Article pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Single-Crystal Study of a Low Spin Co(II) Molecular Qubit: Observation of Anisotropic Rabi Cycles Mei-Xing Xu,† Zheng Liu,† Bo-Wei Dong,† Hui-Hui Cui,‡ Ye-Xin Wang,† Jie Su,† Zhenxing Wang,§ You Song,‡ Xue-Tai Chen,*,‡ Shang-Da Jiang,*,†,⊥ and Song Gao*,†,⊥
Inorg. Chem. Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 01/16/19. For personal use only.
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Beijing National Laboratory for Molecular Sciences, Beijing Key Laboratory of Magnetoelectric Materials and Devices, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China ‡ State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China § Wuhan National High Magnetic Field Center & School of Physics, Huazhong University of Science and Technology, Wu-han 430074, P. R. China ⊥ Beijing Academy of Quantum Information Sciences, West Bld. #3,No. 10 Xibeiwang East Rd., Haidian District, Beijing 100193, P. R. China S Supporting Information *
ABSTRACT: A mononuclear low spin (S = 1/2) Co(II) molecule crystallized in a 4-fold symmetry is fully investigated by CW and pulsed EPR on a single crystal sample. The quantum phase memory time of the molecule around 1 μs at 5 K is direction-independent, while the Rabi oscillation frequency is anisotropic. The spin Hamiltonian analyses reveal that the anisotropic Landé factor and hyperfine tensor do not influence the anisotropy apparently when the microwave magnetic field is applied along a certain direction. It is considered that the possibly involved nuclear spin forbidden transitions may be responsible for the small distinction of Rabi frequencies in two directions.
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INTRODUCTION Quantum information processing (QIP) offers the potential to create new frontiers of quantum technology.1 QIP relies on the manipulation of quantum bits (qubits), such as electron spin, which can be characterized by pulsed electronic paramagnetic resonance (EPR) in ensemble. Among various physical systems proposed, qubits based on magnetic molecules are found to be prominent candidates due to their facile synthetic tunability.2 Notably, transition-metal-ion-based magnetic molecules can offer long phase memory times.3 Furthermore, the coupling between electron spin and nuclear spin can also promote the quantum entanglement for the controlled NOT gate within a single molecule.4 Recent reported qubits based on magnetic molecules are usually constructed with low spin (S = 1/2) or small anisotropic high spin systems.3a,5,6 This is majorly due to that large zero-field splitting and forbidden transitions cause EPR silence and prohibit the spin state manipulation by present techniques.7 Meanwhile, polycrystalline samples make the EPR spectra more complicated and unsuitable for electronic structure studies due to the random orientations. High magnetic field has been utilized to enhance EPR transition resolution and to suppress both electron and nuclear-dipolar decoherence pathways.8 Single crystals with fixed orientation offer another convenient way to study the © XXXX American Chemical Society
electronic structure and eliminate unwanted transitions with better selectivity.9 High-order symmetric crystals provide further ease in the EPR spectra analysis as the principal axes of the Landé factor tensor (g̿) and the hyperfine coupling tensor (A̿ ) are collinear with the crystallographic axes. We recently reported a complex Co(12-TMC)(CH3CN)](PF6)2 (12-TMC = 1,4,7,10-tetramethyl-1,4,7,10-tetraazacyclododecane), which exhibits spin crossover behavior at room temperature and features S = 1/2 in the low spin state below 250 K.10 The slight residual orbital momentum affords us an anisotropic system, with axial g̿e and A̿ tensor. Ensuring the good alignment of the anisotropic magnetic centers, we investigate its quantum coherence behavior from various directions on the diluted single crystal sample. Relying on the enhanced spectrum resolution, it is unexpected to observe the anisotropic Rabi oscillation in various directions. Possible causes have been explored to explain the directional discrepancy of Rabi frequency from both experimental and theoretical aspects. This study provides further understanding of quantum behaviors in favor of better manipulation of electron spin. Received: September 20, 2018
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DOI: 10.1021/acs.inorgchem.8b02685 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
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EXPERIMENTAL METHODS
