$^{17}$O NMR study of charge ordered La$_{1.885}$Sr$_{0.115}$CuO$_4$
T. Imai K. Hirota
cond-mat.supr-con cond-mat.str-el







 
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S4M1, Canada
Canadian Institute for Advanced Research, Toronto, Ontario M5G1Z8, Canada
Deceased
Department of Physics, Tohoku University, Aramaki Aoba, Sendai 980-8578, Japan


             


We successfully isolated the ^17O NMR signals at the planar sites in La_1.885Sr_0.115CuO_4 (T_c=30 K) by applying an external magnetic field along the a-axis of a single crystal.  We demonstrate that charge order enhances incommensurate Cu spin fluctuations below T_charge≃ 80 K.



^17O NMR study of charge ordered La_1.885Sr_0.115CuO_4
    K. Hirota
    December 30, 2023
======================================================




Soon after the discovery of charge “stripe" order at T_charge = 65 K in La_1.6-xNd_0.4Sr_xCuO_4 (x ∼ 1/8) <cit.>, we identified peculiar NMR anomalies at and below the charge order transition <cit.>: (i) ^63Cu NMR intensity is gradually wiped out below T_charge, even if we take into account the transverse relaxation effects on the spin echo intensity, (ii) the Gaussian spin echo decay induced by the indirect nuclear spin-spin coupling becomes unobservable, and  (iii) low frequency Cu spin fluctuations as probed by ^139La nuclear spin-lattice relaxation rate 1/T_1 are enhanced.  We observed all of these peculiar “NMR fingerprints" of charge order also in  La_1.885Sr_0.115CuO_4 (T_c =  30 K), and hence concluded the existence of charge ordered phase in the superconducting cuprate <cit.>.  

Our 1999 conclusion became controversial in the ensuing years, because diffraction experiments  failed to detect the Bragg peaks arising from charge density modulation.   Moreover, a widely shared view at the time was that charge order was a byproduct of the low temperature tetragonal (LTT) structural phase transition at ∼70 K in La_1.48Nd_0.4Sr_0.12CuO_4.  Superconducting La_1.885Sr_0.115CuO_4 does not undergo the LTT transition.  Recent advances in the instrumental technologies have finally led to successful detection of charge order Bragg peaks of La_1.885Sr_0.115CuO_4 at as high as T_charge≃ 80 K <cit.>.  The new revelation also indicated that our original estimation of T_charge≃ 50 K <cit.> overlooked the gradual onset of charge order.   

We recently revisited the issue of charge order based on ^63Cu and ^139La NMR using a new single crystal sample of La_1.885Sr_0.115CuO_4 <cit.>.  Owing to the state-of-the-art NMR technologies, we were able to show that the lost spectral weight of the ^63Cu NMR signals below T_charge≃ 80 K reemerges as a very broad, wing-like NMR signal <cit.>.  The relaxation rates of the wing-like signal are so fast that one can detect the NMR signal only with extremely short NMR pulse separation time τ∼ 2 μs.  We also demostrated that the volume fraction of the CuO_2 planes under the influence of charge order does not reach 100 % until the temperature is lowered to ∼ 20 K.  

In this Short Note, we report ^17O single crystal NMR study of La_1.885Sr_0.115CuO_4.  From early days, accurate ^17O NMR measurements below ∼ 100 K at the planar ^17O sites in La_2-xSr_xCuO_4 have been known to pose a technical challenge, because it is difficult to properly resolve the planar and apical ^17O NMR signals even with a single crystal sample.   Our ^17O single crystal NMR measurements conducted in an external magnetic field B_ext applied along the crystal c-axis <cit.> covered only the temperature range down to ∼ 100 K for that very reason.     



Here we show that there is a way to circumvent the superposition problem by using an alternate field configuration, and explore the crucial temperature range below T_charge≃ 80 K.  In the inset of Fig. 1, we present the ^17O NMR lineshape measured at 77 K in B_ext = 6 T applied along the a-axis.  In this field geometry, B_ext is along the Cu-O-Cu bond for 50 % of the planar ^17O sites, whereas the remaining 50 % has the field applied perpendicular (⊥) to the Cu-O-Cu bond.  Luckily, the nuclear quadrupole frequency ν_Q^(bond)≃ 0.66 MHz and ν_Q^(⊥)≃ 0.44 MHz along the bond and perpendicular direction of the planar sites are much larger than  ν_Q^(ab)≃ 0.10 MHz for the apical sites, and hence the upper satellite peaks are isolated even below 100 K.  We found no evidence for quadrupole broadening of ^17O as well as ^63Cu <cit.> and ^139La <cit.> NMR peaks below T_charge, suggesting that the amplitude of charge density modulation is very small.



In the main panel of Fig. 1, we summarize the temperature dependence of 1/T_1 for the planar ^17O sites.  1/T_1 exhibits a plateau below ∼ 100 K, followed by strong enhancement below ∼ 35 K due to the onset of strong short range order.  We note, however, that 1/T_1 does not diverge at the spin ordering temperature T_spin = 30 K as determined by elastic neutron scattering for this crystal <cit.> due to the glassy nature of spin ordering <cit.>.  These findings are consistent with our observation for the ^63Cu <cit.> and ^139La <cit.> sites.  In Fig. 2, we also summarize 1/T_1T ∝Σ_ q | A( q) |^2 Im χ( q, ω_o), where | A( q) | ^2∝ cos^2 (q_x/2) is the hyperfine form factor <cit.>, Im χ( q, ω_o) is the imaginary part of the dynamical spin susceptibility, and ω_o is the NMR frequency.  Above T_charge, 1/T_1T monotonically decreases with temperature, similarly to the optimally superconducting x = 0.15 <cit.>.  Moreover, at the phenomenological level <cit.>, 1/T_1T closely follows the temperature dependence of the uniform spin susceptibility as measured by the NMR Knight shift <cit.>, because the antiferromagnetic Cu spin fluctuations are geometrically cancelled out by the hyperfine form factor <cit.>.  It is worth noting that commensurate antiferromagnetic spin fluctuations in undoped CuO_2 planes are almost completely filtered out by the form factor, and 1/T_1 hardly exhibits any noticeable anomaly at the Néel transition at T_N = 257 K, as shown in Fig. 2 for Sr_2CuO_2Cl_2 <cit.>.   

Below T_charge, 1/T_1T for La_1.885Sr_0.115CuO_4 begins to grow, leading us to two significant conclusions.  First, charge order triggers the growth of antiferromagnetic spin fluctuations, in agreement with our earlier report that the aforementioned wing-like ^63Cu NMR signals have extremely fast 1/T_1 <cit.>, and 1/T_1T at the ^139La sites are enhanced below T_charge <cit.>.  Second, in view of the fact that the commensurate spin fluctuations are filtered out by the hyperfine form factor, the enhanced spin fluctuations below T_charge must be incommensurate.  Our results are consistent with the inelastic neutron scattering measurements with low energy transfer <cit.>.  

Acknowledgement: We acquired the NMR data at M.I.T. in 1998 - 1999 with the  support from NSF DMR 96-23858 and 98-08941.   The work at McMaster was supported by NSERC and CIFAR.  
T. I. expresses his sincere gratitude to K. H. for his support for our NMR investigation of charge order before his passing in 2010. 

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