# On the Magnetization and Entanglement Plateaus in One-Dimensional Confined Molecular Magnets

^{*}

## Abstract

**:**

## 1. Introduction

_{12}acetate or Fe

_{8}[1,2,5]. For example, Ni

_{4}has no tunneling in a zero magnetic field, and the electron paramagnetic-resonance EPR spectra exhibited unusual double sets of low-temperature peaks corresponding to slightly different easy magnetization axes [31]. Unlike Mn

_{12}acetate and Mn

_{4}dimer or Fe

_{x}$(x=4,8)$, encapsulated Ni molecular magnets seemed not to be equally spaced from each other [31,33] and did not have effective giant spins. Furthermore, the couplings of Cr-Ni molecular rings were studied by using different ligand-transition metal bridges, and the different sizes of the ligands could tailor the intermolecular interactions in Ni-based molecules as well [32,34,35].

_{4}Mo

_{12}molecule was studied within a post-Hartree–Fock approach, taking into account the contribution of delocalized electrons involved in complex exchange processes [36]. These contributions are favored when intricate exchange-bridge structures are present. Although such contributions are beyond the scope of this present study, they could be relevant within a framework that considers interactions between SMMs and the confining nanotubes’ electronic degrees of freedom or focuses on other ferroic order parameters.

## 2. Trimetric Ni-Based Single Chain Magnets and Quantum Methods

#### 2.1. Spin Chains: Hamiltonian Modeling

_{13}between two of the Ni ions (1 and 3 in Figure 1), which end up antiferromagnetically sharing the “central” Ni while breaking the triangular symmetry for the smaller nanotube diameters; the symmetric exchange coupling between the central Ni and its two nearest-neighbors, i.e., J

_{12}and J

_{23}, are initially ferromagnetic, giving rise to a frustrated-like state for comparatively larger nanotube dimensions [26].

_{2}-filled SWCNTs (single-wall carbon nanotubes) as the SMMs are being wrapped. To model the precise arrangement of the SMMs inside the SWCNTs would likely require a mixture of experimental, ab initio, and/or Hamiltonian techniques; however, there have been only a limited amount of approaches to form ordered structures inside the nanotube channels [26,42], and recent experiments with magnetic molecules still lack enough insight on this particular inquiry [44]. In this work, we explore three of the highest-symmetry configurations with respect to the axis of the tube and the planes perpendicular to it, which could be used to screen and/or interpret other energetically stabilized molecular arrangements.

_{2}case with a ferromagnetic superexchange coupling between $(1,2)$ and $(2,3)$ local nickel atoms, and ${J}_{13}=-0.89y$ meV, with $y=1$ representing the antiferromagnetic superexchange between ($1,3$) local molecular spins [26]. Also, ${\mathcal{J}}_{L}={\mathcal{J}}_{31}$, ${\mathcal{J}}_{A}={\mathcal{J}}_{21}$, and ${\mathcal{J}}_{P}={\mathcal{J}}_{22}$, where the subscripts refer to two nn molecules, respectively. Note the difference between the intra (J) and intermolecular ($\mathcal{J}$) couplings and that $(x,y)$ are parameters that allow us to follow the differences between the experimental exchange interactions and those simulated here, which, without loss of generality, could represent other molecular systems. In addition, the local magnetic moments for nickel are considered to have originated on a 3D shell with two unpaired electrons, i.e., $S=1$, as suggested in several previous results [26,33,41].

#### 2.2. Quantum Many-Body Methods: DMRG and MPS

## 3. 3D and 1D Molecular Magnets

#### 3.1. SMM Solutions

_{2}-filled SWCNTs simulated here.

