordered ground state. Here, the combination of the Cu2+ Jahn–Teller (J–T) effect and orbital ordering produces a square lattice Heisenberg antiferromagnet, with highly two-dimensional magnetism.[13,21,22] The tetragonal unit cell has square lattice a–b planes of Cu2+ cations in which superexchange is described using in-plane J1 (NN) and J2 (NNN) interactions, but with additional weak interplane interactions (J3 and J4) along c (Figure b).[11,21] Following the principles of the d10/d0 effect, Sr2CuTeO6 is Néel ordered, while a strong J2 leads to columnar ordering for Sr2CuWO6.[13,14,20,23−25] Using the d10/d0 effect by making a Sr2CuTe1–WO6 solid solution allows for the direct tuning of magnetic interactions on the square lattice between the strong J1 (x = 0) and strong J2 (x = 1) limits.[8,26] The d10/d0 substitution results in the strong suppression of magnetic order as a quantum disordered ground state is observed for a wide composition range of x = 0.05–0.6.[8,12,26−29] The 50:50 mixture Sr2CuTe0.5W0.5O6 closely resembles a quantum spin liquid, an exotic magnetic state in which the moments remain dynamic at 0 K and have been highly sought since they were first proposed in the 1970s.[30−33]

The question of whether d10/d0 doping can be used to tune magnetic interactions and induce exotic magnetic states in other magnetic lattices than the square lattice remains, and whether this can be extended from perovskites to perovskite-derived structures. Depending on the choice of A and B′/B″ cations, B′–O–B″–O–B′ linkers form between corner-sharing or/and face-sharing octahedra, generating the classic double perovskite structure in the purely corner-sharing case, while the introduction of face sharing creates the hexagonal perovskite structure.[34−36] The observation of tunable magnetic interactions in structures with different octahedral connectivity would suggest d10/d0 substitutions can be employed in a range of materials to access novel quantum states, many of which are hard to realize experimentally.[37]

Ba2CuTeO6 is an excellent system for testing this due to its hexagonal perovskite structure that results in a spin ladder magnetic geometry.[38−41] Within the spin ladder, Cu2+ cations are linked via three key Cu–O–Te–O–Cu exchange interactions illustrated in Figure c. These are the intraladder Jleg and Jrung interactions via the corner-sharing Te(1)O6 units and the interladder interaction via the face-sharing Te(2)O6 units within the Cu–Te(2)–Cu trimers.[42] The intraladder interactions are antiferromagnetic and equally strong with Jrung/Jleg ∼ 1, while the interladder interaction is weaker.[38,39] In principle, W6+ could be doped onto either of the Te6+ B″ sites. This offers the possibility of tuning the Jleg and Jrung interactions independently of the Jinter, forming a more complex phase space than cubic perovskites. For clarity, the two B″ sites are henceforth labeled B″(c) and B″(f), where c and f denote corner and face sharing, respectively. The B″(c) and B″(f) sites are indicated in Figure d(ii), which shows the Cu2+ spin ladders running along the b-axis of the Ba2CuTeO6 structure. The intraladder interactions in Ba2CuTeO6 are quite similar to the Cu–O–Te–O–Cu interactions within the square lattice of Sr2CuTeO6. Both structures share the structural motif shown in Figure d(i) involving four corner Cu2+ cations interacting via Cu–O–B″–O–Cu superexchange. In addition, the significant Jinter leads to the formation of a Néel ordered ground state for Ba2CuTeO6, the same type of ordering observed for Sr2CuTeO6.[39] Hence, in a manner analogous to that of Sr2CuTe1–WO6, one might expect similar strong suppression of magnetic order upon site-specific doping of B″ d0 cations onto the intraladder B″(c) sites in Ba2CuTe1–WO6.[26,28,29]

To answer these questions, we prepared the Ba2CuTe1–WO6 solid solution (0 ≤ x ≤ 0.3). Using a combination of crystallographic and spectroscopic techniques, we show that W6+ can be site-selectively doped onto the corner-sharing B″(c) site in Ba2CuTe1–WO6. This site selectivity allows for the direct tuning of intraladder interactions, which show a strong decrease in Jrung/Jleg with an increase in x. Our work demonstrates the d10/d0 effect can be extended to perovskite-derived structures such as hexagonal perovskites.

Experimental Section

Synthesis

Conventional solid-state chemistry techniques were used to synthesize polycrystalline samples of Ba2CuTe1–WO6. The x = 0, 0.05, 0.1, 0.2, and 0.3 compositions were prepared by thoroughly mixing stochiometric quantities of high-purity BaCO3 (99.997%), CuO (99.9995%), TeO2 (99.995%), and WO3 (99.998%) (all purchased from Alfa Aesar) in an agate mortar. The reactant mixtures were pelletized and calcined at 900 °C in air, before being fired at 1000–1100 °C for 24 h periods with intermittent grinding. The phase purity was monitored using X-ray diffraction (Rigaku Miniflex, Cu Kα). A total of 72–120 h was required to achieve phase purity in all compositions, with the heating time increasing as the W content increased. The synthesis was stopped once single-phase samples were obtained. The sample color changed from yellow to a darker yellow-brown across the solution from x = 0 to x = 0.3, which may be indicative of a gradual modification of the band gap as the W6+ content increased.

