Qiang Wang

Julien Trébosc

Yixuan Li

Oliver Lafon

Shaohui Xin

Jun Xu

Bingwen Hu

Ningdong Feng

Jean-Paul Amoureux

Feng Deng
email: dengf@wipm.ac.cnjean-paul.amoureux@univ-lille1.fr

Uniform signal enhancement in MAS NMR of half-integer quadrupolar nuclei using quadruple-frequency sweeps

Keywords: Half-integer quadrupolar nuclei, Quadruple-frequency sweeps, Signal enhancement, Satellite transitions, Central transition. I

We introduce two MAS schemes that allow manipulating the satellite-transition (ST) populations of half-integer quadrupolar nuclei, and which both exhibit improved robustness to the quadruplar coupling constant (C Q ). These schemes, called quadruple frequency sweep (QFS) or quadruple WURST (QWURST) are the sums of two DFS or four WURST to efficiently invert the ST populations of nuclei subject to large or small quadrupole interactions, simultaneously. These quadruple sweeps methods only require 6% more rf-power than the double sweeps ones. We demonstrate, both numerically and experimentally, that the QFS and QWURST schemes benefit from robustness to C Q and rf amplitude and offset and hence achieve uniform enhancement of the CT signal for 27 Al nuclei subject to different quadrupole interactions. Although the version of QFS with repetitive accumulation can achieve higher enhancement in the S/N of the 27 Al MAS spectrum, the final sensitivity gains mainly depend on the longitudinal relaxation time of different 27 Al sites. We also confirm that these schemes provide an improved acceleration of the 31 P-{ 27 Al} coherence transfer in PT-J-HMQC experiments.

Introduction

Nuclear Magnetic Resonance (NMR) spectroscopy of half-integer spin quadrupolar nuclei, with spin number S = n/2 , is widespread because (i) these isotopes represent about two thirds of stable NMR active nuclei and (ii) they are present in materials ranging from catalysts, glasses, ceramics and superconductors to biological systems [1][START_REF] Fernandez | Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances[END_REF][3][START_REF] Fyfe | One-and two-dimensional high-resolution solid-state NMR studies of zeolite lattice structures[END_REF][START_REF] Kong | Variable-temperature 17O NMR studies allow quantitative evaluation of molecular dynamics in organic solids[END_REF][6][START_REF] Wu | NMR studies of alkali metal ions in organic and biological solids[END_REF][8]. In solids, the large interaction between the quadrupole moment of these isotopes and the electric field gradients splits the NMR resonance into 2S single-quantum transitions, which include the central transition (CT) between energy levels +1/2 and -1/2, as well as 2S -1 satellite transitions (STs) between energy levels m and m -1 with m 1/2. The splitting depends on the crystallite orientation, and hence for powder samples the quadrupole interaction results in severe anisotropic broadenings, thus reducing the resolution and the sensitivity of the NMR spectra of these isotopes. The CT is not subject to the first-order quadrupole interaction, whereas STs are. Therefore, most of the time, on powder samples only the CT is observable. However, its line width can be as large as hundreds of kHz [8], and the S/N ratio hence can be very small.

Much effort has thus been devoted to the development of techniques aimed at enhancing the sensitivity of solid-state NMR experiments for half-integer quadrupolar nuclei. In particular, an ingenious and general method to increase the CT polarization, and hence the signal, consists in the manipulation of the ST populations [6b,9]. This increase can be obtained by saturating or selectively inverting the ST populations without irradiating the CT. The theoretical maximum enhancement of CT polarization is equal to S + 1/2 for the saturation and 2S for the perfect inversion of the STs converging from the external to internal transitions [10]. The maximum enhancement of 2S, corresponding to a perfect selective convergent inversion of the STs and an unaffected CT, has been achieved for spin-3/2 and -5/2 nuclei in static single crystals [11].

For static powders, the enhancements are lower because: (i) the STs cover large frequency ranges up to 3(S 1/2)C Q , with C Q = e 2 qQ being the quadrupolar coupling constant, and (ii) the STs always overlap with the CT and hence it is difficult to selectively excite them without perturbing the CT. Nevertheless, different schemes have been designed in order to manipulate ST populations for static powders. These schemes include the frequency-swept (SW) fast-amplitude-modulated (FAM) pulses [12], which generally lead to ST saturation, as well as the frequency swept pulses, such as the double frequency sweep (DFS) technique [START_REF]F1 of Fig.12 for the three 31 P sites obtained by conventional J-HMQC (bottom) and PT-J-HMQC with QFS (top) experiments[END_REF].

In the rotating frame, the DFS pulse has a constant rf-field strength (

) and it generates two radio-frequency (rf) spikelets, which are linearly swept in a symmetric manner over a frequency interval. For static powders, DFS with a large frequency sweep range is used so that the rf-spikelets are swept from the external STs towards the CT. This convergent DFS scheme achieves an adiabatic inversion of the outer STs before the inner ones in order to reach a maximum enhancement of the CT polarization. Furthermore, for static powders the simultaneous irradiation of STs on both sides of the CT by DFS is advantageous since it inverts all STs in a twice shorter time than two sequential frequency swept irradiations on either side of the CT. Hence, DFS minimizes the losses produced by spin lattice relaxation.

For static powders, DFS generally yields the best CT signal enhancement [6b]. This enhancement is below the theoretical one of 2S because: (i) the quadrupolar splitting depends on the crystallite orientation, and (ii) the frequency sweep can achieve adiabatic inversion only for crystallites exhibiting quadrupolar splittings much larger than [START_REF] Van Veenendal | Frequency stepped adiabatic passage excitation of half-integer quadrupolar spin systems[END_REF]. Otherwise, i.e. for crystallites exhibiting small quadrupolar splitting, the frequency sweep does not produce the anticipated effects and the gain of CT polarization of those crystallites is lower than the theoretical one.

To enhance the resolution, Magic-Angle Spinning (MAS) of the sample is often used. For each crystallite, the frequencies of STs are modulated by the MAS frequency, R , and their resonances break up into several spinning side-bands (ssbs).

For frequency swept pulses, such as DFS, the effective frequency sweep is the sum of the carrier frequency sweep and the modulation of the quadrupole interaction by the rotation. Therefore, the effective sweep frequency, and hence the enhancement of CT polarization by broadband DFS, depend on the crystallite orientation [START_REF] Iuga | Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra[END_REF]. As a result, broadband DFS produces lower enhancements under MAS than under static conditions. SW -FAM [12] was also proved to generate frequencies spreading over the range of their sweep width, which could lead under MAS to a better signal enhancement than the original FAM [10]. In fact, there is no essential difference between SW-FAM and DFS from a physical point of view, since they can provide very similar results for the frequency sweep. However, due to their simple amplitude modulation, FAM and it variants can be employed on spectrometers for which frequency modulation of the very short RF pulse is not feasible.

Under MAS, an alternative to the broadband excitation is the selective irradiation of one or a few ssbs [16]. This selective irradiation can be achieved by FAM pulses, which saturate the STs. This method was also named Rotor-Assisted Population Transfer (RAPT) [START_REF] Yao | Sensitivity enhancement of the central transition NMR signal of quadrupolar nuclei under magic-angle spinning[END_REF]. More conventional shaped inversion pulses, such as hyperbolic secant (HS) pulse [START_REF] Siegel | Signal enhancement of NMR spectra of half-integer quadrupolar nuclei in solids using hyperbolic secant pulses[END_REF] and wideband uniform-rate and smooth-truncation (WURST) [START_REF] Dey | Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion[END_REF], have been employed to irradiate ssbs of STs. In principle, the use of an adiabatic inversion pulse ensures a perfect inversion of the STs magnetization, provided the adiabaticity condition is satisfied. The largest enhancements for these frequency-swept adiabatic pulses are obtained when the width of their frequency Nevertheless, all techniques that manipulate the populations of STs by irradiating a single or two symmetric ssbs, have a common limitation: they are sensitive to the quadrupole interaction. Indeed, the sites with large C Q values require using ssb selective pulses with (i) large rf-field to achieve an efficient inversion and (ii) large frequency offset with respect to the CT so that the latter is not perturbed by rf irradiation. This is the contrary for sites with small C Q values. Hence, sites with different quadrupole interactions often exhibit distinct enhancements of the CT polarization. This non-uniform gain has been used for spectral editing [21,23].

Herein, we introduce two improved MAS schemes that allow manipulating the ST populations of half-integer quadrupolar nuclei, and which both exhibit improved robustness to the C Q value. These schemes, called quadruple frequency sweep (QFS)

or quadruple WURST (QWURST) are the sums of two sideband-selective DFS or four sideband-selective WURST with offsets and rf-fields that are both either large or small to efficiently invert the ST populations of nuclei subject to large or small quadrupole interactions, respectively. We demonstrate on crystalline aluminophosphate materials, through numerical simulations and experiments, that the QFS and QWURST schemes benefit from high robustness to C Q and rf amplitude and offset and hence achieve uniform enhancement of the CT signal for 27 Al nuclei subject to different quadrupole interactions. Similar to multiple RAPT/FAM [21a,b] and repetitive DFS [21c] strategies, repeating the QFS scheme and signal readout without allowing for longitudinal relaxation can lead to further sensitivity enhancement. However, the uniform enhancement of the CT of different 27 Al sites cannot be maintained due to their different T 1 relaxation times. We also show that these schemes provide an improved acceleration of the 31 P- 27 Al coherence transfer in PT-J-HMQC experiments with the indirect detection of 27 Al isotopes via 31 P spy nuclei ( 31 P-{ 27 Al}).