#### 3.2. Two Coupled Molecules

## 4. Chain Magnets

#### 4.1. Beyond Two SMMs

#### 4.2. ($J$, ${J}_{13}$) Quenching

#### 4.2.1. ${\mathcal{J}}_{L}$ Configuration

#### FM ${\mathcal{J}}_{L}$

#### AFM ${\mathcal{J}}_{L}$

#### 4.2.2. ${\mathcal{J}}_{A}$ Configuration

#### FM ${\mathcal{J}}_{A}$

#### AFM ${\mathcal{J}}_{A}$

#### 4.2.3. ${\mathcal{J}}_{P}$ Configuration

#### FM ${\mathcal{J}}_{P}$

#### AFM ${\mathcal{J}}_{P}$

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Ni(acac)_{2} | trimetric nickel(II) acetylacetonate |

SMM | single-molecule magnet |

nn | nearest-neighbor |

L | linear |

A | alternated |

P | perpendicular |

SWCNT | single-wall carbon nanotube |

MPSs | Matrix Product States |

DMRG | density-matrix renormalization group |

Tenpy | Tensor Network Python |

TDVPs | time-dependent variational principles |

TEBDs | time-evolving block decimations |

S | entanglement entropy or von Neumann’s |

FM | ferromagnetism |

AFM | antiferromagnetism |

## Appendix A. Exact Solution for One and Two SMM

Energy (meV) | State |
---|---|

$-4.76$ | $\frac{1}{\sqrt{2}}(|\downarrow \downarrow 0\rangle -|0\downarrow \downarrow \rangle )$ |

$-4.76$ | $\frac{1}{2}(|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle -|00\downarrow \rangle -|\uparrow \downarrow \downarrow \rangle )$ |

$-4.76$ | $\frac{1}{2\sqrt{3}}(|0\downarrow \uparrow \rangle -|0\uparrow \downarrow \rangle +2|\downarrow 0\downarrow \rangle +|\downarrow \uparrow 0\rangle -2|\uparrow 0\downarrow \rangle -|\uparrow \downarrow 0\rangle )$ |

$-4.76$ | $\frac{1}{2}(|00\uparrow \rangle +|\downarrow \uparrow \uparrow \rangle -|\uparrow 00\rangle -|\uparrow \uparrow \downarrow \rangle )$ |

$-4.76$ | $\frac{1}{\sqrt{2}}(|0\uparrow \uparrow \rangle -|\uparrow \uparrow 0\rangle )$ |

$-4.18$ | $\frac{1}{\sqrt{3}}(|0\downarrow \downarrow \rangle +|\downarrow 0\downarrow \rangle +|\downarrow \downarrow 0\rangle )$ |

$-4.18$ | $\frac{1}{\sqrt{15}}(2|00\downarrow \rangle +2|0\downarrow 0\rangle +2|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle +|\downarrow \uparrow \downarrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$-4.18$ | $\frac{1}{\sqrt{10}}\left(2\right|000+|0\downarrow \uparrow \rangle +|0\uparrow \downarrow \rangle )+|\downarrow 0\uparrow \rangle +|\downarrow \uparrow 0\rangle +|\uparrow 0\downarrow \rangle +|\uparrow \downarrow 0\rangle $ |

$-4.18$ | $\frac{1}{\sqrt{15}}(2|00\uparrow \rangle +2|0\uparrow 0\rangle +2|\uparrow 00\rangle +|\downarrow \uparrow \uparrow \rangle +|\uparrow \downarrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$-4.18$ | $\frac{1}{\sqrt{3}}(|0\uparrow \uparrow \rangle +|\uparrow 0\uparrow \rangle +|\uparrow \uparrow 0\rangle )$ |

$-4.18$ | $|\uparrow \uparrow \uparrow \rangle $ |

$-3.56$ | $\frac{1}{\sqrt{3}}(-|0\downarrow 0\rangle +|\downarrow \downarrow \uparrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$-3.56$ | $\frac{1}{\sqrt{3}}(-|000\rangle +|\downarrow 0\uparrow \rangle +|\uparrow 0\downarrow \rangle )$ |

$-3.56$ | $\frac{1}{\sqrt{3}}(-|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$1.2$ | $\frac{1}{2}(|00\downarrow \rangle -|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle -|\uparrow \downarrow \downarrow \rangle )$ |