Magnetization and Heat Capacity Measurements

Magnetic characterization was performed using a Quantum Design MPMS3 magnetometer (Magnetic Property Measurement System). Approximately 100 mg of powder was sealed in a gelatin capsule, which was then secured in a polymer straw sample holder. Zero-field-cooled (ZFC) and field-cooled (FC) curves were measured between 2 and 300 K in dc superconducting quantum interference device mode using an external field of 0.1 T. ac measurements were taken between 2 and 100 K using a dc field of 25 Oe and an ac field of 5 Oe using ac frequencies between 10 and 467 Hz. Heat capacity measurements were performed using a Quantum Design Physical Property Measurement System instrument. The samples were mixed with silver (99.999%) in a 1:1 gravimetric ratio to enhance the low-temperature thermal conductivity. The Ba2CuTe1–WO6:Ag powder was pressed into a pellet. The pellet was broken, and ∼10 mg shards were selected; the heat capacity was measured between 2 and 120 K using the thermal relaxation method. The silver contribution was removed on the basis of a measurement of pure silver powder.

Neutron Powder Diffraction

The nuclear structure of x = 0.05, 0.1, and 0.3 compounds was investigated using the High Resolution Powder Diffractometer (HRPD) at the ISIS Neutron and Muon Source. Approximately 8 g of each sample powder was loaded into an Al-alloy slab-can and sealed using vanadium windows. The exposed surfaces of the slab-can were shielded using highly absorbing Gd and Cd foils so that only the vanadium windows of the can were exposed to the neutron flux. After the slab-can had been aligned perpendicular to the neutron beam, time-of-flight neutron powder diffraction patterns were recorded between 2 and 300 K using a cryostat to cool the sample. The data can be found online.[43] The data were corrected for sample absorption, and Rietveld refinements were performed using GSAS-2.[44,45] VESTA was used to visualize the crystal structures.[46]

Synchrotron X-ray Diffraction

The x = 0.1, 0.2, and 0.3 samples were loaded into 0.6 mm diameter glass capillaries and measured at room temperature on the P02.1 beamline at the PETRA III X-ray radiation source (DESY) using a wavelength λ of 0.20742 Å. The capillary was located 1169.45 mm from the PerkinElmer XRD1621 two-dimensional (2D) detector and spun during the measurement. The 2D data were processed using DAWN Science. The one-dimensional data obtained were refined using GSAS-2. The X-ray and neutron data (as well as the bulk magnetization data) were collected using samples from the same batch.

Extended X-ray Absorption Fine Structure (EXAFS)

EXAFS measurements were performed on the Beamline for Materials Measurement (6-BM) at National Synchrotron Light Source II (NSLS-II). Room-temperature X-ray absorption spectra (XAS) of the x = 0.3 compound were recorded in transmission mode near the W L3 edge, using a finely ground specimen dispersed in polyethylene glycol to achieve a thickness of one absorption length. Incident and transmitted beam intensities were measured using ionization chambers, filled with mixtures of He and N2, operated in a stable region of their I/V curve. A tungsten foil was used as an internal energy calibration where the first inflection point in the measured W L3 edge was defined to be E0 = 10206.8 eV. Data reduction and analysis were performed using Athena, Artemis, and Hephaestus.[47] The EXAFS data were then analyzed using ATOMS and FEFF in the Artemis package with the monoclinic structural model.

Results

Crystal Structure

Initial structural characterization was achieved using laboratory X-ray diffraction. The laboratory X-ray diffraction (XRD) patterns confirm phase purity from x = 0 to x = 0.3. Attempts were made to synthesize richer W6+ samples, but beyond x = 0.3, significant W6+ impurities formed. These impurities were not diminished on further heating, showing the x = 0.3 composition lies close to the solubility limit for our synthesis procedure. Rietveld refinement showed all of the Ba2CuTe1–WO6 structures adopt the same C2/m symmetry as the Ba2CuTeO6 parent structure. The unit cell volume decreases linearly with x (see the inset of Figure S1); this showing Vegard’s law behavior indicates successful doping of W6+ into the Ba2CuTeO6 structure. Synchrotron X-ray diffraction, EXAFS, and neutron diffraction studies provided further insight into the structural effects of doping across the solution.

