Knight Shift Measurements Research Articles

Large Reduction in the a-axis Knight Shift on UTe2 with Tc = 2.1 K

Spin susceptibility in the superconducting (SC) state was measured in the higher-quality sample of uranium-based superconductor UTe$_2$ by using Knight-shift measurements for a magnetic field $H$ along all three crystalline axes. In the higher-quality sample, the SC transition temperature $T_{\rm c}$ is about 2.1 K, and the residual electronic term in the specific heat is almost zero. The NMR linewidth becomes narrower and is almost half of that in the previous sample with $T_{\rm c} \sim 1.6$ K when $H \parallel a$ and $c$. Although the Knight-shift behavior was not so different from the previous results for $H \parallel b$, and $c$, a large reduction in Knight shift along the $a$ axis was observed, in contrast with the previous $a$-axis Knight shift result. We discuss the origin of the difference between the previous and present results, and the possible SC state derived from the present results.

An experimental procedure to determine quantitative muon Knight shifts

Muon Knight-shift measurement are experimentally rather challenging as in most setups one does not have a direct way of measuring the external magnetic field applied to the sample. Here we show, a way to overcome this problem and suggest a suitable sample mounting and correcting scheme. This enables us to quantitatively determine the correct Knight-shift values even in extreme sample environments where a separate measurement of the externally applied magnetic field by means of NMR or additional µSR is not feasible or practical.

Tuning the Fermi liquid crossover in Sr2RuO4 with uniaxial stress

We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr2RuO4, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasiparticle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi-liquid coherence scale is shown to be tunable by strain, and driven to low values as the associated Lifshitz transition is approached.

Leading superconducting instabilities in three-dimensional models for Sr2RuO4

The superconductor Sr2RuO4 has been the subject of enormous interest over more than two decades, but until now the form of its order parameter has not been determined. Since groundbreaking NMR experiments revealed that the pairs are of dominant spin-singlet character, attention has focused on time-reversal symmetry breaking linear combinations of $s$-, $d$- and $g$-wave one-dimensional (1D) irreducible representations. However, a state of the form $d_{xz}+id_{yz}$ has also been proposed. We present a systematic study of the stability of various superconducting candidate states, assuming that pairing is driven by the fluctuation exchange mechanism, including a realistic three-dimensional Fermi surface, full treatment of both local and non-local spin-orbit couplings, and a wide range of interaction parameters $U,J,U',J'$. The leading superconducting instabilities are found to exhibit nodal even-parity $A_{1g} (s')$ or $B_{1g} (d_{x^2-y^2})$ symmetries, similar to the findings in two-dimensional models without longer-range Coulomb interaction which tends to favor $d_{xy}$ over $d_{x^2-y^2}$. Within the so-called Hund's coupling mean-field pairing scenario, the $E_g (d_{xz}/d_{yz})$ solution can be stabilized for large $J$ and specific forms of the spin-orbit coupling, but for all cases studied here the eigenvalues of other superconducting solutions are significantly larger when the full fluctuation exchange vertex is included in the pairing kernel. Additionally, we compute the spin susceptibility in relevant superconducting candidate phases and compare to recent neutron scattering and NMR Knight shift measurements.

Enhanced superconductivity and moderate spin fluctuations suppressed at low energies in heavily electron-doped La1111-based superconductor

To elucidate the origin of re-enhanced high-$T_c$ phase in the heavily electron-doped Fe-pnictides, systematic $^{75}$As NMR studies are performed on heavily electron-doped LaFe$Pn$O$_{0.75}$H$_{0.25}$ by controlling the pnictogen height ($h_{Pn}$) from the Fe plane through the substitution at $Pn$(=As) site with Sb or P. The measurements of nuclear spin relaxation rate (1/$T_1$) and Knight shift ($K$) reveal that the moderate spin fluctuations at high temperatures are suppressed toward low temperatures. Such characteristic spin fluctuations with gap like feature at low energies are more enlarged in higher $T_c$ compounds with higher $h_{Pn}$, while those are totally suppressed in non-superconducting compounds with lower $h_{Pn}$. This implies that the contribution of the finite energy part in the spin fluctuation spectrum is crucial for enhancing $T_c$ in the heavily electron-doped regime. This is in contrast to many cases of typical Fe-based compounds with hole and electron Fermi surfaces of similar sizes, where the spin fluctuations at low energies develop significantly at low temperatures. The features in the heavily electron-doped states are discussed in relation with the characteristics of the faint hole Fermi surface derived from $d_{xy}$ orbital that rises when $h_{Pn}$ is high, together with the enhanced electron correlation effects.