Synthetic Procedures and Crystallography. Single crystals of [M(12-TMC)(CH3CN)](PF6)2 (M = Zn, Co) were synthesized following the previously described method reported in ref 10. The diluted sample, [Zn 0.995 Co 0.005 (12-TMC)(CH 3 CN)](PF 6 ) 2 , (Zn0.995Co0.005) was prepared by dissolving the crystals of [Zn(12TMC)(CH3CN)](PF6)2 and [Co(12-TMC)(CH3CN)](PF6)2 with a ratio of 100:1 in CH3CN. The pale pink crystals were obtained from the mixture by diffusion of diethyl ether into CH3CN solution. The actual doping concentration of Co was determined by inductively coupled plasma mass spectrometry (ICP, Leeman PROFILE SPEC), around 0.5% ± 0.01%. The identity of Zn0.995Co0.005 single crystal was confirmed by an Agilent Super Nova Dual Atlas CCD diffractometer. CW EPR Experiments. Continuous-wave (CW) and pulsed EPR experiments were performed on a Bruker ElexSys E580 spectrometer operating at the X-band (ca. 9.7 GHz) with an Oxford Instruments ESR900 and CF935 continuous helium flow cryostat, also equipped with a goniometer convenient for rotation and angle determination. After face indexing on an Agilent Super Nova Dual Atlas CCD diffractometer, a qualified slice-shape crystal sample was mounted on the Teflon sample holder in a quartz tube (Figure S1), with the crystallographic a axis parallel to the B1 field of the microwave which is also the rotation axis. The rotation angle θ is defined by the angle between crystallographic c axis and external B0 field, varying from −90° to 270°. Pulsed EPR Experiments. The echo-detected field-swept (EDFS) EPR spectra were obtained with a standard Hahn echo pulse sequence, π/2−τ−π−τ-echo, under variation of the static B0 magnetic field. The pulse lengths were optimized to minimize the electron spin echo envelope modulation (ESEEM) effect, giving a proper π pulse length of 500 ns and τ equal to 1100 ns. The phase memory times, Tm, were measured with the above sequence at selected B0 field positions as marked with asterisks in the spectra (Figure 2). The spin−lattice relaxation times, T1, were determined with a standard magnetization inversion recovery sequence, π−t−π/ 2−τ−π−τ-echo with varying t and fixed τ. In the nutation experiments, a detection sequence, tp−tw−π/2−τ−π−τ-echo (tw > 5Tm), was used to measure the Rabi oscillation to determine the Rabi frequency via a fast Fourier transform (FFT). The Rabi frequency was measured in three distinctive microwave powers (attenuating the full power of 300 W with 0, 6, and 12 dB) so as to vary the B1 field. In all cases, all EPR spectra were simulated with the MATLAB toolbox “EasySpin” (http://www.easyspin.org/).11
Figure 1. (a) View of the molecular structure of Zn0.995Co0.005. (b) View of crystal packing looking along the c-axis.
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RESULTS AND DISCUSSION Molecular Structure. The cation of Zn0.995Co0.005 is comprised of a five-coordinated ZnII/CoII ion with a macrocyclic 12-TMC ligand in the equatorial positions and a CH3CN ligand in the axial position. As shown in Table S1, Zn0.995Co0.005 was crystallized in the tetragonal P4/nmm space group with two inversion related sets of molecules in a unit cell. It is worth noting that the 4-fold axis passes through the metal centers while the molecule has a lack of inversion symmetry (Figure 1). Even though there are some disorders in the structure, the high symmetric molecular structure offers the ease of EPR characterization in a single crystal sample. According to Neumann’s principle, the principal axes of the molecule must be collinear with the crystallographic axes a, b, and c. The bond lengths between a ZnII/CoII ion and coordinated nitrogen atoms in the equatorial positions are 2.126 Å, and the one in the axial position is 1.989 Å. The nearest distance between the ZnII/CoII ion and fluorine nuclear in the counteranion is 4.524 Å. Electronic Structure. The field-domain X-band EPR spectra on the powder sample of Zn0.995Co0.005 were recorded at 5 K. The CW EPR spectrum features a typical low spin anisotropic Co(II) behavior (Figure 2a). In the high-field
Figure 2. (a) CW EPR spectrum (black) measured at 5 K and (b) corresponding EDFS spectrum for a powder sample. The red curve inset is an enlarged view for the high-field range in (a). The green line represents the position of peak overlap. (c) CW EPR spectrum (blue) measured at 5 K and (d) corresponding EDFS spectrum for a crystal sample in the perpendicular direction (θ = 90°). (e) CW EPR spectrum (purple) measured at 5 K and (f) corresponding EDFS spectrum for a crystal sample in the parallel direction (θ = 0°). (g) Energy level diagram (blue for the perpendicular direction and purple for the parallel direction). All simulations are represented as gray curves.