II. Method

II.1 Frequency-swept pulses

During a pulse, in the rotating frame the rf-Hamiltonian is given by ( 1)

where and are the instantaneous rf amplitude and phase.

During a WURST pulse, the rf-amplitude is given by [24]:

(

with the peak amplitude of the rf-field. T p is the WURST pulse duration and the index N determines the extent to which the edges of the pulse are rounded off. The phase is modulated as a quadratic function of time and for a decreasing frequency sweep equal to , it is equal to:

(3) where is the average offset angular frequency at the center of the pulse (t = T p /2). This phase modulation can be described in a frame, known as the frequency-modulated frame [START_REF] Garwood | The return of the frequency sweep: designing adiabatic pulses for contemporary NMR[END_REF], rotating in concert with the rf-field as a linear sweep of the carrier frequency:

In this article, we introduce double WURST (DWURST) pulses, which irradiate two symmetric sets of ST ssbs (Fig. 1b). These pulses consist of the sum of two identical WURST pulses with peak amplitudes, and opposite offsets, ± . For each species, the ssbs are situated at the sum of the isotropic chemical shift and the quadrupolar induced shift (QIS) associated to each transition, plus a multiple of R . It has been shown that for the m m -1 transition, in units of (1 + Q 2 /3) Q 2 /(10 0 ) the QIS can be written as [START_REF] Fernandez | Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances[END_REF][START_REF] Trébosc | Comparison of high-resolution solid-state NMR MQMAS and STMAS methods for half-integer quadrupolar nuclei[END_REF]:

QIS = 1 I(I + 1) + 36m(m 1)/4 (5)
where Q = 3C Q /[2S(2S-1)] is the quadrupole frequency and 36m(m 1) = -9, 27, 135, 315, 567 for the CT, ST 1 (inner), ST 2 (2 nd ), ST 3 (3 rd ) and ST 4 (4 th ) transitions, respectively. The ssbs of the CT are often very limited in number and amplitude, and they are not relevant for the CT signal enhancement. For a given species and sideband order, the ssbs of the STs (i) are always in the same frequency order: ST 1 < ST 2 < ST 3 < ST 4 (Eq.5), and (ii) they cover a frequency range which is often much smaller than R because the frequency difference in between ssbs of the external and internal STs is small:

QIS ext QIS ST1 = 3/128, 9/245 and 243/4000 (6) in units of (1 + Q 2 /3)C Q 2 / 0 , for S = 9/2, 7/2 and 5/2, respectively. For each species, the most efficient way to increase its CT magnetization is to irradiate one of its sets of close ssbs, and sweep it with decreasing order, i.e. from the outer ST to the inner one.

Therefore, we have always swept down the frequency in the WURST, DWURST or QWURST pulses (Fig. 1b,d).

The DFS pulse produces a linearly oscillating rf-field, which can be decomposed into the sum of two counter-rotating rf-fields. In the rotating frame this creates two rf-spikelets with constant amplitude, , irradiating in opposite directions at ± off (t) with respect to the carrier frequency (Fig. 1a). With a frequency sweep equal to , is given by Eq.4.

In this article, we also introduce the quadruple WURST (QWURST) pulse, which consists of four WURST pulses with the same decreasing sweep to irradiate the STs by decreasing order, and with rf angular offsets and peak amplitudes of (± , )

and (± , ) (Fig. 1d). We have chosen these two sets of rf offsets and amplitudes because they allow similar efficiencies for the ST CT transfers of nuclei with C Qs in the ratio of ca. 2, as shown by comparing Figs.8a and 9a simulated for DWURST with C Q = 3 and 1.5 MHz, respectively. This quadruple simultaneous excitation makes the QWURST pulse robust with respect to the quadrupole interaction.

In a similar way, we also introduce the QFS pulse (Fig. 1c), which consists of the sum of two DFS pulses with rf offsets and fields of (± , ) and (± ,

), and the four rf-spikelets converging towards the CT. With DFS and QFS, only half of the STs are irradiated by decreasing order.

Note that the rf-power, which is proportional to the square of the rf-amplitude, is hence only 6% higher for the QFS and QWURST pulses than for the DFS and DWURST ones.

II.2 The employed NMR sequences

In Fig. 2a, the previous frequency-swept pulses are used to manipulate the ST populations during T p to enhance the CT one. Then a CT-selective pulse converts the enhanced CT polarization into a CT single-quantum coherence, which is detected during the acquisition period. Fig. 2b represents the repetitive applications of sideband-selective QFS and acquisitions without allowing the system to relax.

These swept pulses can also be incorporated into the 31 P-{ 27 Al} PT-J-HMQC sequence in order to accelerate the 31 P- 27 Al coherence transfer through the J-coupling.

This sequence, displayed in Fig. 2c, derives from the conventional 31 P-{ 27 Al} J-HMQC sequence, but the coherence transfer related to J 31P-27Al during the defocusing and refocusing delays, mix , is accelerated by applying M frequency-swept pulses, which manipulate the 27 Al ST populations [22]. Furthermore, the initial transverse 31 P magnetization is created herein by a 1 H 31 P CPMAS scheme.

III. Details of simulations and experiments

In Fig. 4, 5, 9 and 10 the experimental or simulated signal has been normalized to its maximum value. All experiments and simulations were performed with a static magnetic field of B 0 = 9.4 T.

III.1. Numerical simulations

To rationalize the ST CT transfers, numerical simulations were carried out using SIMPSON software [START_REF] Bak | SIMPSON: a general simulation program for solid-state NMR spectroscopy[END_REF]. The powder averaging was accomplished using 2460 { MR , MR , MR } Euler angles that describe the orientation of the Molecule in the Rotor frame. The 615 { MR , MR } pairs were selected according to the REPULSION algorithm [START_REF] Bak | REPULSION, a novel approach to efficient powder averaging in Solid-State NMR[END_REF], whereas the four MR angles were regularly stepped from 0 to 360°.

The spin system was an isolated 31 P- 27 Al spin pair with J = 100 Hz. The 27 Al quadrupole interaction was considered up to the second order with Q = 0 and C Q = 3.0 (Fig. 9) or 1.5 MHz (Fig. 10). The other spin interactions were discarded. For all simulations, the MAS frequency was = 25 kHz. We simulated in a 1D way (t 1 = 0) the signal of the 31 P-{ 27 Al} PT-J-HMQC sequence (Fig. 9,10), starting from the 31 P transverse magnetization and selecting the +1Q 27 Al coherence. An ideal -pulse was employed on 31 P channel and the nutation frequency was 8 kHz for the two 27 Al CT selective /2-pulses. The recoupling delay was fixed to mix = 1.68 ms 1/6J.

III.2. Experiments

All experiments were carried out at = 15 kHz on a Bruker Avance-400 spectrometer operating with a Bruker 3.2 mm HXY probe. Acquisitions were performed by observing 27 analyze the robustness of these schemes to the average offset frequency, (Fig. 7) [START_REF] Massiot | Chemical bonding differences evidenced from J-coupling in solid state NMR experiments involving quadrupolar nuclei[END_REF].

Fig. 2a shows the 1D pulse sequence, with a frequency sweep before the CT--pulse, used to measure the 27 Al CT signal enhancement. Fig. 2b represents the repetitive version of QFS. Inversion recovery method was used to measure the T 1 of the different 27 Al sites on AlPO 4 -14. In the case of 31 P-{ 27 Al} 2D experiments (Fig. 2c), an initial 1 H 31 P CPMAS transfer was used with a contact time of 3 ms and rf-fields of 40 kHz and 55 kHz (ramped). The central 31 P -pulse used an rf-field of 52 kHz, and the two 27 Al CT-selective -pulse-lengths were of 7.5 s ( 11 kHz). The 31 P resolution was enhanced with two simultaneous 1 H and 27 Al decoupling sequences. A SPINAL-64 1 H decoupling, with an rf-field of 75 kHz was applied after the CP transfer, whereas during t 2 acquisition a 27 Al rotor-asynchronized multiple-pulse (RA-MP) decoupling [START_REF] Delevoye | Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei[END_REF], was also applied. This decoupling consisted of 27 Al pulses with rf-field strength of 40 kHz, lasting 5 s each, and separated by windows of 83 s. In PT-J-HMQC experiments, the ST CT transfers were performed with the four different schemes depicted in Fig. 1 whose parameters (Table 1) were optimized by using the pulse sequence in Fig. 2a. A fixed frequency sweep pulse length of T p = 500 s was employed and repeated M times during mix for each experiment. The conventional J-HMQC experiment was obtained by removing during mix the adiabatic frequency sweep pulses.

IV. Results and discussion

IV.1. Single pulse excitation

Actually, the application of multiple frequency sweeps has already been explored in previous studies. For example, (i) Iuga used two simultaneous broadband DFS to optimize the performance of the DFS theoretically and experimentally [START_REF] Iuga | Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra[END_REF]; (ii) Siegel performed HS frequency sweeps at two different frequencies ( and -/2) [START_REF] Siegel | Signal enhancement of NMR spectra of half-integer quadrupolar nuclei in solids using hyperbolic secant pulses[END_REF]; and (iii) the four-point FAM [10] or two subsequent FAM with different timings [12] presented by Brauniger also generated irradiations at two positive and two negative frequencies. Here, we aim to illustrate the feasibility of the combination of sideband-selective adiabatic inversion pulses and weighted rf-fields applied on different offsets in quadruple frequency sweep scheme, which should alleviate the saturation effect on the central transition of half-integer quadrupolar nuclei.