$1.2$ | $\frac{1}{2}(-|0\downarrow \uparrow \rangle -|0\uparrow \downarrow \rangle +|\downarrow \uparrow 0\rangle +|\uparrow \downarrow 0\rangle )$ |

$1.2$ | $\frac{1}{2}(-|00\uparrow \rangle +|\downarrow \uparrow \uparrow \rangle +|\uparrow 00\rangle -|\uparrow \uparrow \downarrow \rangle )$ |

$4.18$ | $\frac{1}{\sqrt{6}}(-|0\downarrow \uparrow \rangle +|0\uparrow \downarrow \rangle +|\downarrow 0\uparrow \rangle -|\downarrow \uparrow 0\rangle -|\uparrow 0\downarrow \rangle +|\uparrow \downarrow 0\rangle )$ |

$4.76$ | $\frac{1}{\sqrt{6}}(|0\downarrow \downarrow \rangle -2|\downarrow 0\downarrow \rangle +|\downarrow \downarrow 0\rangle )$ |

$4.76$ | $\frac{1}{2\sqrt{3}}(-|00\downarrow \rangle +2|0\downarrow 0\rangle -|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle -2|\downarrow \uparrow \downarrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$4.76$ | $\frac{1}{2}(-|0\downarrow \uparrow \rangle +|0\uparrow \downarrow \rangle +|\downarrow \uparrow 0\rangle -|\uparrow \downarrow 0\rangle )$ |

$4.76$ | $\frac{1}{2\sqrt{3}}(-|00\uparrow \rangle +2|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle -|\uparrow 00\rangle -2|\uparrow \downarrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$4.76$ | $\frac{1}{\sqrt{6}}(|0\uparrow \uparrow \rangle -2|\uparrow 0\uparrow \rangle +|\uparrow \uparrow 0\rangle )$ |

$10.72$ | $\frac{1}{2\sqrt{15}}(-3|00\downarrow \rangle +2|0\downarrow 0\rangle -3|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle +6|\downarrow \uparrow \downarrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$10.72$ | $\frac{1}{2\sqrt{15}}\left(4\right|000\rangle -3|0\downarrow \uparrow \rangle -3|0\uparrow \downarrow \rangle +2|\downarrow 0\uparrow \rangle -3|\downarrow \uparrow 0\rangle +2|\uparrow 0\downarrow \rangle -3|\uparrow \downarrow 0\rangle )$ |

$10.72$ | $\frac{1}{2\sqrt{15}}(-3|00\uparrow \rangle +2|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle -3|\uparrow 00\rangle +6|\uparrow \downarrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

Energy (meV) | State |
---|---|

$-0.48$ | $\frac{1}{2\sqrt{15}}(-3|00\downarrow \rangle +2|0\downarrow 0\rangle -3|\downarrow 00\rangle )+|\downarrow \downarrow \uparrow \rangle +6|\uparrow \downarrow \uparrow \rangle +|\uparrow \downarrow \downarrow \rangle $ |

$-0.48$ | $\frac{1}{2\sqrt{15}}\left(4\right|000\rangle -3|0\downarrow \uparrow \rangle -3|0\uparrow \downarrow \rangle +2|\downarrow 0\uparrow \rangle -3|\downarrow \uparrow 0\rangle +2|\uparrow 0\downarrow \rangle -3|\uparrow \downarrow 0\rangle )$ |

$-0.48$ | $\frac{1}{2\sqrt{15}}(-3|00\uparrow \rangle +2|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle -3|\uparrow 00\rangle +6|\uparrow \downarrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$-0.32$ | $\frac{1}{\sqrt{6}}(-|0\downarrow \uparrow \rangle +|0\uparrow \downarrow \rangle +|\downarrow 0\uparrow \rangle -|\downarrow \uparrow 0\rangle -|\uparrow 0\downarrow \rangle +|\uparrow \downarrow 0\rangle )$ |

$-0.16$ | $\frac{1}{2}(|00\downarrow \rangle -|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle -|\uparrow \downarrow \downarrow \rangle )$ |

