Dynamic Relaxation Rate Research Articles

Flux creep and flux pinning behavior in Cu-doped FeSe0.4Te0.6 single crystals

This paper presents the preparation and comparative study of the superconducting properties and magnetic flux dynamics of FeSe and Fe1-xCuxTe0.6Se0.4 (x = 0, 0.005, 0.01, 0.015) single crystals, with the aim of investigating the origin of the second peak in FeTe0.6Se0.4. The Cu element significantly suppresses the superconducting transition temperature (Tc) of Fe1-xCuxTe0.6Se0.4 from 14.5 K at x = 0 to 9.23 K at x = 0.015, which is close to the 9 K of FeSe, while also suppressing the second peak effect. Additionally, the critical current density anisotropy (γ) is reduced. Dynamic relaxation rates (Q) indicate a crossover from rapid single-vortex pinning near the second peak to collective pinning, linking fast and slow magnetic flux relaxation with the second peak effect. By comparing the pinning properties of FeSe and Fe1-xCuxTe0.6Se0.4 (x = 0, 0.005, 0.01, 0.015), it is found that the second peak effect is closely related to the transition from δl - pinning to δTc - pinning in Fe1-xCuxSe0.4Te0.6 (x = 0, 0.005, 0.01, 0.015). While surface pinning centers dominate in FeSe, the pinning in Fe1-xCuxSe0.4Te0.6 (x = 0, 0.005, 0.01, 0.015) originates from the interaction between the core and normal centers. Furthermore, the electronic transport properties of the FeSe and Fe1-xCuxSe0.4Te0.6 (x = 0, 0.005, 0.01, 0.015) series are also studied. Te substitution suppresses the nematic transition in FeSe, while Cu substitution suppresses the superconducting transition in Fe1-xCuxSe0.4Te0.6 (x = 0, 0.005, 0.01, 0.015) and reduces the residual resistivity. Additionally, the upper critical field is reduced from 150 T in FeSe0.4Te0.6 to 41 T in Fe0.085Cu0.015Se0.4Te0.6, but still higher than the 12.5 T observed in FeSe.

Spatial and Temporal Control of 3D Hydrogel Viscoelasticity through Phototuning.

The mechanical properties of the extracellular environment can regulate a variety of cellular functions, such as spreading, migration, proliferation, and even differentiation and phenotypic determination. Much effort has been directed at understanding the effects of the extracellular matrix (ECM) elastic modulus and, more recently, stress relaxation on cellular processes. In physiological contexts such as development, wound healing, and fibrotic disease progression, ECM mechanical properties change substantially over time or space. Dynamically tunable hydrogel platforms have been developed to spatiotemporally modulate a gel's elastic modulus. However, dynamically altering the stress relaxation rate of a hydrogel remains a challenge. Here, we present a strategy to tune hydrogel stress relaxation rates in time or space using a light-triggered tethering of poly(ethylene glycol) to alginate. We show that the stress relaxation rate can be tuned without altering the elastic modulus of the hydrogel. We found that cells are capable of sensing and responding to dynamic stress relaxation rate changes, both morphologically and through differences in proliferation rates. We also exploited the light-based technique to generate spatial patterns of stress relaxation rates in 3D hydrogels. We anticipate that user-directed control of the 3D hydrogel stress relaxation rate will be a powerful tool that enables studies that mimic dynamic ECM contexts or as a means to guide cell fate in space and time for tissue engineering applications.

Upper critical field and peak effect in (Li0.8Fe0.2)OHFeSe single crystal

The transport properties, magnetization and dynamic magnetization relaxation rate measurements of (Li0.8Fe0.2)OHFeSe single crystals are presented at various magnetic fields and temperatures. The temperature dependence of upper critical field Hc2 exhibits an upward curvature. The Hc2 has been determined based on the orbital limiting and the Pauli limiting effect. The peak effect occurs in both the magnetic hysteresis loops and critical current density, which associates with the vortex motion. The field dependence of ∆M measured at different field sweeping rates is distinguished, which indicates a giant vortex creep. The magnetic relaxation rate Q has been investigated, indicating a transition between the two different vortices motion with increasing field. Our results suggest that the peak effect originates from the vortex transition from the elastic motion to the plastic motion.

