# Antiferromagnetic Ordering in the Frustrated Rare-Earth Chain Systems M2Cl3 (M = Gd, Tb)

Reinhard K. Kremer, Walter Schnelle, Roland Eger, Arndt Simon, P. Jane

Brown, Bachir Ouladdiaf, Klaus-Ulrich Neumann

► To cite this version:

Reinhard K. Kremer, Walter Schnelle, Roland Eger, Arndt Simon, P. Jane Brown, et al. Antiferromagnetic Ordering in the Frustrated Rare-Earth Chain Systems M2Cl3 (M = Gd, Tb). Chemistry of Materials, 2024, 36 (14), pp.7036-7045. 10.1021/acs.chemmater.4c01317. [https://doi.org/10.1021/acs.chemmater.4c01317](https://doi.org/10.1021/acs.chemmater.4c01317)

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# Antiferromagnetic Ordering in the Frustrated Rare-Earth Chain Systems $M_2Cl_3$ (M = Gd, Tb)

*Published as part of Chemistry of Materials* virtual special issue “In Memory of Prof. Francis DiSalvo”.

Reinhard K. Kremer,* Walter Schnelle, Roland Eger, Arndt Simon, P. Jane Brown, Bachir Ouladdiaf, and Klaus-Ulrich Neumann

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Cite This: *Chem. Mater.* 2024, 36, 7036–7045

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**ABSTRACT:** The magnetic properties of the two isostructural rare-earth condensed octahedral-cluster chain compounds $M_2Cl_3$ (M = Gd, Tb) have been investigated by magnetization, heat capacity, and single-crystal neutron diffraction experiments. Both compounds exhibit antiferromagnetic order below ~23 and ~43 K for $Gd_2Cl_3$ and $Tb_2Cl_3$, respectively. For $Gd_2Cl_3$, the large negative Curie–Weiss temperature of ~209 K indicates substantial magnetic frustration. The magnetic moments of Gd at the two different crystallographic atom positions are aligned along the chains. Whereas at ~14.5 K the magnetic moments at the shared edge approach the theoretically expected spin-only value of ~7 $\mu_B$, the moments at the geometrically frustrated apical position of the octahedra are significantly reduced. In $Tb_2Cl_3$, the magnetic moments lie in the plane perpendicular to the chains and are inclined with respect to each other. The Tb cations in the shared edges have a magnetic moment of 9.3 $\mu_B$, slightly exceeding the maximum value of 9 $\mu_B$ that is expected for $Tb^{3+}$ with $J = 6$ for the Russell–Saunders ground state. Neutron scattering with polarization analysis on a $Tb_2Cl_3$ crystal in a magnetic field reveals enhanced polarizability of the Tb moments at the frustrated apical octahedral sites.

## INTRODUCTION

The most common oxidation state of the rare-earth (RE) elements is +3, while some RE elements can also have an oxidation state +4, or with fewer electronegative anions, they can assume the oxidation state +2. Prominent examples are the two boundary elements in the RE series, Ce and Yb. But in general, the variety of oxidation states is more limited as compared to other transition-metal group elements, such as, for example, the 3d elements. It therefore came as a surprise when, in the middle of the 1960s, Corbett and collaborators reported a compound with the composition $GdCl_{1.6}$.¹ Later, the exact composition was determined by Lokken and Corbett as $Gd_2Cl_3$, suggesting an average formal oxidation state of +1.5 for Gd.² However, the first high-temperature magnetic susceptibility data of $Gd_2Cl_3$ proved an effective magnetic moment corresponding well to the $^8S_0$ 4f⁷ spin-only electronic ground state, indicating Gd to be in the oxidation state +3.³

Subsequently, Simon et al., in addition to $Gd_2Cl_3$, reported the phases $Gd_2Br_3$ and $Tb_2Cl_3$, and with the space group $C2/m$, they gave the correct centrosymmetric description of the crystal structure.⁴ The crystal structure of the $M_2Hal_3$ (M = Gd, Tb; Hal = Cl, Br) phases has been described as composed of trans-edge-connected $M_6$ metal-atom octahedra (see Figure 1) linked via opposite edges to infinite chains which run along the monoclinic *b*-axis. The metal-atom octahedra are significantly distorted. Along the chains, the octahedra are elongated, whereas the distances between the metal atoms in the shared edge are even

Received: May 6, 2024

Revised: June 20, 2024

Accepted: June 21, 2024

Published: July 10, 2024

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>**Figure 1.** Chain of trans-edge-connected M metal-atom octahedra running along [010] in the crystal structure of the M₂Cl₃ phases. The symmetry-equivalent pairs of M metal atoms are labeled by 1, 1' and 2, 2', respectively.</figcaption></figure>

smaller than typical atom distances in Gd or Tb metal. The connected octahedra are reminiscent of cluster compounds of the heavy transition-metal elements, and the formation of chains has been interpreted in terms of cluster condensation.⁵

The octahedra chains are embedded in a halogen matrix (see Figure 2), separating them from each other. The halogen

