Korringa Relation Research Articles

Planar Cu and O NMR and the Pseudogap of Cuprate Superconductors

Recently, an analysis of all available planar oxygen shift and relaxation data for the cuprate high-temperature superconductors showed that the data can be understood with a simple spin susceptibility from a metallic density of states common to all cuprates. It carries a doping dependent but temperature independent pseudogap at the Fermi surface, which causes the deviations from normal metallic behavior, also in the specific heat. Here, a more coherent, unbiased assessment of all data, including planar Cu, is presented and consequences are discussed, since the planar Cu data were collected and analyzed prior to the O data. The main finding is that the planar Cu shifts for one direction of the external magnetic field largely follow from the same states and pseudogap. This explains the shift suppression stated more recently, which leads to the failure of the Korringa relation in contrast to an enhancement of the relaxation due to antiferromagnetic spin fluctuations originally proposed. However, there is still the need for a second spin component that appears to be associated with the Cu 3d(x2−y2) hole to explain the complex Cu shift anisotropy and family dependence. Furthermore, it is argued that the planar Cu relaxation which was reported recently to be rather ubiquitous for the cuprates, must be related to this universal density of states and the second spin component, while not being affected by the simple pseudogap. Thus, while this universal metallic density of states with a pseudogap is also found in the planar Cu data, there is still need for a more elaborate scenario that eludes planar O.

Fast nuclear spin relaxation rates in tilted cone Weyl semimetals: redshift factors from Korringa relation

Spin lattice relaxation rate is investigated for 3D tilted cone Weyl semimetals (TCWSMs). The nuclear spin relaxation rate is presented as a function of temperature and tilt parameter. We find that the relaxation rate behaves as with α ≈ 9 where 0 ⩽ ζ < 1 is the tilt parameter. We demonstrate that such a strong enhancement for ζ ≲ 1 that gives rise to very fast relaxation rates, is contributed by a new hyperfine interactions arising from the tilt itself. This can be attributed to the combination of anisotropy of the Fermi surface and an additional part related to the structure of the spacetime: extracting an effective density of states (DOS) from the Korringa relation, we show that it is related to the DOS ρ of the tilted cone dispersion by the ‘redshift factor’ as . We interpret this relation as NMR manifestation of an emergent underlying spacetime structure in TCWSMs.

Landau diamagnetism and Weyl-fermion excitations in TaAs revealed by As75 NMR and NQR

The electronic and superconducting properties associated with the topologically non-trivial bands in Weyl semimetals have recently attracted much attention. We report the microscopic properties of the type-I Weyl semimetal TaAs measured by $^{75}$As nuclear magnetic (quadrupole) resonance under zero and elevated magnetic fields over a wide temperature range up to 500 K. The magnetic susceptibility measured by the Knight shift $K$ is found to be negative at low magnetic fields and have a strong field ($B$) dependence as ln$B$ at $T$ = 1.56 K. Such nonlinear field-dependent magnetization can be well accounted for by Landau diamagnetism arising from the 3D linearly dispersed bands, and thus is a fingerprint of topological semimetals. We further study the low-energy excitations by the spin-lattice relaxation rate 1/$T_{1}$. At zero field and 30 K $\leq T\leq$ 250 K, 1/$T_{1}T$ shows a $T^{2}$ variation due to Weyl nodes excitations. At $B \sim$ 13 T, $1/T_1T$ exhibits the same $T$-dependence but with a smaller value, scaling with $K^2\propto T^2$, which indicates that the Korringa relation also holds for a Weyl semimetal. Analysis of the Korringa ratio reveals that the energy range of the linear bands is about 250 K in TaAs.