$-0.16$ | $\frac{1}{2}(-|0\downarrow \uparrow \rangle -|0\uparrow \downarrow \rangle +|\downarrow \uparrow 0\rangle +|\uparrow \downarrow 0\rangle )$ |

$-0.16$ | $\frac{1}{2}(-|00\uparrow \rangle +|\downarrow \uparrow \uparrow \rangle +\uparrow 00-|\uparrow \uparrow \downarrow \rangle )$ |

$-0.16$ | $\frac{1}{\sqrt{6}}(|00\downarrow \rangle -2|\downarrow 0\downarrow \rangle +|\downarrow \downarrow 0\rangle )$ |

$-0.16$ | $\frac{1}{2\sqrt{3}}(-|00\downarrow \rangle +2|0\downarrow 0\rangle -|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle -2|\downarrow \uparrow \downarrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$-0.16$ | $\frac{1}{2}(-|0\downarrow \uparrow \rangle +|0\uparrow \downarrow \rangle +|\downarrow \uparrow 0\rangle -|\uparrow \downarrow 0\rangle )$ |

$-0.16$ | $\frac{1}{2\sqrt{3}}(-|00\uparrow \rangle +2|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle -\uparrow 00-2|\uparrow \downarrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$-0.16$ | $\frac{1}{\sqrt{6}}(|0\uparrow \uparrow \rangle -2|\uparrow 0\uparrow \rangle +|\uparrow \uparrow 0\rangle )$ |

$0.0$ | $\frac{1}{\sqrt{3}}(-|0\downarrow 0\rangle +|\downarrow \downarrow \uparrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$0.0$ | $\frac{1}{\sqrt{3}}(-|000\rangle +|\downarrow 0\uparrow \rangle +|\uparrow 0\downarrow \rangle )$ |

$0.0$ | $\frac{1}{\sqrt{3}}(-|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$0.16$ | $\frac{1}{\sqrt{2}}(-|0\downarrow \downarrow \rangle +|\downarrow \downarrow 0\rangle )$ |

$0.16$ | $\frac{1}{2}(-|00\downarrow \rangle +|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle -|\uparrow \downarrow \downarrow \rangle )$ |

$0.16$ | $\frac{1}{2\sqrt{3}}(|0\downarrow \uparrow \rangle -|0\uparrow \downarrow \rangle +2|\downarrow 0\uparrow \rangle +|\downarrow \uparrow 0\rangle -2|\uparrow 0\downarrow \rangle -|\uparrow \downarrow 0\rangle )$ |

$0.16$ | $\frac{1}{2}(|00\uparrow \rangle +|\downarrow \uparrow \uparrow \rangle -|\uparrow 00\rangle -|\uparrow \uparrow \downarrow \rangle )$ |

$0.16$ | $\frac{1}{\sqrt{2}}(|0\uparrow \uparrow \rangle -|\uparrow \uparrow 0\rangle )$ |

$0.32$ | $|\downarrow \downarrow \downarrow \rangle $ |

$0.32$ | $\frac{1}{\sqrt{3}}(|0\downarrow \downarrow \rangle +|\downarrow 0\downarrow \rangle +|\downarrow \downarrow 0\rangle )$ |

$0.32$ | $\frac{1}{\sqrt{15}}(2|00\downarrow \rangle +2|0\downarrow 0\rangle +2|\downarrow 00\rangle +|\downarrow \downarrow \uparrow \rangle +|\downarrow \uparrow \downarrow \rangle +|\uparrow \downarrow \downarrow \rangle )$ |

$0.32$ | $\frac{1}{\sqrt{10}}\left(2\right|000\rangle +|0\downarrow \uparrow \rangle +|0\uparrow \downarrow \rangle +|\downarrow 0\uparrow \rangle +|\downarrow \uparrow 0\rangle +|\uparrow 0\downarrow \rangle +|\uparrow \downarrow 0\rangle )$ |

