Andrea Simion

Tobias Schubeis

Tanguy Le Marchand

Mihai Vasilescu

Guido Pintacuda

Anne Lesage

Claudiu Filip
email: claudiu.filip@itim-cj.ro

Heteronuclear decoupling with rotor-synchronized phase-alternated cycles

published or not. The documents may come

I. INTRODUCTION

Resolution and sensitivity are the traditional Achille's heel of solid-state nuclear magnetic resonance (ssNMR) spectroscopy. In static conditions, the chemical shift information is usually masked by the presence of strong anisotropic interactions, such as the chemical shift anisotropy (CSA), the homonuclear and heteronuclear dipolar couplings, or the quadrupolar couplings. 1,2 The effect of these anisotropic interactions can be averaged out in two ways: (i) by manipulating the spatial part of the Hamiltonian, spinning the sample around the magic angle, i.e., around an angle of 54.7° with respect to the external magnetic field, 3,4 or (ii) manipulating the spin part of the Hamiltonian, which is achieved by applying radio-frequency (RF) pulses. For heteronuclear dipolar interactions, which are the focus of this paper, a variety of heteronuclear decoupling pulse sequences have been developed over the last few decades. [7][8][9][10] Figure 1 presents the most used of them in a hierarchical form. Continuous-wave (CW) heteronuclear decoupling has been the most commonly used heteronuclear sequence for many years. CW variants, such as MLEV, 14 WALTS, 15 DIPSI, 16 and GARP, 17 and adiabatic inversion RF pulses, such as WURST 18 and SWIRL, 19 designed originally to decouple the isotropic heteronuclear J-couplings in solution nuclear magnetic resonance (NMR) experiments, were subsequently adapted to multiaspect signaling (MAS) NMR, at a high RF power to reduce the anisotropic interactions. The introduction of the two-pulse phase-modulated (TPPM) sequence in 1995 by Bennett et al. 8 was a key step, as it was shown to provide a significant improvement over CW decoupling in solids with dense homonuclear coupling networks. Since then, many variants of TPPM were designed that yielded improved decoupling performances, such as frequencymodulated and phase-modulated (FMPM), 20 small phase angle rapid cycling (SPARC), 21 small phase incremental alternation (SPINAL) and its variants, 22,23 amplitude-modulated TPPM (AMPM), 24 GT-n sequences, 25 cosine-modulation (CM), 26 swept-frequency TPPM (sw-TPPM) 27 and its variants, [31][32] and refocused TPPM (rTPPM). 33

FIG. 1. Hierarchy of heteronuclear decoupling pulse sequences.

A second family was associated with the understanding of the importance of phase-inversion, which is incorporated in the X inverse X (XiX) sequence, 34,35 its variants, such as amplitude-modulated XiX (Am-XiX) and super-cycled amplitude-modulated XiX (SC-AM-XiX), 36 refocused XiX (rXiX), 37 and derivate sequences, such as a phase-inverted super-cycled sequence for attenuation of rotary resonance (PISSARRO). 38 A third family was based on the use of rotor-synchronized πpulses, i.e., Rotor-Synchronized Hahn-Echo pulse train (RS-HEPT) sequence, 39,40 which, unlike the previous ones, uses time-reversal of the lowest-order effective Hamiltonian (i.e., Heff (1) from Eq. (9) in Ref. 41) under ultra-fast MAS, and not the additional modulation by the RF field, as the main decoupling mechanism. Derivate heteronuclear decoupling sequences were developed to remove the broadening of the spin-1/2 nuclei arising from the scalar coupling with quadrupolar nuclei, such as rotor-asynchronized multiple-pulse (RA-MP). 42 A fourth family was conceived based on the demonstration that the insertion of rotor-synchronized π-pulses in the CW sequence can enhance the decoupling's efficiency. This leads to the development of the refocused CW (rCW) sequence, 43 and its variant, where π-pulses are non-rotorsynchronized, such as rCW A or rCW Apa sequences. 44,45 Recently, Equbal et al. demonstrated that the rCW Apa sequence is robust regarding experimental parameters, such as pulse length and offset irradiation, and provides efficient heteronuclear decoupling in the low-power and fast MAS regimes. 46 Finally, a unified strategy of two-pulse-based heteronuclear decoupling sequences (UTPD) 47,48 was presented, demonstrating the importance of combined time-and phase-modulation. In the present work, we introduce a new heteronuclear decoupling pulse sequence, named Rotor-Synchronized Phase-Alternated Cycles (ROSPAC). Our results show that ROSPAC offers good 1 H offset robustness for a large chemical shift range under low-power irradiation, and performs well in the ultra-fast MAS regime, where it is almost independent of RF power, thus, avoiding rotaryresonance recoupling conditions. Moreover, being a pulsed sequence, ROSPAC has the advantage of a lower duty cycle compared to the conventional decoupling schemes relying on a continuous RF irradiation.

II. MATERIALS AND METHODS

A. Samples 98% uniform labeled 13 C, 15 N-glycine, and 13 C, 15 N-alanine were purchased from Cambridge Isotope Laboratories (CIL). The GB1 (β1 immunoglobulin binding domain of protein G) protein domain was expressed in Escherichia coli cultures, grown in an M9 medium containing 1,3-13 C-glycerol and 15 NH4Cl as sole carbon and nitrogen sources, purified by ion exchange and size-exclusion chromatography, and batch crystallized as described previously.

B. Simulations

Simulations for ROSPAC and RS-HEPT sequences were performed using the SIMPSON simulation software package 52,53 for a CH2 spin system assuming conditions of an 800 MHz NMR spectrometer, chemical shift anisotropy of protons of 𝛿CSAH = -2450 Hz, and dipolar couplings of 𝜔𝐷𝐶-H1/2𝜋=𝜔𝐷𝐶-H2/2𝜋= -21.9 kHz, 𝜔𝐷H1-H2/2𝜋=-23.3 kHz. Isotropic chemical shifts, Jcouplings, and asymmetry parameters were set to zero. The chemical shift anisotropy (CSA) of carbon spin was not taken into consideration, as it does not influence the decoupling performance. Simulations were carried out with 65 536 points and a spectral width of 12 000 Hz. Powder averaging was accomplished with a REPULSION scheme 54 employing 168 crystallite orientations and eight gamma angles.