Nuclear spin-lattice relaxation time in TaP and the Knight shift of Weyl semimetals

We first analyze the recent experimental data on the nuclear spin-lattice relaxation rate of the Weyl semimetal TaP. We argue that its non-monotonic temperature dependence is explained by the temperature dependent chemical potential of Weyl fermions. We also develop the theory of the Knight shift in Weyl semimetals, which contains two counteracting terms. The diamagnetic term follows $-\ln[W/\max(|\mu|,k_BT)]$ with $W$, $\mu$ and $T$ being the high energy cutoff, chemical potential and temperature, respectively, and is always negative. The paramagnetic term scales with $\mu$ and changes sign depending on the doping level. Altogether, the Knight shift is predicted to vanish or even change sign upon changing the doping or the temperature, making it a sensitive tool to identify Weyl points. We also calculate the Korringa relation for Weyl semimetals which shows an unusual energy dependence rather than being constant as expected for a non-interacting Fermi system.

Nuclear magnetic relaxation and Knight shift due to orbital interaction in Dirac electron systems

We study the nuclear magnetic relaxation rate and Knight shift in the presence of the orbital and quadrupole interactions for three-dimensional Dirac electron systems (e.g., bismuth–antimony alloys). By using recent results of the dynamic magnetic susceptibility and permittivity, we obtain rigorous results of the relaxation rates (1/T1)orb and (1/T1)Q, which are due to the orbital and quadrupole interactions, respectively, and show that (1/T1)Q gives a negligible contribution compared with (1/T1)orb. It is found that (1/T1)orb exhibits anomalous dependences on temperature T and chemical potential μ. When μ is inside the band gap, (1/T1)orb∼T3log(2T/ω0) for temperatures above the band gap, where ω0 is the nuclear Larmor frequency. When μ lies in the conduction or valence bands, (1/T1)orb∝TkF2log(2vFkF/ω0) for low temperatures, where kF and vF are the Fermi momentum and Fermi velocity, respectively. The Knight shift Korb due to the orbital interaction also shows anomalous dependences on T and μ. It is shown that Korb is negative and its magnitude significantly increases with decreasing temperature when μ is located in the band gap. Because the anomalous dependences in Korb is caused by the interband particle-hole excitations across the small band gap while (1/T1)orb is governed by the intraband excitations, the Korringa relation does not hold in the Dirac electron systems.

Cr3 Triangles induced competing magnetic interactions in the new metal boride TiCrIr2B2: An NMR and DFT study

The presence of one-dimensional trigonal arrangements of chromium atoms (Cr3) in the structure of TiCrIr2B2 leads to a magnetic transition near ambient temperature. Herein we report an investigation of the nature of electronic and magnetic properties of TiCrIr2B2 via ab initio calculations together with 11B NMR Knight shift (K) and spin-lattice relaxation rate (1/T1) analysis. The presence of a characteristic rectangular powder pattern below 280K, absence of a Korringa relation, strong enhancement of 1/T1.T at low temperatures and weak temperature dependence of K indicate competition between antiferromagnetic and ferromagnetic spin fluctuations in the itinerant d-band electrons, in agreement with ab initio calculations. One-dimensional trigonal arrangements of magnetically active elements in intermetallic compounds, as is found in TiCrIr2B2, are quite rare and could lead to exotic phenomena such as spin-chirality and quantum criticality in low-dimensional frustrated lattices.

Paramagnetic-to-nonmagnetic transition in antiperovskite nitride Cr3GeN studied by 14N-NMR and µSR

The antiperovskite-related nitride Cr3GeN forms a tetragonal structure with the space group at room temperature. It shows a tetragonal () to tetragonal (I4/mcm) structural transition with a large hysteresis at 300–400 K. The magnetic susceptibility of Cr3GeN shows Curie-Weiss type temperature dependence at high temperature, but is almost temperature-independent below room temperature. We carried out µSR and 14N-NMR microscopy measurements to reveal the magnetic ground state of Cr3GeN. Gradual muon spin relaxation, which is nearly temperature-independent below room temperature, was observed, indicating that Cr3GeN is magnetically inactive. In the 14N-NMR measurement, a quadrupole-split spectrum was obtained at around 14K = 0. The temperature dependence of 14(1/T1) satisfies the Korringa relation. These experimental results indicate that the ground state of Cr3GeN is Pauli paramagnetic, without antiferromagnetic long-range order.

