# Thermal Spin Transport Properties in Diarylethene-Based Molecule Devices

Authors: Gang Xu; Xingyi Tan; Dahua Ren
Journal: Advances in Condensed Matter Physics
 (2022)

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## Abstract

Spin caloritronic devices, as multifunctional devices, combining spintronics, and caloritronics, are essential for the sustainable development of humans. Here, a novel spin caloritronic device is presented using a diarylethene molecule photoswitch sandwiched among two semi-infinite zigzag graphene nanoribbons containing asymmetrical edge hydrogenation electrodes. We demonstrate that the temperature gradient between the right and the left electrodes can generate spin-up (SU) and spin-down (SD) currents moving in opposite orientations. Moreover, the mentioned currents possess approximately the same magnitudes, indicating a nearly nondissipative spin Seebeck effect. We also find that these currents are significantly dissimilar for the two photochromic isomers at different temperature gradients, demonstrating the excellent system’s switching nature. The obtained results reveal that the light can control the thermal spin transport properties.


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## Body

## 1. Introduction

Spin caloritronics, focusing on the interconnection between heat currents and spin and taking advantage of spintronics and thermoelectronics, has stimulated much recent interest [1–8]. The mentioned field has emerged since the study of Uchida et al. [3] observed the spin Seebeck effect (SSE) in a ferromagnetic metal (NiFe alloy). This novel phenomenon substantially enhances studies on novel green energy of thermoelectricity and low-power-consumption devices. Thus, various studies have been devoted to controlling SSE using the external physical field. For instance, Ni et al. [9] found SSE in the zigzag graphene nanoribbon heterojunction by applying a sufficiently strong magnetic field. Fu et al. [10] utilized the MoS2 monolayer or bilayer intercalated by TiP single-molecule magnets to construct spin caloritronic devices. It was found that the spin-Seebeck currents could be driven in numerous MoS2 layers while applying a temperature gradient to the TiP-MoS2-bilayer device and regulating the external electric field orientation. However, finding a new physical field to control the SSE is an exciting area of spin caloritronics research.On the other hand, as photochromic molecules, photoswitches withstand a reversible transformation between their corresponding stable and metastable isomers caused by light [11]. A different light wavelength is usually employed to return to nature and generate a more thermodynamically stable isomer. Among them, diarylethene, exhibits a photochromic, thermally irreversible reactivity [12]. They often show light-influenced switching in solution and individual crystals through reversibly varying aromaticity within the open-closed (closed-open) transitions, determined by visible ultraviolet lights, respectively [13, 14]. The mentioned feature has increased the interest in studying the derivatives of diarylethene as potential photochromic molecular switches [15, 16]. Theoretically, Motta et al. [17] obtained the conductivity of two isomers of molecules based on diarylethene as well as the verification of the function of the graphene leads. They found that the switch could work electrically by applying short pulses. Photochromic diarylethene derivatives have been verified on single-walled carbon nanotube (SWCNT) as outlook single-molecule devices containing more precisely described connections to the electrodes. Experimentally, Jia et al. [18] successfully constructed photoswitches through graphene nanoribbon (GNR) electrodes and molecules of diarylethene having a dual-mode switch performance, driven by electric field and light with significant precision and repeatability. However, to the best of our knowledge, spin caloritronic devices constructed by diarylethene-based molecules have not been reported.The current study employed diarylethene-based molecules and zigzag graphene nanoribbons to construct spin caloritronic devices. From the theoretical computations, the spin-dependent currents could be driven by applying a temperature gradient to these devices.


## 2. Computational Approach

In the Atomistix ToolKit (ATK) package, spin density functional theory was combined with the nonequilibrium Green’s function technique to perform electronic structures and geometrical optimization calculations [19, 20]. To determine the exchange-correlation potential, the double numerical plus polarization (DNP) basis set and the generalized gradient approximation (GGA) technique were utilized [21, 22]. To enable the convergence of the optimization, the spatial locations of the atoms were relaxed, and the maximum force tolerance was set to 0.01 eV/Å. The standard for energy convergence and the cut-off energy were selected as 1 × 10−5 eV and 150 Hartree, respectively. In order to derive the thermal spin-related transport currents, similar core electrons, cut-off energy, and exchange-correlation potentials were chosen. A 1 × 1 × 100 Monkhorst-Pack k-point grid was employed to achieve precise outcomes.In the Landauer–Büttiker formalism, the subsequent relation can be employed to derive the devices’ spin-related currents [23](1)I↑↓=eh∫−∞∞T↑↓EfLE,TL−fRE,TRdE,where e describes the charge of an electron, h stands for the Planck constant, TLR describes the temperature of the left (right) electrode, and fLRE,TTR stands for the average Fermi–Dirac distribution (FDD) of the left (right) electrode, described as follows:(2)fLRE,TLR=1+expE−μLRkBTLR−1,where μLR and TLR stand for the chemical potential of the left (right) electrode and temperature, respectively, kB denotes the Boltzmann constant, and T↑(↓) (E) indicates the spin-related transport parameter described as follows:(3)T↑↓E=TrΓLGrΓRGa,where Gr(a) stands for the central area’s retarded (advanced) Green’s function, and ΓL(R) describes the interconnection between a central dispersion region and the left/right contact. In our system, the left electrode’s temperature (TL) is more significant than the right (TR), while the temperature difference described as ΔT = TR − TL generates the thermal spin-related currents. Additionally, the previous studies found that the disorder can increase the phonon scattering and decrease the lattice thermal conductance [24, 25]. The central dispersion area (diarylethene molecule) breaks the spatial symmetry of the nanoribbons, which increases the phonon scattering and decreases the lattice thermal conductance. At the same time, it should be noted that the electron-phonon coupling is weak in ZGNRs [26], and the electron-phonon mean-free path in ZGNRs is tens of microns at room temperature [27]. Therefore, the lattice thermal conductance and the electron-phonon interaction were ignored in our calculations.