The 27 Al MAS spectra of AlPO 4 -14 using the four frequency sweep schemes of experiments, the spectra were recorded with = 150 (Fig. 3d,f) or 300 kHz (Fig. 3e,g). In case of QFS and QWURST, we employed frequency sweeps with simultaneous offsets of 150 and 300 kHz (Fig. 3b,c). Compared to the normal CT--pulse-acquire spectrum (Fig. 3a), the enhancement factors of the four different 27 efficient for all Al species simultaneously. Since the purpose of this manuscript is not to obtain the most efficient method for one particular species, but for all, we will focus now our discussion on the way to make the population transfers the most robust possible versus C Q values. Compared to the other three Al sites, Al 1 reveals a rather different enhancement evolution with DWURST and DFS (Fig. 6a andc). It increases very fast and is maximum (ca. 2.5) with 170 kHz, when simultaneously the gain is of only ca.

2.0 for Al 3 . However, when the gain is maximum with 300 kHz for Al 2 , Al 3 and Al 4 , that for Al 1 has decreased rapidly to ca. 1.8-1.9. On the contrary, QWURST and QFS make the enhancement factor build-up curves to be little C Q dependent (Fig. 6b andd). This improvement may thus offer an acceptable route to employ this ST CT transfer strategy in some hetero-/homo-correlation MAS experiments involving half-integer quadrupolar nuclei, without significant influence of the local electric field gradients in different chemical environments.

Here, we would like to explore in more detail the robustness of these sweeping methods with respect to versus the total shift (isotropic chemical plus quadrupolar-induced). This analysis is difficult to perform with AlPO 4 -14 which contains four Al species and thus four different shifts, and this sample should hence only lead to an averaged evaluation. For such an analysis, we have thus used a berlinite sample, since it only has a single aluminum site with a moderate quadrupole interaction (C Q = 4.7 MHz). In Fig. 7 we show the signal that is observed with the frequency sweep bandwidth of = 15 kHz, and varied from 170 to 200 kHz with a step of = 1 kHz for DFS/DWURST and from 340 to 400 kHz with = 2 kHz for QFS/QWURST. One observes that D/Q-WURST signal is subject to a non-negligible modulation with frequency. This means that the signal depends largely on the value, and hence on the experimental optimization. This is much less the case with DFS and particularly with QFS, which is very robust with respect to the particular value of .

IV.2. Repetitive quadruple frequency sweep

It has been demonstrated that the remaining polarization of the satellites after a single RAPT/FAM/DFS manipulation can be used to achieve a further enhancement of the CT by employing these schemes several times before waiting for the re-equilibration of the spin system.

[21] Here, we have also explored the interest of repetitive manipulation for QFS. Fig. 8a and 8b show the experimental results obtained for AlPO 4 -14 using a single pulse and the repetitive QFS sequence of Fig. 2b with N = 16, respectively. Although much higher S/N gains, larger than 3.7, can be obtained with the weighted addition of the individual FIDs recorded with the repetitive QFS, a uniform enhancement cannot be maintained for the four Al sites (Fig.

8c-f), as compared with the regular QFS scheme. Especially, after N = 16 accumulations, the Al 3 site exhibits an enhancement of ca. 4.5 (Fig. 8e), which is 20 % higher than for the other three sites. This difference can be attributed to its much shorter relaxation time (T 1,Al3 6.9 ms) compared to the others sites: T 1,Al1 25.9, T 1,Al2 25.8 and T 1,Al4 45.7 ms. This result demonstrates that the enhancement factor is affected by the longitudinal relaxation time in the repetitive strategy.

IV.3. 31 P-{ 27 Al} PT-J-HMQC experiments

One of the main applications of the ST CT transfer of populations is to speed up the J-recoupling, which is required to acquire J-HMQC 2D spectra, between spin-1/2 and half-integer quadrupolar nuclei. Indeed, these small J couplings require long mixing times, during which the signal is largely attenuated due to losses which are often important when dealing with quadrupolar nuclei. To demonstrate the feasibility of such strategy, we have first simulated the PT-J-HMQC 31 P-{ 27 Al} signal for one isolated 27 Al-31 P spin-pair with J = 100 Hz and the 4 different ST CT transfer schemes in Fig. 1. Two quadrupolar constants were selected for 27 Al, C Q = 1.5 and 3 MHz, and this interaction was considered Q = 0 to the second order. The signal intensities of the 31 P 27 Al 31 P transfers are plotted in Fig. 9 and 10 for C Q = 3 and 1.5 MHz, respectively, versus peak rf-field ( ) and offset ( ), for the four sweep schemes. These two figures demonstrate that the QFS/QWURST schemes can cover a much broader range of parameter compared to conventional DFS/DWURST schemes, especially with small C Q values (Fig.10b,d). This shows that the quadruple frequency sweep strategy is also available for our very recently developed PT-J-HMQC experiment. transfer, versus mix either with J-HMQC (Fig. 11b) or PT-J-HMQC (Fig. 11a) with the QFS sequence, as shown in Fig. 2c. In order to show the robustness of the QFS population transfer with respect to rf-field and also to alleviate its interference with proton decoupling, we have used a peak value of only 14 kHz. The offset was pre-optimized with the pulse sequence in Fig. 2a, and its value was of = 300 kHz. On the 27 Al channel, except for the QFS irradiation, all pulses selectively excited the CTs. The maximum overall transfer efficiency was significantly enhanced by PT-J-HMQC (Fig. 11c). Moreover, the optimal mixing time of PT-J-HMQC was shortened by a factor of ca. 1.7 compared to J-HMQC. In Fig. 12, we have represented the experimental 2D 31 P-{ 27 Al} 2D spectra of AlPO 4 -14 acquired with QFS PT-J-HMQC (Fig. 12a) and conventional J-HMQC (Fig. 12b). Representative vertical slices from these 2D spectra are displayed in Fig. 13. It must be noted that the application of this low rf-field of QFS ( 14 kHz) leads to the lower gain (1.8-2.1) of Al 1 compared with that (2.3-2.6) of the other three Al sites in PT-J-HMQC experiment. However, this gain is still higher than that (1. 4 -1.6) obtained by using DFS/DWURST schemes at the same conditions (results not shown).

It must be noted that our previous study showed that the maximum efficiency was observed with PT-J-HMQC when was set at the most intense sideband of ST 1

[22b], and the efficiency dropped when was small.

Nevertheless, these results demonstrate that the quadruple sweep strategy always leads to an improved robustness of ST CT transfer to accelerate the J recoupling between the two nuclei, which improves the sensitivity when used with the J-HMQC sequence due to reduced losses.

Conclusion

In

Fig. 1

 1 Fig.1 are shown with = 26.4 kHz in Fig.3b-g. For DFS and DWURST

Fig. 6

 6 Fig.6 displays the experimental CT enhancement factor versus off of the four Al sites of AlPO 4 -14 with = 26.4 kHz and the four sweep schemes shown in Fig.1.

Fig

  Fig.11 displays the 31 P signal observed on AlPO 4 -14 after a 31 P

Fig. 1 .Fig. 2 .

 12 Fig.1. Schematic representations of adiabatic frequency sweeps. Double frequency sweeps: DWURST (a) and DFS (c); Quadruple frequency sweeps: QWURST (b) and QFS (d).

Fig. 3 .

 3 Fig.3. AlPO 4 -14 27 Al 1D MAS spectra obtained with /2-CT-selective pulse: (a) alone, or (b-g) preceded with STs manipulation by QWURST (b), QFS (c), DWURST (d,e), DFS (f,g) with 1max = 26.4 kHz, = 150 (d,f), 300 (e,g) or 150 and 300 (b,c) kHz (indicated on the spectra). B 0 = 9.4 T, R = 15 kHz, T p = 500 s, 16 scans with a relaxation delay of 2 s.

Fig. 4 .

 4 Fig.4. AlPO 4 -14 Al 1 (C Q = 1.7 MHz) normalized signal versus 1max and off in MAS spectra obtained with sequences shown in Fig.2a with sweeps either at off with (a) DWURST and (c) DFS, or off and off /2 with (b) QWURST and (d) QFS. B 0 = 9.4 T, R = 15 kHz and T p = 500 s.

Fig. 5 .

 5 Fig.5. AlPO 4 -14 Al 3 (C Q = 5.6 MHz) normalized signal versus 1max and off in MAS spectra obtained with sequences shown in Fig.2a with sweeps either at off with (a) DWURST and (c) DFS, or off and off /2 with (b) QWURST and (d) QFS. B 0 = 9.4 T, R = 15 kHz and T p = 500 s.

Fig. 6 .

 6 Fig.6. AlPO 4 -14 experimental enhancement factor for the four 27 Al sites (Al 1 : --, Al 2 : --, Al 3 : --, Al 4 : --) versus with: (a) DWURST, (b) QWURST, (c) DFS and (d) QFS. B 0 = 9.4 T, R = 15 kHz, T p = 500 s and 1max = 26.4 kHz.

Fig. 7 .

