#
Mapping the Magnetic Anisotropy inside a Ni_{4} Cubane Spin Cluster Using Polarized Neutron Diffraction

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

^{‡}

## Abstract

**:**

_{4}(L)

_{4}(MeOH)

_{4}] (H

_{2}L = salicylidene-2-ethanolamine; MeOH = methanol), by the means of angular-resolved magnetometry and polarized neutron diffraction (PND). We show that better than other usual characterization techniques—such as electron paramagnetic resonance spectroscopy (EPR) or SQUID magnetometry—only PND enables the full determination of the local magnetic susceptibility tensor of the tetranuclear cluster and those of the individual Ni(II) ions and the antiferromagnetic pairs they form. This allows highlighting that, among the two antiferromagnetic pairs in the cluster, one has a stronger easy-axis type anisotropy. This distinctive feature can only be revealed by PND measurements, stressing the remarkable insights that they can bring to the understanding of the magnetic properties of transition metals clusters.

## 1. Introduction

^{3+}and Co

^{2+}ions [9,10]. In this paper we report the study, by angular-resolved magnetometry and polarized neutron diffraction, of the magnetic anisotropy of the [Ni

_{4}(L)

_{4}(MeOH)

_{4}] cluster (Figure 1), so-called [Ni

_{4}]. This complex presents a S = 4 paramagnetic ground spin-state resulting from dominant ferromagnetic interactions between two weakly antiferromagnetic Ni pairs, but shows no SMM behavior. The nature of the magnetic anisotropy of the [Ni

_{4}] cluster was previously investigated by the means of inelastic neutron scattering (INS) on powder [11] which showed the existence of a large easy-axis type anisotropy. The aim of the present study is to show how PND permits to map precisely the local magnetic anisotropy inside polynuclear complexes in the weak exchange limit, here in the case of a paramagnetic cubane-like tetranuclear Ni

^{2+}complex.

_{4}] cluster crystallizes in the monoclinic space group P2

_{1}/n, with cell parameters a = 13.0750(9) Å, b = 18.2933(10) Å, c = 18.7624(13) Å and β = 110.260(7) deg, with two different molecular orientations in the cell [11]. Following the classification of polynuclear complexes with cubane like structure [12] [Ni

_{4}] is a class II cluster, characterized by a distorted [Ni

_{4}O

_{4}] cubane core with alkoxo bridges, presenting four short and two long Ni…Ni distances (type 4+2 structure), with an approximate S

_{4}symmetry (Figure 1c). Angular-resolved SQUID measurements provide the crystal (lattice) magnetic anisotropy but not the individual molecular principal magnetic axes because of the existence of two different molecular orientations in the cell, nor the local magnetic anisotropy on each Ni site. In contrast, PND measurements under a moderate magnetic field applied along different directions of the crystal allows to determine the local susceptibility tensor of the cluster and the directions of its principal axes with respect to its geometry. This cluster tensor can be written as the sum of so-called effective tensors [10], which are defined as single ion tensors perturbed by the magnetic exchange between Ni(II) ions. In the following, we show how PND gives access to both the single ion and effective tensors of the antiferromagnetic pairs in the cluster.

## 2. Materials and Methods

#### 2.1. Synthesis

_{4}(L)

_{4}(MeOH)

_{4}] cluster was prepared as described in [11], where L

^{2−}is the bis-deprotonated ligand represented in Figure 1a. Large single crystals (size 9–12 mm

^{3}) were obtained by slow diffusion of methanol to a solution of [Ni

_{4}(L)

_{4}(MeOH)

_{4}] in ethyl acetate (EtOAc): the green precipitate of [Ni

_{4}(L)

_{4}(MeOH)

_{4}] was solubilized in a small quantity of EtOAc, then the obtained solution was filtered and carefully transferred into a long glass tube. The tube was inserted inside a HLC TK13 heating-block thermostat keeping the crystallization temperature constant. The solution was carefully layered with the same volume of pure EtOAc in order to avoid immediate mixing. Finally, a small volume of methanol was carefully added, the tube was closed and left undisturbed for about a month. The bottom part of the tube was constantly heated to 40 °C. After one month, large green single crystals were formed.

