Knight Shift Research Articles

As75NMR study of the antiferromagnetic Kondo lattice compound CeNiAsO

We revisit the magnetic properties of the antiferromagnetic Kondo lattice CeNiAsO by $^{75}$As nuclear magnetic resonance measurements. Our results confirm two successive antiferromagnetic transitions of Ce moments at $T_{N1}=9.0(3)$ K and $T_{N2}=7.0(3)$ K. Incommensurate and commensurate antiferromagnetic orders are suggested for $T_{N2}<T<T_{N1}$ and $T<T_{N2}$ respectively, consistent with previous neutron and muon experiments. A Knight shift anomaly, characterized by the failure of $K(T)-\chi(T)$ scaling, is observed below $T^*\sim15$ K, which gives a measure of the onset of coherent $c-f$ correlations. This energy scale is further confirmed by the spin-lattice relaxation rate ($1/T_1$). The analysis of spin dynamics also reveals a quasi-two-dimensional character of spin fluctuations in CeNiAsO. This work paves the way for further $^{75}$As nuclear magnetic resonance studies under pressure.

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.

NMR evidence for a Peierls transition in the layered square-net compound LaAgSb2

We measured the central ($1/2\leftrightarrow -1/2$) and first satellite ($\pm3/2\leftrightarrow \pm1/2$) lines of the \la\ NMR spectra as a function of temperature in LaAgSb$_2$, in order to elucidate the origin and nature of the charge-density-wave (CDW) transitions at $T_\text{CDW1}=207$ K and $T_\text{CDW2}=186$ K. In the normal state, the Knight shift K reveals a fairly linear relationship with decreasing temperature, which is ascribed to a pseudogap in the spin excitation spectrum, pointing towards the material being an unconventional metal. Upon further cooling, K decreases more steeply below $T_\text{CDW1}$, indicative of the partial Fermi surface gap opening on top of the pseudogap. The most remarkable finding in our study is a clear splitting of the satellite lines at $T_\text{CDW1}$ observed for $H\parallel c$, whose temperature dependence behaves as the BCS order parameter in the weak-coupling limit, evidencing that the CDW transition induces the periodic lattice distortion. Our NMR findings therefore demonstrate that the CDW transition in LaAgSb$_2$ is of Peierls type, being driven by the electronic instability in the vicinity of the Fermi level.

Al27 NMR insight into the phase transition in BaFe2Al9

We have applied $^{27}\mathrm{Al}$ nuclear magnetic resonance (NMR) spectroscopy to investigate the iron-based aluminide of $\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{Al}}_{9}$. This material has been a subject of current interest due to indications of charge density wave behavior below the transition temperature ${T}_{C}\ensuremath{\simeq}100$ K. Two sets of the $^{27}\mathrm{Al}$ NMR resonance lines that are associated with two nonequivalent crystallographic aluminum sites have been well resolved. We have discussed the obtained electric field gradient and anisotropic Knight shift for each individual aluminum site, revealing the strong $ab$ plane bonding configuration for the structural properties of $\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{Al}}_{9}$. Pronounced features in the isotropic Knight shift and nuclear spin-lattice relaxation rate have been observed in the vicinity of ${T}_{C}$. Furthermore, the detailed $^{27}\mathrm{Al}$ NMR analyses have provided evidence for the decrease of the electronic density of states upon lowering temperature below ${T}_{C}$.

Electron spin dynamics in a hexaboride superconductor YB6 probed by 89Y and 11B NMR

Normal-state properties of hexaboride superconductors YB6 with Tc = 7.4 and 4.2 K were studied using 89Y and 11B NMR at temperatures from 6 to 300 K. Both the spin-lattice relaxation rate and the Knight shift of 89Y were found to be higher in the sample with higher Tc indicating a respectively higher density of states at the Fermi level. Along with the enhancement of electron-phonon coupling, these are the two main factors that increase Tc in YB6. The spin-lattice relaxation rate of 11B includes a contribution that can be associated with a transition into a dynamic disordered state at 50-70 K.