<figure><img src="image_11.png" /><figcaption>**Figure 2.** Crystal structure of M₂Cl₃ (M = Gd, Tb) projected along [0–10].⁴ The M atoms are represented by small black circles and the Cl atoms by larger yellow circles. The chains of trans-edge-connected M-atom octahedra (see Figure 1) are depicted as black diamonds.</figcaption></figure>

environment of the M atoms matches closely that of isolated M₆Hal₈ clusters observed for heavier transition-metal elements, with the halogen atoms capping the triangular faces of the M₆ octahedra.⁴

A first investigation of the electronic properties of the M₂Hal₃ phases was carried out by electrical conductivity measurements by Bauhofer and Simon.⁶ They found semiconducting behavior with bandgaps of ~0.8 and ~1 eV for Gd₂Cl₃ and Tb₂Cl₃, respectively. For the isostructural nonmagnetic phase Y₂Cl₃, a band gap of ~0.8 eV was reported later.⁷

Using LCAO calculations, Bullet showed that hybridized doubly occupied bonding *d*-bands located about 1 eV below the Fermi energy accept the electron excess and stabilize the

structure of the M₂Hal₃ phases.⁸,⁹ Recent GGA band structure calculations within the Materials Project (mp-1088829) confirm these results and give similar band gaps.¹⁰

A comprehensive investigation of the low-temperature bulk magnetic properties of the M₂Hal₃ compounds was carried out on Gd₂Cl₃ by Kremer.¹¹ Strong evidence for one-dimensional (1d) antiferromagnetism in the chains of octahedra was found by magnetic susceptibility, heat capacity, ESR, and NMR measurements.

A first neutron powder diffraction study on Tb₂Cl₃ by Schmid et al. detected long-range antiferromagnetic order below ~41 K with largely different magnetic moments for Tb1 (8.7 µB) and Tb2 (2.4 µB) at 5 K.¹² Subsequently, Beck performed a neutron powder diffraction investigation on a sample prepared by electrochemical synthesis, followed by a tetrahydrofuran extraction of a possible trihalide surplus.¹³ Using the correct symmetry constraints for the orientation of the Tb moments, they found ordered moments within the *a*–*c* plane of 9.3 and 1.8 µB for Tb1 and Tb2 at 25 K, respectively. While below 25 K the magnitude of the moment at Tb1 leveled off, the moments at Tb2 sites decreased and changed orientation.¹⁴ In addition to the sharp magnetic Bragg reflections, a broad temperature-dependent diffuse shoulder centered at *d* ≈ 5 Å was detected, the integrated intensity of which correlated with the temperature dependence of the magnetic moment at Tb2 atoms. This behavior was ascribed to the unconventional synthesis method, apparently inducing some structural disorder with repercussions, particularly on the magnetic coupling of the Tb2 atom sites.

Here, we report on detailed single crystal neutron diffraction, magnetization, and specific heat investigations on Gd₂Cl₃ and Tb₂Cl₃ to not only establish the magnetic structure of Gd₂Cl₃ but also to resolve some of the inconsistencies left, e.g., by the neutron powder diffraction studies on Tb₂Cl₃ summarized before. We used crystal samples prepared by the conventional metal-trihalide route.¹ Our neutron diffraction investigations on Gd₂Cl₃ and Tb₂Cl₃ indicated long-range antiferromagnetic order below 23 and 43 K, respectively, consistent with specific heat and magnetization measurements. In Gd₂Cl₃, the magnetic moments are oriented along the chains, whereas in Tb₂Cl₃, they lie in the *a*–*c* plane, and both moments are inclined with respect to each other. In contrast to the earlier studies, the Tb moments do not reorient at low temperatures. Using neutron polarization analysis on a Tb₂Cl₃ crystal placed in an external magnetic field along the *b*-axis perpendicular to the Tb moments revealed significantly larger magnetic polarizability of the Tb2 moments, which we ascribe to the magnetic frustration of the Tb2 moments. A fit of the isothermal magnetization using a semiclassical model is consistent with this interpretation. Gd₂ moments in Gd₂Cl₃ are significantly reduced as compared to the expected Gd³⁺ spin-only moment of 7 µB, which we ascribe to the magnetic frustration of the magnetic moments at the apical sites of the metal-atom octahedra.

## EXPERIMENTAL SECTION

Samples of M₂Cl₃ (M = Y, Gd, Tb) were prepared by reacting stoichiometric amounts (total ~2 g) of chips of the respective metals (Johnson Matthey Co., purity 99.99%) and anhydrous MCl₃ powder in sealed tantalum capsules outer diameter ~12 mm, length ~10 cm, filled with a 1 bar Ar atmosphere for an extended period of up to several months at 610 °C in a tube furnace with a uniform (~± 6 K) temperature profile. Anhydrous MCl₃ was prepared from the RE oxides (Rare Earth Products Ltd., purity 99.9%) via the ammonia route and subsequently purified by several repeated sublimations in high
$$f = l\theta / T_N \approx 9.5$$

which points to significant magnetic frustration, most likely of the Gd2 magnetic moments, residing at the apical sites of the octahedra, i.e., at the tip of the triangle formed by two Gd1 atoms and one Gd2 atom.