#### 2.2. Magnetic Measurements

^{3}) under a magnetic field of 0.1 T and at 10 K, temperature of the PND study. The orientation of the crystal on the magnetometer was set manually:

**Set 1**: the crystal was set with the $\overrightarrow{c}$ axis along the rotation axis;

**Set 2**: the crystal was set with the $\overrightarrow{b}$ axis along the rotation axis. In both cases, the $\overrightarrow{a}$ axis was initially set along the magnetic field (rotation angle Φ = 0).

#### 2.3. Simulation of Angular-Resolved Magnetic Measurements

**Set 1**: Considering a crystal rotating around the $\overrightarrow{c}$ axis and a magnetic field initially parallel to the $\overrightarrow{a}$ axis, one may write, in the ($\overrightarrow{i}$,$\overrightarrow{j}$,$\overrightarrow{k}$)frame (with $\overrightarrow{i}$//${\overrightarrow{a}}^{*}$, $\overrightarrow{j}$//$\overrightarrow{b}$, $\overrightarrow{k}$//$\overrightarrow{c}$), the magnetic field as:

**Set 2**: It was not possible to simulate the experimental data considering a rotation around the $\overrightarrow{b}$ axis and the magnetic field initially along the $\overrightarrow{a}$ axis. A rotation around an axis comprised in the ($\overrightarrow{b}$,${\overrightarrow{c}}^{*}$) plane was instead considered, with a field initially parallel to $\overrightarrow{a}$. Calling ω the angle between the rotation axis and the crystal $\overrightarrow{b}$ axis, and Φ the rotation angle we can express the orientation of the magnetic field in the ($\overrightarrow{i}$,$\overrightarrow{j}$,$\overrightarrow{k}$) frame as:

#### 2.4. Neutron Diffraction

#### 2.4.1. Polarized Neutron Diffraction

^{+}and I

^{−}are the intensities which are diffracted by the crystal when the incident neutron beam has alternate up (+) and down (−) directions of vertical polarization.

_{ij}of the susceptibility tensor, provided the data are collected under a moderate magnetic field in order to ensure a linear magnetization behavior, for three successive orthogonal orientations with respect to the crystal.

^{3}, for three different orientations of the crystal with respect to the vertical applied magnetic field (see Table 1). The same sample was used on the 5c2 diffractometer. From the magnetization curve at 10 K, it appears magnetization remains linear with field at 2 T, whatever the field orientation with respect to the crystal lattice. Therefore, data collection for the magnetic susceptibility tensor determination were performed at 10 K under 2 T.

#### 2.4.2. Unpolarized Neutron Diffraction

_{iso}(C), U

_{iso}(N), U

_{iso}(O), U

_{iso}(H)) using 109 constraints. The following thermal parameters were obtained: U

_{iso}(C) = 0.008(6), U

_{iso}(N) = 0.013(14), U

_{iso}(O) = 0.018(19), U

_{iso}(H) = 0.070(13) and used to calculate the nuclear structure factors that are necessary for the PND data analysis.

## 3. Results and Discussion

#### 3.1. Bulk Magnetic Anisotropy from Magnetometry

^{−1}(Figure 2a), which is higher than the expected value for four uncorrelated Ni

^{2+}ions. The χT product continuously increases upon cooling to reach a maximum of 11.83 cm

^{3}·K·moL

^{−1}at 8 K, indicating the dominant ferromagnetic interactions within the cluster. The maximum value is close to the expected value for an S = 4 ground spin-state with a g-value of 2.2. However, this g-value is quite high, in agreement with ground spin-state anisotropy. At 2 K, magnetization increases continuously with the field (Figure 2b) but does not reach saturation at 5 T.

_{4}], with its easy axis directed along the applied field. It shows a rapid increase and reaches a saturation value of 9 µ

_{B}which corresponds to a ground spin-state S = 4 with g = 2.2.