C. Solid-state NMR spectroscopy

All spectra were recorded on a Bruker Avance III narrow-bore NMR spectrometer operating at a 1 H Larmor frequency of 800 MHz using a triple-resonance HCN 0.7 mm probe-head. Measurements on glycine and alanine were carried out by applying a 90° pulse on the 13 C channel with a 3.5 µs duration, followed by the acquisition of the 13 C FID under heteronuclear decoupling (TPPM, sw-TPPM, SPINAL, rCW ApA , or ROSPAC) applied on 1 H channel. For the case of rCW ApA , optimizations were performed as described by Equbal et al. 46 The two-pulse phase difference was 15° for sw-TPPM and TPPM, while the phase alternation angles were α = 10° and β = 5° for SPINAL and ROSPAC. The measurements were made at different rotation frequencies, i.e., 40, 60, and 100 kHz, respectively. All spectra were recorded with 16 scans, eight dummy scans, and a recycle delay of 10 s. Spectra of the protein GB1 were recorded at 100 and 60 kHz rotation frequencies, with a CP-HSQC pulse sequence 55 incorporating a non-selective spin-echo period on the 13 C channel (Fig. 10) with ROSPAC or sw-TPPM heteronuclear decoupling applied on the 1 H channel. The 90° pulse length was set to 1.25 µs on the 1 H channel and 5.18 μs on the 13 C channel. Contact times were 3 ms for the direct CP (i.e., 1 H -> 13 C) and 1 ms for the inverse CP (i.e., 13 C -> 1 H). Water suppression was performed with the MISSISSIPPI pulse scheme 56 applied on the 1 H channel without homospoil gradient, for a duration of 200 ms, and 1 H signal was recorded under Waltz-16 decoupling 15 applied on the 13 C channel at 10 kHz rf-field amplitude. NMR spectra were recorded with 16 scans in the former experiments, two dummy scans, and a recycle delay of 1 s.

III. RESULTS AND DISCUSSION

A. ROSPAC heteronuclear decoupling pulse sequence

Rotor-Synchronized Phase-Alternated Cycle (ROSPAC) (Fig. 2) is a heteronuclear decoupling pulse sequence designed for fast MAS NMR. It consists of 16 rotor-synchronized π-pulses, separated by a distance between them of d = nτr, where τr is the rotor period and n is an integer number, having different values, depending on the rotation frequency, as discussed in the Result section. The 16 phases of the pulses are {10, 350, 15, 345, 20, 340, 15, 345, 350, 10, 345, 15, 340, 20, 345, 15} and were optimized experimentally. The sequence is based on partial refocusing of the coherences responsible for transverse spin-polarization dephasing, on increasing the resonance frequency range in the rotating frame, and on a significant minimization of the cross-terms between the 1 H chemical shift anisotropy and dipolar couplings. Its performance was analyzed both numerically and experimentally and compared to that of sw-TPPM, TPPM, SPINAL, rCW Apa , and RS-HEPT.

B. Numerical simulations 1. Importance of phase alternation and supercycling

Robustness with respect to rotary-resonance conditions (i.e., v1 = nvr, where vr is the rotation frequency, v1 is the RF power, and n is a positive integer number) was observed when using two πpulses separated by a rotor period (RS-HEPT decoupling sequence) [Fig. 3(a)]. The anti-periodic symmetry of single-spin operators (i.e., Ix, Iy, and Iz) in the interaction frame, in the sense defined in Ref. 57, leads to the minimization of cross-terms between 1 H-1 H homonuclear dipolar coupling and 1 H chemical-shift anisotropy (CSA) in the effective Hamiltonian. The introduction of such symmetry can be done by applying π-pulses separated by a rotor period, which, in the lowest order approximation of the effective Hamiltonian, refocuses the coherences responsible for dephasing transverse spin-polarization. 39 However, even if RS-HEPT has good performances in the ultra-fast MAS regime, good sensitivity and resolution can be achieved only in compounds with small 1 H chemical shielding parameters, and under high-power RF irradiation. By increasing the number of π-pulses to 16 and modulating their phases (as done in the ROSPAC decoupling sequence), a significant minimization of CSA is achieved, leading to a strong improvement in the decoupling efficiency, as can be seen in the simulated spectra of Fig. 3(b), where ROSPAC is compared with the RS-HEPT scheme previously introduced by us. i.e., τr, 2τr, 4τr, and 6τr (peak intensity was normalized to that obtained with 300 kHz RF power and a distance between the π-pulses of τr). (b) Simulated carbon-13 spectra of a CH2 group, using RS-HEPT (the distance between the π-pulses was τr) and ROSPAC (the distance between the π-pulses was 6τr) heteronuclear decoupling at 100 kHz rotation frequency and three different RF powers: 20, 70, and 160 kHz, respectively (peak intensity was normalized to that obtained with 20 kHz RF power and 100 kHz rotation frequency using ROSPAC heteronuclear decoupling).

The proton line is partly inhomogeneous and, thus, difficult to saturate with a single frequency irradiation (e.g., using TPPM decoupling). Phase alternation overcomes this issue by enabling the irradiation of a larger pattern of frequencies in the rotating frame, i.e., over a broader range of different proton chemical shifts in the spectrum, 22 this effect being more significant in the lowpower regime, where the RF power and chemical shifts are of the same order of magnitude. Moreover, if the π -pulses are separated by a rotor period, the irradiation pattern is extended in the ultra-fast MAS regime, proof being that better performances were obtained using ROSPAC with respect to SPINAL, which is also a phase-alternated sequence. The second key element that contributes to the enhanced efficiency is the supercycling. Interference effects that influence the decoupling performances will depend on (i) sample spinning frequency, (ii) modulation of irradiation frequencies, and (iii) static components of the RF Hamiltonian. In supercycled sequences, higher-order Fourier components play a significant role, being directly responsible for their superior performance in comparison to lower-order supercycle schemes. 58

Choosing the number of π-pulses in the heteronuclear decoupling pulse sequence

The normalized peak height of the CH2 group as a function of the number of π-pulses in the sequence was simulated for ROSPAC heteronuclear decoupling, at 60 kHz rotation frequency, with 10, 80, and 160 kHz RF powers (Fig. 4). For Using more than two π-pulses, and alternating the phases, an improvement was observed in the decoupling performance. The minimum number of π-pulses for which the same good performance was obtained in all the three RF power regimes, i.e., low-power, intermediate, and high-power regime, is 16. Increasing the number of pulses does not yield any improvement, i.e., a constant peak height of the CH2 group was obtained. Therefore, 16 π-pulses were experimentally considered for the ROSPAC heteronuclear decoupling sequence.