Figure 4 displays the temperature dependence of the heat capacities of Gd₂Cl₃ and of the isostructural diamagnetic

<figure><img src="image_12.png" /><figcaption>**Figure 4.** Heat capacities of Gd₂Cl₃ (red dots) and Y₂Cl₃ (black dots). The solid cyan line is a fit of the heat capacity of Y₂Cl₃ with a sum of a Debye and two Einstein terms. Parameters are given in the text. The inset displays the anomaly in the heat capacity of Gd₂Cl₃ at ≈23 K on an enlarged scale.</figcaption></figure>

compound Y₂Cl₃. Cₘag(T) of Gd₂Cl₃ exposes a small ordering anomaly at ≈23 K, in agreement with the magnetic susceptibility data. The comparisons with the heat capacity of Y₂Cl₃ reveal a broad continuum, apparently of magnetic origin, extending up to ~100 K. At sufficiently high temperatures, the magnetic contributions to Cₚ(T) of Gd₂Cl₃ become negligible, and the heat capacities of Gd₂Cl₃ and Y₂Cl₃ exhibit a similar temperature dependence. In order to extract the magnetic contributions to the heat capacity of Gd₂Cl₃, we constructed a lattice reference by fitting Cₚ(T) of Y₂Cl₃ with a sum of a Debye-type heat capacity term and a contribution of two Einstein terms, with intensity ratios of 1.19:1.94:1.87 and a Debye temperature of 146 K and of 231 and 633 K for the two Einstein temperatures, respectively. To compensate for the different molecular weights of Gd₂Cl₃ and Y₂Cl₃, we multiplied the fitted heat capacities of Y₂Cl₃ by the factor 1.06 to make the heat capacities of both compounds coincide above ~100 K, where magnetic contributions to Cₚ(T) of Gd₂Cl₃ fade out.

Figure 5 shows the magnetic contribution to the heat capacity of Gd₂Cl₃ and the magnetic entropy per Gd atom obtained by integrating Cₘag(T)/T. At high temperatures, the magnetic entropy approaches a value of 2 × R ln 8, as expected for the S = 7/2 8-fold degenerate ground state of two Gd³⁺ species. At ~23 K, only about one-half of the magnetic entropy has been removed, leaving the remainder, i.e., the entropy corresponding to one Gd atom, to be taken out below. This temperature dependence of the magnetic entropy is a consequence of the broad bulge in Cₘag developing below ~23 K, with a maximum at ~10 K. Such broad humps in Cₘag at ~T_N/2 are frequently observed for magnetic systems with degenerate ground states, e.g., for compounds containing Gd³⁺ or Eu³⁺ cations.¹⁸,²²,²³ The temperature dependence of the magnetic heat capacity and the entropy of Gd₂Cl₃ strongly suggest a gradual thermal

<figure><img src="image_13.png" /><figcaption>**Figure 5.** Magnetic heat capacity of Gd₂Cl₃ and magnetic entropy of Gd₂Cl₃.</figcaption></figure>

depopulation of weakly exchange split Gd³⁺ S = 7/2 spin multiplets below T_N, which we attribute to the geometrical frustration of the Gd2 atoms residing at the tip of the triangle with the Gd1 atoms at the base edge. As also indicated by the magnetic structure (see below), as a consequence of magnetic frustration, the Gd2 moments are far from being fully ordered at ~14 K, in contrast to the Gd1 moments, which exhibit an ordered moment close to 7 µB.

**Magnetic Structure Determination.** A set of 350 nuclear Bragg reflections was collected with D9's single detector at 14.5 K with the C-centering symmetry conditions h + k even. Following absorption correction, the data were merged into 250 independent reflections. Table 1 lists the refined atom positions

<table><caption>**Table 1.** Atom Positional Parameters of Gd₂Cl₃ Refined from Single-Crystal Neutron Diffraction Data Collected at 14.5 Kᵃ</caption><thead><tr><th>atom</th><th>x (RT)</th><th>x (14.5 K)</th><th>z (RT)</th><th>z (14.5 K)</th></tr></thead><tbody><tr><td>Gd1</td><td>0.40983(6)</td><td>0.4097(6)</td><td>0.05192(9)</td><td>0.052(2)</td></tr><tr><td>Gd2</td><td>0.13690(6)</td><td>0.1355(5)</td><td>0.29308(9)</td><td>0.290(2)</td></tr><tr><td>Cl1</td><td>0.65905(35)</td><td>0.6505(7)</td><td>0.51165(40)</td><td>0.510(3)</td></tr><tr><td>Cl2</td><td>0.76925(33)</td><td>0.7681(7)</td><td>0.88245(46)</td><td>0.882(3)</td></tr><tr><td>Cl3</td><td>0.95035(33)</td><td>0.9488(8)</td><td>0.26901(51)</td><td>0.268(3)</td></tr></tbody></table>

at 14.5 K in comparison with those determined by single-crystal X-ray diffraction at RT.⁴ The lattice contraction is rather uniform and amounts to ≈0.4% for a, b, and c and ≈0.1% for the monoclinic angle β.

At 14.5 K, the reciprocal space was searched with D9's multidetector for magnetic Bragg scattering with no symmetry restrictions on h, k, l and h, k, l covering half integer in all possible combinations.

