Room temperature memory device using single-molecule magnets

Abstract

To make memory devices based on an individual single-molecule magnet work far above the blocking temperature, we propose a new route, where the information is contained in the charge state of the molecule, and it works through charging and discharging the molecule by applying gate voltages. Here, a model device built on a single-molecule magnet, Fe₄, is taken as an example to exhibit the validity of our proposed route. Ab initio calculations show that the two different charge states with a moderately large energy shift of 1.2 eV are responsible for the low and high conductances in this device: one corresponds to the neutral state of the molecule, and the other to its anionic state. Moreover, the transition from the neutral state to the anionic state is accompanied by a giant increase of nearly two orders of magnitude in the conductance. Additionally, the low and high conductances before and after charging the molecule are hardly dependent on the different spin configurations of the Fe₄ molecule, which indicates that the performance of the Fe₄ memory device is probably preserved even at room temperature.

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1 Introduction

In molecular spintronics,^1–3 single-molecule magnets (SMMs) have attracted great interests due to their outstanding chemical characteristics and impressive magnetic properties.⁴ Particularly, SMMs’ magnetization relaxation times are extremely long below their blocking temperature (T_B).⁵ As a result, a memory device can be constructed using SMMs, where the information is contained in the magnetization direction of the SMMs, and the on/off-states are achieved by switching their magnetization direction. Nevertheless, the SMMs’ blocking temperatures mostly remain in the liquid-helium temperature range (∼4 K),⁶ in spite of great efforts to improve the SMMs’ magnetic properties.^7–12 Such a low blocking temperature possibly causes the paramagnetic state of the SMMs in practical environments,^13,14 and the memory devices based on the magnetization direction of the SMMs may fail to work, since the ambient temperature is generally far above the liquid-helium temperature or even in the room-temperature range. Consequently, new working mechanisms are necessary to build practical memory devices using SMMs.

In this work, we propose an alternative route to greatly raise the working temperature of a SMM-based molecular memory device. In this memory device, two different charge states are used to represent the low and high conductances, and the device works on charging and discharging the central molecule by applying gate voltages. Here, we take a model device of the SMM Fe₄ (ref. 15–17) as an example to show the performance of the memory device based on the charge-state transition. Numerical calculations demonstrate that the low and high conductances of the Fe₄ memory device can be denoted by the neutral state and the anionic state of the molecule, and the conductance difference between the two charge states reaches two orders of magnitude. Moreover, the switching between the high and low conductances is hardly achieved by thermal perturbations (∼26 meV at room temperature) and low bias voltages (≤0.16 eV), since the charge-state transition is closely associated with a moderately large energy shift of 1.2 eV. Further studies reveal that the low and high conductances before and after charging the Fe₄ molecule are independent of the spin configurations (magnetic states) of the SMM Fe₄. Based on these facts, the Fe₄ memory device can work far above its blocking temperature or even at room temperature. The rest of this paper describes our calculations and results in greater detail.

2 Computational details

The model Fe₄ device is displayed in Fig. 1(a), in which the sulphur-functionalized Fe₄ molecule is connected to two semi-infinite nanoscale Au(100) electrodes. For the Fe₄ molecule, the 3-fold symmetry¹⁸ leads to two nonequivalent Fe³⁺ ions: one is the central Fe³⁺ ion marked as Fe^I in Fig. 1(b); the other is the peripheral Fe³⁺ ion marked as Fe^II. Four spin configurations depicted in Fig. 1(c) are considered in this work: the ground spin configuration (GS) and the three excited spin flip configurations (Flip1, Flip2, Flip3). The parallel (antiparallel) arrows mean the ferromagnetic (antiferromagnetic) coupling between the Fe³⁺ ions. Nanoelectrodes have been adopted by many authors in the study of molecular devices.^19–21 A large enough vacuum layer around the electrode in the x and y direction was chosen so that the device had no interactions with its mirror images. Electron transport properties were calculated using the SMEAGOL program,²² which combines the non-equilibrium Green’s function approach with density functional theory calculations, implemented in the SIESTA code.^23,24 The capability of the code has been well verified to consider the electron transport properties of SMMs.^25,26 Specifically, the exchange–correlation potential takes the form of the Ceperley–Alder parameterization of the local density approximation.²⁷ Only valence electrons were self-consistently calculated, and the atomic cores were described by scalar relativistic norm-conserving pseudopotential.²⁸ The valence wave functions were expanded by localized numerical atomic orbitals²⁹ and the basis set was constructed as follows: SZP for Au and DZ for other atoms (SZ = single-ζ, DZ = double-ζ). Molecular structures were fully relaxed until the force tolerance was reached at 0.03 eV Å⁻¹. It is pointed out that although the spin-polarized calculations were performed to correctly simulate the different spin configurations of the Fe₄, only the total transmission and current were necessary and are presented in this paper.