Superconducting Order Parameter in UTe2 Determined by Knight Shift Measurement

This study investigates the spin susceptibility in U-based superconductor UTe$_2$ in the superconducting (SC) state by using Knight shift measurements for a magnetic field $H$ along the $a$ axis, which is the magnetic easy axis of UTe$_2$. Although a tiny anomaly ascribed to the SC diamagnetic effect was observed just below the SC transition temperature $T_{\rm c}$, the $a$-axis Knight shift in the SC state shows no significant decrease, following the extrapolation from the normal-state temperature dependence. This indicates that the spin susceptibility is nearly unchanged below $T_{\rm c}$. Considering the previous Knight shift results for $H \parallel b$ and $H \parallel c$, the dominant SC state is determined to be $B_{\rm 3u}$ in the spin-triplet pairing, which is consistent with the spin anisotropy in the normal state. The present result shows that UTe$_2$ is a spin-triplet superconductor with spin degrees of freedom.

Transport signatures of the pseudogap critical point in the cuprate superconductor Bi2Sr2−xLaxCuO6+δ

Five transport coefficients of the cuprate superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ were measured in the normal state down to low temperature, reached by applying a magnetic field (up to 66 T) large enough to suppress superconductivity. The electrical resistivity, Hall coefficient, thermal conductivity, Seebeck coefficient, and thermal Hall conductivity were measured in two overdoped single crystals, with La concentration $x=0.2$ (${T}_{\mathrm{c}} =18$ K) and $x=0.0$ (${T}_{\mathrm{c}} =10$ K). The samples have dopings $p$ very close to the critical doping ${p}^{★}$ where the pseudogap phase ends. The resistivity displays a linear dependence on temperature whose slope is consistent with Planckian dissipation. The Hall number ${n}_{\mathrm{H}}$ decreases with reduced $p$, consistent with a drop in carrier density from $n=1+p$ above ${p}^{★}$ to $n=p$ below ${p}^{★}$. This drop in ${n}_{\mathrm{H}}$ is concomitant with a sharp drop in the density of states inferred from prior NMR Knight shift measurements. The thermal conductivity satisfies the Wiedemann-Franz law, showing that the pseudogap phase at $T=0$ is a metal whose fermionic excitations carry heat and charge as do conventional electrons. The Seebeck coefficient diverges logarithmically at low temperature, a signature of quantum criticality. The thermal Hall conductivity becomes negative at low temperature, showing that phonons are chiral in the pseudogap phase. Given the observation of these same properties in other, very different cuprates, our study provides strong evidence for the universality of these five signatures of the pseudogap phase and its critical point.

Evidence for even parity unconventional superconductivity in Sr2RuO4

Unambiguous identification of the superconducting order parameter symmetry in [Formula: see text] has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