 7 Fig.7. Berlinite experimental 27 Al CT-signal optimization versus off of sequence in Fig.2a with: (a) DWURST, (b) QWURST, (c) DFS, (d) QFS. B 0 = 9.4 T, R = 15 kHz, T p = 500 s, 1max = 26.4 kHz and NS = 16.

Fig. 8 .

 8 Fig.8. Experimental 27 Al MAS spectra of AlPO 4 -14 obtained using: (a) a /2-CT-selective pulse, (b) a repetitive QFS adding N = 16 individual FIDs acquired with the sequence shown in Fig.2b. Statistic enhancement of the four 27 Al sites (c-f) with repetitive QFS: black squares: S/N for each of the N individual FIDs; red circles: enhancement of S/N if the sum of the N individual FIDs is used; blue triangles: enhancement of S/N for the weighted sum of the N individual FIDs. B 0 = 9.4 T, R = 15 kHz, T p = 500 s, 1max = 26.4 kHz and a relaxation delay of 2 s.

Fig. 9 .

 9 Fig.9. Simulation results of the normalized signal intensities of 31 P 27 Al 31 P transfer in PT-J-HMQC experiments for one isolated 27 Al-31 P spin-pair with J = 100 Hz and C Q = 3.0 MHz as a function of peak rf-field ( 1max ) and offset ( off ) obtained by the pulse sequence described in Fig.2c with different frequency sweeps: (a) DWURST, (b) QWURST, (c) DFS and (d) QFS. B 0 = 9.4 T, mix = 1.68 ms 1/6J, R = 25 kHz and T p = 500 s.

Fig. 10 .

 10 Fig.10. Simulation results of the normalized signal intensities of 31 P 27 Al

Fig. 11 .

 11 Fig.11. AlPO 4 -14 31 P-{ 27 Al} 1D (t 1 = 0) spectra at B 0 = 9.4 T with R = 15 kHz. 31 P signal intensities versus mix for (a) PT-J-HMQC (Fig.2c) with QFS using T p = 500 s, off = 300 kHz and 1max = 14 kHz, and (b) conventional J-HMQC. (c) Expansion of optimal 31 P spectra obtained with (b) ( mix = 5.0 ms) and (a) ( mix = 3.0 ms) experiments, respectively.

Fig. 12 .

 12 Fig.12. AlPO 4 -14 31 P-{ 27 Al} J-HMQC TPPI spectra at B 0 = 9.4 T with R = 15 kHz, T p = 500 s, TD (F1) = 140, t 1 = 66.67 s, NS = 16, D1 = 2 s, experimental time 1.3 h, and skyline projections along F1 and F2. These spectra have been obtained: (a) with QFS ( 1max = 14 kHz) and mix = 3.0 ms, and (b) conventional sequence with mix = 5.0 ms, and they are represented with same contour levels.

  Al and 31 P of AlPO 4 -14 at the Larmor frequencies of 104.3 and 162.0 MHz, respectively. This sample contains three P and four Al sites exhibiting very different quadrupole coupling constants with C Q = 1.7, 4.2, 5.6 and 2.6 MHz for Al 1 , Al 2 , Al 3 and Al 4 , respectively [29]. This compound is thus adequate to demonstrate the advantages of quadruple frequency sweep schemes. We have also used AlPO 4 berlinite with a single Al site (C Q = 4.7 MHz) as a model sample to

  Al sites with the above sweep schemes are summarized in Table 1. As discussed previously, AlPO 4 -14 consists of four crystallographically distinct Al sites DFS and DWURST may be very slightly more efficient than QFS and QWURST for one particular species, but then this is the opposite for the other Al resonances. On the contrary, QFS and QWURST are very

	even Al 3 with	> 200 kHz.
	with different C Q s which exhibit quite distinct ST ssb patterns. It is hence difficult to
	obtain optimal ST	CT transfers for all 27 Al species by just sweeping at two
	symmetric offsets. Indeed, using DFS and DWURST with	= 150 kHz yields CT
	enhancements of ca. 2.4 for Al 1 sites, while smaller enhancements of 1.3 -1.6 are
	observed for the other three sites with larger C Q values (Table 1). Oppositely, with
	= 300 kHz one obtains gains of ca. 2.5-2.6 for the later three Al sites, but of 1.84
	for Al 1 site with the smallest C Further experimental investigations have been done to optimize off and 1max of
	the different schemes by using the pulse sequence in Fig.2a. The signal intensities of
	Al 1 and Al 3 sites as a function of	and	are plotted in Fig.4 and 5,
	respectively. One observes that the optimal peak rf-field is always in the range of
	15-30 kHz. With DFS and DWURST, the best enhancement of Al 1 site is
	achieved with	160-200 kHz, while it decreases above this range. Due to the
	simultaneous irradiations at	and	, this decrease for Al 1 is negligible with
	QFS and QWURST, which also allows a very good transfer for all other Al species,

Q . On the contrary, using the QFS and QWURST quadruple sweep schemes with simultaneous offsets of 150 and 300 kHz, results in enhancements of ca. 2.5 0.1 for all four Al sites of AlPO 4 -14 (Table

.

1). It is clear that the quadruple frequency sweep schemes have improved the robustness of frequency sweep to the quadrupole interactions. Actually, the QFS and QWURST sequences can be considered as the independent combinations of two DFS and DWURST pulses, simultaneously irradiating at two sets of ST ssbs. The much lower peak rf-field amplitude of 6.6 kHz of the inner adiabatic pulses at 150 kHz is required to avoid the interference of these two frequency sweep irradiations with the CT. It must be emphasized that the WURST shape pulse can be replaced by other adiabatic pulses, such as HS, in our quadruple frequency sweep strategy, which yield uniform sensitivity gains for the four Al sites of AlPO 4 -14, similar to those of QWURST (results not shown).

  this work, we have demonstrated the advantages of the improved strategy of Financial support from the IR-RMN-THC Fr-3050 CNRS for conducting the research is gratefully acknowledged. static and magic-angle-spinning NMR of quadrupolar nuclei by frequency-swept fast amplitude-modulated pulses, Chem. Phys. Lett., 383 (2004) 403-410. (b) T. Brauniger, G. Hempel, P.K. Madhu, Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in static NMR of half-integer spin quadrupolar nuclei, J. Magn. Reson., 181 (2006) 68-78; (c) T. Brauniger, Enhancing the central-transition NMR signal of quadrupolar nuclei by spin population transfer using SW-FAM pulse trains with a tangent-shaped sweep profile, Solid State Nucl. Magn.Reson., 45-46 (2012) 16-22.

	STs manipulation by using the quadruple frequency sweep technique. Instead of
	sweeping only one pair of symmetrical ST spinning sidebands, sweeping two different
	such pairs makes the ST	CT transfer much less sensitive to the offset of the sweep
	pulses. This method, which only requires 6% more rf-power than the double sweep,
	allows manipulating efficiently the STs of several sites with quite different C Q values,
	thus achieving similar signal enhancements for samples containing several
	nonequivalent sites. This robustness with respect to C Q is simultaneously obtained
	with a good robustness with respect to the sweeping rf-field. Both advantages are
	mandatory when analyzing samples whose spectra have a low S/N ratio. Indeed, it is
	then very difficult and time consuming to optimize carefully the rf-field and offset
	parameters.
	We have demonstrated this strategy in the case of pulse-acquire 1D experiments, and
	shown that it can also be employed in our recently developed PT-J-HMQC 2D
	experiment. This scheme can also be combined with many other 2D experiments
	involving half-integer quadrupolar nuclei to improve the experimental sensitivity. We
	have proposed two quadruple frequency sweep techniques based on
	sideband-selective DFS and WURST excitations, called QFS and QWURST,
	respectively. We have shown that (i) both sweepings provide the same signal gain of
	ca. 2.5, independent on the C Q value, but (ii) that QFS is slightly more robust than
	QWURST with respect to the offset, hence requiring less offset optimization.
	ACKNOWLEDGMENTS:
	Science Foundation of China (21733013, 21573278, 91745111, 21611130104 and
	21622311 .

J. Trébosc, O. Lafon and J.-P. Amoureux are grateful for funding provided by Region Nord/Pas de Calais, Europe (FEDER), CNRS, French Minister of Science, USTL, ENSCL, CortecNet, and contract ANR-2010-jcjc-0811-01.

Table 1 .

 1 Enhancement factors of the four Al sites on AlPO 4 -14 with different sweep schemes by using the pulse sequence in Fig.2a.