range (2970−3670 G), the septet of triplets are recognized as the parallel transitions, originating from the hyperfine interaction of 59Co (I = 7/2) and 14N (I = 1) nuclei with the electron spin (S = 1/2). The eighth set of triplets in parallel B
DOI: 10.1021/acs.inorgchem.8b02685 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry transition peaks (around 2950 G marked with green line in Figure 2a) is hardly resolvable because it is overlapped with the perpendicular ones. The separation between the two directional transitions demonstrates the g̿ tensor anisotropy of this molecule. Moreover, the peak separation in parallel transitions is much larger than that of the perpendicular ones, indicating the highly anisotropic nature of the hyperfine interaction between 59Co nuclear spin and electron spin. The EDFS spectrum was also recorded on the powder sample as shown in Figure 2b. This integration spectrum is consistent with the derivative one recorded from the CW EPR measurement discussed above. Considering the molecular structure and the spectrum feature, the spin Hamiltonian of the system can be described by ̂ A̿ Co S ̂ + IN̂ A̿N S ̂ Ĥ = μB Bg ̿ S ̂ + ICo
(1)
where μB is the Bohr magneton, g̿ is the Landé factor tensor, A̿ Co and A̿ N are the hyperfine coupling tensor for 59Co or 14N ̂ , IN̂ , and Ŝ are the spin operators nucleus, respectively, the ICo for nuclear spin (59Co (I = 7/2) and 14N(I = 1), respectively) and electron spin, respectively (only one kind of coordinated 14 N atom was considered as a result of the obvious triplets in each set). Since the complex is crystallized in a tetragonal space group and the magnetic center locates on the 4-fold axis, it is convenient to conclude that the above g̿, A̿ Co, and A̿ N tensors are of axial symmetry and that their uniaxial principal axes are collinear with the crystallographic c axis. The best simulation of both CW EPR and EDFS spectra is given with g∥ = 2.022, g⊥ = 2.337, ACo∥ = 286 MHz, ACo⊥ = 68 MHz, AN∥ = 36 MHz, and AN⊥ = 32 MHz, as shown in Figure 2 a and b. Rotating a single crystal sample around the crystallographic a axis in the external B0 magnetic field (Figure S1), we are able to record the angular-dependent CW EPR spectrum. The resonant field varies as a sinusoidal function of the angle θ (Figure 3), while θ = 0° and θ = 90° correspond to the crystallographic c axis parallel and perpendicular to the B0 field, respectively. The hyperfine splitting features are well resolved (Figure 2c and e). Considering the angle between the B0 and caxis, these angular-resolved spectra can be reproduced by the simulated parameters mentioned above. The sine curve feature of the angular-resolved spectra is originated from the large g̿ tensor anisotropy in consistent with the powder data. The octet of triplets in a parallel orientation are clearly resolved. And in perpendicular directions, the peak−peak mixing is extensive due to the comparable in-plane component of A̿ Co and A̿ N tensors. The EDFS spectra of the single crystal were measured for the two orientations as shown in Figure 2d and f, which are corresponding to the CW EPR spectra. In parallel direction, the spectrum reveals very sharp absorption with a well-resolved octet of triplets separated by 100 G, which are further split into 3-fold peaks by 15 G. In the perpendicular direction, the multiple transitions are not well split with complicated fine structures. Quantum Coherence. The definitely separated peaks on the single crystal provide clear selectivity to study the spin dynamics and quantum coherence of the multiple hyperfine transitions and the orientation dependence. The spin−lattice relaxation time (T1) and the quantum phase memory time (Tm) are determined by pulse sequences described in the Experimental Methods. As shown in Figure S2a, T1 at 5 K is determined to be 1.3 ms at 2950 G in the parallel direction.
Figure 3. (a) Angular-dependent CW EPR spectrum with the angle θ varying from −90° to 270°. Panels (b) and (c) correspond to fine structures in perpendicular (θ = 90°) and parallel (θ = 180°) directions, respectively. Gray solid lines represent the relevant simulations.