_{B}at 2 T, while, for the minimum ($\overrightarrow{H}$//${\overrightarrow{a}}^{*}$), it increases up to 3.4 µ

_{B}. For the $\overrightarrow{b}$ axis rotation (Figure 5b), close values (3.3 and 3.7 µ

_{B}) are observed at 2 T for both the minimum and two maxima of Figure 4b.

#### 3.2. Local Susceptibility Tensor from PND

_{F}) and antiferromagnetic (W

_{AF}) exchange between the Ni(II) ions:

_{4}O

_{4}cube. This approximation is justified by the weakness of the magnetic exchange interactions in the cluster, as shown by the coupling constants deduced from magnetic measurements, J

_{F}= 8(1) cm

^{−1}and J

_{AF}= −3(1) cm

^{−1}from [11]:

_{ij}for each Ni ion were first refined, on the joint basis of the three datasets, but only those for which the obtained value was larger than 1.5 times the error bar were included in the final refinement. The refinement of the local susceptibility tensors ${\overleftrightarrow{\chi}}_{Ni}^{\mathit{l}}$ (with l = 1, 4) evidences a strong similarity between the Ni1 and Ni4 susceptibilities on one side and between Ni2 and Ni3 on the other side as showed by the reported components in Table 1. This suggests that the two Ni atoms belonging to a same antiferromagnetic (AF) pair, (Ni1, Ni4) and (Ni2, Ni3), respectively, have similar magnetic behaviors with respect to the applied magnetic field. Furthermore, the refined eigenvalues of each Ni local tensor, reported in Table 2, show that the Ni1 and Ni4 tensors are more anisotropic than those of Ni2 and Ni3. This feature is reflected by the magnetic ellipsoids drawn in Figure 7, together with the directions of the eigenvectors, whose components are reported in Table S1.

_{4}pseudo-symmetry axis, but the hard ($\overrightarrow{{\chi}_{3}}$) and intermediate ($\overrightarrow{{\chi}_{2}})$ axes are found nearly perpendicular to each other axes, as well.

#### 3.3. Discussion

_{4}] are reported in Table 5. The deformation of the coordination octahedron around each Ni atom of this cluster is due a tetragonal elongation along the O–Ni–O direction involving the coordinated methanol and the bridging alkoxide [15]. The local geometries around Ni1 and Ni4 (Ni2 and Ni3, respectively) are very similar, as exemplified by the longest distance between opposite edge atoms in the octahedron (which reflects the distortion of the octahedron): 4.246 Å for Ni1, and 4.254 Å for Ni4. Noteworthy, this distance is slightly larger (4.275 Å) for both Ni2 and Ni3.

_{2}O

_{2}bridges of the cubane are summarized in Table 6. The AF bridges present longer Ni…Ni distances (3.19 Å) with two short and two long Ni–O bonds and bridging angles of 100–101 deg., while the ferromagnetic bridges display shorter Ni…Ni distances (3.04 Å) with three short and one long Ni–O bonds and bridging angles of 91 to 97 deg, as shown in Figures S1 and S2 in the Supplementary Information.

_{2}Ni4 and Ni2O

_{2}Ni3 bridges, the directions of the $\overrightarrow{{\chi}_{3}}$ hard magnetic axes for Ni1, Ni3 and Ni4 are close to the local distortion axes, i.e., along the O–Ni–O direction involving methanol and bridging alkoxide, as speculated in [15]. This is not verified for the Ni2 ion. However, from Table 4, the eigenvalues of the Ni2 local tensor corresponding to the mean and hard axes are close to each other (χ

_{2}= 0.42(20)μ

_{B}/T and χ

_{3}= 0.33(6)μ

_{B}/T) with overlapping error bars, showing that it is difficult to discriminate between these two directions and that the exact direction of the hard axis in the plane perpendicular to the easy axis cannot be determined from the Ni2 local tensor.