Symmetry Properties of Superconducting Order Parameter in Sr2RuO4

Soon after the discovery of superconductivity in Sr2RuO4 (SRO) a quarter-century ago, it was conjectured that its order parameter (OP) has a form similar to that realized in the superfluid phases of 3-He, namely, odd parity and spin triplet. While the chiral p-wave pairing believed to be realized in the A phase of that system was favored by several early experiments, in particular, the muon spin rotation and the Knight shift measurements published in 1998, the original Knight shift result was called into question in early 2019, raising the question as to whether the “chiral p-wave”, or even the spin-triplet pairing itself, is indeed realized in SRO. In this brief pedagogical review, we will address this question by counterposing the currently accepted results of Knight shift, polarized neutron scattering, spin counterflow half-quantum vortex (HQV), and Josephson experiments, which probe the spin and orbital parts of the OP, respectively, with predictions made both by standard BCS theory and by more general arguments based only on (1) the symmetry of the Hamiltonian including the spin-orbital terms, (2) thermodynamics, and (3) the qualitative experimental features of the material. In the hope of enhancing readers’ intuitive grasp of these arguments, we introduce a notation for triplet states alternative to the more popular “d-vector” one which we believe well suited to SRO. We conclude that the most recent Knight shift and polarized neutron scattering experiments do not exclude in the bulk the odd-parity, spin-triplet “helical” states allowed by the symmetry group of SRO but do exclude the “chiral p-wave”, ${{{\varGamma }}}_{5}^{-}$ state. On the other hand, the Josephson and in-plane-magnetic-field stabilized HQV experiments showed that the pairing symmetry in SRO cannot be of the even-parity, spin-singlet type, and furthermore, that in the surface region or in samples of mesoscopic size the d-vector must be along the c axis, thus excluding all bulk p-wave states except ${{{\varGamma }}}_{5}^{-}$ . Possible resolution of this rather glaring prima facie contradiction is discussed, taking into account implications of other important experiments on SRO, including that of the muon spin rotation, which are touched upon briefly only towards the end of this article.

Interorbital p - and d -wave pairings between dxz/yz and dxy orbitals in Sr2RuO4

We study the pairing symmetry of Sr$_2$RuO$_4$ through the group-theoretical approach. We emphasize the role of pairing interaction between the quasi-one-dimensional(Q1D) $d_{xz/yz}$ and quasi-two-dimensional(Q2D) $d_{xy}$ orbitals. It is found that two degenerate inter-orbital time-reversal-invariant(TRI) p-wave pairings, one is spin-singlet and the other spin-triplet with out-of-plane $\bm{d}$-vector, could be the most promising candidates. Several important physical quantities are presented, including the near-nodal gap structure, the unchanged out-of-plane Knight shift, and no split transition under strain, which are consistent with the experiments. In addition, these p-wave pairings shed light on resolving the contradiction between the time-reversal breaking and reduced in-plane Knight shift measurements. As the system reaches the Van Hove singularity under applied strain, the pairing symmetry would become a d-wave pairing mainly consisting of inter-orbital components, which could be responsible for the strained 3$K$ phase.

Persistent spin dynamics and absence of spin freezing in the H−T phase diagram of the two-dimensional triangular antiferromagnet YbMgGaO4

We report results of muon spin relaxation and rotation ($\mu$SR) experiments on the spin-liquid candidate~YbMgGaO$_{4}$. No static magnetism $\gtrsim 0.003\mu_B$ per Yb ion, ordered or disordered, is observed down to 22~mK, a factor of two lower in temperature than previous measurements. Persistent (temperature-independent) spin dynamics are observed up to 0.20~K and at least 1~kOe, thus extending previous zero-field $\mu$SR results over a substantial region of the $H$-$T$ phase diagram. Knight shift measurements in a 10-kOe transverse field reveal two lines with nearly equal amplitudes. Inhomogeneous muon depolarization in a longitudinal field, previously characterized by stretched-exponential relaxation due to spatial inhomogeneity, is fit equally well with two exponentials, also of equal amplitudes. We attribute these results to two interstitial muon sites in the unit cell, rather than disorder or other spatial distribution. Further evidence for this attribution is found from agreement between the ratio of the two measured relaxation rates and calculated mean-square local Yb$^{3+}$ dipolar fields at candidate muon sites. Zero-field data can be understood as a combination of two-exponential dynamic relaxation and quasistatic nuclear dipolar fields.

Direct observation of muonium reacting with uncapped gold nanoparticles in porous silica and nature of the final state.

We report the reaction of muonium (Mu = [μ+e-]), a light isotopic analog of hydrogen, with uncapped gold nanoparticles embedded in mesoporous silica. Using the radio-frequency muon spin rotation (RF-μSR) technique, we directly observe and characterize the resulting final state on the nanoparticle surface, showing conclusively its diamagnetic nature. The magnetic environment experienced by the reacted muons is only weakly perturbed compared to that of muons in a silica reference, consistent with the surface of the gold nanoparticles being metallic and non-magnetic. We demonstrate the potential of RF-μSR for the investigation of the surface properties of nanoparticles and show the feasibility of Knight shift measurements of muons on metal surfaces.