Fig. 1 (a) The structure of the model device: an individual Fe₄ molecule is sandwiched between two Au(100) nanoelectrodes. z denotes the electron transport direction. Different atoms are distinguished by different colors. (b) The magnetic core of the Fe₄ molecule at different angles. The central Fe³⁺ ion is named Fe^I, and the three equivalent peripheral Fe³⁺ ions are named Fe^II. (c) Different spin configurations for the Fe₄ molecule. The arrows denote the spin directions of the Fe³⁺ ions.

3 Results and discussion

In the neutral state of the ground spin configuration (or GS-NS), Fig. 2(a) shows that the electron transmission is quite weak near the Fermi level (∼10⁻⁶). To understand the negligible transmission, the local density of states (LDOS) is calculated using the formula n(E,r⃑,σ) = ∫|ψ_σ(r⃑)|²δ(E − ε_σ)dE integrated over (−0.1, 0.1 eV), where E is the energy, r⃑ is the spatial coordinates, σ is the spin, and ψ_σ(r⃑) is an eigenstate with eigenenergy ε_σ. This quantity returns the spatially resolved density of states in a molecular device, and allows one to know which atoms in space are contributing to electron tunnelling. From the LDOS displayed in the inset of Fig. 2(a), it is found that the electronic states for electron tunneling are only distributed on Au electrodes and S–Au interfaces near the Fermi level, and totally absent in the magnetic-core region of the Fe₄ molecule. Obviously, the absence of electronic states in such a region is responsible for the poor transmission near the Fermi level in the Fe₄ device. By analyzing the projected density of states (PDOS) displayed in Fig. 2(b), it is noted that the electronic states of the nanoelectrodes are distributed over the whole energy range (−1.6, 1.6 eV), however, the lowest unoccupied molecular orbital (LUMO) of the Fe₄ molecule is 1.2 eV above the Fermi level, and its highest occupied molecular orbital (HOMO) is 1.0 eV below the Fermi level. It is well known that electron transmission from one electrode to another in a molecular device must be meditated by a certain molecular orbital. Hence, the poor transmission around the Fermi level fundamentally arises from the fact that both the HOMO and the LUMO are far away from the Fermi level in this device. In a word, a low conductance or the off-state can be denoted by the GS-NS.

Fig. 2 (a) The total transmission spectrum of the neutral state in the ground spin configuration (GS-NS); (b) the projected density of states for the Fe₄ devices in the GS-NS; (c) the total transmission spectrum of the anionic state in the ground spin configuration (GS-AS). The insets in (a) and (c) show the local density of states for the Fe₄ devices integrated from −0.1 to 0.1 eV with an isosurface criterion of 0.1e/nm³. Au and Mol in (b) denote the Au nanoelectrodes and the Fe₄ molecule; HOMO and LUMO denote the highest occupied molecular orbital and the lowest unoccupied molecular orbital.