Higher angular momentum pairing states in Sr2RuO4 in the presence of longer-range interactions

The superconducting symmetry of Sr$_2$RuO$_4$ remains a puzzle. Time-reversal symmetry breaking $d_{x^2-y^2} + ig_{xy(x^2-y^2)}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in Sr$_2$RuO$_4$, including the effects of spin-orbit coupling (SOC), in the presence of both local and longer-range interactions within a random phase approximation. We show that the inclusion of second nearest neighbor repulsions, together with non-local SOC in the $B_{2g}$ channel or orbital-anisotropy of the non-local interactions, can have a significant impact on the stability of both $d_{x^2-y^2}$- and $g$-wave pairing channels. We analyze the properties, such as Knight shift and spontaneous edge current, of the realized $d_{x^2-y^2} + ig$, $s^{\prime}+id_{xy}$ and mixed helical pairings in different parameter spaces and find that the $d_{x^2-y^2} + ig$ solution is in better agreement with the experimental data.

Magnesium-rich intermetallic compounds RE 3Ag4Mg12 (RE = Y, La–Nd, Sm–Dy, Yb) and AE 3Ag4Mg12 (AE = Ca, Sr)

Abstract The magnesium-rich intermetallic compounds RE 3Ag4Mg12 (RE = Y, La–Nd, Sm–Dy, Yb) and AE 3Ag4Mg12 (AE = Ca, Sr) were synthesized from the elements in sealed tantalum ampoules through heat treatment in an induction furnace. X-ray powder diffraction studies confirm the hexagonal Gd3Ru4Al12 type structure, space group P63/mmc. Three structures were refined from single crystal X-ray diffractometer data: a = 973.47(5), c = 1037.19(5) pm, wR2 = 0.0296, 660 F 2 values, 30 variables for Gd3Ag3.82(1)Mg12.18(1), a = 985.27(9), c = 1047.34(9) pm, wR2 = 0.0367, 716 F 2 values, 29 variables for Yb3Ag3.73(1)Mg12.27(1) and a = 992.41(8), c = 1050.41(8) pm, wR2 = 0.0373, 347 F 2 values, 28 variables for Ca3Ag3.63(1)Mg12.37(1). Refinements of the occupancy parameters revealed substantial Ag/Mg mixing within the silver-magnesium substructure, a consequence of the Ag@Mg8 coordination. The alkaline earth and rare earth atoms build Kagome networks. Temperature dependent magnetic susceptibility measurements indicate diamagnetism/Pauli paramagnetism for the compounds with Ca, Sr, Y and YbII, while the others with the trivalent rare earth elements are Curie-Weiss paramagnets. Most compounds order antiferromagnetically at T N = 4.4(1) K (RE = Pr), 34.6(1) K (RE = Gd) and 23.5(1) K (RE = Tb) while Eu3Ag4Mg12 is a ferromagnet (T C = 19.1(1) K). 151Eu Mössbauer spectra confirm divalent europium (δ = −9.88(1) mm s−1). Full magnetic hyperfine field splitting (18.4(1) T) is observed at 6 K. Yb3Ag4Mg12 shows a single resonance in its 171Yb solid state NMR spectrum at 6991 ppm at 300 K indicating a strong, positive Knight shift.

Distinguishing dxz+idyz and dx2−y2 pairing in Sr2RuO4 by high magnetic field H−T phase diagrams