	1max = 26.4 kHz	C Q (MHz)	QWURST	QFS	DWURST	DFS
	off (kHz)		300 + 150	300 + 150	300	150	300	150
	Al 1	1.7	2.45	2.43	1.85	2.40	1.84	2.43
	Al 2	4.2	2.43	2.50	2.65	1.49	2.60	1.61
	Al 3	5.6	2.47	2.50	2.50	1.58	2.54	1.64
	Al 4	2.6	2.55	2.57	2.58	1.35	2.59	1.44


Bei Hu

Fushan Geng

Chong Zhao

Bertrand Doumert

Julien Trebosc

Olivier Lafon

Chao Li

Ming Shen

Bingwen Hu

Bei Hu

Julien Trébosc

Bingwen Hu

Deciphering the Origin of High Electrochemical Performance in a Novel Tisubstituted P2/O3 Biphasic Cathode for Sodium-Ion Batteries

Keywords: Ti-substitution, oxygen redox, Mn charge compensation, structure stability

published or not. The documents may come

Deciphering the origin of high electrochemical performance in a novel ti-substituted p2/o3 biphasic cathode for sodium-ion batteries

INTRODUCTION

Rechargeable sodium-ion batteries (SIBs), as an emerging category of electrochemical energy storage device, are advantageous over currently commercial lithium-ion batteries (LIBs) due to the use of abundant, geographically dispersed, and inexpensive Na resource. [START_REF] Dunn | Electrical Energy Storage for the Grid: A Battery of Choices[END_REF][START_REF] Kundu | The Emerging Chemistry of Sodium Ion Batteries for Electrochemical Energy Storage[END_REF] However, the energy density and durability of SIBs are still significantly lower than those of LIBs, owing notably to the scarcity of suitable Nabased cathode materials. Recently, a wide variety of Na-ion host cathodes have been developed toward high energy density and long cycle lifespan. [START_REF] Li | Towards High Power High Energy Aqueous Sodium-Ion Batteries: The NaTi2(PO4)3/Na0.44MnO2 System[END_REF][START_REF] Han | A Comprehensive Review of Sodium Layered Oxides: Powerful Cathodes for Na-ion Batteries[END_REF][START_REF] Clément | Review-Manganese-Based P2-Type Transition Metal Oxides as Sodium-Ion Battery Cathode Materials[END_REF][START_REF] Li | High-Energy Nanostructured Na3V2(PO4)2O1.6F1.4 Cathodes for Sodium-Ion Batteries and a New Insight Into their Redox Chemistry[END_REF] Among them, layered sodium oxides NaxTMO2 (TM = transition metal) with high theoretical capacities have aroused extensive interests over recent years. These layered oxides share similar structural characteristics with TMO6 edge-sharing octahedra along the c-axis that form parallel slabs but with different stacking arrangement. Delmas et al. proposed the structural classification for layered AxTMO2 (A = alkaline metal, TM = transition metal) materials using O2, O3 and P2, etc., where the letter indicates the form of coordination for A site (O: octahedral, P: prismatic) and the number (2 or 3) indicates the number of different (TMO2)n-layers per cell unit. [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Among these layered oxides, the P2 and O3-type NaxMnO2 compounds have garnered greater interest due to their superior electrochemical behavior and the lowcost of Mn. Compared with the O3 structure, the P2-type NaxMnO2 materials generally exhibit better electrochemical performance because of its low diffusion barrier for Na ions (Scheme S1) and applicable phase stability. [START_REF] Han | A Comprehensive Review of Sodium Layered Oxides: Powerful Cathodes for Na-ion Batteries[END_REF][START_REF] Guo | A Layered P2and O3-Type Composite as a High-Energy Cathode for Rechargeable Sodium-Ion Batteries[END_REF] However, when P2-type NaxMnO2 is employed as a cathode material, the extraction of Na + at high voltage usually causes drastic structural changes, and the insertion of Na + at low voltage results in large Jahn-Teller distortions induced by Mn 3+ ions, thus preventing reversible desodiation and sodiation upon long cycles. [START_REF] Yabuuchi | P2-Type Nax[Fe1/2Mn1/2]O2 Made From Earth-Abundant Elements for Rechargeable Na Batteries[END_REF][10][START_REF] Pang | Interplay between Electrochemistry and Phase Evolution of the P2-Type Nax(Fe1/2Mn1/2)O2 Cathode for Use in Sodium-Ion Batteries[END_REF] For the O3-type NaxMnO2, the sufficient Na ions reserved in alkaline layer guarantees the Na supply upon long cycles, which is an advantage for commercial applications. [START_REF] Fouassier | Evolution Structurale Et Proprietes Physiques Des Phases AXMO2 (A = Na, K; M = Cr, Mn, Co) (X ⩽ 1)[END_REF] However, the structural stability of the O3 phase is worse than that of P2 phase, which arises from the inevitable complex phase transition under ambient condition. [START_REF] Li | O3-Type Na(Mn0.25Fe0.25Co0.25Ni0.25)O2: A Quaternary Layered Cathode Compound for Rechargeable Na Ion Batteries[END_REF] To overcome the above bottlenecks of pure P2-or O3-type NaxMnO2 cathodes, multiple-phase composites were proposed to enhance the physical and electrochemical properties . [START_REF] Lee | Layered P2/O3 Intergrowth Cathode: Toward High Power Na-Ion Batteries[END_REF][START_REF] Chen | Stable Layered P3/P2 Na0.66Co0.5Mn0.5O2 Cathode Materials for Sodium-Ion Batteries[END_REF] Nonetheless, the combination of P2-and O3-type materials still suffer from irreversible structural transition that results in large capacity loss during long cycles. [START_REF] Lee | Layered P2/O3 Intergrowth Cathode: Toward High Power Na-Ion Batteries[END_REF] In recent works, chemical substitution by inactive elements has been introduced as a modification method to improve structural stability and promote the cycling performance of NaxMnO2 materials [START_REF] Yoshida | P2-Type Na2/3Ni1/3Mn2/3-xTixO2 as a New Positive Electrode for Higher Energy Na-ion Batteries[END_REF][START_REF] Wang | Suppressing the P2-O2 Phase Transition of Na0.67Mn0.67Ni0.33O2 by Magnesium Substitution for Improved Sodium-Ion Batteries[END_REF] . For instance, Bruce et al. have used Mg substitution in P2-Na0.67Ni0.3-xMgxMn0.7O2 to inhibit the irreversible P2-O2 phase transition and optimize the reversible P2-OP4 transition. [START_REF] Singh | High Voltage Mg-Doped Na0.67Ni0.3-xMgxMn0.7O2 (X = 0.05, 0.1Na-Ion Cathodes with Enhanced Stability and Rate Capability[END_REF] Therefore, chemical doping is perhaps a rational route to achieve better electrochemical performance for the multiple-phase composite cathodes.

In this work, we develop a novel Ti-substituted Li-containing P2/O3-intergrown Na0.8Li0.27Mn0.68Ti0.05O2 (P2/O3-NLMTO) cathode material for SIBs, which demonstrates highly reversible structural evolution upon Na + intercalation and deintercalation. The oxygen redox capacity in P2/O3-NLMTO, compared with that of Tifree Na0.8Li0.27Mn0.73O2 (P2/O3-NLMO), has been effectively promoted by increasing the electron density around oxygen ions, yet without sacrificing oxygen redox reversibility. Furthermore, the notorious Mn 3+ /Mn 4+ redox at low-voltage region has been greatly suppressed after Ti substitution. Ex-situ HRTEM and [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li solid-state NMR studies were employed to probe the crystal structure and the fate of lithium atoms, revealing retarded surface crack and lithium loss during cycling. These findings could offer practical guidelines for formulating rational strategies to improve structure rigidity and electrochemical performance of Mn-based cathode materials in SIBs.

EXPERIMENTAL SECTION

2.1. Materials synthesis. The Na0.8Li0.27Mn0.73O2 (P2/O3-NLMO) and Na0.8Li0.27Mn0.68Ti0.05O2 (P2/O3-NLMTO) samples were synthesized by using a facile solid-state reaction. Na2CO3•H2O (Aladdin, 99.999%), Li2CO3 (Aladdin, 99.99%), MnO2 (Aladdin, 99.95%), and TiO2 (Aladdin, 99.99%) powders were used with stoichiometric amounts. Excess of Na and Li sources (3%) were used to compensate for their loss at high temperature. The starting materials were thoroughly mixed by wet ball milling in ethanol at 250 rpm for 2 h and then dried at 70 ℃ for 30 min in air. After pressing into pellets, the precursor mixture was calcined in air at 700 ℃ for 12 h with a heating rate of 2 ℃/min and then naturally cooled down to room temperature. The final product was ground in an agate mortar and stored in an Ar-filled glovebox before use.

Electrochemical testing.

Both P2/O3-NLMO and P2/O3-NLMTO laminated electrodes consisted of 80 wt% active material, 10 wt% Super P (conductive additives), and 10 wt% PVDF (polyvinylidene fluoride) binder. Note that carbon nanotube conductive additives were used in all electrodes subjected to EPR experiments in order to avoid the interference of strong signal arising from Super P. The mass loading of cathode materials on the electrode was 3.0-4.0 mg cm -2 . Metallic sodium and glass fibers were used as the negative electrode and separator, respectively. The electrolyte was 1.0 M NaPF6 in ethylene carbonate (EC) and propylene carbonate (PC) [1:1 in volume] with 5% fluorinated ethylene carbonate (FEC) as an electrolyte additive. CR2032-type coin cells were then assembled in an Ar-filled glovebox (O2, H2O < 0.1 ppm). The assembled electrodes were dried overnight at 110 ℃ in a vacuum oven before electrochemical measurements. Galvanostatic charge-discharge measurements at room temperature were conducted using a Land 2001A battery test system. The cyclic voltammetry (CV) with 0.05 mV s -1 and electrochemical impedance spectra (EIS) with frequency range from 0.01 Hz to 100 kHz were tested by a CHI660e electrochemical workstation. For all ex-situ characterizations, the cells were held for at least 6 h after reaching the given states-of-charge (SoC) and then disassembled inside an Ar-filled glovebox. The electrodes were then washed with dimethyl methyl carbonate (DMC) for three times and dried for at least 12 h in Ar-filled glovebox.

