Session K16: Spin-Sensitive Experiments on Singlet and Triplet Superconductors

Cuprate universal electronic spin response and the pseudogap from NMR

It is shown that three independently measured NMR shifts in the cuprates in their whole temperature dependence are linearly related to each other with a doping and family dependent, but temperature independent constant. It is the Cu shift anisotropy that changes in proportion to the planar O shift for all materials found in the literature, independent of sample origin or details of the measurements. Such a relation involving three shifts rules out a single spin component description of the cuprates. It is argued that the relation is so robust since it depends for Cu on ($A_perp-A_parallel$), the hyperfine coefficient $A_alpha$ for the Cu $3d(x^2-y^2)$ hole, and not on the isotropic Cu  term $B$ from transferred spin. The Cu $3d(x^2-y^2)$ spin together with a second spin that determines the planar O shift can explain the data.

For overdoped metallic samples, both become temperature dependent only at the critical temperature of superconductivity, $T_mathrm{c}$, where both begin to decrease. However, the Cu spin component turns increasingly negative until the second spin has disappeared. In the presence of a small pseudogap the onset temperature of this process coincides with the onset of the temperature dependence of the shifts, which is now above $T_mathrm{c}$. As the pseudogap increases further, the behavior does not change even as $T_mathrm{c}$ begins to decrease again. The temperature independent constant in the linear relationship describing the negative spin is related to the size of the uncoupled spin components and depends on the planar oxygen hole content that is known to correlate with the maximum $T_mathrm{c}$. The Cu spin component does not appear to carry significant entropy as the nuclear relaxation ceases in the condensed state.   

Random Fields from Quenched Disorder in an Archetype for Correlated Electrons: the Parallel Spin Stripe Phase of La1.6-xNd0.4SrxCuO4 at the 1/8 Anomaly

The parallel stripe phase is remarkable both in its own right, and in relation to the other phases it co-exists with. Its inhomogeneous nature makes such states susceptible to random fields from quenched magnetic vacancies. We argue this is the case by introducing low concentrations of nonmagnetic Zn impurities (0-10%) into La_1.6-xNd_0.4Sr_xCuO₄ (Nd-LSCO) with x = 0.125 in single crystal form, well below the percolation threshold of ~ 41% for two-dimensional square lattice. Elastic neutron scattering measurements on these crystals show clear magnetic quasi-Bragg peaks at all Zn dopings. While all the Zn-doped crystals display order parameters that merge into each other and the background at ~ 68 K, the temperature dependence of the order parameter as a function of Zn concentration is drastically different. This result is consistent with meandering charge stripes within the parallel stripe phase, which are pinned in the presence of quenched magnetic vacancies. In turn it implies vacancies that preferentially occupy sites within the charge stripes, and hence that can be very effective at disrupting superconductivity in Nd-LSCO (x = 0.125), and, by extension, in all systems exhibiting parallel stripes.   

Microscopic characterization of Pb10-xCux(PO4)6O by 31P, 63Cu, and 65Cu NMR measurements

The report of the first room-temperature ambient-pressure superconductivity in Pb_10-xCu_x(PO₄)₆O has attracted lots of attention. However, the Meissner effect, which is a more decisive property of superconductors, has never been observed in this material. Later studies show that quite a lot of impurity phases exist in the polycrystalline samples, and the sharp superconducting-like transition is most likely due to a reduction in resistivity caused by the first-order structural phase transition of Cu₂S at around 385 K, from the β phase at high temperature to the γ phase at low temperature. Till now, only bulk measurements have been performed on Pb_10-xCu_x(PO₄)₆O samples, which would be easily affected by the impurity phases, and the intrinsic properties of Pb_10-xCu_x(PO₄)₆O could be masked. Nuclear magnetic resonance(NMR)  is a  powerful technique to investigate the structural and magnetic properties of materials from a microscopic point of view. In this study, ³¹P, ⁶³Cu, and ⁶⁵Cu nuclear magnetic resonance (NMR) measurements have been performed on Pb_10-xCu_x(PO₄)₆O powder sample. The structural and magnetic properties of Pb_10-xCu_x(PO₄)₆O have been revealed.   

