MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}}); π-Electron-Assisted Relaxation of Spin Excited States in Cobalt Phthalocyanine Molecules on Au (111) Surface
  Chinese Journal of Chemical Physics  2017, Vol. 30 Issue (2): 161-165

The article information

Xiao-gang Liu, Hong-jian Du, Bin Li, Ye-liang Zhao, Ai-di Zhao, Bing Wang
刘小刚, 杜宏健, 李斌, 赵烨梁, 赵爱迪, 王兵
π-Electron-Assisted Relaxation of Spin Excited States in Cobalt Phthalocyanine Molecules on Au (111) Surface
Au (111) 表面钴酞菁分子自旋激发态的π电子辅助自旋弛豫
Chinese Journal of Chemical Physics, 2017, 30(2): 161-165
化学物理学报, 2017, 30(2): 161-165
http://dx.doi.org/10.1063/1674-0068/30/cjcp1609178

Article history

Received on: September 9, 2016
Accepted on: October 17, 2016
π-Electron-Assisted Relaxation of Spin Excited States in Cobalt Phthalocyanine Molecules on Au (111) Surface
Xiao-gang Liu, Hong-jian Du, Bin Li, Ye-liang Zhao, Ai-di Zhao, Bing Wang     
Dated: Received on September 9, 2016; Accepted on October 17, 2016
Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Author: Bin Li, E-mail:libin@mail.ustc.edu.cn; Bing Wang, E-mail:bwang@ustc.edu.cn, Tel.:+86-551-63601747, +86-551-63602177, FAX:+86-551-6360626
Abstract: We present our investigation on the spin relaxation of cobalt phthalocyanine (CoPc) films on Au (111) (CoPc/Au (111)) surface using scanning tunneling microscopy and spectroscopy.The spin relaxation time derived from the linewidth of spin-flip inelastic electron tunneling spectroscopy is quantitatively analyzed according to the Korringa-like formula.We find that although this regime of the spin relaxation time calculation by just considering the exchange interaction between itinerant conduction electrons and localized d-shells (s-d exchange interaction) can successfully reproduce the experimental value of the adsorbed magnetic atom, it fails in our case of CoPc/Au (111).Instead, we can obtain the relaxation time that is in good agreement with the experimental result by considering the fact that the π electrons in CoPc molecules are spin polarized, where the spin polarized π electrons extended at the Pc macrocycle may also scatter the conduction electrons in addition to the localized d spins.Our analyses indicate that the scattering by the π electrons provides an efficient spin relaxation channel in addition to the s-d interaction and thus leads to much short relaxation time in such a kind of molecular system on a metal substrate.
Key words: Scanning tunneling microscopy     Spin relaxation     Single molecule     s-d coupling    
Ⅰ. INTRODUCTION

It is of fundamental importance to understand the dynamics of spin states of the magnetic molecules on electrodes for their potential applications in miniaturized molecular spintronic devices [1-4]. Due to the requirement of a long enough spin relaxation time to exceed the duration of spin manipulations [5], a wide research interest has been stimulated in searching the molecular magnetic systems with long spin relaxation time [6-10]. However, it has been observed that the spin relaxation time of magnetization excitations in magnetic molecules are very short in the presence of electrodes, typically in the order of 10-14 s [11, 12]. This time scale is even shorter by over one order of magnitude than those of the magnetic atoms on metal surfaces [13-17] or in bulks of metals [18, 19] and semiconductors [20-22].