Metal-insulator transition and magnetic fluctuations in polycrystalline Ru1−xRhxP investigated by P31 NMR

$^{31}\mathrm{P}$ NMR measurements have been made on polycrystalline samples to study a metal-insulator (MI) transition and magnetic fluctuations in ${\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Rh}}_{x}\mathrm{P}$ which has metallic (M), pseudogap (PG), insulating (I), and superconducting (SC) phases. We find that RuP undergoes a crossover from the high-temperature (high-$T$) M phase to the PG phase with the pseudo spin-gap behavior probed by the nuclear spin-lattice relaxation rate at ${T}_{\mathrm{PG}}=330\phantom{\rule{4pt}{0ex}}\mathrm{K}$. The first-order MI transition is observed to take place from the PG phase to the low-$T$ nonmagnetic I phase with the spin-gap energy of 1250 K at ${T}_{\mathrm{MI}}=270\phantom{\rule{4pt}{0ex}}\mathrm{K}$. In the PG phase of ${\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Rh}}_{x}\mathrm{P}$ with $0\ensuremath{\le}x&lt;0.45$, an analysis based on the modified Korringa relation, which is applicable to an itinerant paramagnet with weak electron correlation, shows that antiferromagnetic (AFM) fluctuations described in the random-phase approximation are enhanced in the low-$T$ and low-$x$ region. Around the PG-M phase boundary at ${x}_{\mathrm{c}}\ensuremath{\sim}0.45$, there is the SC phase whose normal state has negligible electron-electron interaction. We discuss the MI transition, the crossover from the M phase to the PG phase, and the magnetic properties of each phase based on the band structure.

Quest for the Origin of Heavy Fermion Behavior ind-Electron Systems

Spin fluctuation is presumed to be one of the key properties in understanding the microscopic origin of heavy-fermion-like behavior in the class of transition-metal compounds, including LiV$_2$O$_4$, Y(Sc)Mn$_2$, and YMn$_2$Zn$_{20}$. In this review, we demonstrate by our recent study of muon spin rotation/relaxation that the temperature ($T$) dependence of the longitudinal spin relaxation rate ($\lambda\equiv 1/T_1$) in these compounds exhibits a common trend of leveling off to a constant value ($\lambda\sim const$.) below a characteristic temperature, $T^*$. This is in marked contrast to the behavior predicted for normal metals from the Korringa relation, $\lambda\propto T/\nu$, where the spin fluctuation rate ($\nu$) in the Pauli paramagnetic state is given as a constant, $\nu\simeq 1/[h D(E_F)]$ [with $D(E_F)$ being the density of states at the Fermi energy]. Thus, the observed behavior of $\lambda$ implies that the spin fluctuation rate becomes linearly dependent on temperature, $\nu\propto T$, suggesting that heavy quasiparticles develop in a manner satisfying $D(E_F)\propto (m^*)^{\sigma}\propto 1/T$ at lower temperatures ($\sigma$ determined by the electronic dispersion). Considering that the theory of spin correlation for intersecting Hubbard chains as a model of pyrochlore lattice predicts $\nu\propto T$, our finding strongly indicates the crucial role of $t_{2g}$ bands which preserve the one-dimensional character at low energies due to the geometrical frustration specific to the undistorted pyrochlore lattice.

Sub-millisecond 125Te NMR spin-lattice relaxation times and large Knight shifts in complex tellurides: Validation of a quadratic relation across the spectrum

125Te NMR spectra and spin-lattice relaxation times, T1, have been measured for several GeTe-based materials with Te excess. The spectra show inhomogeneous broadening by several thousand ppm and a systematic variation in T1 relaxation time with resonance frequency. The quadratic dependence of the spin-lattice relaxation rate, 1/T1, on the Knight shift in the Korringa relation is found to be valid over a wide range of Knight shifts. This result confirms that T1 relaxation in GeTe-based materials is mostly dominated by hyperfine interaction between nuclei and free charge carriers. In GeTe with 2.5% excess of Te, about 15% of the material exhibits a Knight shift of ≥4500ppm and a T1 of only 0.3ms, indicating a high hole concentration that could correspond to close to 50% vacancies on the Ge sublattice in this component. Our findings provide a basis for determining the charge carrier concentration and its distribution in complex thermoelectric and phase-change tellurides, which should lead to a better understanding of electronic and thermal transport properties as well as chemical bonding in these materials.