## 3. Results and Discussion

First, the open and closed frameworks of two different diarylethene molecules were verified, as presented in Figure1(a). Upon ultraviolet light irradiation, the ring-open colorless diarylethene molecules undergo electrocyclization to form a ring-closed isomer that can be transformed back.Figure 1
(a) The studied diarylethene derivative frameworks closed and open states.R stands for the functional class that connects the molecule to graphene, equal to CH2 or CONH. (b) The thermal spin device’s schematic description (R = CONH, closed state as an example).To the ring-open structure with visible light [13, 14], as shown in Figure 1(a), all molecules have similar central diphenylmethane components, connected to the electrodes via-R-with R = CO–NH (denoted by R1) and R = CH2 (indicated by R2). The graphene electrodes have zigzag edges containing one edge C atom fulfilled by single H atoms and various edge C atoms fulfilled by double H atoms. One edge C atom is sp2 hybridized and the other edge C atoms are sp3 hybridized, as presented in Figure 1(b). Figure 1(b) presents the molecular switch’s schematic diagram. The molecules of diarylethene are covalently connected to two 6-ZGNR electrodes with six zigzag carbon chains along with their width. The considered system is categorized into three components: the central dispersion area, the right electrode, and the left electrode. A supercell containing three repeated carbon modules along with the transport orientation (Z-orientation) is employed to describe the semi-infinite electrodes. The central dispersion area involves a part of the semi-infinite ZGNR electrodes, in which a screen impact happens. A supercell containing a significant vacuum layer (15 Å) in the x- and y-orientations is utilized to remove interactions from the near neighbors. Before performing electronic transport calculations, the central dispersion area is entirely relaxed through a force convergence criterion of 0.02 eV/Å.Next, we concentrate on the zero-bias transmission spectra (TS) of open and closed isomers (R1 and R2), as presented in Figure2. Apparently, each transmission spectra have two transmission peaks and a noticeable transmission gap can be observed near the Fermi level, while the 6-ZGNR band structures (shown in Supplementary materials Figure S1) induce the mentioned transmission properties. Figure 2 presents the spin-down (SD) electrons’ transmission in a range of energies higher than the Fermi level (FL). Thus, there exists an SD negative current for this range. Besides, the behaviors of spin-up (SU) and SD currents are opposite, while there is an SU positive current. The differences between the four devices are that the closed isomers’ transmission coefficients are very higher than open isomers, while the transmission channel of closed isomers is a little wider than that of open isomers. This heterogeneous distribution of TS leads to various transport capacities of the four forms.Figure 2
The spin-dependent TS of the thermal spin device, (a)R = CONH, closed state, (b) R = CONH, open state, (c) R = CH2, closed state, and (d) R = CH2, open state. The red and black lines indicate the SU and SD electrons, respectively.
(a)(b)(c)(d)In order to understand the primary structure of spin-related currents caused by the temperature difference, the current spectraJ (E) is first chosen as the multiplication of the TS and the Fermi functions difference T↓ (↑) [fL (E, TL)− fR (E, TR)]. Since the right and left electrodes have the same materials and state densities, the FDD fL (E, TL)− fR (E, TR) indicates the carrier nature and concentration via the constructed device, relying on electron temperature at two leads, as presented in Figure 3(a).Figure 3
(a) The thermal spin device’s Fermi distribution of theTL and TR. (b) The difference of Fermi functions (TL = 320 K, TR = 300 K). The spin-related current spectra at ΔT = 20 K and TL = 320 K (c) R = CONH, closed state, (d) R = CONH, open state, (e) R = CH2, closed state, and (f) R = CH2, open state.
