Random Local Fields Research Articles

Orientational Ordering in Solid N2-Argon Mixtures: Collective Versus Non-Collective Behavior

Abstract We compare the temperature variation of the local orientaional order parameters and the Edwards-Anderson glass order parameter decduced from available NMR data, With the variations expected for a non-Collective local random quadrupolar field model. The analysis of the experimental results for solid N2-Argon allowy indicates a weak collective behavior and new experiments are suggested to test for true glassy behavior.

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).

On zero-field anisotropic static Kubo-Toyabe relaxation functions

For muons which have thermalized in the allowed stopping sites of a given crystal, zero-field static Kubo-Toyabe spin dynamics is expressed in terms of the crystal frame spherical harmonic coefficients of the local classical random magnetic field distributions associated with each stopping site. The resulting muon spin polarization involves nine observable relaxation functions which are the counter frame spherical tensor expansion coefficients of the second-rank dynamic motion tensor. These relaxation functions can be measured simultaneously using the skewed field technique for the same experimental conditions, that is, with a single apparatus and with a single crystal-counter frame orientation. The local field distributions of, in general, arbitrary symmetry are classical approximations to the magnetic field interactions between the spin of the muon and the spins of the nuclei associated with each site at which the muon has stopped. They are characterized by equating their moments with the quantal moments generated by the quantal magnetic fields. The observable consequences of the anisotropic second-order moments associated with the planar sites of hexagonal crystals are used as an illustration.

Local anisotropy and strain effects in Pd 1− xCo x

Small angle neutron scattering (SANS) and magnetic measurements on annealed and cold worked dilute PdCo alloys show local moment disalignment, with SANS signals proportional to q -4.3 and strong hysteresis effects. In field S AN S anisotropy is not consistent with a simple random local anisotropy field model.

Excitation energies of multilevel tunneling states in the presence of large local strain fields: A possible model for the glassy state.

The density of states, ${P}_{0}$(E), of the elementary excitation energies E is obtained for a single two-level and four-level tunneling state in the presence of a distribution ${P}_{1}$(\ensuremath{\xi}) of random local strain fields \ensuremath{\xi} and a fixed tunneling matrix element \ensuremath{\Delta}. Whereas the two-level states have low-energy excitations only when both \ensuremath{\Delta} and \ensuremath{\xi} are small, the four-level (or six-level) states have very-low-energy excitations, E\ensuremath{\propto}${\ensuremath{\Delta}}^{2}$/\ensuremath{\xi}, even for large values of \ensuremath{\Delta}, provided the strain fields \ensuremath{\xi} are sufficiently large. We thus obtain the unexpected result that the excitation energies become smaller with increasing local strain fields for the multilevel states but not for the two-level states. For the case when ${P}_{1}$(\ensuremath{\xi})\ensuremath{\propto}\ensuremath{\Vert}\ensuremath{\xi}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}k}$ for large \ensuremath{\xi}, the density of the low-energy excitations for the four-level states is ${P}_{0}$(E)\ensuremath{\propto}${E}^{k\mathrm{\ensuremath{-}}2}$ for E\ensuremath{\ll}\ensuremath{\Delta}. For k=2, ${P}_{0}$(E) is a constant for low E for the four-level states. We also show that for a number of physically interesting probability distributions of strain fields ${P}_{0}$(E) is approximately constant for the four-level states but not for the two-level states. In particular we find that the probability for low \ensuremath{\xi} is not relevant in determining the low-temperature thermodynamic properties of the four-level (and six-level) states. The possible significance of our results to the low-temperature thermodynamic properties of glasses is discussed.

Muon-spin relaxation in AuFe and CuMn spin glasses.