From δl- to δT c-pinning in CaKFe4As4 single crystals obtained by adjusting their defect structures

We have investigated the vortices pinning behaviors of CaKFe4As4 with two types of defect structures by alternating current and direct current susceptibility measurements under the Ginzburg-Landau theory and collective pinning model. We observed a new dissipative peak at temperature T J in each out-of-phase () curve even at low magnetic field in the samples with thick CaFe2As2 intercalations, which has been ascribed to the weak Josephson-like link. The unrelaxed current J c and the normalized pinning energy g(t) have been investigated for both types of the CaKFe4As4 crystals based on the dynamic relaxation rate Q and transient current J s by means of generalized inversion scheme. For the samples with monolayer-KFe2As2 intercalations, the temperature dependence of J c and g(t) is found to be in agreement well with the model of single vortex δT c-pinning. But for the samples with thick CaFe2As2 intergrowths, both the δT c- and δl-pinning are in functioning at low magnetic field, but the δl pinning will play a leading role at magnetic field above 3.0 T. Differential charge analysis shows that the intergrowth of KFe2As2 should be normal phase and the CaFe2As2 will become superconducting one due to the charge transfer. The non-superconducting KFe2As2 will induce an abruptly spatial change of T c resulting to strong δT c-pinning, and the superconducting CaFe2As2 phase can mainly cause to fluctuate of mean free path leading to δl-pinning. The present work illustrates how the defect structure affects the flux pinning behaviors and can provide a new clue to design high-performance superconducting wire/tapes and films for strong magnetic field applications.

Unusual spin dynamics in the low-temperature magnetically ordered state of Ag3LiIr2O6

Recently, there have been contrary claims of Kitaev spin-liquid behaviour and ordered behavior in the honeycomb compound Ag$_3$LiIr$_2$O$_6$ based on various experimental signatures. Our investigations on this system reveal a low-temperature ordered state with persistent dynamics down to the lowest temperatures. Magnetic order is confirmed by clear oscillations in the muon spin relaxation ($\mu$SR) time spectrum below 9 K till 52 mK. Coincidentally in $^7$Li nuclear magnetic resonance, a wipe-out of the signal is observed below $\sim$ 10 K which again strongly indicates magnetic order in the low temperature regime. This is supported by our density functional theory calculations which show an appreciable Heisenberg exchange term in the spin Hamiltonian that favors magnetic ordering. The $^7$Li shift and spin-lattice relaxation rate also show anomalies at $\sim$ 50 K. They are likely related to the onset of dynamic magnetic correlations, but their origin is not completely clear. Detailed analysis of our $\mu$SR data is consistent with a co-existence of incommensurate N\'eel and striped environments. A significant and undiminished dynamical relaxation rate ($\sim 5$ MHz) as seen in $\mu$SR deep into the ordered phase indicates enhanced quantum fluctuations in the ordered state.

Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate

The Kitaev quantum spin liquid provides an ideal playground for the spin fractionalization to Majorana and vison excitations. The fingerprints manifest themselves in spin dynamics, which are accessible via many experimental techniques. However, extrinsic disorder effects are inevitable in real materials. Here, the authors compute finite-temperature spin dynamics in disordered Kitaev spin liquids and clarify that disorder seriously affects the vison excitations rather than Majorana quasiparticles. Furthermore, the softening of the vison excitations and Majorana zero modes emerge due to disorder, which will help identify Kitaev magnets.

Muon spin relaxation and fluctuating magnetism in the pseudogap phase of YBa2Cu3Oy

We report results of a muon spin relaxation study of slow magnetic fluctuations in the pseudogap phase of underdoped single-crystalline YBa$_{2}$Cu$_{3}$O$_{y}$, $y = 6.77$ and 6.83. The dependence of the dynamic muon spin relaxation rate on applied magnetic field yields the rms magnitude~$B\mathrm{_{loc}^{rms}}$ and correlation time~$\tau_c$ of fluctuating local fields at muon sites. The observed relaxation rates do not decrease with decreasing temperature~$T$ below the pseudogap onset at $T^\ast$, as would be expected for a conventional magnetic transition; both $B\mathrm{_{loc}^{rms}}$ and $\tau_c$ are roughly constant in the pseudogap phase down to the superconducting transition. Corresponding NMR relaxation rates are estimated to be too small to be observable. Our results put strong constraints on theories of the anomalous pseudogap magnetism in YBa$_{2}$Cu$_{3}$O$_{y}$.

Emergent mesoscopic quantum vortex and Planckian dissipation in the strange metal phase

A major puzzle of condensed-matter physics is the physics behind the linear-in-temperature law of resistivity in many exotic metallic systems, including cuprates, pnictides, and heavy fermions. In this work, we propose, based on a symmetry-breaking analysis, that the strange metal phase is a novel emergent mesoscopic quantum state, beyond Landau’s quasiparticle excitation, which is composed of fluctuating vortices. The model predicts, in a straightforward way, the local magnetic field with a correlation time determined by the Coulomb potential, validated by observations of dynamic muon spin relaxation rates in both 3d cuprates and 5d iridate without fitting parameter. Furthermore, the model resolves the underlying quantum mechanism of the Planckian dissipation in terms of carrier scattering by fluctuating vortex, which predicts a scattering rate proportional to the vortex density, thus deriving both linear-in temperature and linear-in field laws, with a universal scattering coefficient validated by data of several dozens of samples for cuprates and iron pnictides. These findings offer a new phenomenology for non-Fermi liquid in strongly correlated materials.