Materials Characterization.

The crystal structures of the pristine cathode powder were characterized by X-ray diffraction (XRD) in the synchrotron beam line BL14B at Shanghai Synchrotron Radiation Facility (λ = 0.68889Å). The synchrotron XRD patterns were refined using FullProf Suite software. The ex-situ laboratory XRD patterns were conducted on instrument (Smartla SE, Rigaku) with Cu-Kα radiation (V = 40 kV, I = 40 mA, λ = 1.5406 Å). The chemical composition of samples was determined via inductively coupled plasma-atomic emission spectrometry (ICP-AES, Agilent ICP-OES 730). The scanning transmission electron microscopy (STEM) and high-resolution TEM (HRTEM) analyses were performed on EI Tecnai G2 F200 and FEI TECNAI G2 F20 microscopes. The HRTEM patterns were analyzed with the Gatan DigitalMicrograph program. The X-ray photoelectron spectroscopy (XPS) measurements of the as-synthesized samples were conducted using an AXIS Ultra DLD spectrometer (SHIMADZU Ltd., Japan).

The soft X-ray adsorption spectroscopy (sXAS) experiments were carried out at Shanghai Synchrotron Radiation Facility (BL08U). Total-electron-yield (TEY) mode (the probe depth is about 10 nm) was used to obtain the O K-edge and Mn L-edge sXAS spectra. All sXAS experiments were performed under ultrahigh vacuum (10 -7 Torr) condition at room temperature. Hard X-ray absorption spectroscopy (hXAS) experiments at Mn K-edge (E0 = 6539 eV) were monitored at Shanghai Synchrotron Radiation Facility (BL14W1), operating at 3.5 GeV under "top-up" mode with a constant current of 220 mA. The hXAS data was collected under transmission mode and the energy was calibrated according to the absorption edge of pure Mn foil. All the data processing performed prior to analysis, including background subtraction, energy calibration, normalization and Fourier transformation was performed using the Athena program. To get the X-ray absorption near edge structure (XANES) spectra, the hXAS data were processed by background subtraction and normalization procedures. In order to present effective radial distribution function, the k space has been selected to between 2 and 12 Å -1 , and the Rbkg value has been set to 1.0 in the Fourier transformed extended X-ray absorption fine structure (EXAFS) spectra. Note that the phase correction was not applied in these FT spectra, thus the distance value are not the accurate bond lengths. [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li magic-angle spinning (MAS) solid-state NMR experiments were performed on a 2.35 T Bruker AVANCE II spectrometer operating at a [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li Larmor frequency of 38.78 MHz and equipped with a 2.5 mm triple resonance HXY MAS probe used in doubleresonance mode. Temperature was calibrated by measuring the 1 H paramagnetic shift difference of a mixture of ferrocene and nickelocene solids. The temperature of tested samples was maintained at 309 K using temperature regulation system (BVT and BCU unit). The mass loading of cathode materials on the electrode was 6.0-7.0 mg cm -2 for NMR experiments. The cycled electrode materials were scraped from Al foil in Arfilled glovebox and packed into 2.5 mm zirconia rotors and spun at the frequency of 25 kHz. The [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li pj-MATPASS (pj = projection, MAT: magic-angle turning, PASS: phaseadjusted sideband separation) [START_REF] Hung | Isotropic High Field NMR Spectra of Li-Ion Battery Materials with Anisotropy >1 MHz[END_REF] spectra were acquired using π/2 pluse of 1.8 μs and result from averaging of 5k-55k transients with a recycle delay of 40 ms. Chemical shifts were referenced to 1 M LiCl solution at 0 ppm. Continuous-wave electron paramagnetic resonance (CW-EPR) spectra were acquired on a Bruker EMX plus 10/12 spectrometer in X-band (9.4 GHz), using a perpendicularmode microwave cavity and an Oxford ESR910 liquid helium cryostat. The microwave power and modulation amplitude were respectively set to 0.1 mW and 2 G; microwave frequency and modulation frequency were respectively set to 9.647 G and 100 kHz; and temperature was set to 90 K.

RESULTS AND DISCUSSION

3.1. Structure Characterizations. Synchrotron XRD (SXRD) was utilized to identify the crystal structures of the obtained P2/O3-NLMO and P2/O3-NLMTO, as shown in Figures 1a andb. As expected, the diffraction peaks of the two samples can both be well indexed to a mixture of hexagonal lattices with space groups of P63/mmc (P2) and R3 ̅ m (O3). According to the refined results of Table S1, Table S2 and previous studies, [START_REF] Yang | Design of High-Performance Cathode Materials with Single-Phase Pathway for Sodium Ion Batteries: A Study On P2-Nax(LiyMn1-y)O2 Compounds[END_REF][START_REF] Li | Substituted Co-Free Layered P2/O3 Biphasic Na0.67Mn0.55Ni0.25Ti0.2-xLixO2 as High-Rate-Capability Cathode Materials for Sodium Ion Batteries[END_REF] we believe that most of the Li ions enter the transition-metal sites to generate the major P2 phase, and residual Li ions occupy the Na sites to produce a small amount of O3 phase. It is noted that a low-intensity peak at 9.84° (marked with star) is observed for P2/O3-NLMO and P2/O3-NLMTO, which can be assigned to the long range inplane ordering between Li + and Mn 4+ (√3𝑎 √3𝑎 -type supercell). [START_REF] Yabuuchi | New O2/P2-type Li-Excess Layered Manganese Oxides as Promising Multi-Functional Electrode Materials for Rechargeable Li/Na Batteries[END_REF] The calculated crystallographic data of samples are presented in Tables S3. The results demonstrate that the relative ratio between P-and O-type phases is 98.08% (P2): 1.92% (O3) for P2/O3-NLMO and 97.84% (P2): 4.44% (O3) for P2/O3-NLMTO, respectively.

According to previous work, an intergrowth structure can ameliorate complicated phase transitions and accompanied large volume variation upon cycling, [START_REF] Huang | Tailoring Alternating Heteroepitaxial Nanostructures in Na-ion Layered Oxide Cathodes Via an In-Situ Composition Modulation Route[END_REF][START_REF] Yabuuchi | New O2/P2-type Li-Excess Layered Manganese Oxides as Promising Multi-Functional Electrode Materials for Rechargeable Li/Na Batteries[END_REF][START_REF] De La Llave | Improving Energy Density and Structural Stability of Manganese Oxide Cathodes for Na-Ion Batteries by Structural Lithium Substitution[END_REF] therefore the slightly higher proportion of O3 phase in P2/O3-NLMTO than in P2/O3-NLMO may indicates alleviated structure distortion and volume change in NLMTO during cycling.

In addition, the chemical components of the as-prepared P2/O3-NLMO and P2/O3-NLMTO were evaluated via ICP by fixing the Mn content as a reference due to its nonvolatility. The results (Table S4) suggest that the atomic ratios of the obtained-samples are consistent with the expected theoretical values.

To investigate the morphology and microstructure, detailed TEM and HRTEM analyses on the obtained P2/O3-NLMO and P2/O3-NLMTO were performed. The TEM images in Figure 1c and Figure S1a all illustrate hexagonal-shape particles with an average size of 0.5-1.5 μm, which is consistent with the hexagonal symmetry of the lattice. The HRTEM image in Figure 1d manifests two sets of clear lattice fringes, directly showing the intergrowth of P2 and O3 structure at atomic scale. [START_REF] Lee | Layered P2/O3 Intergrowth Cathode: Toward High Power Na-Ion Batteries[END_REF] The coexistence of P2 and O3 phases in P2/O3-NLMO is also observed in Figure S1b. Due to the low content of O3 phase, the major atomic structure of P2/O3-NLMTO shown in of Ti, Na, Mn, and O elements on the sample surface. Furthermore, to confirm that Tidoping uniformly occurs in the bulk material, XPS depth profiles were also collected (Figure S2). With increasing detection depth, the intensity of Ti 2p XPS peaks remain the same, thus suggesting the uniform Ti 4+ distribution from the material surface to the bulk.

Electrochemical Properties.

The electrochemical properties of the designed P2/O3-NLMTO and P2/O3-NLMO were gauged in Na half cells between 2.0 and 4.3

V vs. Na + /Na. Figure 2 shows the initial galvanostatic charge profiles and cycling performance of the P2/O3-NLMO and P2/O3-NLMTO electrodes at a current density of 20 mA g -1 between 2.0 and 4.3 V (vs. Na + /Na). Similar to other reported layered NaxMnO2 cathodes containing pure Mn 4+ , [START_REF] Rong | Structure-Induced Reversible Anionic Redox Activity in Na Layered Oxide Cathode[END_REF][START_REF] Rong | Anionic Redox Reaction-Induced High-Capacity and Low-Strain Cathode with Suppressed Phase Transition[END_REF] the initial charging curves of P2/O3-NLMO and P2/O3-NLMTO show a long plateau, which is likely due to the evolution of oxygen. Considering that the Mn 4+ is unlikely to be oxidized to Mn 5+ below 4.3 V, the initial extraction process of Na + results from pure oxygen oxidation. Interestingly, the initial charging capacity of the P2/O3-NLMTO electrode (127.9 mAh g -1 ) is higher than that of P2/O3-NLMO (111.9 mAh g -1 ), implying an increased anionic activation The voltage profiles of the materials in different cycles at 20 mA g -1 are depicted in Figure 3. In contrast to the initial charge profile, the second charge curve exhibits two stages with a slope at low voltage and a plateau region above 3.3 V, which is related with the oxidation of Mn 3+ and O-related anionic process, respectively. [START_REF] Yang | Lithium-Doping Stabilized High-Performance P2-Na0.66Li0.18Fe0.12Mn0.7O2 Cathode for Sodium Ion Batteries[END_REF][START_REF] Cao | Restraining Oxygen Loss and Suppressing Structural Distortion in a Newly Ti-Substituted Layered Oxide P2-Na0.66Li0.22Ti0.15 Mn0.63O2[END_REF] Intriguingly, the high-potential oxygen oxidative profiles of P2/O3-NLMTO are stable in the following cycles, while the oxygen redox process changes greatly in P2/O3-NLMO, demonstrating a favorable reversibility of the cycling process after Ti substitution.