Only reflections with h + k odd and l half integer showed significant intensity. Most intense reflections were found for k = 0, implying that large magnetic moments aligned along the crystallographic b-axis.

Temperature scans of four selected magnetic reflections were obtained between 14.5 and 30 K in both heating and cooling cycles. The temperature stability was maintained better than

<footnote>ᵃAll atoms are located on Wyckoff site 4i (y = 0) in space group C2/m (no. 12). X-ray data at RT from ref 4 are given for comparison. The refined lattice parameters at 14.5 K amount to a = 1516.0 pm, b = 388.1 pm, c = 1013.0 pm, β = 117.5°. χ² (integr. intensity, 14.5 K) = 0.27; data at RT have been taken from ref 4.</footnote>
0.03 K. Figure 6 shows the typical integrated intensities of two magnetic Bragg reflections.

<figure><img src="image_14.png" /><figcaption>Figure 6. Typical temperature dependence of the integrated intensities of two magnetic Bragg reflections of Gd₂Cl₃. The black solid lines are fits to a critical power law (eq 4) between 22 and 30 K.</figcaption></figure>

A fit of the integrated intensities of four magnetic Bragg reflections with a critical power law

$$I(T) = I_0 t^{2\beta} \qquad (4)$$

where the reduced temperature t is given by $(T_N - T)/T_N$ resulted in an averaged critical temperature $T_N$ of

$$T_N = 27.1(1) \text{ K}$$

and an averaged critical exponent of

$$\beta = 0.32(2)$$

The critical exponent is well within the range expected for 3D universality classes,²⁴ whereas $T_N$ is somewhat higher as compared to the heat capacity and magnetic susceptibility results, the latter agreeing well within error bars. We ascribe this difference to bad thermal coupling of the sample to the Displex cryostat’s coldfinger or to some offset of the sensor calibration.

At 14.5 K, a set of magnetic Bragg reflections were collected using the D9’s single detector, losing C-centering, i.e., h + k odd and l half integer. The data set was merged as for the nuclear reflections to ≈150 independent reflections. Refinements of the nuclear and magnetic structure were performed using standard software (CCSL and Fullprof) program packages.²⁵,²⁶

Figure 7 displays the correlation between the observed and calculated squares of the magnetic and nuclear structure factors, and Figure 8 shows the magnetic structure.

The magnetic structure of Gd₂Cl₃ at 14.5 K is characterized by the moments pointing along the chains and the large difference between the ordered magnetic moments refined for the two different Gd sites. They amount to

$$\mu(\text{Gd1}) = 5.8(3)\mu_B \text{ and } \mu(\text{Gd2}) = 0.9(3)\mu_B$$

Extrapolating to $T \to 0$, the magnetic moment of Gd1 reaches a value close to 7 $\mu_B$, as expected for that of Gd³⁺. In contrast, the moment at Gd2 remains at a magnitude of less than 1 $\mu_B$. The significant discrepancy between Gd1 and Gd2 magnetic moments is attributed to the strong frustration of the Gd2

<figure><img src="image_15.png" /><figcaption>Figure 7. $F_{\text{calc}}^2$ versus $F_{\text{obs}}^2$ of the nuclear and magnetic structure refinement of Gd₂Cl₃.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 8. Magnetic structure of Gd₂Cl₃. The magnetic moments are aligned along ±[010]. The length of the arrows corresponds to the size of the magnetic moments.</figcaption></figure>

sites, as already indicated by the heat capacity data and the large frustration ratio derived from the susceptibility data.

Figure 9 shows the temperature dependence of the integrated intensities of two magnetic reflections combined from measurements carried out at ILL’s instruments D9 and D3 ($T < 14$ K) with the external magnetic field on the latter turned off. It reveals a marked reduction of the magnetic scattering intensity, which we ascribe to a reorientation of the magnetic moments and possibly to a more complete ordering of the Gd2 magnetic moments. Further experiments are needed to determine the full magnetic structure at low temperatures.

**Tb₂Cl₃.** Magnetic and Thermal Properties. Figure 10 displays the inverse magnetic susceptibility of a crystal of Tb₂Cl₃ with the magnetic field aligned along the crystallographic b-axis. Above ~150 K, the susceptibilities follow a Curie–Weiss law according to eq 1 with an effective magnetic moment of

$$\mu_{\text{eff}} = 9.76(2)\mu_B$$

per Tb atom and a Curie–Weiss temperature of

$$\theta = -115(1) \text{ K}$$

with the latter amounting to about one-half of the Curie–Weiss temperature of Gd₂Cl₃. The effective magnetic moment is in very good agreement with the value of 9.72 $\mu_B$ expected for Tb³⁺
<figure><img src="image_17.png" /><figcaption>Figure 9. Two magnetic reflections acquired on a crystal of Gd₂Cl₃ using D9's single counter between T_N and ~14 K and the instrument D3 (external field set to zero) down to ~1.4 K. (Data taken from refs 27 and 28.)</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 10. Inverse magnetic susceptibility of TbCl₁.₅. The red solid line is a fit to the Curie–Weiss law (eq 1) with parameters given in the insets. The lower right inset displays the susceptibility at low temperatures.</figcaption></figure>

with the Landé g-factor gᵢ = 3/2 and J = 6. Using Pascal's increments, the diamagnetic susceptibility, χ₀, was calculated and fixed to -54 × 10⁻⁶ cm³/mol.²⁹