Magnetic anisotropy and spin dynamics in the kagome magnet Fe4Si2Sn7O16 : NMR and magnetic susceptibility study on oriented powder

${\mathrm{Fe}}_{4}{\mathrm{Si}}_{2}{\mathrm{Sn}}_{7}{\mathrm{O}}_{16}$ hosts an undistorted kagome lattice of ${\mathrm{Fe}}^{2+}$ ($3{d}^{6}, S=2$) ions. We present results of bulk magnetization and Sn nuclear magnetic resonance (NMR) measurements on an oriented ${\mathrm{Fe}}_{4}{\mathrm{Si}}_{2}{\mathrm{Sn}}_{7}{\mathrm{O}}_{16}$ powder sample oriented in geometries parallel ($\ensuremath{\parallel}$) and perpendicular ($\ensuremath{\perp}$) to the external applied magnetic field used for orienting the powder (${B}_{\text{ori}}$). The bulk susceptibility $\ensuremath{\chi}$ shows a broad peak at ${T}_{N}\ensuremath{\sim}3$ K associated with antiferromagnetic ordering. NMR spectra indicate the presence of planar anisotropy in the kagome planes. From an analysis of the static NMR shift ($K$) and dynamic spin-lattice relaxation rate ($1/{T}_{1}$) we conclude the presence of dominant magnetic fluctuations in the kagome planes. For the $\ensuremath{\parallel}$ orientation, $K$ scales linearly with the bulk susceptibility for temperatures down to $\ensuremath{\sim}4$ K, while in the $\ensuremath{\perp}$ orientation $K$ starts to deviate strongly below $T\ensuremath{\sim}30$ K. We associate this deviation with the onset of spin-tilting towards the kagome planes. These correlations are also reflected in the $1/{T}_{1}$ data for the $\ensuremath{\parallel}$ orientation, which starts to decrease below $T\ensuremath{\sim}30$ K. In this correlated regime, ${T}_{N}<T< \ensuremath{\sim}30$ K, we discuss the formation of positive chiral spin correlations in the kagome planes.

Vortex Pinning and the Mechanism in CaKFe4As4 Revealed by Dynamical Magnetization Relaxation

We have studied the vortex dynamics of CaKFe4As4 single crystals using a dynamical magnetization relaxation method. A large region of vortex elastic motion is observed indicating strong vortex pinning ability. Temperature dependence of normalized flux pinning energy of g(t) is determined based on the data of transient current density Js and dynamical relaxation rate Q by the generalized inversion scheme (GIS), which suggests that both the δ(Tc)- and δ(l)-pinning may be responsible for the vortex dynamical behaviors in CaKFe4As4 under field parallel to c-axis (H // c). The value of Js for field parallel to ab-plane (H // ab) is obviously larger than that of H // c, this indicates that the flux pinning mechanisms are distinct in different crystal orientations. Under H // ab, a dip structure in the magnetic hysteresis loops (MHLs) is obtained around zero field, which is ascribed to planar defects in ab-plane. We further analyze the flux pinning mechanisms and find that the abnormal flux pinning behaviors should originate from its unique structure in CaKFe4As4.

Coexistence of ferromagnetic fluctuations and superconductivity in the actinide superconductor UTe2.

We report low-temperature muon spin relaxation/rotation (μSR) measurements on single crystals of the actinide superconductor UTe2. Below 5 K we observe a continuous slowing down of magnetic fluctuations that persists through the superconducting transition temperature (T c = 1.6 K), but we find no evidence of long-range or local magnetic order down to 0.025 K. The temperature dependence of the dynamic relaxation rate down to 0.4 K agrees with the self-consistent renormalization theory of spin fluctuations for a three-dimensional weak itinerant ferromagnetic metal. Our μSR measurements also indicate that the superconductivity coexists with the magnetic fluctuations.