$0.32$ | $\frac{1}{\sqrt{15}}(2|00\uparrow \rangle +2|0\uparrow 0\rangle +|\downarrow \uparrow \uparrow \rangle +2|\uparrow 00\rangle +|\uparrow \downarrow \uparrow \rangle +|\uparrow \uparrow \downarrow \rangle )$ |

$0.32$ | $\frac{1}{\sqrt{3}}(|0\uparrow \uparrow \rangle +|\uparrow 0\uparrow \rangle +|\uparrow \uparrow 0\rangle )$ |

$0.32$ | $|\uparrow \uparrow \uparrow \rangle $ |

**Figure A1.**Magnetization plateaus under different temperatures in 3D (

**left panel**) and 1D (

**right panel**) structures, compared to the experimental values (red circles) reported in [26].

**Figure A2.**Magnetization along the field for ${\mathcal{J}}_{L}$, ${\mathcal{J}}_{A}$, and ${\mathcal{J}}_{P}$ exchange-coupled pairs of molecules with (

**a**) 3D molecular unit (upper panel) and (

**b**) 1D molecular unit (lower panel) at 0.0 (K).

**Figure A3.**Magnetization along the field for ${\mathcal{J}}_{L}$, ${\mathcal{J}}_{A}$, and ${\mathcal{J}}_{P}$ exchange-coupled pairs of molecules with (

**a**) 3D molecular unit (upper panel) and (

**b**) 1D molecular unit (lower panel) at 0.1 (K).

**Figure A4.**Entanglement entropy phase diagrams corresponding to ${\mathcal{J}}_{L}$, ${\mathcal{J}}_{A}$, and ${\mathcal{J}}_{P}$ configurations for the 3D molecules (

**a**,

**c**,

**e**) (left column) and 1D ones (

**b**,

**d**,

**f**) (right column), respectively.

## Appendix B. Entanglement of Chain Magnets

**Figure A5.**Entanglement entropy for the corresponding panels in Figure 8. The partitions of the chains are made by cutting them between spins 1 and 2 at molecule 3 for the corresponding cases.

**Figure A6.**Local magnetizations for a 36 spin chain (12 3D SMMs) and ${\mathcal{J}}_{L}=(0.25,-0.25)$ for upper two panels, respectively. Lower two panels have the local magnetizations for a 33 spin chain (11 3D SMMs) and ${\mathcal{J}}_{A}=(0.25,-0.25)$, respectively.

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**Figure 1.**3D trimetric nickel(II) acetylacetonate (Ni(acac)

_{2}) (H atoms are not shown for sake of simplicity). The spins of nickel ions are superexchange-coupled through oxygen ligands, with exchange constant J

_{12,23}between the nearest-neighbor spins and J

_{13}between the terminal spins [26].

**Figure 2.**Nearest-neighbor Ni-trimers conforming the molecular chains; three types of exchange interactions are considered to couple the single magnets in Figure 1, i.e., “linear” ${\mathcal{J}}_{L}$ (

**a**), “alternated” ${\mathcal{J}}_{A}$ (

**b**), and “perpendicular” ${\mathcal{J}}_{P}$ (

**c**). (

**d**) Single-wall nanotube-confined trimers, which give rise to molecular spin chains described by Equation (1).

**Figure 3.**Energy levels of 3D (

**a**) and 1D (

**b**) trimetric nickel(II) acetylacetonate (Ni(acac)

_{2}) [26]. Here, 3D corresponds to ($x=1$, $y=1$), whereas 1D corresponds to ($x=-0.0537$, $y=0$) according to notation in Section 2.1. Colorful lines are for visualization purposes respect to the field-driven breaking of energy degeneration.

**Figure 4.**Three-dimensional SMM magnetization along the field (

**a**,

**c**) and von Neumann entropy (

**b**,

**d**) as a function of y with $x=1$ (

**a**,

**b**) and of x with $y=1$ (

**c**,

**b**). We have used the notation “${S}_{z}$”-plateau to refer to the characteristic constant magnetization of the respective plateaus.

