Mn12

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The molecule Mn₁₂O₁₂(CH₃COO)₁₆(H₂O)₄, commonly abbreviated Mn₁₂ or Mn₁₂Ac₁₆, was the first system in which the tunneling effect in the demagnetization was measured experimentally, when appreciating steps in the magnetic hysteresis curve. These steps have been justified by the fast relaxations of the magnetization when the transitions take place by tunnel effect. It was the first of the monomolecular magnets, and it is still one of the most studied, although much work has recently been done on other, simpler systems. Due to the extensiveness of the studies, it has been called "the drosophila of monomolecular magnetism", referring to the well-known model organism in genetics.

Chemical structure and derivatives

The molecule Mn₁₂ has an Mn core₄^IVO₄ with cubic structure, surrounded by 8 others ${displaystyle Mn^{III}}$ They are arranged in the form of a ring. 8 oxo anions and 16 acetate ligands complete coordination. The molecule has a global form of lentil.

Vista lateral del Mn12. Se ven los carboxilatos superiores e inferiores

It is possible to replace, by chemical reaction, the acetate ligands with others, mainly carboxylates, but there are also known cases of sulfates and phosphates. Generally, the main features of the magnetic properties of the molecule are maintained, but the more or less electronegative character of the ligand has been related to the magnitude of the exchange interaction between the ions it binds.

It is also possible to reduce by one or two Mn electrons ${displaystyle _{12}}$ . This changes the thorn of its fundamental state, but its behavior is generally maintained as a unimolecular magnet.

Magnetic properties and structure

The ${displaystyle Mn_{12}}$ He's a monomolecular magnet. As such, it presents cycles of magnetic hysteresis (at low temperature), quantum tunnel in magnetization (which manifest as steps in the hysteresis cycle), and characteristic variations in the position and height of the peaks of susceptibility in ac measures depending on the frequency of sweeping.

The molecule ${displaystyle Mn_{12}}$ is characterised quantitatively, in its simplest form, by its quantum number value S or total spin (S=10, is the sum of the spins of each constituent Mn atom, its Landé factor, g and its depopulation in the null field, D (effective). The minimum description can serve to rationalize some of the properties in balance, such as magnetization to a given temperature and a given field, but dynamic phenomena require going much further. Thus, occasionally, more subtle parameters are included in the hamiltonian, such as fourth or sixth order terms, or that effective sphin is broken down. S=10 in the magnetic moments of the individual Mns.

Esquema de acoplamiento magnético en el Mn12

The 4 Mn (IV) have an electronic configuration ${displaystyle d^{3}}$ , and. therefore, they each provide an S=3/2. The 8 Mn (III) have an electronic configuration ${displaystyle d^{4}}$ , and bring each one an S=2. The strong antiferromagnetic interaction between the two blocks leads to the fundamental state of S=10: the 4 Mn (IV) result in an S=6, the 8 Mn (III) result in an S=16.

On the other hand, it must be considered that, while Mn (IV) are isotropic, the anisotropy of Mn (III) includes a symmetry term E. Therefore, they present a small splitting at zero field, due to interaction second order spin-orbit. The vector sum of these axial anisotropies will lead to an axis of easy magnetization for the complete molecule.

Since there are no first-order spin-orbit interactions, the value of the Landé parameter g (effective) for all these ions is approximately 2. In this way, the state S=10 will also be described by a g close to 2.

Finally, it should be noted that, at the temperatures of interest (between 1 and 10 K) and at the low camps (about 0.1 T) the different levels of S=10 have been populated. ${displaystyle M_{s}=pm 10,pm 9,...}$ ). Effectively and in the first approach, we have the same case as if we had an ion (fiction) with S=10 and without a spinal-orbit coupling at room temperature. Thus, it is possible to apply simplified formulas such as: ${displaystyle chi T={frac {g^{2}}{8}}cdot Scdot (S+1)}$ , to play part of the magnetic behavior.

Magnetic hysteresis loops

The application of an external magnetic field (during a sweep) can reverse the direction of the magnetic field of a magnet. Once the direction of the magnetization has been reversed, a reverse external field is applied and the magnetization is measured again. The magnitude of the external field necessary to reverse the magnetization is called the coercive field. In the absence of an external magnetic field, the remnant magnetization that is typical of each material can be measured, as in traditional magnets. If the zero (or almost zero) field is maintained above the Neel temperature, a slow relaxation (loss of magnetization) or demagnetization is observed. The residual magnetic field at temperatures below the Neel temperature is called the remaining field and this can last from a few hours to months.

As a differential characteristic of the magnetic hysteresis cycles in Mn12 (and other monomolecular magnets) compared to traditional magnets, there are fast relaxation steps of the magnetization at certain magnetic fields. Conventional magnetic materials do not present these steps, they only show a sigmoid behavior that is a function of temperature.

The position, height and shape of these steps can be rationalized by a combination of three types of processes: (1) thermal excitations (involving phonons) that allow overcoming the potential barrier, which dominate at high temperatures; (2) tunneling processes from the ground state, which dominate at lower temperatures and (3) tunneling processes across the barrier from low-energy excited states, which are important at intermediate temperatures. In these processes, the unimolecular Hamiltonian is perturbed by dipole interactions between molecules.

Relaxation by spin-phonon coupling

At low temperatures (Pocos Kelvin), the Mn12 is trapped in the wells ${displaystyle M_{s}=pm 10}$ . If there is an applied field, the wells are at different heights, and the system will be trapped in the lower energy well, where the magnetic moment is aligned with the external field. Not all molecules will be in the state of maximum ${displaystyle M_{s}}$ (except at K fraction temperatures), there will be populated states ${displaystyle M_{s}=+10,+9,+8...}$

The states with two units of difference in ${displaystyle M_{s}}$ can be mixed, by coupling between the spine states and the fonones (molecular vibrations or the crystalline network). The propagation of this mixture, with less intensity, makes possible the transition between levels ${displaystyle M_{s}=-10}$ and ${displaystyle M_{s}=+10}$ . Obviously, the probability of this transition will be almost zero, and transitions will be much higher as ${displaystyle M_{s}=-6rightarrow M_{s}=+4}$ or ${displaystyle M_{s}=-5rightarrow M_{s}=+5}$ . Thus, this mechanism is only possible at relatively high temperatures.

Quantum tunneling effect on magnetization

If the applied magnetic field is diminished, the levels of the two wells will be crossed (a lot before reaching the point where the two wells are crossed, with energy match for everything. ${displaystyle M_{s}=pm i}$ ). At each inter-level crossing, a quantum tunnel effect transition will be possible. If that transition occurs, the affected molecule will see its magnetization reversed. As a result, the measured hysteresis cycles have steps.

Not all coincidences of energy levels lead to tunnel effect transitions with the same probability: On the one hand, for the transition to be probable, there must be overlap between the involved wave functions. This makes, depending on the parameters of the specific system, crosses or others are more likely (e.g., they can be especially intense between levels ${displaystyle M_{s}(1)=+4}$ and ${displaystyle M_{s}(2)=-6}$ or between levels ${displaystyle M_{s}=pm 5}$ ). On the other hand, the origin of the transition must be populated for this to happen. At sub-Kelvin temperatures, only the state may be populated ${displaystyle M_{s}(1)=+10}$ , but at higher temperatures transitions will occur from higher levels of energy. This is the phenomenon known as "the thermally assisted quantum".

The Landau-Zener method has been used to study the quantum tunneling effect of magnetization.

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