Charge Compensation Mechanism Studies.

To study the oxygen-related charge compensation process of P2/O3-NLMO and P2/O3-NLMTO, spectroscopic studies were conducted via O and Mn soft X-ray absorption spectroscopy (sXAS) (Figure 4a andc). A soft X-ray in energy range from 522 eV to 550 eV excites filled O 1s electrons to empty O 2p (K-edge), allowing direct probe of O unoccupied states. [START_REF] Okubo | Molecular Orbital Principles of Oxygen-Redox Battery Electrodes[END_REF] The O K-edge sXAS is dominated by a broad feature peak above 535 eV, which is attributed to the excitation from the O 1s orbital to the hybridized orbital of transition metal (TM) 4sp and O 2p. The pre-edge peaks at lower energy (529.0 and 531.4 eV) are associated to the transition from the O 1s orbital to the unoccupied hybridized orbital of TM 3d and O 2p. [START_REF] Luo | Charge-Compensation in 3D-Transition-Metal-Oxide Intercalation Cathodes through the Generation of Localized Electron Holes On Oxygen[END_REF][START_REF] Hu | Retarding Phase Transformation During Cycling in a Lithium-and Manganese-Rich Cathode Material by Optimizing Synthesis Conditions[END_REF] In addition, the extra peak at 533.2 eV is assigned to carbonate (Na2CO3 or Li2CO3) in the surface. [START_REF] Lin | Faster Activation and Slower Capacity/Voltage Fading: A Bifunctional Urea Treatment on Lithium-Rich Cathode Materials[END_REF] The TEY mode sXAS spectra of Mn L-edge shown in Figure 4c allow one to assign the valence state of Mn ions. The peaks at 642.8 eV and 640.4 eV correspond to Mn 4+ , whereas the peak at 641.0 eV corresponds to Mn 3+ ions, and the peak at 639.4 eV is associated with Mn 2+ .

As shown in Figure 4a, for both Ti-free and Ti-substituted samples, the changes in the intensity of pre-edge peak at 531.4 eV show a similar trend, displaying an increase of hole state when charging to 4.3 V. Although the presence of electron holes on oxygen cannot be explained by O sXAS alone, the Mn L-edge spectra show no change beyond Mn 4+ after charging to 4.3 V (Figure 4c), thus we conclude that the increased hole states must be located on the O anions. [START_REF] House | What Triggers Oxygen Loss in Oxygen Redox Cathode Materials?[END_REF] In particular, compared with the spectra of P2/O3-NLMO, the pre-edge peak of P2/O3-NLMTO increases more obviously upon charging, suggesting the greater oxygen electron contribution at highly desodiated state.

Considering that there is no valence electron in the 3d 0 configuration of Ti 4+ , we perceive that Ti 4+ is inactive during charging process. Compared with Mn-O bond, the electrons in Ti-O bond are closer to oxygen atoms, which increases the electron density around oxygen (as illustrated in Figure 4b) and thus promote the oxidation of oxygen ion. [START_REF] Zhao | Ti Substitution Facilitating Oxygen Oxidation in Na2/3Mg1/3Ti1/6Mn1/2O2 Cathode[END_REF][START_REF] Kim | Material Design of High-Capacity Li-rich Layered-Oxide Electrodes: Li2MnO3 and Beyond[END_REF][START_REF] Hamaguchi | First-Principles Study on Cathode Properties of Li2MTiO4 (M=V, Cr, Mn, Fe, Co, and Ni) with Oxygen Deficiency for Li-Ion Batteries[END_REF] This result is consistent with the much higher capacity at high-voltage plateau region in P2/O3-NLMTO compared with P2/O3-NLMO.

Upon the reverse discharge process, the intensity of the pre-edge peak in the O Kedge spectra decrease greatly and the broad peak above 535 eV shifts to lower energy for both P2/O3-NLMO and P2/O3-NLMTO samples, which reveals the elongation of TM-O bond owing to the expansion of Mn ions by gaining electrons. The Mn L-edge spectra in Figure 4c also suggest the reduction of Mn 4+ to Mn 3+ and Mn 2+ after discharging. Note that the O K-edge spectra display similar peak intensity for both samples. This is due to the fact that the extra oxidized O 2-in P2/O3-NLMTO is reversibly reduced during the discharge process. Such reversibility of oxygen redox ensures the overall capacity stability during cycle.

0 1 2 3 4 5 P2/O3-NLMTO G(r) (a.u.) R (Å) pristine C-4.3 V D-2.0 V Mn K-edge P2/O3-NLMO (d)
electrochemically inactive as the tetravalent state for both samples. Upon discharge, the spectrum of P2/O3-NLMO shifts to a lower energy position, while the spectrum of P2/O3-NLMTO stays unchanged, which implies the lower Mn valence in nonsubstituted sample. From the Fourier-transformed Mn K-edge EXAFS spectra shown in Figure 4d, the two main peaks, respectively associated with Mn-O bonds and Mn-TM bonds, [START_REF] Nam | Combining in Situ Synchrotron X-Ray Diffraction and Absorption Techniques with Transmission Electron Microscopy to Study the Origin of Thermal Instability in Overcharged Cathode Materials for Lithium-Ion Batteries[END_REF][START_REF] Xu | Identifying the Critical Role of Li Substitution in P2-Nax[LiyNizMn1-Y-Z]O2 (0<X, Y, Z< 1) Intercalation Cathode Materials for High-Energy Na-Ion Batteries[END_REF] are all observable in two cases. Notably, for the P2/O3-NLMO in the fully discharged state, an obvious peak at 1.07 Å (in dashed circle) originating from Jahn-Teller distortion is clearly witnessed. [START_REF] Zhang | Manganese Based Layered Oxides with Modulated Electronic and Thermodynamic Properties for Sodium Ion Batteries[END_REF] However, this peak is hardly observed in discharged P2/O3-NLMTO, evidencing the suppressed reduction of Mn 4+ to Mn 3+ by Ti substitution. This phenomenon can be explained by the retarded lattice oxygen loss during the initial charge process based on the intuitive electroneutrality principle. In fact, the restrained Mn 3+ -triggered Jahn-Teller distortions and lattice oxygen loss by utilizing Ti substitution have also been reported previously in Zhou's work despite the fact that only P2 phase was explored. 29 pristine (red), fully charged (C-4.3V, green), and fully discharged (D-2.0V, blue) state.

To further investigate the electronic state of Mn and O ions before and after Ti substitution, the EPR tests were performed under perpendicular mode to probe the electronic state of Mn and O ions (Figure 5). Both pristine P2/O3-NLMO and P2/O3-NLMTO display a signal with Lorentzian shape centered at g ≈ 1.99, which is ascribed to Mn 4+ ions with antiferromagnetically coupled Mn 4+ -O-Mn 4+ cluster. [START_REF] Wang | Unveiling the Benefits of Potassium Doping On the Structural Integrity of Li-Mnrich Layered Oxides During Prolonged Cycling by Dual-Mode EPR Spectroscopy[END_REF][START_REF] Li | Unraveling the Critical Role of Ti Substitution in P2-NaxLiyMn1-yO2 Cathodes for Highly Reversible Oxygen Redox Chemistry[END_REF] Intriguingly, the symmetrical EPR signal of P2/O3-NLMTO is weaker than that of P2/O3-NLMO.