Antiferromagnetic excitations in very underdoped HgBa2CuO4+δ measured by neutron scattering

It is a distinct possibility that spin fluctuations are the pairing interactions in a wide range of unconventional superconductors [1]. In the case of the cuprates, in which superconductivity emerges upon doping an antiferromagnetic Mott-insulating state, spin correlations might furthermore drive unusual pseudogap phenomena. HgBa₂Cu­O_4+δ (Hg1201) is a model experimental system, as it exhibits a particularly simple crystal structure and the highest superconducting transition temperature (nearly 100 K) among all single-layer cuprates. However, sizable single crystals with low hole concentrations have been unavailable. We have succeeded in preparing a large Hg1201 sample (mass ~ 1 g) with T_c ≈ 30 K and a hole concentration of just above 5%. Here we report both time-of-flight and triple-axis inelastic neutron scattering measurements of the antiferromagnetic response close to the lower edge of the superconducting dome. In contrast to results for other cuprates for this part of the phase diagram, but consistent with prior results for Hg1201 at higher doping [2,3], the data reveal gapped excitations and no evidence for stripe or spin-density-wave correlations.

[1] D. J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012)

[2] M. K. Chan  et al., Phys. Rev. Lett. 117, 1 (2016)

[3] M. K. Chan et al., Nat. Commun. 7, 1 (2016)   

Tuning Triplet Superconductivity States at LSMO/YBCO Interfaces

Triplet superconductivity at a high-T_c-superconductor/Ferromagnetic-oxide (SC/FM) interface potentially has a significant impact on the development of spintronics, quantum information, and the search for Majorana fermions.  Triplet superconductivity has three states: s_z=0 and ±1.  The s_z=0 state, also known as the FFLO state, exhibits short penetration depth and its wave function oscillates over a short distance within the ferromagnetic layer.  In contrast, the s_z=±1 states have a long penetration depth and can be considered a dissipationless spin-polarized current.  To tune the superconductivity within these states, an additional interfacial layer with a magnetic moment perpendicular to that of the ferromagnetic layer is proposed. We have discovered that the induced Cu moment at the interface may function as the magnetic interfacial layer.  Furthermore, its magnetic moment direction can be controlled by using a field-cooling process with a specific range of fields.  The orientation of the Cu moment can be altered by disrupted flipping between three different alignments with respect to that of the FM layer. With an appropriately applied field during the field-cooling process, we observed a significant enhancement of the superconducting critical current due to the generation of triplet superconductivity at s_z= ±1.  In this presentation, we will present the transport measurements to elucidate the collective behavior and polarized neutron reflectivity to reveal the interface conditions.   

Nuclear magnetic resonance study in Nb3Sn

The superconducting compound Nb₃Sn is widely used for applications where high critical temperature and high critical field are important.  However, there has as yet not been any comprehensive investigation of its properties using nuclear magnetic resonance. We have performed ⁹³Nb NMR on high-quality Nb₃Sn powder in 3.2 T and 7 T magnetic fields, with a temperature range from 1.5 K to 300 K. The spectrum measurements indicate that there exists magnetic anisotropy although the sample has a cubic crystal structure. This anisotropy leads to alignment of powder grains under specific temperature and field protocols. We measured the Knight shift and spin-lattice relaxation rate T₁^-1 in the normal state, and the latter in the superconducting state. From this data we obtained the field dependent energy gap and compared with BCS theory.   

51V NMR spectroscopy on single crystal of A15 superconductor V3Si: New insights at milliKelvin temperatures

The A15 superconductor V₃Si, though well-studied for decades, continues to yield insights into its superconducting phase, as made possible by (1) newer methods in NMR spectroscopy, (2) on high-quality, single-crystal samples, and (3) at temperatures down to the milliKelvin range. After finding evidence that the Martensitic transformation (MT) occurs over a range of temperatures in which transformed and untransformed phases coexist [Gapud et al., Physica C, vol. 602, 1354137], new data on (1) the temperature dependence of the Knight shift show effects due to the MT not seen in previous studies, including a possible regime reminiscent of pseudogap phase and/or a Jahn-Teller effect; and (2) the power-law temperature dependence of the NMR longitudinal relaxation time T1 strongly suggests an anisotropic superconducting order parameter -- as will be reported and discussed.   

Absence of bulk charge density wave in low temperature x-ray measurements of UTe2

UTe₂ has been the subject of extensive study since the discovery of its unconventional, potentially spin-triplet superconductivity. Recent evidence has emerged for the formation of a pair density wave (PDW) via scanning tunneling microscopy (STM) measurements [1-3]. However, a clear signature of an associated bulk charge density wave (CDW) transition has not been observed in transport measurements. Here we present high energy and resonant elastic x-ray scattering measurements of UTe₂ taken at temperatures comparable to STM measurements by using Joule-Thomson-supported cooling stages. We find no signatures for the formation of a bulk CDW down to ∼ 2 K, either in non-resonant measurements at 100 keV or in resonant measurements at the U M₄ edge (3.7 keV) or the Te L₁ edge (4.9 keV). Our results suggest that the CDW observed in STM may be a feature of the surface and absent from the bulk of UTe₂ at this temperature. 