Synchrotron X-ray Diffraction

Figure a shows an illustrative synchrotron X-ray diffraction pattern collected for the x = 0.2 sample. Data collected at 300 K for x = 0.1, 0.2, and 0.3 compounds were all used to test three possible site occupancy models. These models are (1) W6+ exclusively on the B″(c) site, (2) W6+ exclusively on the B″(f) site, and (3) W6+ occupying both B″(c) and B″(f) sites. An equal distribution (50:50) was initially assumed in model 3. The results in panels a and b of Figure show model 1 reproduces the observed diffraction profile uniquely well. Figure b shows Rwp is consistently lower when W6+ exclusively occupies the B″(c) site in x = 0.1, 0.2, and 0.3 compounds. This suggests a strong preference for corner-sharing, which was further evaluated by allowing the site occupancies to be refined, within the constraints of sample stoichiometry. This identified a small amount of W6+ on the B″(f) site in each sample, with the site occupancy increasing linearly with x to a maximum value of ∼3% as shown in Table . In each refinement, 5% of the W6+ present in the sample is found on the face-sharing octahedral site. Comparing the Rwp and χ2 values in Table to those in Figure b shows minor occupation of the B″(f) site by W6+ leads to a slight but not negligible improvement in the fit compared to model 1. W6+ occupancy of the B″(f) site was confirmed by refinements using the initial site occupancies from model 1 and model 2 as starting values. Both refinements converged to the same results in Table . Given the energetics for ion migration diminishes on cooling from room temperature, the site preference undoubtedly extends to the low-temperature structures.

Figure 2

(a) Synchrotron X-ray diffraction pattern of Ba2CuTe0.8W0.2O6 at room temperature collected using a wavelength λ of 0.20742 Å. (b) R-Factors obtained from Rietveld refinement using the three different W6+ site occupancy models for Ba2CuTe1–WO6. The crystal structures directly above the R-factors for each model depict the placement of W6+ (pink) on either the corner-sharing B″(c) site, the face-sharing B″(f) site, or both the B″(c) and B″(f) sites (50:50) in the x = 0.1, 0.2, and 0.3 compositions. The Te6+ cations are colored blue, and the Cu2+ cations are colored green in the spin ladder.

Table 1

Refined B″(c) and B″(f) Site Fractions Determined Using the x = 0.1, 0.2, and 0.3 Synchrotron X-ray Diffraction Dataa

	B″(c)		B″(f)
	Te(1)	W(1)	Te(2)	W(2)	percentage of total W6+ on the B″(f) site	Rwp (%)	χ2
x = 0.1	0.809(1)	0.191(1)	0.991(1)	0.009(1)	4.7(2)	1.54	3.39
x = 0.2	0.618(1)	0.382(1)	0.982(1)	0.018(1)	4.7(2)	1.75	4.54
x = 0.3	0.430(1)	0.570(1)	0.970(1)	0.030(1)	5.3(2)	2.60	10.50b

The W(1) and W(2) site fractions were used to calculate the percentage of the total amount of W6+ on the B″(f) site in each composition. Also shown are the Rwp and χ2 values for the Rietveld fits.

The larger χ2 for the x = 0.3 composition reflects a longer counting time compared to those of the x = 0.1 and 0.2 samples.

Extended X-ray Absorption Fine Structure (EXAFS)

Analysis of W L3 EXAFS data considered the following models, (1) full W6+ substitution on the B″(c) site and (2) full W6+ substitution on the B″(f) site, within the monoclinic structure. Model 1 afforded a plausible W6+ environment at the B″(c) site, with reasonable path lengths and positive Debye–Waller factors (Table S11). Figure a shows an excellent fit to the data, with an R-factor of 1.18%. In contrast, model 2 did not afford a plausible W6+ environment at the B″(f) site, with several paths having negative Debye–Waller factors (Table S12). The fit for model 2 in Figure b shows obvious regions of poor fit when compared to model 1 in Figure a and has a comparatively higher R-factor of 9.07%. This is because W6+ substitution at the B″(f) site does not provide adequate scattering paths to fit the significant second-shell contribution observed in the χ(R) transform of the EXAFS data in the R range of 3–4 Å (compare Figures S18 and S20). This supports the strong preference for W6+ doping at the B″(c) site, in agreement with the synchrotron X-ray data, but has the added advantage of providing an element-specific perspective. Attempts were made to fit the EXAFS data using contributions from both models 1 and 2, under a linear constraint, to assess the potential for disorder of a fraction of W6+ from the B″(c) to B″(f) site. However, it was not possible to adequately stabilize such a fit, because the number of variables approached the number of data points.

Figure 3

(a) k2χ(k) and χ(R) W L3 EXAFS data of Ba2CuTe0.7W0.3O6 with model 1, assuming W6+ doping on the B″(c) site (uncorrected for phase shift). (b) k2χ(k) and χ(R) W L3 EXAFS data of Ba2CuTe0.7W0.3O6 with model 2, assuming W6+ doping on the B″(f) site (uncorrected for phase shift). In panels a and b, the solid black lines represent the experimental data and the red lines represent the model fits. Fitting windows are indicated by solid blue lines. The crystal structures in the plots of χ(R) vs radial distance depict the models used in the fits. W6+ on the B″(c) site in model 1 and the B″(f) site in model 2 is colored pink, while the Te6+ cations are colored blue. The Cu2+ cations in the spin ladder are colored green.