Employing a realistic tight-binding model describing the Fermi surface in the normal state of $Sr_2RuO_4$ we map out magnetic field versus temperature phase diagrams for $d_{x^2-y^2} (B_{1g})$ and $d_{xz}+id_{yz} (E_g)$ pairing types. Both produce (i) a similar Knight shift suppression of $\sim\!80\%$ and (ii) a bicritical point at $T=0.88$K separating low field second order phase transitions from high field Pauli limiting first order transitions. We find, however, strikingly different phase behaviour within the high field Pauli limiting region. For $d_{x^2-y^2}$ pairing symmetry an additional lower critical line of first order transitions is found (terminating in a critical point at $T=0.09-0.22$K depending on the choice of Hubbard U parameters) while for $d_{xz}+id_{yz}$ no such additional high field phase transitions are found for any choice of Hubbard U. In conjunction with our earlier finding [{\it Physical Review B} {\bf 102} (23), 235203] for $p$-wave helical pairing of a still different high field phase structure (a lower critical field line meeting the upper critical field line exactly at the bicritical point), we suggest high field Pauli limiting phase structure as a possible route to distinguish pairing symmetries in this material.

Topological superconductivity in Sn/Si(111) driven by nonlocal Coulomb interactions

Superconductivity was recently observed in boron-doped $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\mathrm{Sn}/\mathrm{Si}(111)$. The material can be described by an extended Hubbard model on a triangular lattice. Here, we use the random-phase approximation to investigate the charge and spin fluctuations as well as the superconducting properties of the system with respect to filling and the relative strength of the extended versus the on-site Hubbard interactions. Our calculations reveal that near half-filling and weak extended Hubbard interactions, the superconducting ground state exhibits chiral $d$-wave pairing. Far from half filling and for stronger nearest-neighbor Coulomb interactions, the system shows chiral $p$-wave (hole-doping) and $f$-wave (electron-doping) pairings. The dependence of the pairing symmetry on the extended Hubbard interactions suggests that charge fluctuations play an important role in the formation of Cooper pairs. Finally, the temperature dependence of the Knight shift is calculated for all observed superconducting textures and put forward as an experimental method to examine the symmetry of the superconducting gap function.

Dynamical magnetic response in superconductors with finite-momentum pairs

We derive the dynamical magnetic response functions in the Fulde-Ferrell (FF) state of a superconductor with inversion symmetry. The pair momentum 2q is obtained by minimization of the condensation energy and the resulting quasiparticle states and spectral functions exhibit the segmentation into paired and unpaired regions due to the finite q. The dynamical magnetic susceptibility is then calculated in linear response formalism in the FF state with finite-q condensate resulting from s-wave or d-wave pairing. We show that quasiparticle excitations inside as well as between paired and unpaired segments contribute to the dynamical response. We discuss its dependence on frequency and momentum transfer which develops a characteristic symmetry-breaking parallel to q. Furthermore, we investigate the possible influence on Knight shift and in the case of d-wave pairing on the spin resonance formation in the FF state.

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.

Fragment-orbital-dependent spin fluctuations in the single-component molecular conductor [Ni(dmdt)2]

Motivated by recent nuclear magnetic resonance experiments, we calculated the spin susceptibility, Knight shift, and spin-lattice relaxation rate ($1/T_{1}T$) of the single-component molecular conductor [Ni(dmdt)$_2$] using the random phase approximation in a multi-orbital Hubbard model describing the Dirac nodal line electronic system in this compound. This Hubbard model is composed of three fragment orbitals and on-site repulsive interactions obtained using ab initio many-body perturbation theory calculations. We found fragment-orbital-dependent spin fluctuations with the momentum $\textbf{q}$=$\textbf{0}$ and an incommensurate value of the wavenumber $\textbf{q}$=$\textbf{Q}$ at which a diagonal element of the spin susceptibility is maximum. The $\textbf{q}$=$\textbf{0}$ and $\textbf{Q}$ responses become dominant at low and high temperatures, respectively, with the Fermi-pocket energy scale as the boundary. We show that $1/T_{1}T$ decreases with decreasing temperature but starts to increase at low temperature owing to the $\textbf{q}$=$\textbf{0}$ spin fluctuations, while the Knight shift keeps monotonically decreasing. These properties are due to the intra-molecular antiferromagnetic fluctuations caused by the characteristic wave functions of this Dirac nodal line system, which is described by an $n$-band ($n\geq 3$) model. We show that the fragment orbitals play important roles in the magnetic properties of [Ni(dmdt)$_2$].