First-principles hyperfine tensors for electrons and holes in GaAs and silicon

Understanding (and controlling) hyperfine interactions in semiconductor nanostructures is important for fundamental studies of material properties as well as for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory (DFT) and $\mathbf{k}\cdot\mathbf{p}$ theory, we have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon. Accounting for relativistic effects near the nuclear core, we find contact hyperfine interactions for electrons in GaAs that are consistent with Knight-shift measurements performed on GaAs quantum wells and are roughly consistent with prior estimates extrapolated from measurements on InSb. We find that a combination of DFT and $\mathbf{k}\cdot\mathbf{p}$ theory is necessary to accurately determine the contact hyperfine interaction for electrons at a conduction-band minimum in silicon that is consistent with bulk Knight-shift measurements. For hole spins in GaAs, the overall magnitude of the hyperfine couplings we find from DFT is consistent with previous theory based on free-atom properties, and with heavy-hole Overhauser shifts measured in GaAs (and InGaAs) quantum dots. In addition, we theoretically predict that the heavy-hole hyperfine coupling to the As nuclear spins is stronger and almost purely Ising-like, while the (weaker) coupling to the Ga nuclear spins has significant non-Ising corrections. In the case of hole spins in silicon, we find (surprisingly) that the strength of the hyperfine interaction in the valence band is comparable to that in the conduction band and that the hyperfine tensors are highly anisotropic (Ising-like) in the heavy-hole subspace. These results suggest that the hyperfine coupling cannot be ruled out as a limiting mechanism for coherence ($T_2^{\ast}$) times recently measured for heavy holes in silicon quantum dots.

Review of U-based Ferromagnetic Superconductors: Comparison between UGe2, URhGe, and UCoGe

The discovery in 2000 that the ferromagnetic (FM) compound UGe2 (T_Curie = 52 K at ambient pressure) becomes superconducting under a pressure of P = 1.1 GPa until it enters the paramagnetic (PM) phase above Pc = 1.6 GPa was a surprise. Successive searches for new materials (URhGe and UCoGe) led to the discovery of the coexistence of superconductivity (SC) and ferromagnetism at ambient pressure. Furthermore in UCoGe, it was found that SC survives in the PM regime from P_c = 1.1 to 4 GPa. Focus has been on low-temperature experiments under extreme conditions of magnetic field (H), pressure, and uniaxial stress. In UGe2, strong interplay exists between Fermi surface (FS) reconstructions in the cascade of different FM and PM ground states and their magnetic fluctuations. Similar phenomena occur in URhGe and UCoGe but, at first glance, the SC seems to be driven by the FM fluctuations. In UCoGe, a longitudinal field scan leads to a drastic decrease in the FM fluctuations, while a transverse field scan leads to suppression of the Curie temperature, T_Curie; the consequence is a boost in FM fluctuations, leading to a reinforcement of SC. The singularity in URhGe is the weakness of the anisotropy between c- and b-axes; the most noteworthy feature is the detection of reentrant SC near H_R. All the experimental results give evidence that the SC in these three materials originates from the FM fluctuations, which are amplitude modes of magnetic excitations in the FM state. Spin-triplet pairing has been anticipated in the FM superconductors and was actually observed by Knight-shift measurements in the SC state of UCoGe. Their fascinating (p, T, H) phase diagrams are now well established. Discussion is presented on how different theoretical approaches can describe the various phenomena discovered by experimentalists.

Residual spin susceptibility in the spin-triplet orbital-singlet model

Nuclear magnetic resonance (NMR) and Knight shift measurements are critical tools in the identification of spin-triplet superconductors. We discuss the effects of spin orbit coupling on the Knight shift and susceptibilities for a variety of spin triplet multi-orbital gap functions with orbital-singlet character and compare their responses to "traditional" single band spin-triplet ($p_x+ip_y$) superconductors. We observe a non-negligible residual spin-susceptibility at low temperature.