It is known that when individual quantum spins are placed in close proximity to conducting substrates, the dynamic properties of the localized spins can be significantly affected because of the exchange interaction between itinerant conduction electrons and localized d-shells, so-called s-d exchange interaction. In this regime, the relatively short relaxation time of spin states in magnetic atoms can be described in reasonable time scale by considering the s-d exchange interaction [18, 23, 24], although the observed relaxation times still vary in different magnetic atoms or substrates [13-17]. In particular, the substrate-dependences of spin relaxation times of individual magnetic atoms have been interpreted according to some of other additional processes, like Stoner excitations of the itinerant conduction electrons of the substrate [14] and the spin polarization of nonmagnetic atoms of the substrate [13]. Much longer spin lifetimes have also been observed in the systems with large magnetic anisotropy barrier [15-17, 25-27] and/or by introducing f electrons for the weak coupling of f electrons with both tunneling electrons and itinerant electrons of the conducting substrates [28, 29]. Even in the systems with large magnetic anisotropy barriers, the sequential spin transitions induced by the s-d interaction may still play an important role in the spin lifetime [15, 26]. In comparison, the existences of ligands in molecular systems may introduce additional spin relaxation channels [30], in which the π electrons in ligands have shown important roles in Kondo physics [31-33]. Understanding the effect of π electrons in ligands on the spin relaxation of magnetic molecules, especially at a quantitative level, is crucial toward their applications in the area of molecular spintronics.

Here, we investigate the relaxation time of spin excited states in trilayer cobalt-phthalocyanine (CoPc) films on the Au (111) surface using scanning tunneling microscopy and spectroscopy (STM/STS). Korrigna-like formula [18, 23, 24, 34] is employed to analyze the spin relaxation time by considering s-d interaction between the localized spin of CoPc molecule and the bulk and surface density of states (DOS) of the Au (111) substrate. This calculation regime gives the consistent spin relaxation time with the experimental result in the case of Fe atom adsorbed on Pt (111) surface. However, there exists huge discrepancy between the experimental and the calculated values for the case of CoPc/Au (111). According to our analyses of various interactions in this adsorption system of magnetic molecule, this discrepancy could be attributed to the π-electron assisted process.

Ⅱ. EXPERIMENTS

Our STM experiments were carried out using an ultrahigh vacuum low temperature scanning tunneling microscope (Unisoku) equipped with a sample preparation chamber for film growth with a base pressure of 5 × 10-11 Torr. The Au (111) surface was cleaned by cycles of 1000 eV Ar+ ion sputtering and 650 K annealing. CoPc thin films were deposited on the Au (111) substrates using a Knudsen cell, where the fully covered first layer of CoPc was prepared by keeping the substrates at room temperature, and the second and third island layers were prepared by keeping the substrates at ~150 K. The STM measurements were performed at 4.2 K. An electrochemically etched tungsten tip was used. The dI/dV and d2I/dV2 spectra were measured using a lock-in preamplifier, with a typical sinusoidal modulation of 0.5 mV by root mean square (rms) at 797 Hz.

Ⅲ. RESULTS AND DISCUSSION

Figure 1 (a) and (b) show the representative topography images of the CoPc films with different layers on Au (111). The CoPc molecules in the first layer show nearly uniform four-lobe patterns, and those in the second and third layers are tilted with a certain degree with respect to the surface plane. The Co2+ ion centers are much protruded in the second and third layers. In the images, the colored dots indicate the Co2+ ion centers of CoPc in different layers. From the molecules at the island edge and the indicated centers, the Co2+ ion centers of CoPc in the second layer are shifted with respect to the ones in the first layer by about 3.9 Å, accompanied a rotation of 45° with respect to the latter. The Co2+ ion centers of CoPc in the third layer are further shifted with respect to the ones in the second layer by about 2.2 Å, while the molecules in the second and third layers almost have the same orientation. The derived stacking configuration is shown in Fig. 1(c).

FIG. 1 Self-assembled CoPc trilayer film on Au (111). (a) STM image (size of 13 nm × 11 nm, imaged at 1.0 V and 0.1 nA) illustrating the stacking of the first and second layer of CoPc molecules, (b) STM image (size: 12 nm × 10 nm, imaged at 1.0 V and 0.1 nA) showing the stacking of the second and third layer of CoPc molecules. The green and black dots represent the centers of the molecules in the first and second layer or in the second and third layer, respectively. The black and the white lines indicate the shift of the Co2+ ions between the first and the second layer. (c) Schematic diagram of the stacking of the CoPc trilayer on Au (111). The orientation and the shift between molecules in adjacent layers are also depicted for a vertical chain. In the chain, the shift of the Co2+ ion centers between the first and the second layer is 3.9 Å, and the shift between the second and the third layer is 2.2 Å. The overview structural model of a CoPc molecule is shown.