Neutron Diffraction

In low-dimensional systems, the most striking quantum magnetic behavior may emerge at low temperatures.[48,49] Consequently, variable-temperature neutron diffraction studies were performed on x = 0.1 and x = 0.3 compounds between 2 and 300 K to identify the low-temperature structure across the series. Both x = 0.1 and x = 0.3 compounds undergo the same C2/m to P1 transition as Ba2CuTeO6 on cooling.[42] The transition Ttrans was marked by peak splitting, as one can observe by comparing the neutron diffraction patterns of Ba2CuTe0.7W0.3O6 at (a) 300 K and (b) 1.44 K in Figure . As x in Ba2CuTe1–WO6 increased, peak splitting was suppressed to lower temperatures. Where Ttrans is just below room temperature (287 K) for Ba2CuTeO6,[42] comparing the R-factors from refinements using the C2/m and P1 models places Ttrans between 235 and 240 K in the x = 0.1 compound and 100–120 K in the x = 0.3 compound. The decrease in Ttrans is expected to follow across the series down to the minimum at x = 0.3 as the level of cation disorder increases with x. Importantly, it is clear the low-temperature structure at 2 K is triclinic.

Figure 4

Neutron diffraction data showing the high-resolution powder diffraction (HRPD) patterns of Ba2CuTe0.7W0.3O6 at (a) 300 K and (b) 1.44 K.

The transition from C2/m to P1 is caused by weak symmetry breaking arising from further J–T distortion of the CuO6 octahedra on cooling. The structural integrity of the 12R hexagonal stacking sequence is retained upon the transition to lower symmetry. Like in the C2/m structure, extended Cu–O–B″–O–Cu superexchange occurs via the corner-sharing B″(c)O6 and face-sharing B″(f)O6 units forming the intraladder and interladder exchange interactions depicted in Figure c. While there are changes in the bond lengths and angles, the spin ladder structure can be regarded as almost the same in both the room-temperature monoclinic and the low-temperature triclinic structure. Given the close similarity, the C2/m structure has been previously used to model the low-temperature magnetic interactions as the higher symmetry simplifies the calculations.[39]

The dependence of temperature on the CuO6 octahedra was measured empirically using the J–T distortion parameter (σJT) in eq .[50,51]where (Cu–O) represents the Cu–O neutron bond length on the i-Cu(1)O6 site and ⟨Cu–O⟩ is the mean bond length. σJT is plotted as a function of T for x = 0.1 and x = 0.3 compounds in Figure S15. As expected, σJT was found to be large and non-zero, reflecting uneven elongation of the axial Cu–O bonds to accommodate both corner and face sharing with the B″O6 octahedra. σJT gradually increased with a decrease in temperature for both samples, with the increasing distortion driving the transition to P1 symmetry. It appears the CuO6 octahedra in the x = 0.3 sample are slightly less distorted, possibly due to differences in covalency between W6+ and Te6+. However, compared to x = 0.1, the difference in σJT is minor and both samples plateau to the same distortion limit at 100 K.

The similarity in the neutron scattering lengths of Te and W, and the similarity of the preferred coordination site of these cations, meant it was not possible to determine the B″(c) versus B″(f) site distribution from the neutron diffraction data. Therefore, the B″(c) and B″(f) site occupancies determined from the synchrotron X-ray diffraction data were used in the crystal structural models.

Bulk Characterization

Magnetic Susceptibility

dc magnetic susceptibility data collected for x = 0, 0.05, 0.1, 0.2, and 0.3 compounds using a field of 0.1 T are shown in Figure a. The curve of χ versus T of x = 0 is identical to previous reports.[38,40] Upon cooling, there is a broad maximum at a Tmax of ∼74 K, corresponding to short-range ladder interactions. Below Tmax, the susceptibility decreases before leading onto a small upturn beyond 14 K. The low-temperature behavior is believed to be indicative of the departure from ladder behavior and entry to the long-range ordered Néel state.[38] However, the low-dimensional magnetic behavior means the system does not present a classical AFM ordering cusp, and the low-temperature upturn is not a general sign of magnetic order. Instead, magnetic order has been detected using muon and inelastic neutron scattering techniques placing the magnetic transition at a TN of 14 K.[39,41] It is likely to be coincidental that the upturn occurs close to the TN of Ba2CuTeO6.

Figure 5

(a) dc magnetic susceptibility data for Ba2CuTe1–WO6 (x = 0–0.3) measured using an external field of 0.1 T. ZFC curves are shown as a function of temperature T between 2 and 400 K. The inset shows an expansion of the low-temperature χ vs T curve, where the Curie-tail-like features are observed for the W6+-doped samples. (b) Example Curie–Weiss fit of the 1/χ vs T data for Ba2CuTe0.9W0.1O6 between 200 and 400 K. (c and d) ac susceptibility curves for x = 0.1 and x = 0.3, respectively. The χ′ac vs T data show no frequency dependence with ac frequency between 10 and 467 Hz.