C. Experimental results

Effect of delay between π-pulses

ROSPAC heteronuclear decoupling is a rotor-synchronized pulse sequence, i.e., the delay (Δ) between π-pulses satisfy the condition Δ = nτr -p, where n is an integer number, τr is the rotor period, and p is the π-pulses duration. The decoupling performance was evaluated experimentally for the CH2 group of glycine, for different values of n, and at three rotation frequencies, i.e., 100, 60, and 40 kHz (Fig. 5). Note that the measurements started with RF powers for which a positive value of Δ was obtained, i.e., p < nτr. Three decoupling regimes can be defined: (i) continuous-wave decoupling (i.e., Δ = 0), (ii) pulsed decoupling, where the distance between pulses is at least twice higher than the pulse length (i.e., Δ > 2p), and (iii) an intermediate regime, where the distance between π-pulses is close to the π-pulse length (i.e., Δ ≈ p). It was found that if we are in the intermediate regime, rotary-resonance conditions are avoided for ultra-fast MAS, and optimal decoupling efficiency is obtained independently from the rotation frequency. Good choices are n = 6 for 100 kHz rotation frequency, n = 4 for 60 kHz rotation frequency, and n = 2 for 40 kHz rotation frequency, these values being used for all the measurements from this article. As a general rule, n needs to be an integer number for which Δ ≈ p. In this regime, the effect of chemical shift anisotropy is extremely reduced or eliminated.

Rotary-resonance conditions avoiding and closer to radio frequency power independence

In the ultra-fast (60 kHz and above) MAS regime, the number of resonance conditions increases, which limits the decoupling performance to a restricted range of RF powers. One solution to overcome this issue is to use a low power decoupling. 59,60 However, low-power heteronuclear decoupling schemes are quite intolerant to the offset of the carrier frequency. Developing heteronuclear decoupling sequences that avoid rotary-resonance conditions would be an alternative valuable option that possibly also enabling efficient decoupling at high RF powers. 61 Here, we note that two pulse sequences already exist that avoid the second-order rotary-resonance condition, namely, PISSARRO and rCW Apa . 62,63 However, to the best of our knowledge, there are currently no heteronuclear decoupling schemes that prevent the interference observed at the first-order rotaryresonance condition, due to the reintroduction of the chemical shift anisotropy and dipolar coupling interactions. The performance of ROSPAC as a function of the RF power, with values ranging from 10 to 250 kHz was experimentally investigated at three spinning frequencies, i.e., 100, 60, and 40 kHz, and compared to that of existing heteronuclear decoupling schemes. More precisely, we compared ROSPAC with sw-TPPM by recording a series of carbon-13 spectra of L-alanine and measuring the intensity of the CH3 and CH groups (Fig. 6). We also compared the performance of ROSPAC with that of TPPM, sw-TPPM, SPINAL, and rCW Apa on the CH2 group of glycine (Fig. 7). The data clearly show that for ROSPAC both first-order and second-order rotary-resonance conditions are avoided at each rotation frequency. Notably, a behavior almost RF power independent is observed for rotation frequencies vr ≥ 60 kHz. In addition, in this fast-spinning regime, the decoupling efficiency remains fairly constant over the whole RF range. Thus, if the MAS frequency is decreased, i.e., only 20% loss in signal intensity is observed for 40 kHz rotation frequency and 30 kHz RF power, compared to results obtained for 100 kHz rotation frequency, for measurements on CH3 group of alanine. This is in contrast to sw-TPPM, where the loss in the signal intensity over the whole RF range was observed, up to 90% at the rotary-resonance recoupling conditions. Figure 7 shows similar data recorded on glycine. Several additional decoupling sequences were compared. Again, relatively flat RF power profiles are observed at the three spinning frequencies. ROSPAC has similar performances as the rCW Apa sequence in the low-power regime, while, in the intermediate and high RF power regimes, it outperforms all the analyzed pulse sequences, for ultrafast MAS. At lower spinning frequencies, the signal intensity decreases, due to stronger homonuclear couplings between protons of the methylene group. Overall, at 100 kHz MAS, line widths as narrow as 0.39 ppm were obtained for the CH2 group of glycine in the high-power regime (250 kHz RF) and 0.34 ppm in the low power regime (10 kHz RF). Our results prove that ROSPAC heteronuclear decoupling is a good choice for the fast and ultra-fast MAS regimes.

Robustness toward 1 H offset

In the low-power irradiation regime, decoupling performance is strongly dependent on the 1 H offset, a drop in the peak intensity up to 60% being found at small offsets around 4 ppm. 44 The offset dependence of the ROSPAC sequence was analyzed for three rotation frequencies, i.e., 100, 60, and 40 kHz, and three RF powers, i.e., 20, 70, and 160 kHz (Fig. 8). At 100 kHz rotation frequency, it was found that the low-power regime offers the best robustness regarding 1 H offset. Therefore, carrier frequency dependence was analyzed for 100 kHz rotation frequency and 20 kHz RF power for a larger offset scale, i.e., from -10 to 10 ppm, and compared to that obtained for various decoupling sequences discussed in this work (Fig. 9). It was found that ROSPAC performs slightly worse than SPINAL and rCW Apa but better than TPPM or sw-TPPM decoupling, for small (<6 ppm) 1 H offsets. In the case of larger offsets, however, ROSPAC decoupling outperforms all the analyzed sequences, with a loss in intensity of about 30% at ±10 ppm. We expect this property to become relevant for future applications at ultra-high magnetic fields.

Applications to the β1 domain of the immunoglobulin binding protein G (GB1)

The decoupling efficiency of ROSPAC was then evaluated on a microcrystalline sample of the model protein domain GB1 (β1 immunoglobulin binding domain of protein G), 64 a prototypical example of a biosolid.