Anomalous quantum critical spin dynamics in YFe2Al10

We report results of a muon spin relaxation ($\mu$SR) study of YFe$_2$Al$_{10}$, a quasi-2D nearly-ferromagnetic metal in which unconventional quantum critical behavior is observed. No static Fe$^{2+}$ magnetism, with or without long-range order, is found down to 19~mK\@. The dynamic muon spin relaxation rate~$\lambda$ exhibits power-law divergences in temperature and magnetic field, the latter for fields that are too weak to affect the electronic spin dynamics directly. We attribute this to the proportionality of $\lambda(\omega_\mu,T)$ to the dynamic structure factor~$S(\omega_\mu,T)$, where $\omega_\mu \approx 10^5$--$10^7~\mathrm{s}^{-1}$ is the muon Zeeman frequency. These results suggest critical divergences of $S(\omega_\mu,T)$ in both temperature and frequency. Power-law scaling and a 2D dissipative quantum XY (2D-DQXY) model both yield forms for $S(\omega,T)$ that agree with neutron scattering data ($\omega \approx 10^{12}~\mathrm{s}^{-1}$). Extrapolation to $\mu$SR frequencies agrees semi-quantitatively with the observed temperature dependence of $\lambda(\omega_\mu,T)$, but predicts frequency independence for $\omega_\mu \ll T$ in extreme disagreement with experiment. We conclude that the quantum critical spin dynamics of YFe$_2$Al$_{10}$ are not well understood at low frequencies.

Quantum spin fluctuations in the bulk insulating state of pure and Fe-doped SmB6

The intermediate-valence compound SmB6 is a well-known Kondo insulator, in which hybridization of itinerant 5d electrons with localized 4f electrons leads to a transition from metallic to insulating behavior at low temperatures. Recent studies suggest that SmB6 is a topological insulator, with topological metallic surface states emerging from a fully insulating hybridized bulk band structure. Here we locally probe the bulk magnetic properties of pure and 0.5 % Fe-doped SmB6 by muon spin rotation/relaxation methods. Below 6 K the Fe impurity induces simultaneous changes in the bulk local magnetism and the electrical conductivity. In the low-temperature insulating bulk state we observe a temperature-independent dynamic relaxation rate indicative of low-lying magnetic excitations driven primarily by quantum fluctuations.

Magnetic order and spin dynamics across a ferromagnetic quantum critical point:μSRinvestigations ofYbNi4(P1−xAsx)2

In the quasi-1D heavy-fermion system YbNi$_4$(P$_{1-x}$As$_x$)$_2$ the presence of a ferromagnetic (FM) quantum critical point (QCP) at $x_c$ $\approx 0.1$ with unconventional quantum critical exponents in the thermodynamic properties has been recently reported. Here, we present muon-spin relaxation ($\mu$SR) experiments on polycrystals of this series to study the magnetic order and the low energy 4$f$-electronic spin dynamics across the FM QCP. The zero field $\mu$SR measurements on pure YbNi$_4$(P$_{2}$ proved static long range magnetic order and suggested a strongly reduced ordered Yb moment of about 0.04$\mu_B$. With increasing As substitution the ordered moment is reduced by half at $x = 0.04$ and to less than 0.005 $\mu_B$ at $x=0.08$. The dynamic behavior in the $\mu$SR response show that magnetism remains homogeneous upon As substitution, without evidence for disorder effect. In the paramagnetic state across the FM QCP the dynamic muon-spin relaxation rate follows 1/$T_{1}T\propto T^{-n}$ with $1.01 \pm 0.04 \leq n \leq 1.13 \pm 0.06$. The critical fluctuations are very slow and are even becoming slower when approaching the QCP.

Dynamic Nuclear Polarization of β-Cyclodextrin Macromolecules.

1H dynamic nuclear polarization and nuclear spin-lattice relaxation rates have been studied in amorphous complexes of β-cyclodextrins doped with different concentrations of the TEMPO radical. Nuclear polarization increased up to 10% in the optimal case, with a behavior of the buildup rate (1/TPOL) and of the nuclear spin-lattice relaxation rate (1/T1n) consistent with a thermal mixing regime. The temperature dependence of 1/T1n and its increase with the radical concentration indicate a relaxation process arising from the modulation of the electron-nucleus coupling by the glassy dynamics. The high-temperature relaxation is driven by molecular motions, and 1/T1n was studied at room temperature in liquid solutions for dilution levels close to the ones typically used for in vivo studies.