The W6+-doped samples are similar in that they all display the same broad Tmax feature, but the position of Tmax shifts to lower temperatures as x increases as shown in Table , suggesting weakening of the short-range ladder interactions. More dramatic differences are observed at low temperatures, where the upturn in the susceptibility data gradually becomes stronger with x creating a “Curie-tail”-like feature that is most pronounced for the x = 0.3 sample. These Curie-tail features show no field dependence upon measurement at higher external fields of 1 T.

Table 2

Results from Analysis of dc Magnetic Susceptibility Curves

	x = 0	x = 0.05	x = 0.1	x = 0.2	x = 0.3
Tmax (K)	73.9	72.3	70.5	67.1	63.8
C (cm3 K mol–1)	0.5018(4)	0.4582(3)	0.5189(2)	0.5450(5)	0.5048(4)
θW (K)	–102.9(3)	–94.2(1)	–113.4(1)	–124.1(2)	–102.0(2)
μeff (μB per Cu2+)	2.003(9)	1.914(2)	2.037(1)	2.088(3)	2.009(2)
Jleg (K)	85.35(4)	92.0(4)	98.8(2)	102.8(1)	102(1)
Jrung/Jleg	1.0483(6)	0.816(9)	0.546(6)	0.278(4)	0.11(14)
g	2.2234(9)	2.186(2)	2.190(1)	2.1360(5)	2.08(2)

A spin glass state might be an expected ground state of Ba2CuTe1–WO6 given the full Te/W disorder on the B″(c) site. We did not observe any ZFC/FC divergence in the dc magnetic susceptibility for any of the samples. We further investigated the possibility of a spin glass state by measuring the ac magnetic susceptibility of the x = 0.1 and x = 0.3 samples, shown in panels c and d of Figure , respectively. The χ′ac versus T data for each of these samples show no frequency-dependent shift in the curve between 2 and 100 K. Furthermore, no peaks were detected in the imaginary component (χ″ac vs T) of the ac susceptibility. As such, we find no evidence supporting a spin glass state in Ba2CuTe1–WO6.

The dc magnetic susceptibility data between 200 and 400 K were fitted using the Curie–Weiss law as illustrated for Ba2CuTe0.9W0.1O6 in Figure b. The Curie constants (C) and Weiss temperatures (θW) for each sample are listed in Table . Generally, there is little change in θW across the series, implying the interaction strength remains constant. The value of C was used to calculate the effective magnetic moment μeff. The value of μeff is ∼2 μB per Cu2+ for each sample, larger than expected for a Cu2+ moment, but close to the previously reported value of 1.96 μB per Cu2+ for Cu2+ in Ba2CuTeO6.[38] It is unclear why the effective magnetic moment is enhanced in these samples.

The χ versus T data were fitted using an isolated two-leg spin ladder model.[52] This model is based on highly accurate Quantum Monte Carlo (QMC) calculations and allows us to investigate how the intraladder interactions are modified by W6+ substitution. The model has three fitting parameters: the main interaction Jleg, the ratio Jrung/Jleg, and g. The isolated spin ladder model was previously used to show that intraladder interactions are equally strong in Ba2CuTeO6 (Jrung/Jleg ∼ 1),[38,41] which was in excellent agreement with density functional theory calculations[38] and subsequent inelastic neutron scattering measurements.[39]Figure shows the magnetic susceptibility of all samples is described well by the isolated spin ladder model with the fitted parameters listed in Table . Our fit results for x = 0 are in excellent agreement with previous literature.[38,41] Upon W6+ substitution, the strength of the main Jleg interaction is relatively stable showing a small increase. However, the relative strength of the intraladder interactions changes significantly as x increases. The Jrung/Jleg ratio decreases from near unity (i.e., Jleg and Jrung of equal magnitude) for x = 0, to a value of Jrung/Jleg = 0.11(14) upon reaching x = 0.3. This shows that W6+ doping leads to a strong suppression of the Jrung interaction.

Figure 6

(a–e) Isolated two-leg spin ladder model fits to the Ba2CuTe1–WO6 (x = 0–0.3) susceptibility data. The spin ladder fit (red line) was performed between 35 and 400 K. The legend contains the fitting parameters Jleg, Jrung/Jleg, and g. The strength of the Jleg interaction is largely unchanged, while the Jrung/Jleg ratio of the intraladder interactions decreases with x. (f) Spin chain model fit (blue line) to the x = 0.3 susceptibility data between 35 and 400 K. The spin chain model provides a good description of the χ vs T curve at high values of x, further supporting the lower Jrung/Jleg ratio.