Figure 10 shows 1 H MAS NMR spectra recorded at 100 kHz MAS with a modified 2D CP-HSQC pulse sequence, 52 where a 13 C spin-echo of 100 ms was inserted instead of the t1 period. This setup, coupled with the alternate 1,3-13 C-labeling scheme used here, is adapted to illustrate the efficiency of a decoupling sequence, since the experimental intensities depend uniquely on the heteronuclear T2's for the particular decoupling sequence applied during the spin-echo. While at 10 kHz RF power, ROSPAC and sw-TPPM provide the same efficiency, it is evident that with 40 kHz RF power ROSPAC yields better performance, in agreement with the data obtained on glycine and alanine (see Figs. 6 and7). Overall, these experiments demonstrate the efficiency toward a wide range of experimental conditions and straightforward applicability of ROSPAC decoupling for biomolecular MAS solid-state NMR spectroscopy.

IV. CONCLUSIONS

In this work, a new heteronuclear decoupling pulse sequence was introduced. It was demonstrated that the alternation of phases in a supercycle rotor-synchronized π-pulses sequence leads to a significant minimization of the chemical shift anisotropy and 1 H-1 H multi-spin interactions and irradiation of a larger pattern of RF frequencies. Moreover, in the intermediate decoupling regime, where the distance between π-pulses is close to the π-pulses length, both first and second-order rotary-resonance conditions are avoided. Our results show that ROSPAC heteronuclear decoupling offers improved performances, especially in the ultra-fast (60 kHz and above) MAS regime, in terms of RF power independence, 1 H offset robustness toward a large chemical shift range in the low-power regime, ease of optimization, and efficiency. Notably, there are two main applications where these advantages can be exploited: first, to study (bio)materials with large isotropic chemical shift dispersion in the proton spectrum, as paramagnetic materials; 65 and second, in dynamics experiments, e.g., for an accurate T1ρ relaxation mapping, 66 the sequence being used for decoupling during spin-lock. A more detailed analysis of the ROSPAC sequence using Floquet theory and the development of improved versions of this pulse sequence are currently being worked on and will be presented in a future paper.

SUPPLEMENTARY MATERIAL

See the supplementary material for SIMPSON scripts that are used to obtain the presented simulations.

FIG. 2 .

 2 FIG. 2. ROSPAC heteronuclear decoupling pulse sequence.

39

 39

FIG. 3 .

 3 FIG. 3. (a)Normalized simulated peak height of a CH2 group as a function of the radio frequency power, using RS-HEPT heteronuclear decoupling at 100 kHz rotation frequency for different distances between the π-pulses, i.e., τr, 2τr, 4τr, and 6τr (peak intensity was normalized to that obtained with 300 kHz RF power and a distance between the π-pulses of τr). (b) Simulated carbon-13 spectra of a CH2 group, using RS-HEPT (the distance between the π-pulses was τr) and ROSPAC (the distance between the π-pulses was 6τr) heteronuclear decoupling at 100 kHz rotation frequency and three different RF powers: 20, 70, and 160 kHz, respectively (peak intensity

FIG. 4 .

 4 FIG. 4. Normalized simulated peak height of the CH2 group as a function of the number of π-pulses in the sequence, using ROSPAC heteronuclear decoupling at 60 kHz MAS and 10, 80, and 160 kHz RF powers. Peak intensities were normalized to those obtained for each v1 power, i.e., 10, 80, or 160 kHz, respectively, at 60 kHz MAS.

FIG. 5 .

 5 FIG. 5. Dependence of the normalized experimental peak height of the CH2 group of glycine on the separation between π-pulses, as a function of the ratio between radio-frequency power and rotation frequency, using ROSPAC heteronuclear decoupling at 100 kHz (a), 60 kHz (b), and 40 kHz (c) MAS frequencies. Peak intensities were normalized to those obtained with ROSPAC decoupling at 10 kHz RF power at each particular MAS frequency, i.e., 100, 60, or 40 kHz, respectively.

FIG. 6 .

 6 FIG. 6. Normalized experimental peak height of the CH3 (a) and CH (b) groups of alanine as a function of the radio-frequency power, using sw-TPPM and ROSPAC heteronuclear decoupling at MAS frequencies vr of 100, 60, and 40 kHz. Peak intensities were normalized to those obtained with 10 kHz RF power of ROSPAC decoupling at 100 kHz MAS.

FIG. 7 .

 7 FIG. 7. Normalized experimental peak height of the CH2 group of glycine as a function of the radio-frequency power, using TPPM, sw-TPPM, SPINAL, rCW ApA , and ROSPAC heteronuclear decoupling at MAS frequencies vr of 100, 60, and 40 kHz. Peak intensities were normalized to those obtained with 20 kHz RF power of rCW Apa decoupling at 100 kHz rotation frequency.

FIG. 8 .FIG. 9 .

 89 FIG. 8. Normalized experimental peak height of the CH2 group of glycine as a function of the 1 H offset, using ROSPAC heteronuclear decoupling at 100 kHz (a), 60 kHz (b), and 40 kHz (c) rotation frequencies and 20, 70, and 160 kHz RF powers. Larmor frequency for 1 H nuclei was 800 MHz.

FIG. 10 .

 10 FIG. 10. (a) CP-HSQC scheme employed for the evaluation of heteronuclear decoupling in GB1 and (b) and (c) experimental 1 H MAS NMR spectra of GB1 protein recorded with sw-TPPM (blue lines) and ROSPAC (red lines) heteronuclear decoupling at 10 and 40 kHz RF powers and 100 kHz rotation frequency, on a 800 MHz spectrometer.

Accepted to J. Chem. Phys. 10.1063/5.0098135 Accepted to J. Chem. Phys. 10.1063/5.0098135 Accepted to J. Chem. Phys. 10.1063/5.0098135

Accepted to J. Chem. Phys. 10.1063/5.0098135

ACKNOWLEDGMENTS

We acknowledge financial support from the European Union's Horizon 2020 Research and Innovation Program (Grant No. INFRAIA-02-2020 GA 101008500 "PANACEA" to G.P. and A.L. and Grant No. INFRAIA-01-2018-2019 GA 871037 "iNext Discovery" to G.P.), the European Research Council (Grant No. ERC-CoG-2015 GA 648974 "P-MEM-NMR" to G.P.), and the CNRS (Grant No. FR 2054). A.S. acknowledges a research fellowship from the World Federation of Scientists (WFS), CERN, Geneva, Switzerland, and a Scholarship from the Faculty of Physics, Babeș-Bolyai University, Cluj-Napoca, Romania. We thank Professor M. Ernst for helpful suggestions and discussions.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.