To acquire a high conductance or the on-state in the Fe₄ memory device, a certain gate voltage [V_G = 3.0 V] is applied on the magnetic-core region of the Fe₄ molecule [Fig. 1(b)], and the molecule is then charged by nearly one electron. For such an anionic state of the ground spin configuration (or GS-AS), some electronic states are observed around the Fermi level, in addition to electronic states from the Au electrodes and S–Au interfaces, by analyzing the LDOS [the inset of Fig. 2(c)]. These electronic states naturally result in a transmission peak near the Fermi level in Fig. 2(c), with a magnitude of nearly 10⁻⁴. As a result, the transmission in the GS-AS is about two orders of magnitude larger than that of the GS-NS (∼10⁻⁶), which is consistent with the notable increase in the conductance in the experiment.¹⁷ As a matter of fact, the gate-induced anionic states are always associated with the appearance of some unoccupied molecular orbitals around the Fermi level. Obviously, the LUMO is the direct origin of the transmission peak near the Fermi level for the GS-AS with only one extra electron. As a whole, a high conductance or the on-state is achieved in the GS-AS obtained by applying a gate voltage.

The above results clearly exhibit that the high and low conductances required by a memory device can be accomplished by charging and discharging the Fe₄ molecule. Moreover, it is noted that the LUMO is actually 1.2 eV above the Fermi level in the GS-NS, which indicates that the switching between the off-state and the on-state can hardly be realized by thermal perturbations (∼26 meV at room temperature) and low bias voltages (≤0.16 V). According to these results, it seems that the Fe₄ memory device can work above the blocking temperature of the Fe₄ molecule or even at room temperature. Nevertheless, up to now, only the ground spin configuration has been considered in the above results. To guarantee that the Fe₄ memory device is workable above the blocking temperature, it is very important to study the excited spin configurations of the Fe₄ molecule which will appear above the blocking temperature, and see whether the conductance switching is still observable in these excited spin configurations.

Three excited spin flip configurations marked as ‘Flip1’, ‘Flip2’, and ‘Flip3’ in Fig. 1(c) are respectively considered in the neutral state and the anionic state. The total energy of the Flip1 (Flip2, Flip3) spin configuration is about 17 (34, 51) meV higher than that of the GS in the experiment.¹⁸ It is pointed out that the four considered spin configurations only differ in spin directions or magnetic couplings of the Fe³⁺ ions, while the spin quantum number of the Fe³⁺ ion is kept the same at S = 5/2. Under these three excited spin configurations, the HOMO and LUMO are similarly far away from the Fermi level, as described in Fig. 3(a), thus the poor transmission near the Fermi level is still observed in the neutral state of these excited spin configurations (Flip1-NS, Flip2-NS, and Flip3-NS). This fact proves that the low conductance is independent of the spin configurations of the Fe₄ molecule. More interestingly, we note that the LUMO is found to be at about 1.2 eV above the Fermi level in the neutral state of the four considered spin configurations [see Fig. 2(a) and 3(a)], which implies that the LUMOs of the four considered spin configurations should share some features in common. This predication is verified by analyzing the LDOS of the LUMO presented in Fig. 3(b). In the GS-NS, the LUMO totally lies in the spin-down branch and the corresponding charge distribution is mostly around the three peripheral Fe³⁺ ions. In the Flip1-NS (Flip2-NS), although the LUMO is split into two spin branches, they are degenerate in energy and the total charge distribution of the LUMO is negligibly different from that of the GS-NS. In the Flip3-NS, the charge distribution of the LUMO is also quite close to that of the GS-NS, except for different spin branches. The similar charge distributions of the LUMOs basically guarantee that the high conductance in the anionic state is also independent of the spin configurations of the Fe₄ molecule. Further calculations confirm that when the same gate voltage [V_G = 3.0 V] is applied, the transmission peak arising from electron tunneling through the LUMO also appears near the Fermi level in the anionic state of the three excited spin configurations (Flip1-AS, Flip2-AS, and Flip3-AS), and their transmission magnitudes are all around 10⁻⁴. Consequently, the high conductance is also proven to be independent of the spin configurations of the Fe₄ molecule. Incidentally, the energy positioning of the HOMO is found to be greatly dependent on the spin configurations of the Fe₄ molecule [see Fig. 2(a) and 3(a)], which is the reason why the HOMO or the cationic state is not chosen to generate the on-state of the Fe₄ device.