(a)(b)(c)(d)(e)(f)The FDD function is described asfLRE,TLR=1+expE−μLR/kBTLR−1, where μ describes the chemical potential, taken as zero in our computation. As presented in Figure 3(b) (describing the FDD), the number of electrons on the right, including the energy higher than the FL, is more significant than on the left. Thus, the electrons move from the right to the left. Besides, the number of holes in the right, including the energy lower than the FL, is greater than in the left, while holes also move from the right to the left. The current spectra J (E) of four devices are shown in Figure 3, where ΔT = 20 K and TL = 320 K, (c) R1, closed state, (d) R1, open state, (e) R2, closed state, and (f) R2, open state. The SD and SU current spectra J (E) appear in a range of energies higher and lower than the FL, respectively. The current spectra J (E) of closed isomers are tens of hundreds of times greater than those of open ones.The obtained spin-related currents of R1 devices with respect to the left temperature (TL) and temperature bias (ΔT) are presented in Figure 4. The obtained results in figures 4(a), 4(b), 4(d), and 4(e) belong to the closed and open isomers-based devices, respectively. As presented in Figures 4(a) and 4(d), the values of Iup and Idn are negative and positive, respectively. It is evident that Iup and Idn can be produced using ΔT without external voltage, caused by the holes and spin-splitting electrons moving from the right to the left. Significantly, the Iup and Idn amplitudes are approximately similar in the total temperature area for closed isomers, meaning an SSE. The spin-dependent current characteristic of the open isomer (as shown in Figures 4(b) and 4(e)) is similar to the closed one, except for a coarse SSE.Figure 4
The thermally driven spin-related currentsIup and Idn in the thermal spin devices (R = CONH) with respect to TL and ∆T, (a) and (d) closed state; (b) and (e) open state. (c) and (f) the thermal spin devices’ switching ratio versus TL and ∆T, respectively.
(a)(b)(c)(d)(e)(f)Next, we verify the devices’ optical thermal magnetoresistance varying from the closed state to the open one, derived from the relationship.(4)MR↑,↓%=I↑,↓c−I↑,↓oI↑,↓×100,where I↑,↓c and I↑,↓o stand for the SU/SD currents in the closed and open states, respectively. The MR of the R1 devices is shown in Figures 4(c) and 3(f). As we can see, MR↑ varies from around 1.8 × 104 to 2.7 × 104, while MR↓ varies from around 9.0 × 105 to 3.0 × 106 in the applied temperature range versus the left temperature (TL). The MR↓ varies from around 2.0 × 104 to 3.0 × 104, while MR↓ varies from around 3 × 105 to 1.2 × 106 in the applied temperature range versus the temperature bias (ΔT).Figure5 describes the computed spin-related currents of the R2 device with respect to the source temperature (TL) and temperature bias (ΔT). Results in Figures 5(a), 5(b) and 4(d), 4(e) belong to the closed and open isomers-based devices, respectively. R2 devices have similar laws to those of R1 devices but have smaller currents and on-off ratios.Figure 5
The thermally driven spin-related currentsIup and Idn in the thermal spin devices (R = CH2) versus TL and ∆T, (a) and (d) closed state; (b) and (e) open state. (c) and (f) the corresponding switching ratio of the thermal spin devices versus TL and ∆T, respectively.
(a)(b)(c)(d)(e)(f)In order to better describe the current magnitude, the transmission eigenstates should also be utilized. The transmission eigenstates for the R1 and R2 devices are presented in Figures6 and 7 (the energies are marked with “∗” in Figure 2), respectively. As described in Figures 6 and 7, the eigenstates are distributed more unlocally for I↑, I↓ of the R1 closed state, and I↓ of the R2 closed state. Meanwhile, the transmission eigenstates of the rest currents have a significant amplitude around the left electrode, which will decay from the left electrode to the right electrode. Notably, it disappears near the right electrode. Accordingly, the closed state currents are more significant than open states.Figure 6
Spin-resolved transmission eigenstates of the thermal spin devices (R = CONH) under zero bias, (a) closed state, eV, (b) closed state, eV, (c) open state, eV, and (d) open state, eV. The isovalues are 0.1 Å−3/2.
(a)(b)(c)(d)Figure 7
Spin-resolved transmission eigenstates of the thermal spin devices (R = CH2) under zero bias, (a) closed state, eV, (b) closed state, eV, (c) open state, eV, and (d) open state, eV. The isovalues are 0.1 Å−3/2.
(a)(b)(c)(d)


## 4. Conclusions

An advanced spin caloritronic device is constructed using a diarylethene switch sandwiched between two semi-infinite zigzag graphene nanoribbons containing asymmetrical edge hydrogenation electrodes. By applying a temperature gradient to violate the electron-hole symmetry in the ZGNRs, SU and SD currents were produced with reverse transport orientations and the same order of magnitudes, indicating the appearance of the SSE. Moreover, the SU and SD currents are considerably dissimilar for two photochromic isomers at different temperature gradients, demonstrating the excellent system’s switching action. The obtained outcomes disclose that light can control the thermal spin transport properties.



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*Source: 2149190-2022-09-22.xml*