Pei-Kai Hsu

Yi-Che Chen

Alexandre Gloter

Hong-Chieh Chen

Eric Nestor Tseng

Shih-Yun Chen
email: sychen@mail.ntust.edu.tw

Jenn-Ming Song

Surface-sensitive magnetism of mesoscopic hollow CeO 2 spheres

Keywords:

This study demonstrates magnetism of mesoscopic hollow ceria spheres (H─CeO 2 ) with different defect distribution characteristics. The content and distribution of defect of micro-scale hollow spheres are controlled by varying the reaction with HNO 3 and the annealing process. The obtained spheres are divided into three groups according to the surface structure, defect content and defect distribution of the shell. Group I is characterized by rough sphere surface and with large ceria clusters. Group II has relatively continuous surface defective layers and reduced surface roughness of the sphere. Group III has a continuous and smooth surface defective layer, and a decreasing gradient of Ce 3+ concentration inside this layer. All spheres were ferromagnetic at room temperature. Saturation magnetization from high to low is in the sequence: group III, group II, and group I. The strongest magnetism is obtained for the samples subjected to the reaction with 1 M HNO 3 for 60 min and then annealed, in which defects are distributed homogeneously within the surface thin layer and the sphere surface is smooth. We thus conclude that the surface plays the major role in the magnetic behavior of micro-scale hollow sphere.

Introduction

Several oxides with wide band gaps and high Curie temperatures, notably if their structures and processes are close to those of semiconductors, act as candidate materials in the field of spintronics. Researchers have examined ferromagnetism in such oxides, e.g., TiO 2 , [START_REF] Choudhury | Room temperature ferromagnetism in defective TiO 2 nanoparticles: Role of surface and grain boundary oxygen vacancies[END_REF][START_REF] Karthik | Influence of dopant level on structural, optical and magnetic properties of Co-doped anatase TiO 2 nanoparticles[END_REF] ZnO, [START_REF] Tahir | Surface defects: possible source of room temperature ferromagnetism in Co-doped ZnO nanorods[END_REF][START_REF] Wang | Defects-Induced Room Temperature Ferromagnetism in ZnO Nanorods Grown from ε-Zn(OH) 2[END_REF] CeO 2 , [START_REF] Singhal | Role of electronic structure and oxygen defects in driving ferromagnetism in nondoped bulk CeO 2[END_REF][START_REF] Niu | Oxygen vacancy induced room temperature ferromagnetism in Pr-doped CeO 2 thin films on silicon[END_REF] in the past decade. The occurrence of magnetism in these materials have been experimentally clarified. Scholars attribute magnetism of oxide to the existence of defects in addition to magnetic dopants. [START_REF] Kamble | Investigating thermal stability of structural defects and its effect on d 0 ferromagnetism in undoped SnO 2[END_REF][START_REF] Das | Evidence of oxygen defect induced ferromagnetism in heat treated electrospun ZnO nanowires[END_REF][START_REF] Bernardi | The role of oxygen vacancies and their location in the magnetic properties of Ce 1-x Cu x O 2δ nanorods[END_REF] To further improve the ferromagnetism of oxide, different experimental procedures have been presented to adjust the content as well as defect structure. [START_REF] Tseng | Magnetism and plasmonic performance of mesoscopic hollow ceria spheres decorated with silver nanoparticles[END_REF][START_REF] Ilyas | Enhanced ferromagnetic response in ZnO: Mn thin films by tailoring composition and defect concentration[END_REF][START_REF] Sonsupap | Fabrication, structure, and magnetic properties of electrospun Ce 0.96 Fe 0.04 O 2 nanofibers[END_REF] However, the origin of this magnetism is still unclear. Several models have been developed, including the bound magnetic polaron model [START_REF] Coey | Donor impurity band exchange in dilute ferromagnetic oxides[END_REF] and F-center exchange. [START_REF] Coey | Ferromagnetism in Fedoped SnO 2 thin films[END_REF] Coey et al. recently proposed that magnetic saturation in agglomerations formed with oxide nanoparticles is not derived from collective spin ferromagnetism, but is related to giant magnetic orbitals. [START_REF] Coey | Collective magnetic response of CeO 2 nanoparticles[END_REF] The preferred structure for such orbital magnetism is believed to be a quasi-two-dimensional mesostructure, such as surface layers occurring on aggregates of oxide nanoparticles or granular oxide. [START_REF] Sen | Mesoscopic structure formation in condensed matter due to vacuum fluctuations[END_REF] This magnetic model is expected to be particularly applicable for materials with low electron density, high dielectric constant and surface layers with modified properties relative to the bulk with nearly atomic dimensions. Consequently, a micro-scale hollow sphere with tunable defect distribution such as surface oxygen vacancies is an ideal model structure to reveal the effect of mesoscopic structure on magnetism.

Among oxides with room-temperature ferromagnetism, CeO 2 has attracted extensive interests. Many groups devoted to unravel the relation between defects and magnetism. In undoped CeO 2 nanoparticles, strong magnetic signals correspond with a determinate range of Ce 3+ content at the surface. [START_REF] Li | Relationship between the surface chemical states and magnetic properties of CeO 2 nanoparticles[END_REF][START_REF] Chen | Oxygen vacancy dependent magnetism of CeO 2 nanoparticles prepared by thermal decomposition method[END_REF] Other similar quasi-two-dimensional mesostructures have been developed, including sub-micro core-shell structures and micro-scale hollow spheres. Both these structures are ferromagnetic, with the enhanced magnetism attributed to the presence of a defective thin surface layer. [START_REF] Tseng | Magnetism and plasmonic performance of mesoscopic hollow ceria spheres decorated with silver nanoparticles[END_REF][START_REF] Chen | Interface interactions and enhanced room temperature ferromagnetism of Ag@CeO 2 nanostructures[END_REF] However, the character of this defective surface layer and its relation with magnetic behavior have not been clarified.