Al27 NMR local study of the Al0.5TiZrPdCuNi alloy in high-entropy alloy and metallic glass forms

We report a $^{27}\mathrm{Al}$ nuclear magnetic resonance (NMR) local spectroscopic study of the NMR lineshape and Knight shift of a six-component ${\mathrm{Al}}_{0.5}\mathrm{TiZrPdCuNi}$ metallic alloy that can be prepared either as a crystalline high-entropy alloy (HEA) or as an amorphous metallic glass (MG) at the same chemical composition. For both structural modifications of the material (HEA and MG), we have determined the distribution of electric-field-gradient (EFG) tensors and the local electronic density of states (DOS) $g({\ensuremath{\varepsilon}}_{\mathrm{F}})$ at the Fermi level at the position of $^{27}\mathrm{Al}$ nuclei. A theoretical $I=\frac{5}{2}$ quadrupole-perturbed NMR spectrum, pertinent to both cubic HEAs and amorphous MGs, has been derived using the Gaussian isotropic model of the EFG tensor distribution, and excellent fits of the experimental spectra were obtained. The EFG distribution function of the MG state is about twice broader than that of the HEA state, reflecting the existence of a (distorted) crystal lattice in the latter and its absence in the former. The ${T}^{2}$ dependence of the Knight shift indicates that the DOS is changing rapidly with energy within the Fermi level region for both structural modifications. The local DOS at the $^{27}\mathrm{Al}$ sites of the HEA sample is $\ensuremath{\sim}10%$ larger than that of the MG state, indicating comparable degrees of disorder.

Relationship between electronic inhomogeneity and bandwidth in the organic conductor κ−(BEDT−TTF)2Cu[N(CN)2]I studied by C13 NMR spectroscopy

In $\ensuremath{\kappa}$-(BEDT-${\mathrm{TTF})}_{2}\mathrm{Cu}$[N(${\mathrm{CN})}_{2}]X$ ($X$ = Cl, Br) salts, where BEDT-TTF denotes bis(ethylenedithio)tetrathiafulvalene, the electronic properties can be characterized using a universal pressure-temperature phase diagram. Previous research [T. Kobayashi et al., Phys. Rev. B 100, 195115 (2019)] revealed a low-temperature insulating phase without antiferromagnetic ordering in the isostructural $X$ = I (hereafter, $\ensuremath{\kappa}$-I) salt, which cannot be understood using the universal phase diagram. In addition, the $\ensuremath{\kappa}$-I salt naturally contains electronic inhomogeneity because of the development of a superlattice structure and/or disorder of the ethylene end groups. This could lead to physical properties that are different from those described by the universal phase diagram of $\ensuremath{\kappa}$-type salts. To investigate the relationship between the electronic inhomogeneity and universal phase diagram, $^{13}\mathrm{C}$ NMR measurements were performed under pressure on this material. With increasing pressure, an increase in the bandwidth was revealed from a decrease in the Knight shift. The accompanying suppression of the inhomogeneity at low temperatures was evident from the linewidth. Once the inhomogeneity was suppressed, superconductivity was observed. The temperature dependence of the Knight shift and spin-lattice relaxation rate in the superconducting state is similar to that previously observed for $\ensuremath{\kappa}$-type salts, indicating that the symmetry of the superconducting gap is a $d$ wave. When pressure was applied and the electronic inhomogeneity was suppressed, the physical properties of the $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{I}$ salt were found to be qualitatively identical to those of the high-pressure side on the universal phase diagram. These results indicate that the ratio of electronic inhomogeneity to bandwidth is an essential parameter for this system.