As for Gd₂Cl₃, the negative Curie–Weiss temperature suggests predominant antiferromagnetic exchange interactions between Tb moments. However, crystal electric field splitting effects may also add to the Curie–Weiss temperature. Below ~100 K, 1/χ(T) starts to deviate from the high-temperature Curie–Weiss law, and at low temperatures, the susceptibility follows the Curie–Weiss law again, however with significantly different parameters μₐff and θ

$$ \mu_{\text{eff}} = 5.76(2)\mu_{\text{B}} $$

per formula unit Tb₂Cl₃. The Curie–Weiss temperature amounts to

$$ \theta = -7.5(1) \text{ K} $$

The significantly reduced effective moment is ascribed to the strong antiferromagnetic coupling of one out of the two Tb atoms. As a consequence, the polarization by magnetic fields of the coupled moments is significantly reduced. The large negative high-temperature Curie–Weiss temperature backs this interpretation, whereas the very small Curie–Weiss temperature at low temperatures indicates that the remaining Tb moments are only weakly coupled by spin exchange. This scenario is supported by the polarized neutron diffraction results (see below), which reveal that the strongly antiferromagnetic-coupled large moments at Tb1 positions are less polarizable in an external magnetic field compared to the Tb2 magnetic moments. Finally, at very low temperatures, χ(T) exhibits a rounded peak centered at ~3.6 K, which we ascribe to a TbCl₃ impurity (see inset in Figure 10).

Whereas there is no clear indication for magnetic ordering in the magnetic susceptibility data, the specific heat capacity of Tb₂Cl₃ displayed in Figure 11 shows a small anomaly at ~42.7 K

<figure><img src="image_19.png" /><figcaption>Figure 11. Specific heat of Tb₂Cl₃ highlighting the anomaly at ~42.7 K. The lower inset displays the heat capacity down to 2 K. The upper inset shows a magnified view of the λ-type anomaly at ~3.7 K, which is ascribed to a TbCl₃ contamination of ~0.5(2)%.</figcaption></figure>

comprising an entropy of ~0.45 J/(mol K) per formula unit Tb₂Cl₃. In addition, a small but sharp λ-like anomaly is seen at 3.65 K, which we attribute to the ferromagnetic order of a TbCl₃ contamination, as also indicated by the magnetic susceptibility data. In comparison with the entropy of the ferromagnetic ordering anomaly of concentrated TbCl₃, we estimate an amount for the impurity of ~0.5(2)%.³⁰,³¹

**Magnetic Structure Determination.** Apart from the nuclear Bragg reflections corresponding to the crystal structure of Tb₂Cl₃, temperature-dependent neutron scattering on a crystal of Tb₂Cl₃ showed additional Bragg reflections which can be indexed with a propagation vector ⃗τ = [1,0,0], indicating the loss of the c-centering symmetry operation. These additional Bragg reflections disappear at a temperature of ~42.7 K, coinciding very well with the temperature where the heat capacity anomaly is observed, suggesting the additional reflections to be of magnetic origin (see Figure 12). The intensity of a nuclear test reflection does not show noticeable changes at this temperature, indicating small to negligible spontaneous magnetostriction. A
<figure><img src="image_20.png" /><figcaption>**Figure 12.** Integrated intensities of three magnetic Bragg reflections with indices given in the figure.</figcaption></figure>

fit of the integrated intensities, $I(T)$, of five magnetic Bragg reflections with a critical power law (eq 4) in the temperature range $35 \text{ K} \le T \le 45 \text{ K}$ results in a (averaged) critical temperature of $T_N = 42.68(3) \text{ K}$ and a critical exponent and $\beta = 0.34(2)$. The latter being well within the range of typical critical exponents for standard universality classes of 3D magnetic ordering.²⁴ Figure 13 highlights the integrated intensity of two characteristic

<figure><img src="image_21.png" /><figcaption>**Figure 13.** Integrated intensities of the 300 and 100 magnetic Bragg reflections as a function of temperature in a double-log plot. The red dashed line represents a power law according to eq 4 with a critical exponent of 0.34.</figcaption></figure>

magnetic Bragg reflections as a function of the reduced temperature. The red dashed line represents a power law of the reduced temperature with a critical exponent of 0.34.