In terms of the overall strength of the magnetic interactions, Jleg has twice the impact of Jrung, because Jleg connects any Cu2+ site to two neighboring sites while Jrung connects to only one. Thus, the effect of the small increase in Jleg and the strong suppression of Jrung is a moderate weakening of the overall interactions. This is consistent with the shift in Tmax to lower temperatures, but not with our relatively constant trend in θW obtained from Curie–Weiss fits. The reason for this discrepancy is not known, but it could be related to the strong quantum fluctuations arising from the nearby quantum critical point in Ba2CuTeO6.[39]

The differences in magnetic susceptibility between an isotropic spin ladder with equally strong Jleg and Jrung interactions and more spin chain-type systems with suppressed Jrung are not immediately obvious. The isolated spin ladder fitting function used here is based on QMC calculations of the magnetic susceptibility for different Jrung/Jleg ratios.[52] The QMC calculations show that differences in the high-temperature susceptibility are minor between an isotropic Jrung/Jleg = 1 spin ladder and a spin chain with the latter showing a small increase. The main difference between the two models is found in the broad maximum at Tmax. For isotropic Jrung/Jleg = 1 ladders, this susceptibility is relatively sharp and highly asymmetric. As the Jrung/Jleg ratio decreases, the maximum becomes both broader and much more symmetric, while shifting to lower temperatures. We observe these expected trends in our Ba2CuTe1–WO6 samples: the maximum becomes broader and more symmetric with an increase in x while also shifting to lower temperatures. This further shows that the Jrung/Jleg ratio does decrease with W6+ doping. The differences in the broad maximum are highlighted in Figure a, which shows a comparison of the magnetic susceptibilities of x = 0 and x = 0.2. It should be noted that the Curie-like feature observed at low temperatures is too small to explain the changes in the broad maximum.

Figure 7

(a) Comparison of the susceptibility curves of x = 0 and x = 0.2 compounds. The maximum in susceptibility is more symmetric and broader for x = 0.2 than for x = 0, which is consistent with a lower Jrung/Jleg ratio. In panels b and c, we compare the isotropic spin ladder (with the Jrung/Jleg ratio fixed to 1) and spin chain model fitting to the susceptibility data for x = 0 and x = 0.2, respectively. The spin ladder fits with Jrung/Jleg = 1 are colored red, and the spin chain fits are colored blue. The isotropic spin ladder model fits the x = 0 data very well, but not the x = 0.2 data. The susceptibility of x = 0.2 is better described with a spin chain model confirming that W6+ doping leads to a decrease in the Jrung/Jleg ratio.

To conclusively show that Jrung/Jleg decreases with an increase in x in Ba2CuTe1–WO6, we compare the best fits from an isotropic spin ladder model[52] (Jrung/Jleg = 1) and a spin chain model[53,54] (Jrung/Jleg = 0) for x = 0 and x = 0.2 compounds in panels b and c of Figure . The isotropic spin ladder model fits x = 0 very well, and the Jrung/Jleg ratio of ∼1 has been confirmed by density functional theory calculation and inelastic neutron scattering.[38,39] As expected for the x = 0 compound, the spin chain model provides a poor fit for the maximum in susceptibility, but also for the high-temperature susceptibility. In contrast, the isotropic spin ladder model provides a poor fit for the x = 0.2 data, especially for the broad maximum. The spin chain model, however, describes the x = 0.2 data well and provides a noticeably better fit than the isotropic spin ladder model for the maximum but also at high temperatures. This confirms W6+ doping in Ba2CuTe1–WO6 changes the relative strength of magnetic interactions by decreasing the Jrung/Jleg ratio. Spin chain fits to all compounds are presented in Figure S29, and this model provides a progressively better fit to susceptibility data with an increase in x.

Heat Capacity

Zero-field heat capacity (C) measurements were performed on all samples. The plot in Figure a shows the C/T data as a function of T. Close examination of the curves shows no evidence of an ordering transition in the parent or doped samples. The former observation agrees with previous heat capacity measurements on Ba2CuTeO6.[38,40] Because of weak Néel ordering, Ba2CuTeO6 possesses strong quantum fluctuations that spread out the magnetic entropy. Hence, C/T measurements are largely insensitive to any trace of a λ ordering peak about TN. The lack of a λ peak in the x > 0 curves shows magnetism in the doped samples is similarly weak, as expected from the small S = 1/2 Cu2+ moment and low-dimensional behavior. Consequently, the curves appear to be much the same, so it is not possible to distinguish differences in magnetic ordering. The small variation in the high-temperature data is an artifact of the silver contribution to C/T, which is very well corrected for at low temperatures. However, there are notable trends in the low-temperature C/T data. The expansion of the range of 2–10 K in Figure b shows a linear relationship between C/T and T2 that is readily fitted using the Debye–Einstein model (C = γT + βDT3). The electronic contribution (γ) to the heat capacity was extracted from the intercept of C/T versus T2 and plotted as a function of x in Figure c. For the x = 0 sample, the value of γ is almost zero, in excellent agreement with previous studies.[38] However, as x increases, so does the electronic contribution to C, until γ reaches 29.6 mJ mol–1 K–2 for the x = 0.3 sample. Given these materials are Mott insulators, this electronic contribution can be associated with only magnetic excitations, not conduction electrons.