Quantum criticality and inhomogeneous magnetic order in Fe-dopedα−YbAlB4

The intermediate-valent polymorphs $\alpha$- and $\beta$-YbAlB$_4$ exhibit quantum criticality and other novel properties not usually associated with intermediate valence. Iron doping induces quantum criticality in $\alpha$-YbAlB$_4$ and magnetic order in both compounds. We report results of muon spin relaxation ($\mu$SR) experiments in the intermediate-valent alloys $\alpha$-YbAl$_{1-x}$Fe$_x$B$_4$, $x = 0.014$ and 0.25. For $x = 0.014$ we find no evidence for magnetic order down to 25 mK\@. The dynamic muon spin relaxation rate $\lambda_d$ exhibits a power-law temperature dependence $\lambda_d \propto T^{-a}$, $a = 0.40(4)$, in the temperature range 100 mK--2 K, in disagreement with predictions by theories of antiferromagnetic (AFM) or valence quantum critical behavior. For $x = 0.25$, where AFM order develops in the temperature range 7.5--10 K, where we find coexistence of meso- or macroscopically segregated paramagnetic and AFM phases, with considerable disorder in the latter down to 2 K.

Flux pinning and relaxation in FeSe0.5Te0.5 single crystals

A high-quality FeSe0.5Te0.5 single crystal with Tc ∼ 14.8 K was obtained by the self-flux method. We present the temperature dependence of resistivity at various fields and the magnetization hysteresis loops at various temperatures. The upper critical field Hc2(T) with a criterion of 90% ρn follows Hc2(T) = Hc2(0)[1−T/Tc]n. A second peak (namely the fishtail effect) was observed in a large temperature region ranging from 6.5 K to 12 K. According to the theory of Dew-Hughes, we scaled the flux pinning force density for several fixed temperatures and found its maximum position around h = 0.33, here h is the reduced magnetic field. The dynamical relaxation rate Q of the vortices was measured and discussed.

Spin dynamics in Na4−xIr3O8 (x = 0.3 and 0.7) investigated by 23Na NMR and μSR

We report 23Na nuclear magnetic resonance (NMR) and zero-field (ZF) and longitudinal-field (LF) muon spin relaxation (μSR) measurements of the depleted hyperkagome compounds Na4−xIr3O8 (x = 0.3 and 0.7), which undergo an insulator-semimetal transition as a function of x. The 23Na spin-lattice relaxation rates, , follow a T2.5 power law behavior at accessible temperatures of T = 120–350 K. A substantial temperature dependence of indicates the presence of gapped excitations at elevated temperatures through the transition to a semimetallic phase. ZF-μSR results reveal that hole-doping leads to a melting of quasi-static order to a dynamically fluctuating state. The very slow muon depolarization rate which varies hardly with temperature indicates that spins are close to an itinerant limit in the largest doping x = 0.7. The dynamic relaxation rates extracted from the LF-μSR spectra show a three-dimensional diffusive transport. Our combined NMR and μSR results suggest the occurrence of intriguing spin and charge excitations across the insulator-semimetal transition.

Broken time-reversal symmetry in superconductingPr1−xCexPt4Ge12

We report results of zero-field muon spin relaxation experiments on the filled-skutterudite superconductors~Pr$_{1-x}$Ce$_{x}$Pt$_4$Ge$_{12}$, $x = 0$, 0.07, 0.1, and 0.2, to investigate the effect of Ce doping on broken time-reversal symmetry (TRS) in the superconducting state. In these alloys broken TRS is signaled by the onset of a spontaneous static local magnetic field~$B_s$ below the superconducting transition temperature. We find that $B_s$ decreases linearly with $x$ and $\to 0$ at $x \approx 0.4$, close to the concentration above which superconductivity is no longer observed. The (Pr,Ce)Pt$_4$Ge$_{12}$ and isostructural (Pr,La)Os$_4$Sb$_{12}$ alloy series both exhibit superconductivity with broken TRS, and in both the decrease of $B_s$ is proportional to the decrease of Pr concentration. This suggests that Pr-Pr intersite interactions are responsible for the broken TRS\@. The two alloy series differ in that the La-doped alloys are superconducting for all La concentrations, suggesting that in (Pr,Ce)Pt$_4$Ge$_{12}$ pair-breaking by Ce doping suppresses superconductivity. For all $x$ the dynamic muon spin relaxation rate decreases somewhat in the superconducting state. This may be due to Korringa relaxation by conduction electrons, which is reduced by the opening of the superconducting energy gap.

Dynamical friction in a relativistic plasma

The work of Spitzer on dynamical friction in a plasma [L. Spitzer, Jr., Physics of Fully Ionized Gases, 2nd ed. (Wiley, New York, 1962), Chap. 5] is extended to relativistic systems. We derive the force of dynamical friction, diffusion tensor, and test particle relaxation rates for a Maxwellian background in the same form as Trubnikov [B. A. Trubnikov, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 105], enabling high-temperature laboratory and astrophysical plasmas to be modeled in a consistent manner.