Accordingly, this study systematically tunes the defective layer structures of micro-scale CeO 2 hollow spheres. Hollow sphere is a model structure for the demonstration of surface effect on the modulation of ferromagnetism, but is not yet widely studied, notably due to the 2 difficulty in preparing hollow spheres with different defect gradients. This work uses the spray pyrolysis synthesis method, owing to its large yield possibility for such hollow structures. The spheres are immersed in acidic solutions for different times. Researchers have noted that dissolution of ceria in acid solution promotes reduction of Ce ions. The quantitative dissolution of ceria has been studied by Nikitenko et al. [START_REF] Virot | Catalytic dissolution of ceria under mild conditions[END_REF] A recently study showed that formic acid adsorbed on the CeO 2 surface leads to the partial reduction of Ce 4+ to Ce 3+ . [START_REF] Varalda | Oxygen diffusion and vacancy migration thermally-activated govern high-temperature magnetism in ceria[END_REF] The reductive dissolution of CeO 2 in HNO 3 ─H 2 O 2 and HNO 3 ─HCOOH mixtures can also be accelerated under the effect of 20 kHz ultrasound. [START_REF] Juillet | Ultrasound effects on the dissolution of refractory oxides (CeO 2 and PuO 2 ) in nitric acid[END_REF] Since the dissolution of actinides dioxides is affected by microstructure, temperature and acidity, [START_REF] Horlait | Dissolution of cerium (IV)-Lanthanide (III) oxides: comparative effect of chemical composition, temperature, and acidity[END_REF] this work also presents a post-annealing process to control the densification of spheres. The concentration as well as the distribution of defects in hollow spheres is investigated by using EELS and X-ray absorption spectroscopies, and is then related to the magnetic behavior.

Experimental procedure

Sample preparation

Hollow CeO 2 spheres were first prepared by spray pyrolysis. Ceric ammonium nitrate (CeAN, (NH 4 ) 2 Ce(NO 3 ) 6 , 99.5%, Alfa Aesar) and Glycine (GN, C 2 H 5 NO 2 , 98%, Acros Organics) were used as precursors. CeO 2 particle was prepared first from a 1 wt% solution CeAN and GN in de-ionized water with molar ratio of 4:6. The precursor solution was initially atomized into small droplets (nebulizer, King Ultrasonics Co., Ltd, Taipei, Taiwan), and then underwent solvent evaporation, solute precipitation and precursor decomposition in the heated tubular reactor at 700 • C in atmosphere. The hollow CeO 2 spheres were collected by a cylindrical electrostatic collector with high voltage potential. The obtained spheres are named sample A. The as-prepared spheres were then heated up to 300 • C at 10 • C/min and isothermally held for 2 h in air followed by furnace cooling. The annealed sample was labelled C. The as-prepared and the annealed hollow CeO 2 spheres were then immersed in 1 M HNO 3 solution for different times set as 15, 30, 45, 60, 90 and 120 min.

Characterization

All the spheres were characterized by X-ray Diffractometer (XRD) with Cu K radiation (Bruker D8 Advance). The morphology was investigated using a transmission electron microscope (TEM) operated at 200 keV (FEI Tecnai G2 and Thermo Fisher Scientific Talos F200X). The shell thickness of hollow sphere was estimated from 100 measurements. Electron energy loss spectroscopy (EELS) was performed by using) a C scorrected STEM NION. X-ray absorption measurements were carried out at National Synchrotron Radiation Research Center (NSRRC) in Taiwan. The X-ray absorption near edge structure (XANES) spectroscopy measurements at the Ce L 3 -edge were conducted at Wigger beamline 17C at room temperature through the monochromator silicon (1 1 1) crystal, and its energy resolution at Ce L 3 -edge (5723 eV) was approximately 0.4 eV. The magnetization was measured at room temperature using the vibrating sample magnetometer (VSM) in the Institute of Physics, Academia Sinica, Taiwan.

Results and discussion

Mesoscopic H─CeO 2

Fig. 1 (a) shows a cross-sectional TEM image of as-prepared spheres synthesized by using the spray pyrolysis method, revealing that the spheres are hollow. The insert pattern confirms that the crystal structure of the spheres is CeO 2 . As seen in Fig. 1 (b), the shell had thickness of about 60 nm, and (comprised well crystallized CeO 2 particles with size 4-6 nm. The spatial distribution of defects, i.e. Ce 3+ , was investigated by using STEM combined with EELS. Fig. 1 (c) illustrates the STEM/HAADF image of as-prepared hollow spheres. Hundreds of Ce M edge energy loss near edge structure (ELNES) measurements were taken in this region. As comparing to the standard sample, the content of Ce 3+ can be estimated. The process has been described detailed in elsewhere. [START_REF] Chen | Interface interactions and enhanced room temperature ferromagnetism of Ag@CeO 2 nanostructures[END_REF] The image in Fig. 1 (d) shows that Ce 3+ tends to concentrate at the surface region in these spheres. Fig. 1 (e) displays the variation of ELNES of Ce M 5 edge with position along the red arrow. The green and orange lines denote the peak positions of the M 5 edges contributed by Ce 3+ and Ce 4+ , respectively. Clearly, the peak position of M 5 edge shifts to high energy side as it moves to the bulk region, implying a decrease in Ce 3+ content. Fig. 1 (f) presents the variation of Ce 3+ content from surface layer to bulk region, demonstrating that the Ce 3+ concentration decreases from ca. 100 % to 30 % as the distance from the surface increases from 0 nm to 2 nm.

Fig. S1 (a) shows the microstructure investigations of the spheres annealed in air at 300 • C for 2 h, demonstrating that the annealing process produced a dense shell, with growth and the inter-grain sintering. As for the defect distribution, Ce 3+ was still concentrated at the surface region of the shell, but the width of the Ce 3+ rich layer decreased to only 1.5 nm (Fig. S1 (b)). Moreover, the annealed spheres had a lower Ce 3+ concentration than the unannealed spheres], at only 33% and 17% of the surface layer and bulk region, respectively. The magnetic behavior of all hollow CeO 2 spheres was measured using VSM at room temperature. The diamagnetic behavior of sample holder was subtracted from the magnetization curves. Fig. 2 (a) plots the M/H curves of the A-series, demonstrating clear hysteresis loops. Fig. 2 (b) shows the variation of saturation magnetization M s with reacting times of both A and C series. The value of M s of both as-prepared and annealed CeO 2 hollow spheres before reacting with HNO 3 was about 0.5memu/g. The magnetism M s of both hollow spheres rose after reacting with acid solution, but evolved differently with reaction time in the two systems. The A-series had a two-step transition, where M s rose from 0.5memu/g to 6memu/g as the reaction time increased to 60 min, then declined rapidly with further immersion. Conversely, in the C-series, the value of M s rose gradually from 0.5memu/g to 5memu/g as the reaction time reached 120 min.