Full magnetic data sets were collected at 20, 18, 10, 5, and 2 K. Additionally, nuclear Bragg reflections were measured at 20 K, and the crystal structure was refined. The atom positional parameters (see Table 2) were found to be identical to those refined by Beck from neutron powder diffraction data collected at the DMC diffractometer at the Paul Scherrer Institute (PSI, Switzerland) operated in the high-intensity mode.¹³

<table><caption>**Table 2.** Atom Positional Parameters Refined from Integrated Neutron Scattering Intensities Collected at 20 K<sup>a</sup></caption><thead><tr><th>atom</th><th>x</th><th>z</th><th>B<sub>iso</sub> (10<sup>4</sup> pm<sup>2</sup>)</th></tr></thead><tbody><tr><td>Tb1</td><td>0.4102(2)</td><td>0.0530(4)</td><td>0.05(3)</td></tr><tr><td>Tb2</td><td>0.1376(3)</td><td>0.2904</td><td>0.05(3)</td></tr><tr><td>Cl1</td><td>0.6578(3)</td><td>0.5104(4)</td><td>0.08(3)</td></tr><tr><td>Cl2</td><td>0.7691(2)</td><td>0.8819(4)</td><td>0.08(3)</td></tr><tr><td>Cl3</td><td>0.9505(3)</td><td>0.2699(4)</td><td>0.08(3)</td></tr></tbody></table>

<sup>a</sup>The R-factors of the refinements were $R_1 = \frac{\sum |I_{(\text{obs})} - I_{(\text{calc})}|}{\sum |I_{(\text{obs})} - I_{(\text{calc})}|} = 4.07\%$ and $R_2 = \frac{\sum (\text{obs})^2}{\sum (\text{obs})^2} = 0.21\%$. The refined parameters are identical to the parameters refined from a neutron powder diffraction pattern collected at 7.5 K.¹³ All atoms are located on Wyckoff site 4i ($y=0$) in space group C2/m.

A symmetry analysis based on the propagation vector $\tau = [1,0,0]$ using the program BasIreps included in the Fullprof program package²⁶ indicated the magnetic moments to lie either in the a-c plane or along the b-axis. Inspection of the intensity of some characteristic magnetic Bragg reflections suggested the former option to be more likely. The magnetic structure (magnetic space group C'2/m') at five different temperatures, 5 K $\le T \le 20$ K, was solved employing the Cambridge Crystallographic Subroutine Library (CCSL) programs. Tb1 and Tb2 atoms exhibit markedly different ordered moments which below 20 K do not substantially vary as a function of temperature (see Table 3). This finding contrasts with the previous results obtained by Beck from powder diffraction, who found the moment of Tb2 to markedly decrease below ~15 K.¹³,¹⁴

<table><caption>**Table 3.** Refined Magnetic Moments, $\mu$, for Tb1 and Tb2 and Polar Angles $\phi_i^a$</caption><thead><tr><th>T (K)</th><th>μ (Tb1) (μ<sub>B</sub>)</th><th>φ<sub>1</sub> (deg)</th><th>μ (Tb2) (μ<sub>B</sub>)</th><th>φ<sub>2</sub> (deg)</th><th>χ<sup>2</sup></th></tr></thead><tbody><tr><td>20</td><td>9.56(12)</td><td>-39.7(4)</td><td>2.62(6)</td><td>27(1)</td><td>11</td></tr><tr><td>18</td><td>9.39(16)</td><td>-39.6(3)</td><td>2.65(6)</td><td>28(1)</td><td>9</td></tr><tr><td>10</td><td>9.19(23)</td><td>-39.5(4)</td><td>2.62(8)</td><td>27(2)</td><td>9</td></tr><tr><td>5</td><td>9.21(11)</td><td>-39.6(4)</td><td>2.57(6)</td><td>2882</td><td>14</td></tr><tr><td>2</td><td>9.4(3)</td><td>-39.7(5)</td><td>2.68(10)</td><td>27(2)</td><td>17</td></tr></tbody></table>

<sup>a</sup>Common $\chi^2$ values of the refinements are given in the rightmost column.

The magnetic moments of Tb1 and Tb2 lie in the a-c plane and are inclined with respect to each other, enclosing an angle of ~68° (see Figure 14). Whereas the ordered moment of Tb1 amounts to ~9.3 $\mu_B$ and thus slightly exceeds the expected moment of $gJ = 9 \mu_B$, the moment of Tb2 is significantly reduced to ~2.6 $\mu_B$ (see Table 3).

**Neutron Scattering with Polarization Analysis.** The magnetic susceptibility data of Tb₂Cl₃ indicated a gradual reduction of the magnetic moment below ~100 K so that at low temperature, one out of the two Tb atoms in the formula unit of Tb₂Cl₃ effectively appears to disappear. Analogous to Gd₂Cl₃, this finding suggests a strong antiferromagnetic coupling between the Tb1 moments, which leaves these only weakly magnetically polarizable. This presumption was tested by carrying out polarized neutron scattering experiments on ILL's diffractometer D3. A Tb₂Cl₃ crystal was placed in an external magnetic field ($b \parallel H$, ~4.6 T) at 4.2 K, and flipping ratios of ~60 magnetic Bragg reflections with Bragg indices *h*0l were collected. Fourier transformation resulted in the magnetization densities shown in a contour plot in Figure 15. The magnetization density
<figure><img src="image_22.png" /><figcaption>Figure 14. Magnetic structure of Tb$_{2}$Cl$_{3}$ projected along [010]. The Tb1 and Tb2 atoms and the moment vectors are shown in different colors.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Figure 15. (a) Contour plot of the magnetization density of Tb$_{2}$Cl$_{3}$ at 4.6 T projected on the a-c-plane derived from the polarized neutron flipping ratios collected on ILL's hot neutron diffractometer D3. The large diamonds sketch the projection of the Tb metal-atom octahedra. (b) Section of the crystal structure of Tb$_{2}$Cl$_{3}$ corresponding to the section displayed in Figure 2a.</figcaption></figure>

data reveal strong magnetic polarizability of the Tb2 moments, whereas moments at Tb1 sites exhibit only a small response to the external field. This finding clearly supports the interpretation of the low-field magnetic susceptibility data (Figure 10), indicating a substantial reduction of the effective magnetic moment toward lower temperatures.

