Zero-field Relaxation Rate Research Articles

Nodal Superconducting Gap Structure in the Quasi-One-Dimensional Cs2Cr3As3 Investigated Using μSR Measurements

The superconducting ground state of the newly discovered superconductor Cs$_2$Cr$_3$As$_3$ with a quasi-one-dimensional crystal structure ($T_{\bf c}\sim$ 2.1(1) K) has been investigated using magnetization and muon-spin relaxation or rotation ($\mu$SR), both zero-field (ZF) and transverse-field (TF), measurements. Our ZF $\mu$SR measurements reveal the presence of spin fluctuations below 4 K and the ZF relaxation rate ($\lambda$) shows enhancement below $T_{\bf c}\sim$ 2.1 K, which might indicate that the superconducting state is unconventional. This observation suggests that the electrons are paired via unconventional channels such as spin fluctuations, as proposed on the basis of theoretical models. Our analysis of the TF $\mu$SR results shows that the temperature dependence of the superfluid density is fitted better with a nodal gap structure than an isotropic s-wave model for the superconducting gap. The observation of a nodal gap in Cs$_2$Cr$_3$As$_3$ is consistent with that observed in the isostructural K$_2$Cr$_3$As$_3$ compound through TF $\mu$SR measurements. Furthermore, from our TF $\mu$SR study we have estimated the magnetic penetration depth $\lambda_{\mathrm{L}}$$(0)$ = 954 nm, superconducting carrier density $n_s = 4.98 \times 10^{26}~ $m$^{-3}$, and carrier's effective-mass enhancement $m^*$ = 1.61m$_{e}$.

Paramagnetic relaxation in anisotropic materials in zero and weak constant fields

Paramagnetic relaxation in strongly anisotropic materials is analytically investigated in zero and weak constant magnetic fields. The objectives of the microscopic analytical investigation are (i) the weak-field electron paramagnetic resonance (EPR) linewidth and (ii) the electron spin relaxation rates given by a calorimetric Gorter type experiment in the zero constant field at the arbitrary low-frequency field directions, respectively, to the sample crystallographic axes. The EPR linewidth is calculated under the suggestion of its spin-phonon nature at the one-phonon mechanism of the spin-lattice relaxation in the case of the strong isotropic exchange interaction for the arbitrary direction Z of the constant magnetic field. The EPR linewidth is presented as the half sum of the zero-field relaxation rates, measured by the Gorter experiment with the low-frequency field oriented along the X, Y axes. With the help of the macroscopic consideration, it is shown that the zero-field relaxation rates describe the relaxation of the X and Y magnetization components in a zero or weak constant magnetic field. The relaxation rates of the magnetizations created along a,b,c crystallographic axes by a low-frequency field in a Gorter type experiment follow the obtained expressions in the particular cases and are in the experimentally confirmed relations with the EPR linewidth.

Charge/orbital and antiferromagnetic ordering in LaSr 2Mn 2O 7

First μSR results for the bilayered manganite LaSr 2Mn 2O 7 are reported. We have studied the effect on the relaxation rates of the charge/orbital and antiferromagnetic ordering. Between the charge/orbital ordering temperature ( T CO=220 K) and the antiferromagnetic transition temperature ( T N=170 K), unexpected hysteretic behaviour and field history dependence of the relaxation rates were observed. The field history dependence is observed by increased zero-field relaxation rates after switching the external field on and off again. These effects suggest field induced and residual magnetic correlations above T N which are presumably related to the formation of magneto-elastic polarons. No precession signal was observed for T< T N, the only signature of the magnetic transition being the almost complete loss of asymmetry reflecting the wide field distribution at the muon site.

μ+SR observation of magnetic ordering and non-Fermi liquid scaling in CeCoGe 1.8Si 1.2

Muon spin relaxation investigations of CeCoGe 1.8Si 1.2, which is close to a quantum critical concentration, show magnetic ordering in a volume fraction of ∼50% with a transition temperature of ∼0.5 K. The zero-field relaxation rate λ f of this fraction exhibits a power law of temperatures between 0.7 and 1 K, where the specific heat to temperature ratio ( C/ T) scales with log T , and possibly demonstrate non-Fermi liquid (NFL) scaling. We suggest that the disorder which introduces inhomogenities in Kondo temperatures and RKKY coupling strengths of Ce ions as a possible origin of NFL behaviour in this alloy.

A μ + SR study of the magnetic properties of ferritin

We present a study of the magnetic properties of the superparamagnetic ferritin system by employing zero‐field (ZF) and longitudinal‐field (LF) μ+SR measurements. Two μ+ fractions with different depolarisation behaviour are detected, one arising from muons stopped in the organic shell and one from muons stopped in the mineral core. The freezing of the superparamagnetic moments is evident in the temperature evolution of the ZF relaxation rates of both fractions. It occurs gradually below \approx 60\ K and is essentially complete at \approx 11\ K. The results are consistent with a distribution of blocking temperatures which in turn reflects the distribution of core sizes.

Evidence for static ultrasmall-moment magnetism in CeRu 2Si 2

We report on zero-, transverse- and longitudinal-field μ +SR studies on a high-quality single crystal of CeRu 2Si 2. The development of some sort of static magnetism (Ce-moment ≅0.001μ B) below 1.5 K is observed in the zero-field relaxation rate. Measurements in longitudinal fields demonstrate the static character of this magnetism and reveal in addition the presence of dynamic 4f spin fluctuations (also observed in the transverse-field spectra) which coexist with the static magnetism below 1.5 K.

