Impurity Spin Relaxation Research Articles

Magnetic field noise analyses generated by the interactions between a nitrogen vacancy center diamond and surface and bulk impurities

We investigated the mechanism of magnetic noise due to both surface and bulk impurities. For surface noise, we apply the Langevin method to spin fluctuation theory to calculate the noise for paramagnetic surface impurities absorbed in a thin layer of water. We find that the mechanisms generating noise are spin flip and spin precession which depend on impurity spin relaxation and spin precession time. For the bulk noise, we consider carbon-13 and nitrogen as impurities and employ the correlated-cluster expansion to calculate noise. Carbon-13 noise is a few orders of magnitude larger than nitrogen due to the higher impurity density in the typical NV center diamond system. We also find that the noise in the secular approximation underestimates noise under low applied magnetic field. Overall, the major source of magnetic field noise is spin precession noise, which is more than five orders of magnitude larger than the spin flip noise.

Exploring the anisotropic Kondo model in and out of equilibrium with alkaline-earth atoms

We propose a scheme to realize the Kondo model with tunable anisotropy using alkaline-earth atoms in an optical lattice. The new feature of our setup is Floquet engineering of interactions using time-dependent Zeeman shifts, that can be realized either using state-dependent optical Stark shifts or magnetic fields. The properties of the resulting Kondo model strongly depend on the anisotropy of the ferromagnetic interactions. In particular, easy-plane couplings give rise to Kondo singlet formation even though microscopic interactions are all ferromagnetic. We discuss both equilibrium and dynamical properties of the system that can be measured with ultracold atoms, including the impurity spin susceptibility, the impurity spin relaxation rate, as well as the equilibrium and dynamical spin correlations between the impurity and the ferromagnetic bath atoms. We analyze the non-equilibrium time evolution of the system using a variational non-Gaussian approach, which allows us to explore coherent dynamics over both short and long timescales, as set by the bandwidth and the Kondo singlet formation, respectively. In the quench-type experiments, when the Kondo interaction is suddenly switched on, we find that real-time dynamics shows crossovers reminiscent of poor man's renormalization group flow used to describe equilibrium systems. For bare easy-plane ferromagnetic couplings, this allows us to follow the formation of the Kondo screening cloud as the dynamics crosses over from ferromagnetic to antiferromagnetic behavior. On the other side of the phase diagram, our scheme makes it possible to measure quantum corrections to the well-known Korringa law describing the temperature dependence of the impurity spin relaxation rate. Theoretical results discussed in our paper can be measured using currently available experimental techniques.

Impurity-spin relaxation in a one-dimensional X-Y model

The time evolution of the impurity spin projection in an X-Y chain on the direction of the external magnetic field is considered for a stepwise change in the field acting on the impurity. The mode of relaxation is substantially dependent on the presence of discrete impurity levels in the system, and also on the closeness of these to the edge of the continuum. Low-temperature and high-temperature cases are considered.

Effects of Indirect Coupling upon the Nuclear Spin-Lattice Relaxation in Superconducting Dilute Magnetic Alloys

Host nuclear spin-lattice relaxation associated with the real or virtual excitation of the localized magnetic impurity moment in superconducting dilute magnetic alloys is investigated within the framework of the depairing theory. The relaxation rate due to the real excitation is expected to depend only weakly on the superconductivity, if the drastic change of the impurity spin relaxation time does not occur, but the one due to the virtual excitation is drastically modified in the superconducting state as compared with the normal state.

The magnetic susceptibility of virtual bound state alloys

The static and dynamical longitudinal and transverse magnetic impurity spin susceptibilities of the nondegenerate virtual bound state model are calculated as functions of temperature, magnetic field, virtual level width and for arbitrary separation of the quasibound level from the Fermi surface of an infinite structureless conduction electron band. Within this exactly solvable quantum-mechanical model problem the static spin susceptibilities remain finite at zero temperature and follow power law behaviour for low temperatures; at higher temperatures a Curie-Weiss law is obeyed. The dynamical susceptibilities are shown to exhibit interesting temperature, magnetic field and frequency dependent variation; in particular a continuous transition between quantum-mechanical and classical domains is analytically tractable. The longitudinal resonance lineshape is found to deviate from the Lorentzian Bloch equation form but reduces to such in the classical high-temperature regime. For the transverse absorption spectrum this rate equation description may also be obtained by freezing the fluctuating pseudospin with a strong external magnetic field. The impurity spin relaxation rates are finite and approach a constant at high temperatures.