_{1}/c space group, the crystal susceptibility tensor can be deduced from Equations (10) and (11), which leads to the bulk susceptibility tensor:

_{B}) differs from the expected one (2µ

_{B}) from the PND bulk tensor (Equation (15)) for $\overrightarrow{H}$//$\overrightarrow{c}$, while for the maximum (3.7 µ

_{B}) it is larger than the expected value (3.8 µ

_{B}) from Equation (15) for the intermediate axis $\overrightarrow{H}$//${\overrightarrow{a}}^{*}$. This is very likely due to a tilt of the rotation axis in the ($\overrightarrow{b}$,${\overrightarrow{c}}^{*}$) plane, as the precise orientation of the $\overrightarrow{b}$ axis proved to be very hard to find because of the crystal shape. The simulation of the data reported in Figure 4b only proved possible when considering the true rotation axis was tilted from the $\overrightarrow{b}$ axis in the ($\overrightarrow{b}$,${\overrightarrow{c}}^{*}$) plane, with the magnetic field initially close to the $\overrightarrow{a}$ axis, as already proposed. The best agreement between our simulation and the experimental data, displayed on Figure 4b, was obtained for a tilt angle ω of −65°, suggesting the rotation axis was actually closer to $\overrightarrow{c}$ than to $\overrightarrow{b}$ as first expected. As one can note, with such a hypothesis a very good agreement is reached with the experimental data, both on the locations and magnitudes of the extrema of the curve. Alas, this implies that the orientations in the lattice corresponding to these extrema are rather ill-defined and, thus, prevents a proper assignment of the maxima or the minima.

_{4}axis, in agreement with the conclusion of the previous INS investigation [3]. The following Hamiltonian was used for the full description of the eight transitions in the INS spectra (with selection rules ΔM

_{S}= ±1) [3]:

^{−1}and E =0.023(8) cm

^{−1}(due to deviations from S

_{4}cluster symmetry). The observed axial anisotropy of the cluster magnetic ellipsoid (χ

_{1}>> χ

_{2}, χ

_{3}) confirms the easy axis-type magnetic anisotropy of the cluster predicted by the negative sign of D.

## 4. Conclusions

^{2+}ion, and also for the two different pairs of antiferromagnetically-coupled Ni

^{2+}ions. Our results show that the strength of the local magnetic anisotropy is clearly related to the local geometry of the Ni coordination octahedron. They confirm that the orientation of the hard axes of the Ni

^{2+}ions is governed by the tetragonal elongation along the O-Ni-O direction involving the coordinated methanol and the bridging alkoxide. However, the single ion magnetic anisotropy is not only stemming from this axial distortion, but also originates from the deformation in the equatorial directions of the coordination octahedron, as shown by the strongest axial anisotropy of the AF pair which displays the weakest axial elongation but largest equatorial distortion.

_{4}pseudosymmetry axis as assumed in the INS study, but in addition and exclusively it reveals the easy axis anisotropy of the cluster is mastered by the anisotropy of one of the two antiferromagnetic pairs, which presents stronger axial anisotropy than the other one.

## Supplementary Materials

_{2}Ni bridges; Figure S2. Geometry of the four NiO

_{2}Ni bridges presenting ferromagnetic coupling. The source code of the CalcM program; Manual of information about the algorithm.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) salicylidene-2-ethanolamine (H

_{2}L); (

**b**) molecular structure of [Ni

_{4}] cluster; and (

**c**) the view of the cubane core with labels.

**Figure 2.**Magnetic behavior of a polycrystalline sample. (

**a**) Temperature dependence of the product of the magnetic susceptibility with temperature (χT) under an applied field of 0.1 T. (

**b**) Field dependence of magnetization at 2 K.

**Figure 3.**Field dependence of the magnetization at 2 K fora single crystal of [Ni

_{4}] with the magnetic field set parallel to the magnetic easy axis.

**Figure 4.**Dependence of the product of the magnetic susceptibility with temperature (χT) with the rotation angle Φ at 10 K, under a static field of 0.1 T: (

**a**) for a rotation around the crystal $\overrightarrow{c}$ axis and (

**b**) for a rotation around the crystal $\overrightarrow{b}$ axis . The red curve is the simulation from the PND data.

**Figure 5.**Dependence of the magnetization at 10 K with the magnetic field at the maxima and minima of the χT(Φ) curves:

**a**) for the rotation around the $\overrightarrow{c}$ axis and

**b**) for the rotation around the $\overrightarrow{b}$ axis.

**Figure 6.**Magnetic ellipsoid associated to the cluster susceptibility tensor in projection along the crystal $\overrightarrow{c}$ axis. Easy axis is depicted in black, mean axis in green and hard axis in red. The pseudo-S

_{4}symmetry axis is represented in blue.

