Anomalies in the NMR of silicon:  Unexpected spin echoes in a dilute dipolar solid

Abstract

NMR spin echo measurements of 29 Si in Silicon powders have uncovered a variety of surprising phenomena that appear to be independent of doping. These surprises include long tails and even-odd asymmetry in Carr-Purcell-Meiboom-Gill (CPMG) echo trains, and anomalous stimulated echoes with several peculiar characteristics. Given the simplicity of this spin system, these results, which to date defy explanation, present a new and interesting puzzle in solid state NMR.PACS numbers: 03.65. Yz, 03.67.Lx, 76.20.+q, 76.60.Lz In order to implement quantum computation (QC) based upon spins in semiconductors [1,2,3,4,5], a detailed understanding of spin dynamics in these materials is required. To this end, we carried out a series of NMR measurements that were motivated by a simple question: what is the 29 Si decoherence time (T 2 ) in Silicon? Earlier NMR studies in Silicon addressed other questions [6,7,8].We find that it is possible to detect the 29 Si (4.67% natural abundance (n.a.), spin-1 2 ) NMR signals out to much longer times than was previously thought possible, and so far, we have been unable to explain these results in terms of well-known NMR theory [9]. Surprises in such a simple spin system appear brand new to NMR, and understanding their origin is of fundamental importance. In this paper, we describe the phenomena and recount tests we have made to explore possible explanations.Two standard experiments that measure T 2 are reported. First, using the Hahn echo sequence (HE: 90 X -TE 2 -180 Y -TE 2 -ECHO [10]), the measured decay, with T 2HE ≈ 5.6 msec, is in quantitative agreement with that expected for the static 29 Si-29 Si dipolar interaction. This decay mechanism is commonly encountered in solids, and a number of ingenious pulse sequences have been invented to manipulate the interaction Hamiltonian, pushing echoes out to times well beyond T 2HE [9,11,12,13,14,15,16,17]. A common thread running through those sequences is the use of multiple 90 • pulses, and pulses applied frequently compared to T 2HE , which refocus the homonuclear dipolar coupling. The same cannot be said about the second sequence that we used to measure T 2 , the Carr-Purcell-Meiboom-Gill sequence (CPMG: 90 X -TE 2 -180 Y -TE 2 -ECHO repeat n−times [18]). Specifically, the CPMG sequence is not expected to excite echoes beyond T 2HE , since 180 • pulses should not affect the bilinear homonuclear interaction. This statement is exact in two important limits: either for unlike spins or for magnetically-equivalent spins.Therefore, we were surprised to find that CPMG echoes are detectable long after T 2HE , and the echo peaks appear nearly identical in Silicon samples with very different dopings. This CPMG "tail" appears to be even larger at low temperatures. In addition, as the interpulse

Storage of quantum coherences as phase-labelled local polarization in solid-state nuclear magnetic resonance

“…Similar situations were observed in all the systems that manifest long decay times when CPMG-like sequences are applied [12,43,44].…”

“…We found that, by applying the CPMG1 sequence or the CP2 sequence, a magnetization tail appears, i.e. the signal remains for times much longer than T HE 2 as observed in 29 Si [12]. Figure 1 shows the normalized magnetizations acquired by applying the sequences HE, CP1, CP2, CPMG1 and CPMG2 to polycrystalline C 60 .…”

“…This motivated much NMR work where typical experiments to measure T 2 were reported [12,13,56]. In these studies, after applying the CPMGlike sequences, it was found that it is possible to detect the spin-1/2 NMR signal of 29 Si up to times much longer (more than two orders of magnitude) than the characteristic decay time observed with the Hahn echo sequence (≈ 5.6 ms).…”

“…We summarize our own findings on anomalous long-lived echo signals [12,[41][42][43][44]. In particular, we emphasize the use of a simple stimulated echo sequence to discern whether one is in the presence of true long decoherence times or if the coherences are being saved as polarization and then recovered.…”

“…Within solid-state nuclear magnetic resonance (NMR), the interest focuses on those systems that have been proposed as possible candidates for quantum registers [10][11][12][13], quantum channels [14][15][16], simulators of quantum dynamics [17,18] or probes for specific quantum gates [6].…”