Study of pressure influence on thermal transition in spin-crossover nanomaterials
© Gudyma et al.; licensee Springer. 2014
Received: 19 October 2014
Accepted: 8 December 2014
Published: 20 December 2014
The thermal transition accompanied by the variation of the molecular volume in nanoparticles of spin-crossover materials has been studied on the basis of microscopic Ising-like model solved using Monte Carlo methods. For considered model, we examined the spin-crossover phenomenon with applied hydrostatic pressure and thus was shown the possibility to shift transition temperature toward its room value. The obtained results of numerical simulations are in agreement with the experimental ones.
The spin-crossover molecular magnets are the new class of coordination inorganic complexes with d4 to d7 electronic configuration of metal ion orbitals, situated in the centre of the octahedral ligand field [1–3]. These materials posses two stable states: low-spin (LS) configuration with diamagnetic properties and high-spin (HS) configuration which is showing paramagnetic behavior. The spin configuration of each state is defined by the electronic configuration of transition metal ion. The spin-crossover phenomenon consists in the existence of equilibrium point between LS and HS isomers and ability of interconversion between spin states of the compounds. We focused on iron(II) compounds with coordination number 6, due to their practical applicability as sensors, data storage, switching, display, and visualization systems. The attractiveness of practical applications of these materials lies in the possibility to design IT devices with nanosized unit cells of about 4 nm 3. For these compounds, the total spin number for LS and HS configurations is respectively S=0 and S=2 .
To understand the mechanism of interconversion between LS and HS configuration, we must consider the fine structural features of spin-crossover complexes and the way of populating the high-energy levels. The ligand field action on metal ion provokes the splitting of its d-orbitals into a subset of three orbitals d x ,d y , and d z , which are basis of the irreducible representation of t2g sublevels, and a subset of two orbitals dx 1,dy 1 which are basis of the irreducible representation of e g sublevels. For the LS configuration, the energy difference between metastable 5T2g and ground 1A1g state is large enough, so the strength of electron-electron repulsion is not big enough to provoke transition. In this case according to Hund’s rule, the d-electrons will nicely pair up with antiparalel spins on the t2g sublevels, and we will detect the diamagnetic low-spin ground state. The electrons on t2g sublevels may get additional energy from the environment, and in this way, the electron-electron repulsion is increasing. Bringing additional energy on d-electrons, it is possible by influence of external physical fields: temperature, pressure, magnetic field, light irradiation, and other [5–7]. The very recent studies of spin-crossover nanoparticles open new research subjects in the switchable molecular magnetic materials [8–10].
In the vicinity of transition point, the energy difference between 5T2g and 1A1g states decreases and the equilibrium between ligand field strength and electron-electron repulsion is being reached. Now, when there are no barriers between t2g and e g orbitals, according to the same Hund’s rule, the d-electrons will enter uniformly on the t2g and e g orbitals, but in this case, the spins will not be compensated which leads to a resultant magnetic moment and paramagnetic properties of HS state. For LS configuration, metal-ligand bounds are stronger and shorter due to electron absence on e g , whereas for HS, the situation is opposite.
where Ze is the effective charge of the ligand, R is the metal-ligand distance, and r4 is the mean fourth power radius of the d-electron. This relation is fundamental because it shows that applied pressure may change directly the ligand filed splitting energy.
Thus, we have examined the thermal transition based on Ising-like spin-crossover Hamiltonian with applied hydrostatic pressure, where the stochastic nature of external field also have been taken into account.
Here, Δ is the ligand field splitting energy, describing the energy difference between HS and LS state Δ=E(HS)−E(LS) evaluated at zero temperature and atmospheric pressure, k B is the Boltzmann constant, T is the temperature, and g is the degeneracy ratio between HS and LS states.
The Hamiltonian (2) describes in a convenient way the behavior of spin-crossover system where the control parameter is temperature. Great scientific interest also represents the case with applied hydrostatic pressure, that is one of more informative way to examine phase transition in spin-crossover materials. There are a lot of experimental works [11–13] where spin-crossover phenomena is studied by action of hydrostatic pressure where specific behavior of transition curves and therefore interesting practical properties (like piezochromism for pressure-induced hysteresis) were found.
where p is the external applied pressure, Δ V is the molecular volume change during transition between the spin states. The pressure action is introduced in the model taking into account its additive contribution to ligand field splitting energy. Since the applied pressure changes the molecular volume, the inter-molecular interaction is changed. Therefore, the high-order terms of interaction must be considered, but for simplicity, we use zero approach in molecular volume changes.
Here, L is the lattice size of 2D Ising model.
The obtained numerical results based on these aproaches are presented in the next section.
Results and discussion
The vanishing of hysteresis width and shifts of the transition temperatures toward their higher values take place at the same time. For high values of interaction constant, the temperature shifts may be dominated upon hysteresis collapse, and therefore, the hysteretic behavior of the system at room temperatures may be observed. From a point of view of designing new IT devices based on spin-crossover compounds and their practical application, the hysteretic behavior at room temperature is a very important feature.
We are now turning to the comparison of the collapse of thermal hysteresis by raising the pressure in fluctuationless spin-crossover compound and in thepresence of fluctuations of ligand field. Numerical calculations for chosen interaction constant J=145 K for the system without fluctuations indicate that hysteresis collapses for p Δ V=500 K, whereas in the presence of fluctuations with strength ε=100, the same transition curves which will coincide with presented ones (black dashed line in Figure 4) may be obtained for p Δ V=580 K. If we plot the transition curves for the system with pressure p Δ V=500 K and fluctuations strength ε=100 (red dashed line in Figure 4), the shift toward lower temperature is observed, which is the evidence of opposite to pressure action of fluctuations. Detailed analysis of thermal transition, essentially determined by intermolecular interaction J, which in more rigorous approach depends on the change of molecular volume, is however, beyond the scope of the present letter. It will also be a subject of future studies.
We have presented an analysis of an Ising-like model with free boundary conditions that describes the spin-crossover nanomaterials under applied pressure. From Monte Carlo simulations based on Metropolis transition probabilities, the thermal transition curves for external field accounting its fast random variation in time were obtained. For spin-crossover nanosystems, the decreasing of hysteresis width by increasing of applied hydrostatic pressure is detected. It is found that the fluctuations of ligand field lead to opposite behavior related to applied pressure and widen the thermal hysteresis loop.
The applied pressure increases the energy gap between spin states and leads to the special feature of spin-crossover compounds that lies in the shifting of transition temperatures toward its room values. From a practical point of view, it is a very useful property for designing the nanosized devices based on spin-crossover complexes that may work at room temperature. It is shown that for hysteretic behavior at room temperature, which is an important feature for data storage devices, the spin-crossover systems with applied pressure requires high cooperative effects, i.e., the large interaction constant. It is concluded that the widening of hysteresis loop by fluctuations of ligand field in the presence of pressure may simplify the way to design memory and storage systems that need large hysteresis for their stable functioning.
The work of AIuM is supported in part by the Ministry of Science and Education of Ukraine under grant no. 0113U003249.
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