Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays

Stretched exponential relaxation of a quantity n versus time t according to n = n_0 exp[-(lambda* t)^beta] is ubiquitous in many research fields, where lambda* is a characteristic relaxation rate and the stretching exponent beta is in the range 0 < beta < 1. Here we consider systems in which the stretched exponential relaxation arises from the global relaxation of a system containing independently exponentially relaxing species with a probability distribution P(lambda/lambda*,beta) of relaxation rates lambda. We study the properties of P(lambda/lambda*,beta) and their dependence on beta. Physical interpretations of lambda* and beta, derived from consideration of P(lambda/lambda*,beta) and its moments, are discussed.Comment: 8 pages, 10 figures; version to be published in Phys. Rev.

Magnetic Susceptibility of Collinear and Noncollinear Heisenberg Antiferromagnets

Predictions of the anisotropic magnetic susceptibility chi below the antiferromagnetic (AFM) ordering temperatures TN of local moment Heisenberg AFMs have been made previously using molecular field theory (MFT) but are very limited in their applicability. Here a MFT calculation of chi(T<=TN) is presented for a wide variety of collinear and noncollinear Heisenberg AFMs containing identical crystallographically equivalent spins without recourse to magnetic sublattices. The results are expressed in terms of directly measurable experimental parameters and are fitted with no adjustable parameters to experimental chi(T<=TN) data from the literature for several collinear and noncollinear AFMs. The influence of spin correlations and fluctuations beyond MFT is quantified by the deviation of the theory from the data. The origin of the universal chi(T<=TN) observed for triangular lattice AFMs exhibiting coplanar noncollinear 120 degree AFM ordering is clarified.Comment: 5 pages, 5 figure

Antiferromagnetism in EuCu2As2 and EuCu1.82Sb2 Single Crystals

Single crystals of EuCu2As2 and EuCu2Sb2 were grown from CuAs and CuSb self-flux, respectively. The crystallographic, magnetic, thermal and electronic transport properties of the single crystals were investigated by room-temperature x-ray diffraction (XRD), magnetic susceptibility \chi versus temperature T, isothermal magnetization M versus magnetic field H, specific heat Cp(T) and electrical resistivity \rho(T) measurements. EuCu2As2 crystallizes in the body-centered tetragonal ThCr2Si2-type structure (space group I4/mmm), whereas EuCu2Sb2 crystallizes in the related primitive tetragonal CaBe2Ge2-type structure (space group P4/nmm). The energy-dispersive x-ray spectroscopy and XRD data for the EuCu2Sb2 crystals showed the presence of vacancies on the Cu sites, yielding the actual composition EuCu1.82Sb2. The \rho(T) and Cp(T) data reveal metallic character for both EuCu2As2 and EuCu1.82Sb2. Antiferromagnetic (AFM) ordering is indicated from the \chi(T), Cp(T), and \rho(T) data for both EuCu2As2 (T_N = 17.5 K) and EuCu1.82Sb2 (T_N = 5.1 K). In EuCu1.82Sb2, the ordered-state \chi(T) and M(H) data suggest either a collinear A-type AFM ordering of Eu+2 spins S=7/2 or a planar noncollinear AFM structure, with the ordered moments oriented in the tetragonal ab plane in either case. This ordered-moment orientation for the A-type AFM is consistent with calculations with magnetic dipole interactions. The anisotropic \chi(T) and isothermal M(H) data for EuCu2As2, also containing Eu+2 spins S=7/2, strongly deviate from the predictions of molecular field theory for collinear AFM ordering and the AFM structure appears to be both noncollinear and noncoplanar.Comment: 21 pages, 22 figures, 4 Table

Physical properties of EuPd2As2 single crystals

The physical properties of self-flux grown EuPd2As2 single crystals have been investigated by magnetization M, magnetic susceptibility chi, specific heat Cp, and electrical resistivity rho measurements versus temperature T and magnetic field H. The crystal structure was determined by powder x-ray diffraction measurements, which confirmed the ThCr2Si2-type body-centered tetragonal structure (space group I4/mmm) reported previously. The rho(T) data indicate that state of EuPd2As2 is metallic. Long-range antiferromagnetic (AFM) ordering is apparent from the chi(T), Cp(T), and rho(T) measurements. For H \parallel c the chi(T) indicates two transitions at TN1 = 11.0 K and TN2 = 5.5 K, whereas for H \perp c only one transition is observed at TN1 = 11.0 K. Between TN1 and TN2 the anisotropic chi(T) data suggest a planar noncollinear AFM structure, whereas at T < TN2 the chi(T) and M(H,T) data suggest a spin reorientation transition in which equal numbers of spins cant in opposite directions out of the ab plane. We estimate the critical field at 2 K at which all Eu moments become aligned with the field to be about 22 T. The magnetic entropy at 25 K estimated from the Cp(T) measurements is about $11\%$ smaller than expected, possibly due to an inaccuracy in the lattice heat capacity contribution. An upturn in rho at T < TN1 suggests superzone energy gap formation below TN1. This behavior of rho(T < TN1) is not sensitive to applied magnetic fields up to H = 12 T.Comment: 11 pages, 10 figures, 2 tables and 52 references; To appear in J. Phys.: Condens. Matte

Metallic behavior induced by potassium doping of the trigonal antiferromagnetic insulator EuMn2As2

We report magnetic susceptibility \chi, isothermal magnetization M, heat capacity C_p and electrical resistivity \rho measurements on undoped EuMn2As2 and K-doped Eu0.96K0.04Mn2As2 and Eu0.93K0.07Mn2As2 single crystals with the trigonal CaAl2Si2-type structure as a function of temperature T and magnetic field H. EuMn2As2 has an insulating ground state with an activation energy of 52 meV and exhibits antiferromagnetic (AFM) ordering of the Eu+2 spins S=7/2 at T_N1 = 15 K from C_p(T) and \chi(T) data with a likely spin-reorientation transition at T_N2 = 5.0 K. The Mn+2 3d5 spins-5/2 exhibit AFM ordering at T_N = 142 K from all three types of measurements. The M(H) isotherm and \chi(T) data indicate that the Eu AFM structure is both noncollinear and noncoplanar. The AFM structure of the Mn spins is also unclear. A 4% substitution of K for Eu in Eu0.96K0.04Mn2As2 is sufficient to induce a metallic ground state. Evidence is found for a difference in the AFM structure of the Eu moments in the metallic crystals from that of undoped EuMn2As2 versus both T and H. For metallic Eu0.96K0.04Mn2As2 and Eu0.93K0.07Mn2As2, an anomalous S-shape T dependence of \rho related to the Mn magnetism is found. Upon cooling from 200 K, \rho exhibits a strong negative curvature, reaches maximum positive slope at the Mn T_N ~ 150 K, and then continues to decrease but more slowly below T_N. This suggests that dynamic short-range AFM order of the Mn spins above the Mn T_N strongly suppresses the resistivity, contrary to the conventional decrease of \rho that is only observed upon cooling below T_N of an antiferromagnet.Comment: 21 pages, 22 figures, 4 Table