The echo decay curve for Tm exhibits some higher harmonic modulation due to the ESEEM effect, as shown in Figure S3; a selective 500 ns π/2 pulse was selected to suppress ESEEM after testing a series of excitation pulses. As shown in Figure S2b, the echo decay time was modeled with a single exponential decay affording Tm = 900 ns. T1 and Tm at different fields were measured at selected transitions corresponding to various nuclear spin quantum numbers of 14 N and 59Co. As shown in Figure 4a and Table S2, both T1 and Tm are essentially field independent in the respective
Figure 4. (a) Field dependence of T1 (point) and Tm (circle) for a single crystal sample at 5 K in perpendicular (blue) and parallel (purple) directions (field positions correspond to the transition peaks marked with asterisks in Figure 2d and f). (b) Temperature dependence of T1 (point) and Tm (circle) measured at B0 = 2950 G, for a single crystal sample in perpendicular (blue) and parallel (purple) directions. C
DOI: 10.1021/acs.inorgchem.8b02685 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 5. (a) Rabi oscillations of the single crystal sample measured at 5 K by a range of attenuation settings in perpendicular (blue) and parallel (purple) directions (inset: linear fitting of ΩR versus B1; purple solid line for the parallel direction and blue solid line for the perpendicular direction). (b) FFT of Rabi oscillations of the single crystal sample measured at 0 dB at different fields in two directions (blue, purple, black, and red solid lines correspond to Rabi (perpendicular), Rabi (parallel), 1H Larmor, and 19F Larmor frequencies, respectively, and the dotted lines are for eye-comparison of frequencies). (c) Rabi frequency of the single crystal sample at different fields corresponding to perpendicular (blue solid point) and parallel (purple solid point) directions; 1H (blue and purple circle) and 19F (red circle) nuclear Larmor frequencies are also fitted linearly as black and red solid lines, respectively).
performed a nutation experiment on the powder sample, as shown in Figure S4, and the small bias still remains the same as in single crystal rotation experiments, around 1.42 MHz at 0 dB, as shown in Figure 5c. Meanwhile, the distinction exhibits a positive correlation with power attenuation (or B1 field), as shown in Figure S4. Apparently, the spin Hamiltonian parameter tensors, g̿, A̿ Co, and A̿ N, are highly anisotropic, which may contribute to the above observation. The full Hamiltonian system was considered with S = 1/2 and I = 1/2 so as to investigate the analytical solution of the Rabi frequency in the two directions:
directions because both relaxations are dominated by the electron spin determined process. Along the two principal directions, Tm is almost identical while T1 exhibits a slight difference. The experiments were also performed at different temperatures from 5 to 25 K. As shown in Figure 4b and Table S1, Tm only decreases slightly upon warming while T1 exhibits strong temperature dependence. Although Tm is significantly shorter than that found in some transition-metal-ion-based solution systems,3a,5c it is comparable to those found in solid dilution systems based on single crystals.9b,c In the present system, the quantum phase memory time is 3-orders of magnitude shorter than the spin−lattice relaxation time. Therefore, the electron−phonon coupling does not dominant the decoherence mechanism, and the abundant nuclear spins in the molecule serve as the major decoherence pathway. To check the possibility of putting the spin in an arbitrary superposition state, the nutation experiments for the single crystal were performed in parallel and perpendicular orientations at 5 K. A nutation pulse of duration tp was used to tip the magnetization, followed by a classical Hahn echo detection pulse. The echo intensity is measured as a function of tp. As shown in Figure 5a, the Rabi oscillation decays as a result of the spin decoherence as well as the inhomogeneity of the B1 field in the cavity.12 The FFT affords three groups of distinctive peaks in the frequency domain spectrum (Figure 5b). Two groups shift upon B0 field variation linearly. The slopes of these peaks illustrate the presence of 1H and 19F (as aforementioned existing in the counteranion) with Larmor frequencies of 42.58 MHz/T and 40.08 MHz/T, respectively (Figure 5c). This observation also confirms the aforementioned decoherence pathway by nuclei. The third group of peaks refers to the Rabi frequencies (ΩR) proportional to the driven magnetic field (B1) (Figure 5a inset). The Rabi frequency in perpendicular direction is a bit smaller than that of the parallel direction at the same B1 field. However, the direction of B1 field is along the rotation axis (crystallographic a axis), and thus the same g factor (gx) should be applied in the formula Ω R = gμB B1 S(S + 1) − MS(MS + 1) , leading to the same Rabi frequencies in both directions. The effect of structure disorder can be suppressed at very low temperature. To exclude the influence on B1 field strength in the rotation and measure the frequencies at the same condition, we also
̂ ̿ ̂ Ĥ = μB Bge̿ S ̂ + μ N Bg N̿ I ̂ + IAS
(2)
where the three terms correspond to the electron, nuclear Zeeman effect, and the hyperfine interaction. The g̿e term is the axially anisotropic Landé factor tensor with gx = gy ≠ gz, and the g̿N term is isotropic and the A̿ term is also axially anisotropic with Ax = Ay ≠ Az. The Rabi frequencies in both directions are calculated by the method introduced previously and is discussed in detail in the Supporting Information. One can note that the g̿e and A̿ can indeed affect the frequencies. However, the hyperfine interaction (