Probing the Nuclear Spin-Lattice Relaxation Time at the Nanoscale

Nuclear spin-lattice relaxation times are measured on copper using magnetic resonance force microscopy performed at temperatures down to 42 mK. The low temperature is verified by comparison with the Korringa relation. Measuring spin-lattice relaxation times locally at very low temperatures opens up the possibility to measure the magnetic properties of inhomogeneous electron systems realized in oxide interfaces, topological insulators and other strongly correlated electron systems such as high-Tc superconductors.

Microscopic evidence of a metallic state in the one-pot organic conductor ammonium tetrathiapentalene carboxylate

1H NMR (nuclear magnetic resonance) and high-field ESR (electron spin resonance) measurements were carried out for self-doped organic conductors in the ammonium tetrathiapentalene carboxylate (TTPCOO)2[(NH41+)1–x(NH30)x ] system. While the pristine TTPCOOH molecule is closed-shell, self-doped carriers are generated by substitution of the carboxyl proton by (NH30) and (NH41+), which can be regarded as a charge reservoir. The π-extended system TTPCOO has a uniaxial g -tensor, indicating a 2D isotropic structure such as a herring-bone-like or parallel cross donor arrangement. The NMR-relaxation rate indicated the Korringa relation in the temperature dependence, and the ESR linewidth followed the Elliot mechanism. Both of these observations provide supporting evidence for a stable metallic state. In this paper, we introduce self-doped organic conductors as a branch of materials design, and emphasize that advanced magnetic resonance measurements are powerful tools for developing functional materials. (© 2015 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim)

Magnetic fluctuations and possible formation of a spin-singlet cluster under pressure in the heavy-fermion spinelLiV2O4probed byLi7andV51NMR

$^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ NMR measurements up to 9.8 GPa have been made to elucidate local magnetic properties of a heavy-fermion spinel oxide ${\mathrm{LiV}}_{2}{\mathrm{O}}_{4}$ which undergoes a metal-insulator transition above $\ensuremath{\sim}7$ GPa. The temperature $T$ and pressure $P$ dependences of the $^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ Knight shifts and the nuclear spin-lattice relaxation rates $1/{T}_{1}$ show that in the metallic phase, there is a crossover from a high-$T$ region with weak ferromagnetic fluctuations to a low-$T$ one with antiferromagnetic (AFM) fluctuations. The AFM fluctuations are enhanced below 20 K and 1.5 GPa, where a heavy Fermi-liquid state with the modified Korringa relation is formed. The evolution of the magnetic fluctuations is discussed from the aspect of the competition among several magnetic interactions. Above ${P}_{\mathrm{MI}}\ensuremath{\sim}6.7$ GPa, we find the coexistence of metallic and insulating phases due to the first-order metal-insulator transition. The $^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ NMR spectra coming from the insulating phase have $T$-independent small Knight shifts and ${}^{7}(1/{T}_{1})$ with the thermally activated $T$ dependence, indicating the formation of a spin-singlet cluster. We propose a model of a spin-singlet tetramer as discussed in geometrically frustrated materials.