Dynamic crossover in metallic glass melt detected by NMR

The structure and dynamics of melts have critical influence on the glass formation and solidification of crystals, which attracts broad interest to clarify the underlying mechanisms. In this paper, the quadrupolar spin-lattice relaxation rates of 63Cu and 65Cu nuclei in a Au50Cu25.5Ag7.5Si17 metallic glass melt are studied by using a home-designed high-precision high-temperature NMR equipment. The relaxation rates follow the Arrhenius behavior at high temperatures above 870 K, but become non-Arrhenius at low temperatures, which indicates a non-Arrhenius dynamical crossover. The crossover temperature TA is about 2.3 times of the glass-transition temperature (Tg=378 K). Based on the analysis of Knight shift and magnetic relaxation rates, Cu and Si atoms are found to tend to form stronger covalent-like bonds below TA. Such an increase in bonding strength may promote the connectivity of energetically preferred short-range clusters, which is responsible for the observed sluggish dynamics.

Site-Dependent Local Spin Susceptibility and Low-Energy Excitation in a Weyl Semimetal WTe2

Site-dependent local spin susceptibility is investigated with $^{125}$Te nuclear magnetic resonance in a Weyl semimetal WTe$_2$. The nuclear spin-lattice relaxation rate $1/T_1T$ shows a dependence of the square of temperature $T$ at high temperatures, followed by a constant behavior below 50 K. The temperature dependence features Weyl fermions appearing around the linearly crossing bands. The Knight shift $K$ scales to the square root of $1/T_1T$, corroborating a predominant spin contribution in low-lying excitation. The observed dependence of $K$ and $1/T_1T$ on the four Te sites shows the site-dependent electron correlation and density of states. The angular profile of the NMR spectrum gives the anisotropic hyperfine coupling tensor, consistent with $5p$ hole occupations on Te sites.

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.

Possible quadrupole-order-driven commensurate-incommensurate phase transition in B20 CoGe

The B20-type cobalt germanide CoGe was investigated by measuring the specific heat, resistivity, and $^{59}$Co nuclear magnetic resonance (NMR). We observed a phase transition at $T_Q=13.7$ K, evidenced by a very narrow peak of the specific heat and sharp changes of the nuclear spin-spin ($T_2^{-1}$) and spin-lattice ($T_1^{-1}$) relaxation rates. The fact that the entropy release is extremely small and the Knight shift is almost independent of temperature down to low temperatures as anticipated in a paramagnetic metal indicates that the $T_Q$ transition is of non-magnetic origin. In addition, we detected a crossover scale $T_0\sim30$ K below which the resistivity and the NMR linewidth increase, and $T_1^{-1}$ is progressively distributed in space, that is, a static and dynamical spatial inhomogeneity develops. While the order parameter for the $T_Q$ transition remains an open question, a group-theoretical analysis suggests that the finite electric quadrupole density arising from the low local site symmetry at cobalt sites could drive the crystal symmetry lowering from the P2$_1$3 symmetry that is commensurate to the R3 symmetry with an incommensurate wavevector, which fairly well accounts for the $T_Q$ transition. The quadrupole-order-driven commensurate-incommensurate phase transition may be another remarkable phenomenon arising from the structural chirality inherent in the noncentrosymmetric B20 family.

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.

Two-Dimensional XY-Type Magnetic Properties of Locally Noncentrosymmetric Superconductor CeRh2As2

We performed $^{75}$As-NMR measurements to investigate the normal-state magnetic properties of CeRh$_2$As$_2$, a recently-discovered heavy-fermion superconductor. The magnitude and temperature dependence of the Knight shift at the As(2) site indicate easy-plane-type magnetic anisotropy in CeRh$_2$As$_2$. With regard to spin fluctuations, the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ arising from the 4$f$ electrons decreases from high-temperature constant behavior on cooling at $\sim$ 40~K, which is typical behavior of heavy-fermion systems. In addition, $1/T_1$ becomes constant at low temperatures, suggesting spatially two-dimensional antiferromagnetic fluctuations. Two-dimensional magnetic correlations in the real space are quite rare among heavy-fermion superconductors, and they may be a key factor in the unique superconducting multi-phase in CeRh$_2$As$_2$.