**Isothermal Magnetization.** In order to quantitatively follow the magnetic polarizability of the Tb moments as a function of temperature, we have carried out isothermal magnetization measurements. Figure 16 displays the isothermal magnetization of a crystal of Tb$_{2}$Cl$_{3}$ as a function of the external magnetic field aligned along the b-axis, i.e., perpendicular to the ordered moments. The field dependence of the magnetization is reminiscent of saturation behavior but superposed with an additional linear increase, clearly visible at high magnetic fields. At 2 K, the magnetization at 5.5 T amounts to ~3 µ$_{B}$, suggesting that at low temperatures, essentially the moments at Tb2 positions can be aligned by an external magnetic field.

To quantitatively fit the magnetization as a function of the external magnetic field and the temperature, we assumed that

<figure><img src="image_24.png" /><figcaption>Figure 16. Isothermal magnetization of Tb$_{2}$Cl$_{3}$ per formula unit Tb$_{2}$Cl$_{3}$ as a function of the external magnetic field at three characteristic temperatures. The red solid lines represent the fits by a Langevin function and a linear term assuming fixed moments for Tb2 interpolated for the respective temperature from the results of the magnetic structure refinement. The linear magnetization contribution arises from the slight canting of the Tb1 moments induced by the perpendicular external magnetic field. For more details, see the text.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Figure 17. $\chi_{\text{Tb1}}$ and the molecular field parameter $\lambda$ as a function of temperature gained from a fit of eq 5 to the isothermal magnetization data. The dashed lines are guides to the eye. The moments on Tb2 are given in Table 4.</figcaption></figure>

the Tb1 moments are strongly antiferromagnetically coupled and that the external magnetic field can include only a slight canting of the moments with a linear increase of their magnetization. In contrast, the Tb2 atoms are easily polarizable, and in a sufficiently strong magnetic field, the magnetization can saturate. To model the polarization of the Tb2 magnetic moments, we take a Langevin function, $L(\alpha)$, however with the magnetic field acting on the $\mu_{\text{Tb2}}$ moments magnified by a molecular field term, $\lambda\mu_{0}H_{\text{int}}$. The latter is related to the magnetization of the Tb1 atoms multiplied by a molecular field constant $\lambda$.

$$M = \mu_{\text{Tb2}}L(\alpha) + \mu_{0}H_{\text{ext}}\chi_{\text{Tb1}} \quad (5)$$

where $\alpha$ is given by

$$\alpha = \frac{\mu_0 \mu_{\text{Tb2}} (H_{\text{ext}} + H_{\text{int}})}{k_B T} \quad (6)$$
and

$$ \mu_0 H_{\text{int}} = \lambda \mu_0 H_{\text{ext}} \chi_{\text{Tb1}}(T) \quad (7) $$

Using fixed moments for Tb2 as interpolated from the magnetic structure refinement results, our model fits the data very well with the fit parameters listed in Table 4. $\chi_{Tb1}$ reflects

<table><caption>Table 4. Parameters Obtained from Fits of Eq 5 to the Experimental Magnetization Shown in Figure 17<sup>a</sup></caption><thead><tr><th>T (K)</th><th>μ (Tb2) (μ<sub>B</sub>)</th><th>χ<sub>Tb1</sub> (cm<sup>3</sup>/mol)</th><th>λ</th></tr></thead><tbody><tr><td>2</td><td>2.68</td><td>0.133(2)</td><td>3.9(2)</td></tr><tr><td>4</td><td>2.62</td><td>0.153(2)</td><td>8.9(3)</td></tr><tr><td>6</td><td>2.59</td><td>0.167(1)</td><td>11.3(1)</td></tr><tr><td>10</td><td>2.63</td><td>0.174(41)</td><td>13.2(1)</td></tr><tr><td>15</td><td>2.62</td><td>0.176(1)</td><td>14.6(1)</td></tr></tbody></table>

<sup>a</sup>The moments of the Tb2 atoms were interpolated from the magnetic structure refinement results listed in Table 3.

the canting of the Tb1 moments. It shows a weak temperature dependence and levels off at higher temperatures, consistent with the expectation of the perpendicular susceptibility $\chi_{\perp}$ of an uniaxial antiferromagnet. The molecular field parameter $\lambda$ shows a stronger temperature dependence, possibly due to a varying inclination as a function of the temperature of the Tb1 and Tb2 moments in the external magnetic field.