Phenomenological theory of the superconductivity phase diagram of U1-xThx

Possible phenomenological theories to describe the phase diagram of ${\mathrm{U}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Th}}_{\mathrm{x}}$${\mathrm{Be}}_{13}$ based on a crossing of two different types of anisotropic superconductivity at x\ensuremath{\approxeq}0.018 are examined. In this description the second transition for xg0.018 is interpreted as a further superconducting transition. It is shown that measurements of the critical magnetic field support this assumption. The effects of uniform pressure and the specific-heat measurements are qualitatively in a good agreement with these theories. The large peak in the ultrasonic attenuation in the low-temperature phase in the region xg0.018 is explained by a dissipative domain-wall motion, induced by the sound wave, which in this case couples in both [001] and [111] directions. The theory predicts nonunitary superconducting states below the second phase transition. Such states have a finite local spin polarization in each unit cell, which leads to an explanation of zero-field relaxation rate data in muon-spin-rotation experiments.

Magnetic field penetration depth of La1.85Sr0.15CuO4 measured by muon spin relaxation.

Muon-spin-relaxation measurements have been performed on a high-${T}_{c}$ superconductor (${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$)${\mathrm{CuO}}_{4}$. In an external transverse magnetic field of 500 G, a magnetic field penetration depth \ensuremath{\lambda}=2000 A\r{} at T=10 K has been determined from the muon-spin-relaxation rate which increased with decreasing temperature below ${T}_{c}$. From this \ensuremath{\lambda} and the Pauli susceptibility we estimate the superconducting carrier density to be n=3\ifmmode\times\else\texttimes\fi{}${10}^{21}$/${\mathrm{cm}}^{3}$. The zero-field relaxation rates above and below ${T}_{c}$ were equal, which suggests that the superconducting state in this sample is not associated with detectable static magnetic ordering.

Muon Knight shift and zero-field relaxation in (U,Th)Be13

We report μ+ zero-field relaxation and Knight shift studies of the heavy-fermion superconductors U1−xThxBe13, x=0 and 0.033. The Knight shift in UBe13 shows a strong decrease as the temperature is reduced in the superconducting state, unlike U0.967Th0.033Be13 in which the shift remains at about the normal state value. If the superconducting state in UBe13 has odd-parity, the decrease of Kμ below Tc suggests that the order parameter is pinned to the lattice. Either spin-orbit scattering or the existence of two distinct superconducting states with different spin susceptibilities in the (U,Th)Be13 system would explain the differences observed in the Th-doped and pure UBe13 materials. The latter hypothesis would exclude conventional BCS superconductivity. No evidence for magnetic order is seen in the zero-field relaxation rate for either material down to 0.3 K.

Slowing Down of Rubidium-Induced Nuclear Spin Relaxation ofXe129Gas in a Magnetic Field

The longitudinal relaxation rate of $^{129}\mathrm{Xe}$ nuclear spins slows down substantially in an external magnetic field of about 100 G. From an analysis of the magnetic slowing down and of the dependence of the zero-field relaxation rates on the third-body pressure, the authors have deduced the magnitudes of the spin-rotation and spin-exchange interactions in the ${\mathrm{Rb}}^{129}$Xe molecule, as well as the formation and breakup rates of RbXe in ${\mathrm{N}}_{2}$ gas and the dissociation constant of RbXe. The magnetic slowing down shows directly that binary collisions contribute no more than a few percent to the relaxation rates.

On the longitudinal static and dynamic susceptibility of spin-1/2 Kondo systems

The impurity spin polarization, static susceptibility, and longitudinal impurity spin relaxation rate are calculated for thes-d model as function of temperature and magnetic field for ferromagnetic and antiferromagnetic exchange coupling. The thermodynamic functions and the dynamical susceptibility are obtained from the impurity relaxation spectrum, which is approximated by taking into account the infrared-like singularities. For antiferromagnetic coupling the zero-field susceptibility obeys a Curie-Weiss law1/χ∼4.6(T+θ) for high and intermediate temperatures and it approaches the finite value1/χ∼3.8θ for zero temperature. The zero-field relaxation rate is much larger than the Korringa value; it decreases with temperature and approaches the nonzero value1/T1∼1.2θ for zero temperature. The relaxation rate decreases with increasing field. The results for the spin polarization agree well with the experimental data for the Cu:Fe alloy.

Zero-field relaxation and low-field resonance in MnF 2

The zero-field relaxation rate in MnF 2 has been determined as a function of temperature (63–77 K) from magnetic absorption measurements with r.f. field ‖ c and ⊥ c axis. In the first case a weak temperature dependence is found, whereas the latter exhibits critical behaviour. Additional information about the relaxation rates has been obtained from experiments in moderate static fields. A theoretical approach is given which satisfactorily describes the influence of a static field perpendicular to the r.f. field in terms of zero-field relaxation processes. Combining direct and indirect evidence on the r.f. ⊥ c axis case the critical exponent of the relaxation time is found to be -0.65 ± 0.03 for 0.01 <−1+ T T N <0.2 .