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa_{2}Cu_{3}O_{y}.

We present a detailed study of the temperature (T) and magnetic field (H) dependence of the electronic density of states (DOS) at the Fermi level, as deduced from specific heat and Knight shift measurements in underdoped YBa_{2}Cu_{3}O_{y}. We find that the DOS becomes field independent above a characteristic field H_{DOS}, and that the H_{DOS}(T) line displays an unusual inflection near the onset of the long-range 3D charge-density wave order. The unusual S shape of H_{DOS}(T) is suggestive of two mutually exclusive orders that eventually establish a form of cooperation in order to coexist at low T. On theoretical grounds, such a collaboration could result from the stabilization of a pair-density wave state, which calls for further investigation in this region of the phase diagram.

Study of B11 and C13 NMR on doped MgB2 in the normal and in the superconducting state

We have studied carbon-doped magnesium diboride nanoparticles using $^{13}\mathrm{C}$ and $^{11}\mathrm{B}$ NMR in the normal and superconducting states. Measurements of the line shape reveal the role of carbon as a flux-pinning center and, combined with Knight shift measurements, suggest the doping procedure favors the chemical substitution scenario. We perform ab initio calculations on a structure with a single carbon-boron substitution which yield results that match the experimental data. The $^{13}\mathrm{C}$ and $^{11}\mathrm{B}$ Knight shift data are used to extract the spin susceptibility, which indicates a BCS pairing mechanism; however, we do not observe the Hebel-Slichter coherence peak from 1/${T}_{1}$ data, which we hypothesize is due to a pair-breaking mechanism present in the boron planes.

Metal-insulator transition and pseudogap inBi1.76Pb0.35Sr1.89CuO6+δhigh-Tccuprates

It is inferred from bulk-sensitive muon Knight shift measurement for a Bi$_{1.76}$Pb$_{0.35}$Sr$_{1.89}$CuO$_{6+\delta}$ single-layer cuprate that metal-insulator (MI) transition (in the low temperature limit, $T\rightarrow0$) occurs at the critical hole concentration $p=p_{\rm MI}=0.09(1)$, where the electronic density of states (DOS) at the Fermi level is reduced to zero by the pseudogap irrespective of the N\'eel order or spin glass magnetism. Superconductivity also appears for $p>p_{\rm MI}$, suggesting that this feature is controlled by the MI transition. More interestingly, the magnitude of the DOS reduction induced by the pseudogap remains unchanged over a wide doping range ($0.1\le p\le0.2$), indicating that the pseudogap remains as a hallmark of the MI transition for $p>p_{\rm MI}$.

No Detectable Change in In-Plane 29Si Knight Shift in the Superconducting State of URu2Si2

Using a high-quality single crystal of URu2Si2, we performed 29Si Knight shift measurements with an applied magnetic field Ha along the crystalline a-axis, i.e., along the magnetic hard axis, for temperatures down to 50 mK. The narrow, single-peak 29Si NMR spectrum obtained from this crystal allowed us to examine the temperature variation of the Knight shift K(T), and hence, that of the variation of the spin susceptibility with sensitivity on the order of 0.001%. At this precision, no observable change in K(T) was detected from 50 mK up to the superconducting transition at TSC(Ha) ∼ 1 K. Our results correspond to either an extremely small spin susceptibility in the hidden-order state along the magnetic hard axis or to possible spin-triplet superconductivity in this system.

NMR evidence of anisotropic Kondo liquid behavior inCeIrIn5

We report detailed Knight shift measurements of the two indium sites in the heavy fermion compound CeIrIn$_5$ as a function of temperature and field orientation. We find that the Knight shift anomaly is orientation-dependent, with a crossover temperature $T^*$ that varies by 50% as the field is rotated from (001) to (100). This result suggests that the hybridization between the Ce 4f states and the itinerant conduction electrons is anisotropic, a result that reflects its collective origin, and may lead to anisotropic Kondo liquid behavior and unconventional superconductivity.