The surface structures of hollow CeO 2 spheres after immersing in HNO 3 solution were investigated by AFM, with experimental results displayed in Fig. 3. Six samples with distinct magnetic behavior were investigated. The as-prepared spheres (sample A) had a small clusterlike structure, which became more obvious after immersing in HNO 3 for 60 (sample A-60) to 120 min (sample A-120), the cluster size rising) from several nanometers to tens of nanometers. However, the surface roughness among these samples did not change significantly). The average surface roughness of samples A, A-60 and A-120 was 0.287 nm, 0.256 nm and 0.252 nm, respectively. Conversely, acid treatment had a stronger effect on the surface structure of the annealed series. Sample C had a flat surface before acid treatment. The cluster structure became significant after immersion in acid solution for 60 min (sample C-60),. The average roughness of samples C, C-60 and C-120 was 0.308 nm, 0.818 nm and 0.322 nm, respectively.

The cluster-like surface structure was then examined using TEM. Fig. 4 (a-c) present the top-view TEM images of samples A-60, C-60 and C-120. Clear fringes were initially seen in these three samples, particularly the latter two samples, confirming the high degree of crystallization. Sample A-60 and C-120 had similar substructures, while sample C-60 had large cluster-like structures of about tens of nanometers, being separated with contrast areas due to lower density. These TEM observations were consistent with the AFM results. The formation of cluster-like structure can be explained from the TEM and AFM observations. In the as-prepared spheres (sample A), the shell was formed by CeO 2 particles with no preferred orientation. During the annealing process, CeO 2 particles started to assemble to form a larger cluster, resulting in dense clusters and loose space regions between clusters. These substructures were exposed after immersing in acid solution.

The variation of Ce valence among the spheres was then investigated by XAS. Fig. S3 (a) displays the XANES spectra of the Ce L-edge of the Aseries. The change in valence of Ce can be expressed in terms of the concentration of Ce 3+ , which was estimated by fitting the spectra. As demonstrated in the figure, an arctangent function was subtracted from all spectra to eliminate the electronic transition to continuum states, and the spectra were then fit by five Gaussian functions. Interpretations of these peaks have been given elsewhere. [START_REF] Nachimuthu | The study of nanocrystalline cerium oxide by X-ray absorption spectroscopy[END_REF] The concentration of Ce 3+ impurities in the CeO 2 matrix can be expressed as the ratio I C /I total , where I C denotes the intensity of peak C, and I total refers to the sum of deconvoluted peaks of A, B, and C. The calculated results of both A and C-series are shown together in Fig. S3 (b). The A-series initially had higher Ce 3+ concentration than the C-series, which can be attributed to the oxidization caused by the annealing process. The difference of the Ce 3+ concentration among samples in each series was small. The largest difference was only 0.5%, indicating that the overall Ce 3+ content was only changed slightly by immersion in 1 M HNO 3 even for 120 min.

The spatial distribution of defects, i.e. Ce 3+ was investigated by using STEM combined with EELS. Fig. 5 (a),(b),(c) and (d) show the obtained Ce 3+ distribution throughout the shells of samples A-60, A-120, C-60, and C-120, respectively. In these samples, all the shells were divided into two parts. The first was the Ce 3+ rich surface layer, and the thickness of the layer ranged from 1 nm to 5 nm. Interestingly, the distribution character of Ce 3+ within the layer varied with samples. In sample A-60 particularly as well as sample C-120, Ce 3+ was distributed homogeneously within the layer. In contrast, the distribution of Ce 3+ within the layer was less homogeneous in samples A-120 and C-60, resulting in discontinuous defective layer in the direction along the sphere surface.

The second part was the defect-deficient bulk region. The Ce 3+ content was lower in the bulk region of all samples. The distribution of Ce 3+ inside the bulk region also varied by sample, as seen in Fig. 5 (e) and (f), and was estimated according to the ELNES of Ce M edge obtained along line 1 and 2, respectively. The Ce 3+ -rich region inside the shell could be attributed to the surface of the cluster-like structure caused by the sintering process, as revealed by the AFM and TEM observations.

H-CeO 2 after post annealing

The above analysis results indicate that acid treatment of the hollow spheres causes the formation of cluster-like structures in shells, particularly sintered shells. A sample with such a structure has a weak magnetization. To suppress the formation of cluster structure and improve the homogeneity of defect distribution, a post-annealing process was conducted on the acid-treated spheres. The annealing condition was in air at 300 • C for 2 h. The resulting samples were named as A-30-C, A-60-C, A-120-C, C-30-C, C-60-C, and C-120-C, respectively. The spatial variation of Ce 3+ concentration of these samples was verified using EELS analysis. Fig. 6 (a) and (b) show the obtained Ce 3+ mapping and the distribution curve of Ce 3+ content through the shells of samples A-120-C and C-120-C, respectively, confirming that the post-annealing process improved the homogeneity of Ce 3+ content compared to samples A-120 and C-120. Conversely, the Ce 3+ concentration near the surface dropped to ca. 70 % and 65 % in samples A-120 and C-120, respectively. Fig. S4 (a) illustrates M-H curves of the spheres with post-annealing process, measured with VSM at room temperature. Clear hysteresis loops were observed, indicating that all samples were ferromagnetic with the coercivity, H c , ranging from 80Oe to 120Oe. Notably, the spheres with post-annealing process had higher magnetization than the spheres without post annealing process during acid treatment, in particular based on the as-prepared spheres as start material. As shown in Fig. S4 (b), the rise in magnetization M s was larger than 5memu/g, at 7memu/g, 16memu/g and 10memu/g, in samples A-30-C, A-60-C and A-120-C, respectively. Conversely, annealing had a weak effect on C-30, C-60 and C-120 was weak, even decreasing value of M s in the latter two samples.