NMR relaxation studies in doped poly-3-methylthiophene

NMR relaxation rates $(1/{T}_{1})$, magnetic susceptibility, and electrical conductivity studies in doped poly-3-methylthiophene are reported in this paper. The magnetic susceptibility data show the contributions from both Pauli and Curie spins, with the size of the Pauli term depending strongly on the doping level. Proton and fluorine NMR relaxation rates have been studied as a function of temperature (3--300 K) and field (for protons at 0.9, 9.0, 16.4, and 23.4 T, and for fluorine at 9.0 T). The temperature dependence of ${T}_{1}$ is classified into three regimes: (a) For $Tl(g{\ensuremath{\mu}}_{B}\mathbf{B}/\mathbf{2}{\mathbf{k}}_{\mathbf{B}})$, the relaxation mechanism follows a modified Korringa relation due to electron-electron interactions and disorder. ${}^{1}\mathrm{H}\ensuremath{-}{T}_{1}$ is due to the electron-nuclear dipolar interaction in addition to the contact term. (b) For the intermediate temperature range $(g{\ensuremath{\mu}}_{B}\mathbf{B}/\mathbf{2}{\mathbf{k}}_{\mathbf{B}})lTl{T}_{\mathrm{BPP}}$ (the temperature where the contribution from the reorientation motion to the ${T}_{1}$ is insignificant) the relaxation mechanism is via spin diffusion to the paramagnetic centers. (c) In the high-temperature regime and at low Larmor frequency the relaxation follows the modified Bloembergen, Purcell, and Pound model. ${T}_{1}$ data analysis has been carried out in light of these models depending upon the temperature and frequency range of study. Fluorine relaxation data have been analyzed and attributed to the $\mathrm{P}{\mathrm{F}}_{6}$ reorientation. The cross relaxation among the ${}^{1}\mathrm{H}$ and ${}^{19}\mathrm{F}$ nuclei has been observed in the entire temperature range suggesting the role of magnetic dipolar interaction modulated by the reorientation of the symmetric molecular subgroups. The data analysis shows that the enhancement in the Korringa ratio is greater in a less conducting sample. Intra- and interchain hopping of charge carriers is found to be a dominant relaxation mechanism at low temperature. Frequency dependence of ${T}_{1}^{\ensuremath{-}1}$ on temperature shows that at low temperature $[Tl(g{\ensuremath{\mu}}_{B}\mathbf{B}/\mathbf{2}{\mathbf{k}}_{\mathbf{B}})]$ the system shows three dimensions and changes to quasi one dimension at high temperature. Moreover, a good correlation between electrical conductivity, magnetic susceptibility, and NMR ${T}_{1}$ data has been observed.

NMR study of heavy fermion compound EuNi2P2

We report the results of 31P-nuclear magnetic resonance (NMR) measurements on heavy fermion compound EuNi2P2 in order to investigate the magnetic properties at low temperatures from a microscopic view point. The Knight shift has a negative value in an entire temperature range, and the absolute value increases with decreasing temperature but exhibits a broad maximum around 40 K, which is similar to the behavior of the magnetic susceptibility. Also, the nuclear spin-lattice relaxation rate 1/T1 is almost constant at high temperatures above 200 K, which is reminiscent of the relaxation mechanism dominated by the interaction of the 31P nucleus with fluctuating Eu-4f moments. Below 200 K, 1/T1 gradually decreases on cooling due to the change of the valence in the Eu ion. At low temperatures, 1/T1 does not obey the Korringa relation, in contrast to typical heavy fermion compounds. The nuclear spin-spin relaxation rate 1/T2 shows the similar behavior as 1/T1 at high temperatures. But, below 50 K, 1/T2 increases upon cooling due to the development of the magnetic excitation.

Enhancement of Tc Due to Pressure Application in LaFeAsO1–xHx Studied by NMR

The prototypical iron-based high-Tc pnictide LaFeAsO1–xHx has superconducting double domes in the electronic phase diagram. Pressure application merges the double domes into a single dome, and the minimum Tc of 26K observed at x=0.2 goes up to 45K by applying a pressure of 3.0GPa. 75As nuclear magnetic resonance was performed at 3.0GPa to investigate the high-Tc mechanism. The relaxation rate divided by temperature, 1/T1T exhibits a plateau just above Tc and the value is enhanced by applying pressure. The plateau indicates that 1/T1 can be described by the Korringa relation, which suggests that a key factor to raise Tc is the density of states. So far as our results are concerned, spin fluctuations are not essential to achieve high Tc over 45K.