**Figure 5.**One-dimensional SMM magnetization along the field (

**a**) and von Neumann entropy (

**b**) as a function of x with $y=0$.

**Figure 6.**Robustness of magnetization plateaus under different temperatures in (

**a**) 3D and (

**b**) 1D structures. In the 3D structure, the switching occurs around 5 (T); meanwhile, in the 1D structure, it occurs around $2.76$ and $4.15$ (T).

**Figure 7.**Magnetization phase diagrams corresponding to ${\mathcal{J}}_{L}$, ${\mathcal{J}}_{A}$, and ${\mathcal{J}}_{P}$ configurations for the 3D molecules (

**a**,

**c**,

**e**) (left column) and 1D ones (

**b**,

**d**,

**f**) (right column), respectively.

**Figure 8.**Magnetization along the field for ${\mathcal{J}}_{L,A,P}=(0.25,-0.25)$ (top panels and below panels, respectively) for a different number of coupled SMMs. Inset: scaled magnetization.

**Figure 9.**Entanglement entropy for the corresponding panels in Figure 8. The partitions of the chains are made by cutting between molecules 3 and 4 in each case (left-to-right).

**Figure 10.**Entanglement entropy for the corresponding panels in Figure 8. The partitions of the chains are purposely made such that for even ${N}_{m}$, the cut is between spins 1 and 2 of the first molecule of the right chain with respect to the middle intermolecular point; we call it half-bond+1. For odd ${N}_{m}$, the middle molecules 4, 5, and 6 are included in the left chain for 7 and in the right chain for 9 and 11, respectively, with the half-bond+1 taken at that first molecule of the right chain similarly.

**Figure 11.**Entanglement entropy between each pair of molecular spins along the SWCNTs (columns 1 and 2, left-to-right) for ${\mathcal{J}}_{L}=(0.25,-0.25)$, selected magnetic fields, and ($J$, ${J}_{13}$) being tuned from the 3D to 1D SMMs. Local magnetic moments at each molecular spin center along the spin chains inside the SWCNTs (columns 3, 4).

**Figure 12.**Entanglement entropy between each pair of molecular spins along the SWCNTs (columns 1 and 2, left-to-right) for ${\mathcal{J}}_{A}=(0.25,-0.25)$, selected magnetic fields, and ($J$, ${J}_{13}$) being tuned from the 3D to 1D SMMs. Local magnetic moments at each molecular spin center along the spin chains inside the SWCNTs (columns 3, 4).

**Figure 13.**Entanglement entropy between each pair of molecular spins along the SWCNTs (columns 1 and 2, left-to-right) for ${\mathcal{J}}_{P}=(0.25,-0.25)$, selected magnetic fields, and ($J$, ${J}_{13}$) being tuned from the 3D to 1D SMMs. Local magnetic moments at each molecular spin center along the spin chains inside the SWCNTs (columns 3, 4).

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**MDPI and ACS Style**

Norambuena Leiva, J.I.; Cortés Estay, E.A.; Suarez Morell, E.; Florez, J.M.
On the Magnetization and Entanglement Plateaus in One-Dimensional Confined Molecular Magnets. *Magnetochemistry* **2024**, *10*, 10.
https://doi.org/10.3390/magnetochemistry10020010

**AMA Style**

Norambuena Leiva JI, Cortés Estay EA, Suarez Morell E, Florez JM.
On the Magnetization and Entanglement Plateaus in One-Dimensional Confined Molecular Magnets. *Magnetochemistry*. 2024; 10(2):10.
https://doi.org/10.3390/magnetochemistry10020010

**Chicago/Turabian Style**

Norambuena Leiva, Javier I., Emilio A. Cortés Estay, Eric Suarez Morell, and Juan M. Florez.
2024. "On the Magnetization and Entanglement Plateaus in One-Dimensional Confined Molecular Magnets" *Magnetochemistry* 10, no. 2: 10.
https://doi.org/10.3390/magnetochemistry10020010