Figure 8

Heat capacity data for Ba2CuTe1–WO6 (x = 0–0.3), including (a) C/T vs T curves for all samples, (b) Debye–Einstein fits of C/T vs T2 data between 2 and 10 K, and (c) electronic γ term contribution to C as a function of x in Ba2CuTe1–WO6.

Discussion

Our in-depth structural analysis using a combination of synchrotron X-ray diffraction, neutron diffraction, and EXAFS shows W6+ is site-selectively doped onto the corner-sharing B″(c) site. As illustrated in Figure , this means the intraladder, Jrung and Jleg, interactions are most affected by W6+ doping of Ba2CuTeO6. The minor occupation (<5%) of the B″(f) site is unlikely to have a significant effect on the interladder interactions. Hence, d10/d0 doping on the B″(c) site directly tunes the intraladder Cu–O–B″(c)–O–Cu superexchange, while the interladder Cu–O–B″(f)–O–Cu exchange remains unchanged (Figure ).

Figure 9

Diagram illustrating the strong W6+ preference for the corner-sharing B″(c) site vs the face-sharing B″(f) site in the Ba2CuTe1–WO6 structure. The spin ladder structure shown is the same in the C2/m and P1 phases. The solid black lines represent the intraladder interactions Jleg and Jrung (red arrows) of the Cu2+ spin ladder structure. The dotted lines represent the main Jinter interladder interaction (blue arrow) between the spin ladders. The strong B″(c) site preference means the intraladder interactions are most affected by the W6+ d0 orbitals.

W6+ doping has only a weak effect on the structure of Ba2CuTe1–WO6, as expected from the similar ionic radii of W6+ (0.6 Å) and Te6+ (0.56 Å).[55] The hexagonal layered structure and, hence, the Cu2+ spin ladder geometry remained intact across the solid solution. There are only a few minor differences. Mainly, the variable-temperature neutron diffraction data show W6+ doping reduced the C2/m to P1 structural transition temperature from just below room temperature (x = 0) to ∼100–120 K (x = 0.3). The C2/m to P1 transition is weak; therefore, the spin ladder structure and magnetic interactions remain the same.

The synchrotron X-ray data revealed the strong selectivity for W6+ to reside on the corner-sharing B″(c) site. Across the Ba2CuTe1–WO6 series, the structural model provided the best fit to the data when the majority (∼95%) of the W6+ dopant present in the sample resided on the B″(C) site. The EXAFS data corroborated this result, reproducing the experimental data only when the model placed W6+ exclusively on the B″(c) site. The strong site selectivity appears to be surprising for a few reasons, first due to the aforementioned nearly identical W6+ and Te6+ ionic radii.[56] This, and the identical +6 charge, lends us to expect a random distribution of Te6+ and W6+ across the B″(c) and B″(f) sites. However, this argument neglects consideration of the metal–oxygen bonding differences in Te6+ and W6+ (as well as Mo6+) perovskite structures.

It has been noted that perovskites containing W6+ and Mo6+ exclusively form double perovskite structures, whereas Te6+-containing perovskites can also adopt hexagonal structures.[57] The W6+ and Mo6+ cations inability to form hexagonal structures stems from the differences in metal–oxygen bonding involving d0 versus d10 cations. In the case of Te6+, the filled 4d10 orbitals limit the d-orbital contribution to metal–oxygen bonding, creating a significant s- and p-orbital contribution in Te–O bonding. This directs the electron density toward the oxide anions and away from the octahedral surface, thus helping to weaken cation–cation repulsion between Te6+ and the surrounding B′ cation.[57] The weakened cation–cation repulsion allows Te6+ to occupy face-sharing sites in hexagonal perovskite structures, such as the B″(f) site in Ba2CuTe1–WO6. The opposite is true for W6+ and Mo6+ perovskites where the 5d0 orbitals do contribute significantly to metal–oxygen bonding, leading to a strong π-orbital contribution. These π-bonding interactions generate highly regular [WO6]6– octahedral units, with a more spherical charge distribution.[58] This produces a relatively strong repulsion across shared octahedral faces, making face-sharing unfavorable. Consequently, W6+ and Mo6+ prefer corner-sharing sites where cations are farther apart and therefore do not form hexagonal structures.