**Figure 7.**Magnetic ellipsoids associated to the Ni effective single ion susceptibility tensors: (

**a**) in projection along the crystallographic $\overrightarrow{c}$ axis; and (

**b**) in projection along the pseudo S

_{4}axis. Easy axes are in black, mean axes in green and hard axes in red. The pseudo-symmetry axis S

_{4}is represented in blue.

**Figure 8.**Magnetic ellipsoids associated to the antiferromagnetic pairs: (

**a**) Ni1–Ni4; and (

**b**) Ni2–Ni3. The easy magnetic axes are represented in black, the mean axes in green and hard axes in red.

**Figure 9.**Magnetic ellipsoids associated to the single-ion tensors for the Ni atoms involved in AF pairs, in projection along the S

_{4}pseudo axis: (

**a**) Ni1–Ni4; (

**b**) Ni2–Ni3. The easy magnetic axes are represented in black, the mean axes in green, and the hard axes in red.

PND Data Collections | ||||
---|---|---|---|---|

Instrument | 5c1 (LLB) | |||

Temperature (K) | 10 | |||

Field (T) | 2 | |||

Field components ^{1} | H_{x} | −0.7022 | −0.3395 | −0.0256 |

H_{y} | 0.1858 | −0.9347 | 0.1361 | |

H_{z} | 0.6873 | −0.1054 | 0.9904 | |

Number of observations | 241 | 258 | 273 | |

N_{obs} with |1−R| > 2σ | 47 | 75 | 48 |

^{1}in the($\overrightarrow{i}$,$\overrightarrow{j}$,$\overrightarrow{k}$) cartesian basis set.

4-Circle Neutron Diffraction Data Collection | |
---|---|

Instrument | 5c2 (LLB) |

Temperature (K) | 20 |

N measured reflections | 225 |

N merged reflections | 111 |

N used reflections (I > 3σ) | 91 |

N refined parameters | 5 |

R(F) | 0.124 |

R_{w}(F) | 0.133 |

GOF | 5.96 |

**Table 3.**Susceptibility tensor components in (μ

_{B}/T) from PND for the cluster, individual ions, and antiferromagnetic pairs. As a footnote: the respective goodness-of-fits in the combined refinement are relative to the three different datasets.

χ_{11} | χ_{22} | χ_{33} | χ_{23} | χ_{31} | χ_{12} | ||
---|---|---|---|---|---|---|---|

Cluster ^{1} | [Ni_{4}] | 1.88(24) | 2.32(12) | 1.04(12) | 0.0 | 0.0 | −0.72(28) |

Ions ^{2} | Ni1 | 0.63(18) | 0.68(12) | 0.16(9) | 0.0 | 0.0 | 0.0 |

Ni2 | 0.42(20) | 0.48(8) | 0.33(6) | 0.0 | 0.0 | 0.0 | |

Ni3 | 0.23(18) | 0.58(9) | 0.32(7) | 0.0 | 0.0 | −0.18(12) | |

Ni4 | 0.74(21) | 0.85(11) | 0.20(9) | 0.0 | 0.0 | −0.33(13) | |

Pairs ^{3} | Ni1–Ni4 | 1.40(24) | 1.50(14) | 0.36(10) | 0.0 | 0.0 | −0.26(16) |

Ni2–Ni3 | 0.60(16) | 1.02(10) | 0.66(8) | 0.0 | 0.0 | 0.0 |

^{1}GOF: 2.2, 2.3, 2.9;

^{2}GOF: 2.3, 2.0, 3.2;

^{3}GOF: 2.1, 2.1, 2.9.