We note that there are pure MnO6 structures in P2/O3-NLMO sample, while 30% Mn 4+ -O bonding is influenced by 5% Ti substitution in Mn site in P2/O3-NLMTO, resulting in the subdued signal of the latter one. After charging to 4.3 V, the EPR signal representing Mn 4+ -O coupling decays for the two materials, arising from the decreased coupling between Mn 4+ and oxidized oxygen species O 2-δ . [START_REF] Li | Unraveling the Critical Role of Ti Substitution in P2-NaxLiyMn1-yO2 Cathodes for Highly Reversible Oxygen Redox Chemistry[END_REF] Meanwhile, a broad symmetrical line appears as a shoulder on the narrow Lorentzian line with g ≈ 1.99, which may be assigned to a new Mn 4+ -O coupling environment with much different electron-electron dipolar interaction. The detailed structure investigation is still in progress to draw an explicit explanation. Importantly, at fully discharged state, although the O 2-δ ions were reversibly reduced, the narrow EPR signal keeps decreasing in P2/O3-NLMO electrode, which might be attributed to the high amount of EPR-silent Mn 3+ ions produced during the Na + reinsertion process. In contrast, the corresponding signal increases appreciably in P2/O3-NLMTO at discharged state, indicating the alleviated charge compensation contribution from Mn 3+ /Mn 4+ couple. Such result is also consistent with the result of XANES and EXAFS analysis. This clear difference in the surface structure is indeed a result of the structure rigidity induced by Ti substitution. Previous reports have shown that at high desodiation level, layered sodium manganese oxides and lithium manganese oxides experience grain cracks, which is attributed to an increase of interfacial microstrain and unavoidable volume shrink owing to phase transition and distorted intrinsic oxygen framework. 11,43- 46 We believe that the small amount of Ti 4+ in the transition metal layer can greatly promote physical strength of the particles due to the "pillaring effect" of inactive Ti 4+ . [START_REF] Kim | Electrochemical Properties of LiMxCo1-xO2 [M = Mg, Zr] Prepared by Sol-Gel Process[END_REF] Furthermore, Ti-substitution increases the proportion of interlocked O3 (Table S3), In the past decade, experimental and theoretical studies have proved that the anionic redox in oxide cathode materials arises from the presence of oxygen lone-pair, [START_REF] Okubo | Molecular Orbital Principles of Oxygen-Redox Battery Electrodes[END_REF][START_REF] Ben Yahia | Unified Picture of Anionic Redox in Li/Na-ion Batteries[END_REF][START_REF] Assat | Fundamental Understanding and Practical Challenges of Anionic Redox Activity in Li-ion Batteries[END_REF][START_REF] Perez | Approaching the Limits of Cationic and Anionic Electrochemical Activity with the Li-rich Layered Rocksalt Li3IrO4[END_REF][START_REF] Li | Anionic Redox in Na-based Layered Oxide Cathodes: A Review with Focus On Mechanism Studies[END_REF] that is associated with the 'Na-O-Li' configuration in P2/O3-NLMO and P2/O3-NLMTO in our case. Moreover, the local ordering of Li + /Mn 4+ in TM layer may lock the surrounding O atoms and retard their gliding, which in turn delays the phase transition. Therefore, it is important to follow the fate of Li + ions during cycling as they play a critical role in the O-redox reaction. [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li NMR is a sensitive probe of the local ions in Ti-O bonding upon charge, as well as inhibiting the problematic Jahn-Teller effect of Mn 3+ during discharge, Ti-incorporation effectively promotes the oxygen electron contribution to the redox reaction without sacrificing O-redox reversibility.

which
Especially, analyses based on ex-situ HRTEM and [START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li solid-state NMR characterizations reveal that multiple factors are important to achieve the structure stability for Ti-substituted materials: (1) the irreversible surface crack is eliminated within a voltage range of 2.0-4.3 V; (2) lithium loss in the lattice is effectively alleviated and lithium ions in TM layer is well maintained. Altogether, Ti-substitution is an efficient and broadly applicable strategy for improving the practical performance of Mn-based P2/O3 biphasic cathodes for sodium-ion battery.

ASSOCIATED CONTENT

The Supporting Information is available free of charge at Supporting Information.

Schemes, TEM, XPS, CV, XANES and NMR curves (PDF)

Figure 1 .

 1 Figure 1. Synchrotron XRD patterns and the corresponding Rietveld refinement of (a) P2/O3-

Figure

  Figure 1eis still P2-type with a large interplanar distance of 0.55 nm corresponding to

  /O3-NLMTO in Figures 1f and g display the homogeneous distribution

  process. The CV curves in initial cycle are shown in FigureS3. Apparently, compared to P2/O3-NLMO, P2/O3-NLMTO exhibits enhanced oxidation peak above 3.3 V, furtherly suggesting that Ti substitution activates the reactivity of oxygen. After the activation process, the P2/O3-NLMTO electrode exhibits an outstanding performance in the following cycling, as shown in Figure2. The initial discharge capacity of P2/O3-NLMTO is 143.2 mAh g -1 and the remained capacity after 50 cycles is 112.6 mAh g -1 (90.7% capacity retention as compared to the second cycle). By contrast, the discharge capacity drops from 120.2 mAh g -1 to 95.3 mAh g -1 for the Ti-free P2/O3-NLMO sample. The electrochemical impedance spectra (EIS) of pristine electrodes displaying in FigureS4demonstrate lower charge-transfer impedance (Rct) in P2/O3-NLMTO, thereby exhibiting better Na + diffusion rate.

Figure 2 .

 2 Figure 2. Electrochemical performance and initial charge profiles (insert) of P2/O3-NLMO and

Figure 3 .

 3 Figure 3. Representative charge/discharge profiles of (a) P2/O3-NLMO and (b) P2/O3-NLMTO

Figure 4 .

 4 Figure 4. (a) O K-edge sXAS spectra under TEY mode and (b) Schematic electronic structures of

Figure 5 .

 5 Figure 5. Perpendicular-mode EPR spectra of P2/O3-NLMO and P2/O3-NLMTO electrodes in

3. 4 .

 4 Figures 6aand e, the two electrode materials both show smooth integrated structure in

  Figures 6dand h, microcracks are still detected on the surface of P2/O3-NLMO, in

Figure 6 .

 6 Figure 6. (a)-(d) Ex-situ HRTEM images of the P2/O3-NLMO electrodes after (a) charging to 4.0

7 ,

 7 Li + ions and thus is a vital method to quantitatively monitor changes of Li species during cycling. To this end, 2D pj-MATPASS experiments were performed to disentangle the multiple resonances of[START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li sites. The 2D pj-MATPASS spectra of P2/O3-NLMTO electrode in pristine state are plotted in FigureS7to explain the process of tilt transformation and sum projection. The isotropic slices of[START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li 2D pj-MATPASS NMR spectra obtained after spectral shearing along the F2 dimension for P2/O3-NLMO and P2/O3-NLMTO under various electrochemical states are displayed in Figure7. Generally, the signals resonating at ~1900 ppm and ~1500 ppm are tentatively assigned to Li ions within the TM layer, while the signal at ~750 ppm is attributed to Li ions in the Na layer.[START_REF] Yang | Design of High-Performance Cathode Materials with Single-Phase Pathway for Sodium Ion Batteries: A Study On P2-Nax(LiyMn1-y)O2 Compounds[END_REF][START_REF] Yang | Lithium-Doping Stabilized High-Performance P2-Na0.66Li0.18Fe0.12Mn0.7O2 Cathode for Sodium Ion Batteries[END_REF][START_REF] Li | Unraveling the Critical Role of Ti Substitution in P2-NaxLiyMn1-yO2 Cathodes for Highly Reversible Oxygen Redox Chemistry[END_REF] In addition, the signal observed at 0 ppm can be assigned to diamagnetic Li-containing species (such as Li2CO3 and LiF) residing on the surface of particles. The resulting spectra are normalized according to the number of scans and the mass, permitting semi-quantified comparison. As shown in Figure the relative content of Li atoms in TM layer of the pristine electrodes increases from 65.8% to 77.9% after Ti substitution. It is also noteworthy that cycling the electrodes greatly reduced the total signal of Li + ions and also altered the distribution of Li + ions among TM layers and Na layers. Although we cannot rule out the effect of faster T2 relaxation upon cycling, these results still give useful insights when considering the difference in between the two series of samples. In particular, for the samples that went through 25 cycles, the relative amount of Li in TM layers and the total amount of Li atoms in P2/O3-NLMTO were almost twice that of the Ti-free P2/O3-NLMO, which may be attributed to the stronger Na-O-Li bonding after Ti substitution. Because Li + ions in the TM layers are key stabilizers of materials and their loss upon long-term cycling is one of the most important reasons of capacity degradation, our results of[START_REF] Delmas | Structural Classification and Properties of the Layered Oxides[END_REF] Li pj-MATPASS NMR further confirm the positive effect of Ti substitution into Mn on the structural stability of P2/O3 biphasic NLMO.

Figure 7 .

 7 Figure 7. Isotropic 7 Li pj-MATPASS NMR spectra of (a) P2/O3-NLMO and (b) P2/O3-NLMTO

ACKNOWLEDGEMENTS

This work was supported by National Natural Science Foundation of China (Nos. 21902049, 21703068, 21872055, and 21874045), Shanghai Sailing Program (19YF1413000) and the Fundamental Research Funds for the Central Universities. We also acknowledge the support from the Steady High Magnetic Field Facilities of High Magnetic Field Laboratory (CAS) for the EPR experiments, and the support from Shanghai Synchrotron Radiation Facility for the SXRD (BL14B), sXAS (BL08UA) and XANES (BL14W1) experiments. B. Hu, F. Geng, and C. Zhao are thankful for the financial support from the graduate students overseas visiting project of East China Normal University. Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, Hauts-de-France Region and FEDER are acknowledged for supporting and funding partially this work. O. Lafon acknowledges the financial support from contract ANR-18-CE08-0015-01 (ThinGlass) and Institut Universitaire de France (IUF).

AUTHOR INFORMATION

Corresponding Authors

Chao Li -East China Normal University, Shanghai, P. R. China; orcid.org/0000-0002-0153-7825; Email: lchao@phy.ecnu.edu.cn Ming Shen -East China Normal University, Shanghai, P. R. China; orcid.org/0000-0003-1343-2761;Email: mshen@phy.ecnu.edu.cn. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally.

Author Contributions

Notes

The authors declare no competing financial interest.