Metal-insulator transition in antiferromagnetic Ba1−xKxMn2As2(0≤x≤0.4) single crystals studied by55Mn and75As NMR

The magnetic structure and metal-insulator transition in antiferromagnetic (AFM) BaMn${}_{2}$As${}_{2}$ and Ba${}_{1\ensuremath{-}x}$K${}_{x}$Mn${}_{2}$As${}_{2}$ single crystals have been investigated by ${}^{55}\phantom{\rule{0.16em}{0ex}}$Mn and ${}^{75}$As nuclear magnetic resonance (NMR) measurements. In the parent AFM insulator BaMn${}_{2}$As${}_{2}$ with a N\'eel temperature ${T}_{\mathrm{N}}=625$ K, we observed a ${}^{55}\phantom{\rule{0.16em}{0ex}}$Mn zero-field NMR (ZFNMR) spectrum and confirmed the G-type AFM structure from the field dependence of the ${}^{55}\phantom{\rule{0.16em}{0ex}}$Mn spectra and ${}^{75}$As NMR spectra below ${T}_{\mathrm{N}}$. In hole-doped crystals with $x&gt;0.01$, similar ${}^{55}\phantom{\rule{0.16em}{0ex}}$Mn ZFNMR spectra were observed and the AFM state was revealed to be robust up to $x=0.4$ with the ordered moment nearly independent of $x$. The nuclear spin-lattice relaxation rates ($1/{T}_{1}$) for both nuclei in the doped samples follow the Korringa relation ${T}_{1}T=\text{const}$, indicating a metallic state. This confirms the coexistence of AFM ordered localized Mn spins and conduction carriers from a microscopic point of view. From the $x$ dependence of ${({T}_{1}T)}^{\ensuremath{-}1/2}$ for both nuclei, we conclude that this transition is caused by vanishing of the hole concentration as the transition is approached from the metallic side.

Evidence for two energy gaps and Fermi liquid behavior in the SrPt2As2superconductor

We report a detailed calorimetric study on single crystals of the 5$d$-transition metal pnictide SrPt2As2 with a superconducting critical temperature $T_c$ $\sim$5K. The peculiar field dependence of the electronic specific heat coefficient $\gamma$ can be decomposed into two linear components. Moreover, the temperature evolution of the electronic specific heat below $T_c$ is best described by a two-gap model. These findings suggest that two energy gaps are associated with the superconductivity. In parallel, we show that the spin-lattice relaxation time $T_1$, through nuclear magnetic resonance measurement, obeys the so-called Korringa relation well. This, along with the $T^2$ dependence of resistivity at low temperatures, points to a Fermi liquid ground state in this material.

NMR Study of Layered Transition Metal Ditelluride (Ir,Pt)Te2

We report the results of 125Te and 195Pt NMR measurements on (Ir,Pt)Te2 in order to elucidate the characteristic electronic states. For PtTe2, the NMR spectrum exhibits a sharp line, which shows the uniaxially symmetric powder pattern due to the anisotropic Knight shift. The Knight shift is almost independent of temperature and is larger than that for IrTe2. Also, the nuclear spin-lattice relaxation rate 1/T1 of PtTe2 is proportional to the temperature in a wide temperature range, that is, obeys the Korringa relation as expected for simple metallic systems. From the analyses of the Knight shift and 1/T1, it is suggested that the antiferromagnetic correlations slightly exist.

P-concentration dependence of the quasiparticle density of states in BaFe2(As1-xPx)2

31P-NMR measurements were performed in the iron pnictides BaFe2(As1−xPx)2 for 0.07 ≤ x ≤ 0.64 in order to investigate evolution of electronic state with isovalent substitution. In general, the spin part of the Knight shift Kspin and (T1T)−1/2 are proportional to the quasiparticle density of states at the Fermi level N(EF) at high temperature where the Korringa relation holds. We found that Kspin and (T1T)−1/2 are almost unaffected by the P-substitution, indicating that N(EF) is nearly constant. These results are quantitatively consistent with our band calculation. We claim that the slight changes of N(EF) by P-substitution in BaFe2(As1−xPx)2 is not enough to explain the Tc variation ranging from 30 K to 0 K, and thus suggest that antiferromagnetic correlations related to the quantum critical character are essential for the high Tc superconductivity.