Fig. 3 (a) The total transmission spectra in the neutral state of the three excited spin configurations (Flip1-NS, Flip2-NS, and Flip3-NS). HOMO and LUMO denote the transmission peaks generated by electron tunneling through the highest occupied molecular orbital and the lowest unoccupied molecular orbital. (b) The local density of states for the lowest unoccupied molecular orbital for the four considered spin configurations, with an isosurface criterion of le/nm³. Some atoms are removed for clarity, on which none of the electronic states are distributed.

Furthermore, the non-equilibrium transport properties were also examined under a bias voltage ranging from 0.02 V to 0.16 V, which is far away from the Coulomb blockade. The current is approximately 0.002 nA in the neutral state for the four considered spin configurations, as displayed in Fig. 4(a). In the anionic state, the current can generally jump to around 0.2 nA, when a certain bias voltage (≥0.08 V) is applied. To quantify this notable increase in the conductance, we define the conductance increase ratio as (G_AS − G_NS)/G_NS. The value of such a ratio can reach nearly 100 for the four considered spin configurations [see Fig. 4(b)], accompanied by the charge-state transition. Accordingly, the low and high conductances required by a memory device can be denoted by these two charge states even under bias voltages, and they are also independent of the spin configurations of the Fe₄ molecule.

Fig. 4 (a) I–V curves in the neutral state and the anionic state for the four considered spin configurations. (b) The conductance increase ratio of the four considered spin configurations under bias.

It is pointed out that our proposed route can be applied to building high-temperature memory devices (or memory devices working far above the blocking temperature) using other SMMs, as long as the molecular structures are highly symmetric in the transport direction and the ground charge states are greatly retained when they are anchored on a metallic surface, and is not limited to the SMM Fe₄. Besides, although the magnetic properties of SMMs are not used in our proposed memory device, SMMs are still good candidates for building such devices, since their chemical characteristics are superior to those of other molecules (see ref. 4). For example, SMMs consist of an inner core with a surrounding shell of organic ligands. The surrounding ligands can be tailored to strongly bind the SMMs onto surfaces or into junctions. Meanwhile, their electron transport properties which are generally dependent on the inner cores can be preserved in the different device environments due to the protection of the surrounding ligands. This easily enhances the robustness of the device performance, which is an important merit for practical applications. Moreover, SMMs allow selective substitutions of the ligand (or metallic ions) to alter the coupling to the environment (or their physical properties without modifying the structure or coupling), which is another merit for rationally building practical molecular devices.

4 Conclusion

In conclusion, we propose a memory device based on an individual SMM, Fe₄, which works through charging and discharging the Fe₄ molecule by applying gate voltages. Numerical calculations show that the switching between the neutral state and the anionic state leads to a change of nearly two orders of magnitude in the conductance. Moreover, the LUMO, responsible for the high conductance in the anionic state, is found to be 1.2 eV above the Fermi level in the neutral state, thus the low and high conductances are well separated even when considering the thermal perturbations (∼26 meV) and the low bias voltages (≤0.16 V). Importantly, it is proven that the different spin configurations of the SMM Fe₄ have little impact on the performance of the memory device. According to the above facts, the proposed Fe₄-based memory device can work far above its blocking temperature or even at room temperature.

Acknowledgements

This work was supported by the National Science Foundation of China under Grant nos 11104277, 11374301, 11174289, 11204309, and U1230202 (NSAF), the Special Funds for Major State Basic Research Project of China (973) under Grant no. 2012CB933702, Hefei Center for Physical Science and Technology under Grant no. 2012FXZY004 and Director Grants of CASHIPS. The calculations were performed at the Center for Computational Science of CASHIPS, the ScGrid of Supercomputing Center and Computer Network Information Center of Chinese Academy of Science.

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