[1] Aishwarya, A., et al. (2023). Nature, 618(7967), 928–933. 10.1038/s41586-023-06005-8

[2] Gu, Q., et al. (2023). Nature, 618(7967), 921–927. 10.1038/s41586-023-05919-7

[3] Lafleur, A., et al. (2023). arXiv.2308.03721   

NMR and NQR studies in candidate triplet superconductor LaNiGa2

LaNiGa₂ is a layered centrosymmetric superconductor with an orthorhombic crystal structure. μSR experiments have observed spontaneous magnetic fields at the onset of superconducting state, implying time-reversal symmetry breaking and suggesting the possibility of triplet pairing. Here, we report on the microscopic investigations in the normal and superconducting (SC) states of LaNiGa₂ using nuclear magnetic resonance (NMR) and quadrupole resonance (NQR). Single-crystal NMR measurements were used to determine the anisotropy of the electric field gradient (EFG) at the two non-equivalent ⁶⁹Ga sites and one ¹³⁹La site. The field orientation dependence of the spectra revealed a large asymmetry in the EFG tensor for the ⁶⁹Ga sites, whereas EFG had axial symmetry at the ¹³⁹La site. Band structure calculations based on density functional theory provided a good agreement with these results. Zero-field powder NQR measurements were performed in the SC state down to dilution-fridge temperature. We discuss the size and structure of the SC gap and the type of order parameter based on the temperature dependence of the spin-lattice relaxation rate 1/T₁ at ¹³⁹La. The sizes of SC critical fields and the penetration depth have been examined in relation to the grain size.   

Quasi-two-dimensional Antiferromagnetic Spin Fluctuations in the Spin-triplet Superconductor Candidate CeRh2As2

Spin-triplet superconductors may harbor topological states and Majorana fermions relevant to quantum computation. A major challenge is identifying compounds that may realize this phase and establishing the nature and pairing mechanism of the superconductivity. In the tetragonal heavy-fermion superconductor CeRh₂As₂ ( = 0.26 K), a phase transition between superconducting states for c-axis-oriented magnetic fields has been proposed to be a spin-singlet to spin-triplet transition [1]. In an effort to characterize the superconductivity and the underlying pairing mechanism, we use neutron scattering to probe the antiferromagnetic (AF) spin fluctuations in CeRh₂As₂. In the absence of static magnetic order, we reveal the presence of quasi-two-dimensional commensurate AF spin fluctuations centered at  = (1/2 1/2) with a spectrum extending up to at least 1.0 meV.  connects large areas of the Fermi surface calculated with Ce electrons in the core using density functional theory. Since the dominant low-energy excitations in CeRh₂As₂ are magnetic, these findings indicate superconductivity in CeRh₂As₂ is mediated by AF spin fluctuations.

[1] Khim, S., et al. "Field-induced transition within the superconducting state of CeRh2As2." Science 373.6558 (2021): 1012-1016.   

Superfluid density through a Van Hove singularity: Sr2RuO4 under uniaxial strain

Strontium ruthenate (Sr₂RuO₄) is an archetype in the field of unconventional superconductivity; yet, after nearly three decades of strenuous effort, our understanding of superconductivity in Sr₂RuO₄ remains incomplete. To understand how the Van Hove singularity (VHS) impacts the superconductivity, we report on scanning superconducting quantum interference device (SQUID) microscopy measurements of the London penetration depth as the system is strain-tuned through the VHS. We found that the zero-temperature superfluid density increases by ~15%, coinciding with the peak in the superconducting transition temperature, and that the penetration depth varies quadratically with temperature,  Δλ(T) ~ T² over the entire strain range. In addition, we performed scanning tunneling spectroscopy to determine the superconducting gap in uniaxially strained samples. Under zero strain, we resolved a superconducting gap with a magnitude of Δ₀ ≈ 350 μeV, and under a uniaxial compression of ≈0.4%,  we observed an enhanced gap of Δ₀ ≈ 600 μeV. With a nodal order parameter, an increase in the superconducting gap could bring about an increase in the superfluid density through reduced sensitivity to defects or through reduced non-local effects in the Meissner screening. Our data indicate that tuning to the VHS increases the gap throughout the Brillouin zone, and that non-local effects are likely more important than reduced scattering.