This electrostatic energetic penalty explains why W6+ strongly prefers the corner-sharing B″(c) site, where the distance to the Cu2+ cation is significantly larger than that of the face-sharing B″(f) site in the Cu–B″(f)–Cu trimer, e.g., Te6+–Cu2+ distances of 3.962(2) Å (face-sharing) and 2.738(1) Å (face-sharing) in x = 0.3 at 300 K. The unfavorability of the B″(f) site also explains why attempts to synthesize richer W6+ compositions beyond x = 0.3 failed. Furthermore, this reasoning is also the basis for why Ba2CuTeO6 and Ba2CuWO6 adopt different structures. The difference in metal–oxygen bonding drives W6+ to form tetragonal Ba2CuWO6 to maximize the cation distances, while Te6+ can accommodate face-sharing in hexagonal Ba2CuTeO6.[57] Note that while seemingly stronger covalency in Te–O may imply stronger superexchange interactions, this is not necessarily the case. Superexchange between corner-sharing CuO6 and TeO6 octahedra mainly occurs via a Cu–O–O–Cu pathway without a significant contribution from the Te6+ 4d10 states, which lie far below the Fermi level, or the Te6+ 5s and 5p states.[12,13] In contrast, the empty W6+ 5d0 orbitals hybridize strongly with O 2p, resulting in significant Cu–O–W–O–Cu superexchange. This results in different dominant interactions for Te6+ and W6+ compounds, although the prediction of the overall strength of magnetic interactions remains difficult due to competing effects.

The d0 W6+ cations were site-selectively doped onto the B″(c) site, which connects the intraladder Jleg and Jrung interactions via Cu–O–B″(c)–O–Cu superexchange. Therefore, one would expect the d10/d0 doping to result in the direct tuning of these intraladder interactions in Ba2CuTe1–WO6. This does in fact happen as confirmed by our isolated spin ladder fits to magnetic susceptibility data. Tungsten doping has a significant effect on the relative strengths of the intraladder interactions: the Jrung/Jleg ratio decreased from ∼1 for the x = 0 sample as the W6+ content increased, reaching a Jrung/Jleg value of ∼0.1 for the x = 0.3 sample. Jleg was approximately constant with an increase in x, therefore showing decreases in Jrung/Jleg originate from a weakening of the Jrung interaction. Such a modification of the relative intraladder strength by W6+ means that as Jrung/Jleg approaches zero, the system is progressively tuned from a spin ladder toward an isolated spin chain.

While our results show that W6+ doping has a significant effect on the magnetic interactions in Ba2CuTe1–WO6, the true magnetic ground states of the doped samples remain unknown. We are unable to rule out the presence of magnetic order in the doped samples despite the lack of magnetic Bragg peaks in the neutron diffraction patterns. This is because magnetic scattering from Cu2+S = 1/2 moments is very weak and HRPD is an instrument optimized for structure solution as opposed to magnetism.

Magnetic susceptibility and heat capacity data provide hints that the magnetic ground state of Ba2CuTe1–WO6 might change upon doping. We observe an increasing Curie tail in the dc susceptibility with an increase in the level of d10/d0 doping. More importantly, a significant T-linear γ term is observed in the heat capacity data for doped samples, but not for pure Ba2CuTeO6. This large γ term has no obvious origin in a magnetically ordered insulator. The high degree of Te/W disorder on the B″(c) site along with magnetic frustration could lead to a spin glass state, which would explain the γ term in the heat capacity.[59] However, our ac susceptibility measurements show no evidence of a spin glass state down to 2 K. Another possibility is that a quantum disordered state, such as a random singlet state, might form in Ba2CuTe1–WO6 as it forms in Sr2CuTe1–WO6. This would explain both the Curie-tail feature in the magnetic susceptibility and the γ term in the heat capacity.[60,61] For the x = 0.3 sample, the γ term approaches 50% of the value for Sr2CuTe0.5W0.5O6.[8] The ground state of the doped samples could be further investigated using muon spin rotation and relaxation and additional neutron scattering experiments.

Conclusions

Chemical doping of the hexagonal perovskite Ba2CuTeO6 delivers a Ba2CuTe1–WO6 solid solution (0 ≤ x ≤ 0.3). Structural differences among the x = 0, 0.05, 0.1, 0.2, and 0.3 samples were investigated using a combination of neutron diffraction, synchrotron X-ray diffraction, and EXAFS. This revealed a strong site selectivity for W6+ cations to occupy the corner-sharing B″(c) site within the intraladder structure. The site selectivity results from differences in molecular bonding that leads W6+ to prefer the corner-sharing site. Site-specific d10/d0 doping directly modifies the intraladder interactions by suppressing Jrung as the level of W6+ doping increases, while Jleg remains constant. While it is unclear what type of ground state this creates, it is clear the direct d10/d0 effect has a significant effect on the magnetic interactions. As the level of W6+ doping increases, Jrung is further suppressed, and the system is tuned from a spin ladder toward a spin chain as Jrung/Jleg approaches zero.

Overall, this work demonstrates that the d10/d0 effect can be extended beyond double perovskite structures to modify the magnetic interactions in hexagonal perovskites. Furthermore, the effect could be extended to any structural type that contains corner-sharing octahedra, such as perovskite-derived two-dimensional structures (e.g., Ruddlesden–Popper phases and Dion–Jacobson phases). This could even be done in a site-selective manner as we have shown here for Ba2CuTe1–WO6. Therefore, our work highlights the d10/d0 effect as a powerful tool for tuning magnetic interactions and ground states in perovskite-derived oxides.