The dI/dV spectra measured on top of Co2+ ions of CoPc molecules in different layers on Au (111) substrates are shown in Fig. 2(a). In the first layer, the dI/dV spectra almost show no feature in the concerned energy range, which can be attributed to quenching of magnetic-moment of Co2+ ions in the first CoPc layer [35]. Hence, the first CoPc layer may act as a decoupling layer. There is no feature observed from the second CoPc layer on Au (111), different from the case of the second CoPc layer on Pb (111) in which a Kondo resonance peak appeared [12]. It is noted that the second-layer Co2+ ion centers are shifted with respect to the first-layer Co2+ ion centers for CoPc on Au (111), while in the case of CoPc films on Pb (111) the second-layer Co2+ ions are just located on top of the first-layer ones [12]. The off-top configuration of the second CoPc layer on Au (111) may release the molecular spin from Kondo screening of the substrate and thus the Kondo resonance cannot be observed, as suggested in Ref.[12].

FIG. 2 (a) dI/dV spectra measured on top of the Co2+ ions of CoPc in the first, second, and third layer on Au (111). The arrows indicate the spin-excitation threshold voltages for the spectra acquired at the Co2+ ion in the third layer. The spectra are shifted vertically for clarity. (b) d2I/dV2 spin-excitation spectrum acquired at Co2+ ion in the third layer on Au (111). All of the spectra were acquired at 50 mV and 0.3 nA. The bias voltage modulation was 0.5 mV (rms) at 797 Hz.

We focus on the relaxation times of the excited spin states measured at the Co2+ ion centers in the third layer. The step-like features in the dI/dV spectra of the Co2+ ion centers in the third layer originate from the magnetization excitation from the antiferromagnetic (AFM) coupling to the ferromagnetic (FM) coupling between the spins of Co2+ ions in the second and third layers [12]. The Co2+ ion of a single CoPc molecule in the second and the third layer has a spin of 1/2. The total spin Sc is thus 0 and 1 for the AFM and the FM coupling, respectively. The spin excitation energy is 20.9 meV on Au (111), which can be much clearly seen in the second derivative spectrum (d2I/dV2 spectrum), as shown in Fig. 2(b). The variation of the peak positions of different Co2+ ion centers in the third layer is observed within 2 meV. The full width at half maximum (FWHM) of the peak reads W=11.1±0.5 meV for CoPc on the Au (111) substrate. Using the following equation [36],

(1)

where Vmod(=0.5 mV, rms) is the modulation of the bias voltage, e is the electron charge, kB is the Boltzmann constant, Winst (0.15 meV) is the instrumental broadening of our STM [37], we get the intrinsic line width Win=10.9 meV for CoPc on Au (111) substrates. Considering the uncertainty relation τWinħ/2, where ħ is the Plank constant, we then have the lifetime τ=3.1 × 10-14 s for the magnetization excitations of CoPc on Au (111).

The relaxation rate of the excited spin state of CoPc through s-d exchange interaction can be described by the Korringa-like formula [23, 24]

(2)