## SUMMARY AND CONCLUSIONS

The experimental results summarized above provide a first complete picture of the magnetic properties of the RE sesquihalide phases $M_2Cl_3$ (M = Gd, Tb), which for the first time realized the formal oxidation state +1.5 for RE elements. In spite of this, the effective magnetic moments found for $Gd_2Cl_3$ and $Tb_2Cl_3$ compare well with those expected for Gd and Tb in the oxidation state +3. The crystal structure of the $M_2Cl_3$ phases is characterized by condensed octahedral clusters of RE metal atoms and as such bears close analogies to the cluster and condensed cluster compounds of the heavy d-transition elements. The octahedra condense via opposite edges to infinite chains. Metal-metal bonding in the shared edge leads to a very short bonding distance of the RE atoms, being even smaller than those in the metals themselves.

The arrangement of the magnetic RE ions in octahedra puts the apical M2 atoms in geometrically frustrated triangles with a severe impact for their magnetic properties. This becomes particularly evident for $Gd_2Cl_3$. There, the Gd2 moments at the apical sites of the octahedra exhibit a largely reduced ordered moment as compared to the Gd moments at the shared edges. There, a fully developed Gd moment close to $7 \mu_B$ is observed. As a consequence of magnetic frustration, long-range antiferromagnetic order in $Gd_2Cl_3$ appears only at $T_N \sim 23$ K, whereas a very large negative Curie-Weiss temperature of $\sim -209$ K indicates substantial spin exchange between the Gd magnetic moments. The magnetic heat capacity results indicate that about 50% of the magnetic entropy is gradually removed below $T_N$, corresponding to the entropy of one Gd atom in the formula unit $Gd_2Cl_3$. The very small heat capacity anomaly at $T_N$ comprises only a very small fraction (<1%) of the total magnetic entropy per Gd atom. The comparison of $T_N$ and Curie-Weiss temperature reveals a large frustration ratio of $\approx 10$.

For $Tb_2Cl_3$, the magnetic structure solution indicates a similar frustrated scenario with largely different magnetic moments for the Tb1 and Tb2 atoms. In contrast to $Gd_2Cl_3$, the Tb moments

lie in the a-c plane of the monoclinic crystal structure and are inclined with respect to each other. Whereas the size and arrangement of the spin-only Gd moments in $Gd_2Cl_3$ crystalline electric field effects and crystal anisotropy can be expected to be small to negligible, $Tb^{3+}$ has a large orbital moment, and the reduced moment at Tb2 may also be a consequence of crystal field splitting effects. Neutron diffraction with polarization analysis reveals a substantially larger magnetic polarizability of the Tb2 moments residing at the highly frustrated positions at the apical sites of the distorted Tb octahedra. Interestingly, the neutron diffraction results show that the moment at Tb1 is enlarged as compared to the maximum possible moment of $9 \mu_B$. This finding is ascribed to some polarization by the rather large localized Tb moments of d-electrons in filled d-electronic bands, located below the Fermi energy. Similar polarization effects have also been detected in Gd metal or in $GdI_2$.18,32,33

## ASSOCIATED CONTENT

### Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.4c01317.

Details of how the temperature dependence of the low-temperature intensities of two magnetic Bragg reflections of $Gd_2Cl_3$ was acquired using ILL's polarized neutron diffractometer D3 in a modified configuration, including magnetization of a crystal of $Gd_2Cl_3$ showing a peak at $\sim 8$ K, pointing to a second antiferromagnetic ordering of the magnetic structure of $Gd_2Cl_3$ at low temperatures, as also indicated by the temperature dependence of the intensities of the magnetic Bragg reflections shown in the main panel (PDF)

## AUTHOR INFORMATION

### Corresponding Author

Reinhard K. Kremer - Max-Planck-Institut für Festkörperforschung, Stuttgart 70569, Germany;
orcid.org/0000-0001-9062-2361; Email: R.Kremer@fkf.mpg.de

### Authors

Walter Schnelle - Max-Planck-Institut für Festkörperforschung, Stuttgart 70569, Germany; Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden 01187, Germany

Roland Eger - Max-Planck-Institut für Festkörperforschung, Stuttgart 70569, Germany

Arndt Simon - Max-Planck-Institut für Festkörperforschung, Stuttgart 70569, Germany

P. Jane Brown - Institut Max von Laue Paul Langevin, Grenoble 38042, France

Bachir Ouladdiaf - Institut Max von Laue Paul Langevin, Grenoble 38042, France

Klaus-Ulrich Neumann - Department of Physics, Loughborough University, Loughborough, Leics LE11 3TU, U.K.

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.chemmater.4c01317

### Author Contributions

The manuscript has been jointly prepared by all coauthors, R.K.K., W.S., R.E., A.S., P.J.B., B.O., and K.-U.N., who reviewed and approved its content.
## Funding

Open access funded by Max Planck Society.

## Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

This paper is a part of a Virtual Special Issue of Chemistry of Materials dedicated to the memory of Professor Francis J. DiSalvo. We thank E. Brücher for experimental assistance, B. Krauter for preparing some of the RE trihalides, and H.-J. Mattausch for clarifying discussions concerning the chemistry of the sesquihalide compounds.

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