The above structural analysis demonstrates that acid treatment and annealing on the hollow spheres mainly affected the surface region. Therefore, zeta potential measurement was conducted to reflect the difference of surface state of hollow spheres. The relationship between M s and zeta potential of hollow CeO 2 spheres including A-series, C-series, A-C-series, and C-C series were investigated. As demonstrated in Fig. 7, it can be divided into three groups, which are labeled as group I (yellow), group II (purple), and group III (blue). Several phenomenon should be noted. At first, it is found that the relation is independent on either the synthesis or the treatment. Second, the magnetization of the three groups of samples was proportional to the zeta potential, which is expected because the zeta potential is related to the number of surface defects. However, the magnetization of the three groups of samples rose at different rates with increasing zeta potential. The highest rate of increase occurred in group III, followed by group II, and finally group I. Furthermore, the difference in magnetization of these three groups of samples with the same zeta potential could reach more than one order of magnitude, indicating that the regulation of magnetism may be different in the three groups of samples.

Accordingly, the structural characteristics of the three groups of samples should be considered. The microstructure analysis reveals most of the samples in group I were from the C-series, characterized by rough sphere surface and with large clusters. Sample C-60 is representative of this type of sample. Most samples in group II were from the A-series and part of the third series, having relatively continuous surface defective layers and reduced surface roughness of the sphere compared to group I, thus having similar characteristics to sample A-60. The sample in group III had a continuous and smooth surface defective layer, and a decreasing gradient of Ce 3+ concentration inside this layer is. Sample A-120-C is representative of this type of sample.

Several interesting features can be summarized from the above results. First, introducing separated clusters with Ce 3+ -rich surfaces into the shell did not enhance the overall magnetic properties of the hollow spheres. Second, the magnetism of the mesoscopic hollow spheres depended not only on the defect concentration of the defective layer, but also on its substructure, including the surface roughness and homogeneity. As the defective layer was uniform with a continuous defect distribution , the magnetic saturation of the hollow sphere was high. For example, the M s of sample A-30-C reached 16memu/g, which is comparable to the thin CeO 2 layer deposited on Ag [START_REF] Chen | Interface interactions and enhanced room temperature ferromagnetism of Ag@CeO 2 nanostructures[END_REF], and higher than that of undoped CeO 2 nanoparticles. [START_REF] Li | Relationship between the surface chemical states and magnetic properties of CeO 2 nanoparticles[END_REF][START_REF] Ackland | Room temperature magnetism in CeO 2 -A review[END_REF] Present results support the feasibility of the collective orbital paramagnetism developed recently by Coey et al. [START_REF] Coey | Collective magnetic response of CeO 2 nanoparticles[END_REF][START_REF] Coey | Magnetism in d 0 oxides[END_REF] Additionally, the hollow sphere could be further improved by reducing the shell thickness and suppressing the agglomeration phenomenon between the grains in the shell layer caused by sintering.

Conclusion

This work successfully obtains micro-scale CeO 2 hollow spheres with different defect distribution character by varying the immersion in acid solution and the annealing process. Magnetic behavior is found to depend closely on the nature of defective layer at surface, but not the total defective volume of the sphere. A stronger magnetism is observed in hollow spheres with a thin defective layer and continuous surface structure. The experimental results provide guidance for handling the magnetic properties of micro-scale oxides.

Fig. 1 .

 1 Fig. 1. (a) TEM image of cross-section of CeO 2 sphere. (b) High-resolution TEM image of CeO 2 shell. (c) STEM/HAADF image and (d) EELS mapping of Ce 3+ of H-CeO 2 . (e) Variation of ELNES of Ce M 5 edge from surface to bulk region, as represented by the red line. (f) The intensity profile of Ce 3+ obtained from surface to bulk region. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .

 2 Fig. 2. M-H curves of the (a) as-prepared and (b) annealed hollow spheres after reacting with 1 M HNO 3 for different times.

Fig. 3 .

 3 Fig. 3. Surface roughness of hollow CeO 2 spheres after immersing in 1 M HNO 3 for different times measured by AFM for samples (a) A, (b) A-60, (c) A-120, (d), C, (e) C-60 and (f) C-120.

3. 2 .

 2 H─CeO 2 after acid treatment Both the as-prepared and annealed hollow spheres were then immersed in 1 M HNO 3 for different times. The acid treated hollow spheres were named samples A-15, A-30, A-45, A-60, A-90 and A-120 for the as-prepared series, and C-15, C-30, C-45, C-60, C-90 and C-120 for the annealed series. The crystal structure of the spheres after acid treatment was identified with XRD, and the results are plotted in Figs. S2 (a) and (b). These plots demonstrate that the acid treatment did not change the crystalline phase of any of the hollow spheres. All the characteristic peaks of CeO 2 were still clearly visible even after a reaction time of 120 min. Cross-sectional TEM observations in Fig. S2 (c) and (d), indicate that both systems maintained the hollow structures even at a reaction time of 120 min.

Fig. 4 .

 4 Fig. 4. Top-view TEM images of samples (a) A-60, (b) C-60 and (c) C-120. The scale bar represents 10 nm.

Fig. 5 .

 5 Fig. 5. Variation of the Ce 3+ /Ce 4+ ratio throughout the shell in samples (a) A-60, (b) A-120, (c) C-60 and (d) C-120; Ce 3+ concentration distribution curves of samples (e) A-60 and (f) C-60.

Fig. 6 .

 6 Fig. 6. Effect of post-annealing process on the acid treated spheres. (a) Ce 3+ mapping and Ce 3+ distribution profile throughout the shell of the sample A-120-C. (b) Ce 3+ mapping and Ce 3+ distribution profile throughout the shell of the sample C-120-C. The distribution profiles of sample without post-annealing (sample A-120 and sample C-120) are plotted together in both figures.

Fig. 7 .

 7 Fig. 7. The relation between M s and zeta potential of H─CeO 2 with different post-treatments. A-series and C-series represent acid-treated as-prepared spheres and acid-treated annealed spheres, respectively. A-C series and C-C series represent A-series and C-series with post-annealing process.

Acknowledgement

The authors would like to thank the Ministry of Science and Technology (MOST), Taiwan, for financially supporting this research under Contract No. MOST 107-2112-M-011 -002 -MY3.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.mseb.2021.115481.