The de Haas-van Alphen effect in Kondo systems

In Kondo systems, de Haas-van Alphen experiments determine a spin-splitting term in the conduction-electron self-energy. It is shown that for all temperatures and magnetic fields, and in the presence of normal potential scattering from the magnetic impurity, spin-splitting of Landau levels is given exactly with Re Sigma spindown(0)-Re Sigma spinup(0)=cJ(Sz)K Sigma sigma (0) is the conduction-electron self energy at the Fermi level and (Sz)K is the expectation value for the impurity spin including Kondo effects. This equation also applies for both the large-U (Kondo) and small-U limits of the Anderson model, with (Sz)K to (Sz)A for the small-U case. (Sz)K,A does not obey the field and temperature dependence of the Brillouin function, but instead follows the Langevin function. This is so because the Friedel-Anderson impurity d orbitals are populated successively by many electrons during the impurity-spin relaxation time.

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.

63Cu spin lattice relaxation in Cu-Mn and Cu-Cr. Electron spin dynamics

The 63Cu nuclear spin lattice relaxation rate (T1)-1 in Cu-Mn and Cu-Cr dilute alloys, measured between 0.32 and 20K, are interpreted in the light of recent spin diffusion studies done by the authors (1972) in Cu-Mn alloys. It is shown that, the most important impurity contribution to (T1)-1 is through the RKY coupling with the transverse fluctuations of the impurity moment. The impurity spin relaxation rate involved in the NMR data is different from the ESR linewidth and is associated with simple impurity fluctuations.

Retardation effects in the longitudinal spin relaxation in metals

Abstract The longitudinal impurity spin relaxation due to isotropic exchange coupling to the conduction electron spins is calculated as a function of impurity spin, magnetic field, and temperature. For small exchange coupling (nuclear spins) and relaxation rate saturates for low temperatures at a value proportional to the magnetic field. For large coupling constants (electron spins) the relaxation rate passes through a maximum with increasing field. The anomalous behavior is attributed to freezing out of spin flip scattering in a magnetic field at low temperatures.

On the influence of spin-orbit scattering on the Kondo effect

The question of whether spin-orbit interaction of the conduction electrons of dilute magnetic alloys has an influence on the low temperature properties of such alloys is investigated. It is assumed that the spin-orbit interaction is induced by nonmagnetic impurities present in the alloy. In the course of this study, two different models for the interaction between the conduction electrons and the magnetic impurities, thes-d exchange model and the Anderson model, are considered. It is shown that for neither of these models the spin-orbit interaction of the conduction electrons gives rise to a characteristic change in the temperature dependence of the impurity-spin relaxation time and of the electrical resistivity.

Onsager-Zerlegung und Entropieproduktion für einen Defektspin in der linearen Spinkette mitX-Y-Kopplung

The autocorrelation function of an impurity spin in an infinite chain of spins withX-Y-coupling in thermal equilibrium is shown to be an example of “Onsager separation”. This separability ensures that the statistical entropy production associated with the impurity spin relaxation contains a phenomenological part which proves to be always positive.

Onsager-Zerlegung für einen Defektspin in der linearen Spinkette mitX-Y-Kopplung im kritischen Magnetfeld

The autocorrelation function of an impurity spin in an infinite chain of spins withX-Y-coupling moving in a critical magnetic field is shown to be an example of “Onsager separation” with a hydrodynamic branch point singularity. By reason of this type of singularity the hydrodynamic part of the autocorrelation function is longranged in time. It appears that the phenomenological part of the statistical entropy production associated with the impurity spin relaxation in the critical field is positive.

Kondo anomaly of impurity spin resonance linewidth

Suhl's theory of the Kondo effect is extended to calculate the impurity spin relaxation anomaly caused by s-d interactions.

93. Impurity spin relaxation via the conduction electrons in silicon

93. Impurity spin relaxation via the conduction electrons in silicon