where ρs is the DOS of the conduction electrons at the Fermi level of substrate, Js-d is the s-d exchange integral with a value of about 0.25 eV [38], △ is the energy difference between the total states of |1〉 and |0〉 and |0〉 by using the observed excitation energies, Sa is the spin matrix. The contributions of the effective DOSs, that is, the conduction electrons around the localized spins, are from both of the surface and bulk states in the case of Au (111) substrate. Here, we use ρs(Au)=4/3πr3nAu-b+πr2nAu-s to count the effective DOSs of the substrates which scatter the localized spin moment of Co2+ ion, where nAu-b eV-1Å-3 and nAu-s eV-1Å-2 are the bulk DOS [39] and the surface DOS [40] of Au respectively, and r=1.26 Å is the ionic radius of Co2+ ions in CoPc [41], giving ρsJs-d=0.049 for Au (111) substrate. We get the calculated lifetimes τ1→0=8.4 × 10−12 for CoPc on Au (111). However, there is a huge discrepancy by about two orders of magnitude between the experimental and calculated values. It is noticed that in the calculations we do not include the contribution of the DOS from the tungsten tip and the decay of the bulk and surface DOSs at the vacuum side [42]. If taking into consideration of the DOS decay, the calculated lifetimes will be longer. On the other hand, since the localized spin of Co2+ ion is more weaker coupled to the tip than to the substrate, the contribution of the tip DOS to the relaxation rate is still too small to compensate the huge discrepancies even if the tip is considered. Therefore, only considering the scattering of the itinerant electrons by the localized spin of Co2+ ion is obviously insufficient.

As a comparison, let us consider the spin relaxation of Fe atom on Pt (111) and Cu (111), where Pt has the bulk DOS [39] of nPt-b=0.11 eV-1Å-3 and the surface DOS [43] of nPt-s=0.012 eV-1Å-2, and Cu has the bulk DOS [39] of nCu-b=0.025 eV-1Å-3 and the surface DOS [40] of nCu-s=0.017 eV-1Å-2. Then we have ρsJs-d=0.25 for Pt substrate and ρsJs-d=0.074 for Cu substrate respectively. Adopting the measured energies of the first order excitations and the magnetic moments of Sc(Fe/Pt)=5/2 and Sc(Fe/Cu)≈2 for Fe atom on Pt (111) and Cu (111) [13, 14], respectively, we then get the calculated relaxation times as 1.7 × 10-12 and 1.5 × 10-11 s. The calculated relaxation time of Fe atom on Pt (111) is well consistent with the experimental value [13]. Our calculations indicate that the strong s-d interaction due to the relatively large DOSs of Pt can well describe the spin relaxation process of Fe atom on Pt (111). While, the calculated relaxation time of Fe atom on Cu (111) is longer by 2 orders of magnitude than the experimental value [14], which has been attributed to the contribution of the strong Stoner excitations [44]. Although the decay into the Stoner excitations is a possible channel to shorten the spin relaxation time in the case of CoPc films on Au (111), it is not clear that in what degree of this substrate may participate the process of Stoner excitations.

Alternatively, we here consider the possible effects of Pc macrocycle. It was reported that the spin relaxation time was 5.9 × 10-2 s in the mixture of CuPc/H2Pc films on insulating substrate at 5 K [6]. Except the absence of conduction electrons, this system is very similar to the CoPc films in our experiment. Analogous to analysis of the s-d exchange interaction above, by considering , we can get an estimated dimensionless parameter, ρπJπ-d ≈ 1 × 10−6, for the π-d exchange interaction. Here, we assume that the π-d interaction dominates the spin relaxation because of the absence of the conduction electrons in the system. In fact, it has been found that the intramolecular exchange coupling between the π electrons of Pc macrocycle and the localized d spins is as large as Jπ-d ≈ 20−30 meV in the quite similar molecular systems [30, 33]. Some other interactions, like hyperfine interaction [45], and spin-phonon interaction [30], are generally much weaker than the observed π-d coupling. The magnetic dipole-dipole interaction between the lateral chains is also smaller by several orders of magnitude when considering the relatively large lateral distance of 1.4 nm between Co2+ ions in the films. It is believed that the similar intramolecular π-d interaction should exist in CoPc. However, it is seen that even after we consider the π-d interaction as an extra relaxation channel in addition to the s-d interaction, that is, 1/τ ≈ 1/τs-d+1/τπ-d, it cannot explain the huge discrepancy.