**Table 4.**Eigenvalues of the susceptibility tensors in (μ

_{B}/T) from PND for the cluster, individual ions, and antiferromagnetic pairs.

χ_{1} | χ_{2} | χ_{3} | ||
---|---|---|---|---|

cluster | [Ni_{4}] | 2.84 | 1.36 | 1.04 |

ions | Ni1 | 0.68(12) | 0.63(18) | 0.16(9) |

Ni2 | 0.48(8) | 0.42(20) | 0.33(6) | |

Ni3 | 0.66 | 0.32 | 0.15 | |

Ni4 | 1.13 | 0.46 | 0.20 | |

pairs | Ni1–Ni4 | 1.72 | 1.18 | 0.36 |

Ni2–Ni3 | 1.02(10) | 0.66(8) | 0.60(16) |

**Table 5.**Ni local geometry in [Ni

_{4}] from the X-ray structure [3]: distance between opposite atoms of the NiO

_{5}N octahedral.

Central Atom | Axial d(O…O) (Å) | Equatoriald(O…O) (Å) | Equatoriald(N…O) (Å) | |||
---|---|---|---|---|---|---|

Ni1 | O8…O9 | 4.246 | O1…O2 | 3.990 | N1…O6 | 4.008 |

Ni2 | O6…O10 | 4.275 | O3…O4 | 4.007 | N2…O2 | 3.995 |

Ni3 | O4…O11 | 4.275 | O5…O6 | 3.987 | N3…O8 | 3.977 |

Ni4 | O2…O12 | 4.254 | O7…O8 | 3.997 | N4…O4 | 4.007 |

**Table 6.**Structural characteristics of the Ni

_{2}O

_{2}bridges in [Ni

_{4}] from the X-ray structure [3].

Coupling | Ni…Ni Distance | Ni–O–Ni Angles | Short Ni–O Bond Lengths | Long Ni–O Bond Length | |
---|---|---|---|---|---|

ferromagnetic | Ni1–Ni2 | 3.038 | 96.5–96.6 | 2.030, 2.040, 2.051 | 2.116 |

Ni1–Ni3 | 3.032 | 94.0–96.3 | 2.019, 2.024, 2.051 | 2.121 | |

Ni2–Ni4 | 3.042 | 91.1–96.3 | 2.033, 2.040, 2.050 | 2.115 | |

Ni3–Ni4 | 3.039 | 93.1–97.3 | 2.023, 2.024, 2.050 | 2.136 | |

antiferromagnetic | Ni1–Ni4 | 3.184 | 100.4 | 2.022, 2.030 | 2.115, 2.121 |

Ni2–Ni3 | 3.195 | 100.1–101.2 | 2.019, 2.033 | 2.116, 2.136 |

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## Share and Cite

**MDPI and ACS Style**

Iasco, O.; Chumakov, Y.; Guégan, F.; Gillon, B.; Lenertz, M.; Bataille, A.; Jacquot, J.-F.; Luneau, D.
Mapping the Magnetic Anisotropy inside a Ni_{4} Cubane Spin Cluster Using Polarized Neutron Diffraction. *Magnetochemistry* **2017**, *3*, 25.
https://doi.org/10.3390/magnetochemistry3030025

**AMA Style**

Iasco O, Chumakov Y, Guégan F, Gillon B, Lenertz M, Bataille A, Jacquot J-F, Luneau D.
Mapping the Magnetic Anisotropy inside a Ni_{4} Cubane Spin Cluster Using Polarized Neutron Diffraction. *Magnetochemistry*. 2017; 3(3):25.
https://doi.org/10.3390/magnetochemistry3030025

**Chicago/Turabian Style**

Iasco, Olga, Yuri Chumakov, Frédéric Guégan, Béatrice Gillon, Marc Lenertz, Alexandre Bataille, Jean-François Jacquot, and Dominique Luneau.
2017. "Mapping the Magnetic Anisotropy inside a Ni_{4} Cubane Spin Cluster Using Polarized Neutron Diffraction" *Magnetochemistry* 3, no. 3: 25.
https://doi.org/10.3390/magnetochemistry3030025