Phenomenologically, instead of considering the radius of Co2+ ion only, we take into consideration of the Pc macrocycle, by modeling it as a plate with a thickness of 3.0 Å for the CoPc [46] and a radius of rπ=3.9 Å for the extension of the polarized π electrons, which is adopted by considering the observed extended Kondo resonance over the pyrrole ring in Pc macrocycle [31]. Using Eq.(1), we then obtain the calculated relaxation time of 3.7 × 10-14 s for CoPc on Au (111), with phenomenological dimensionless parameters ρJ ≈ 0.7, which is consistent with the value by considering the spatially extended Kondo state [32]. The calculated relaxation time is now in better agreement with the experimental result. To rationalize this analysis, we may consider a system consisting of a localized spin and delocalized spin (s), where the coupling between the localized spin and the delocalized spins may be either FM or AFM, as shown in Fig. 3. In the presence of itinerant conduction electrons, both of the localized spin and the delocalized spins scatter the conduction electrons, leading to a faster spin relaxation of the whole system. This scenario should depend on the spin polarization of π electrons in the Pc macrocycle and the participation of the polarized π electrons as scattering centers. The observed spatially extended Kondo state at Pc macrocycle in the similar systems [30-32] well supports our scenario, even though the intramolecular π-d coupling can be either FM or AFM in different molecular systems [33]. It is noted that the large value of ρJ ≈ 0.7 may be already beyond the limit of the perturbation approach [24]. For a better understanding of the spin relaxation in such molecular systems, one may need to consider the many-body effect [47]. Nevertheless, our analysis here provides useful information to address the importance of the Pc macrocycle due to the spin polarization of the π electrons.

FIG. 3 Schematic drawing of the scattering of conduction electrons by localized d spins and the polarized π electrons in the Pc macrocycles, where FM π-d coupling is shown within the extension of the polarized π electrons (the plate in green).
Ⅳ. CONCLUSION

In summary, we measured the relaxation time of the excited spin states in CoPc films on Au (111). The spin relaxation time estimated using the Korringa-like formula by just considering the s-d exchange interaction is much longer than the experimental result by about two orders of magnitude. However, since the intramolecular π-d coupling and other weaker couplings are smaller than the s-d coupling by over 1 orders of magnitude, the huge discrepancy can not be explained by considering these interactions in a single-particle picture. Our estimation by including the spin polarized π electrons in Pc marcocycle as scattering centers can phenomenologically accord with the experimental value. Our analyses srongly suggest the involvement of many-body effect to efficiently relax the spin states through π electrons in such a kind of molecular systems.

Ⅴ. Acknowledgments

This work was supported by the National Natural Science Foundation of China (No.91321309, No.91421313, No.21421063, and No.21273210), the "Strategic Priority Research Program" of the Chinese Academy of Sciences (No.XDB01020100), and the Fundamental Research Funds for the Central Universities (No.2340000050 and No.2340000074).

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Au (111) 表面钴酞菁分子自旋激发态的π电子辅助自旋弛豫
刘小刚, 杜宏健, 李斌, 赵烨梁, 赵爱迪, 王兵     
中国科学技术大学合肥微尺度物质科学国家实验室 (筹), 量子科技前沿协同创新中心, 合肥 230026
摘要: 利用扫描隧道显微镜和扫描隧道谱方法, 研究了Au (111) 表面钴酞菁分子薄膜 (CoPc/Au (111)) 的自旋弛豫现象.首先通过测量非弹性自旋翻转谱展宽获得自旋弛豫时间, 然后根据类Korringa公式对其进行了定量分析.发现计算自旋弛豫时间时, 如果只考虑导带电子与局域d电子间的自旋交换相互作用 (s-d交换作用), 尽管可以解释磁性原子在金属表面上的弛豫时间, 但不能解释CoPc分子在Au (111) 表面的情况.如果考虑CoPc分子中的π电子是自旋极化的, 可以很好地解释实验现象, 因为分布在Pc大环上的π电子也可能散射导带电子.分析表明, 在s-d交换作用基础上, π电子对导带电子的散射为自旋激发态提供了有效的自旋弛豫通道, 导致在这种金属表面的分子系统中的自旋弛豫时间非常短.
关键词: 扫描隧道显微镜     自旋弛豫     单分子     s-d交换作用