Zero- and longitudinal-field muon-spin relaxation (ZF \ensuremath{\mu}SR and LF \ensuremath{\mu}SR) measurements have been applied to dilute-alloy spin glasses AuFe(1.0 and 1.4 at %) and CuMn(1.1, 3, and 5 at. %). A stochastic theory of muon-spin relaxation has been formulated, and an analytic form of zero-field (ZF) muon-spin-relaxation function has been derived to describe the depolarization of muon spins in static, dynamic, and coexisting static and dynamic random local fields from magnetic impurities. The observed experimental results for the muon-spin-relaxation function ${G}_{z}$(t) in all the specimens have been well explained by the model functions based on the present theory. Depolarization of muon spins due to the rapidly fluctuating dynamic local field has been indicated by the ``root-exponential'' shape of ${G}_{z}$(t) observed above the susceptibility-cusp temperature ${T}_{g}$. The spin correlation time ${\ensuremath{\tau}}_{c}$ of Mn (or Fe) moment, deduced from the dynamic depolarization rate of muon spins, shows a rapid change from ${\ensuremath{\tau}}_{c}$\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}12}$ sec at T\ensuremath{\gtrsim}2${T}_{g}$ towards ${\ensuremath{\tau}}_{c}$\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}9}$ sec at T\ensuremath{\sim}${T}_{g}$ in all the specimens. Coexistence of static and dynamic random fields at each muon site has been found by ZF and LF \ensuremath{\mu}SR below ${T}_{g}$. The average amplitude ${\mathrm{scra}}_{s}$ of static random fields, determined precisely by ZF \ensuremath{\mu}SR, attains finite values only below ${T}_{g}$, and increases towards the full amplitude ${\mathrm{scra}}_{0}$ at T=0. ${\mathrm{scra}}_{s}$/${\mathrm{scra}}_{0}$ is proportional to the static polarization of Mn (or Fe) moment, and its temperature dependence has been found to be consistent with a M\"ossbauer-effect study in AuFe. The squared quantity (${\mathrm{scra}}_{s}$/${\mathrm{scra}}_{o}$${)}^{2}$ of ZF \ensuremath{\mu}SR shows good agreement with the static order parameter Q(T) determined by ac-susceptibility (${\ensuremath{\chi}}_{\mathrm{ac})}$ and by neutron-spin-echo (NSE) measurements for cut-off pieces of the same specimen. In view of the fundamental difference of the hyperfine-field--type from the susceptibility-type measurements, this comparison reveals that spin freezing is characterized by a rather homogeneous amplitude of static spin polarization among different spins in spin glasses, i.e., ``homogeneous freezing.'' The combined results of ZF \ensuremath{\mu}SR, ${\ensuremath{\chi}}_{\mathrm{ac}}$ and NSE measurements in AuFe and CuMn spin glasses have demonstrated rapid slowing down of impurity spin fluctuations above ${T}_{g}$, and the appearance of long-time, persisting static spin polarization below ${T}_{g}$.

Zero-fieldμSR in a spin glass CuMn (1.1 at.%): precise measurement of static and dynamic effects belowT g

Zero-field muon spin relaxation is observed in a spin glassCuMn (1.1 at.%) using surface muon beam. The static amplitude of random local field onμ+ is obtained belowTg, and the static spin polarization of Mn moments is found to set on belowTg.

The dynamical behavior of a small probe molecule dissolved in a nematic liquid crystal studied by NMR

The dynamical behavior of a small probe molecule CH3CN dissolved in a nematic liquid crystal is studied by NMR relaxation measurements on 1H, 13C, and 14N nuclei measured at six different field strengths. The results show a strong frequency dependent relaxation behavior that can be described by order director fluctuations in the nematic solvent. A major contribution from slowly relaxing local structures, as introduced by Polnaszek and Freed, is unlikely. Values for the rotational anisotropy, random local field contributions to the relaxation of the 13C and 1H nuclei, and order director fluctuation parameters are given. A comparison has been made with other studies of analogous systems and the necessity is demonstrated of extended frequency dependent measurements for a complete description of the dynamical processes involved.

Dynamics of disordered spin systems studied by zero- and longitudinal-field μSR: I. (FeTiO3)88(Fe2O3)12

Zero-field muon spin relaxation measurement in a spin glass (FeTiO3)88(Fe2O3)12 exhibited a gradual slowing down of dynamical fluctuation of Fe moments between 170 K >T > 50 K, while an onset of static random local fields starts around T ≈ 30 K. Different sharpness of the temperature dependence of muon relaxation in different spin glasses is also pointed out.

Tricritical line in a transverse Ising model with random local fields

A transverse Ising model, in presence of a local quenched random longitudinal field is studied in the mean-field approximation. The phase diagram of the model exhibits a line of tricritical points separating the surfaces of second and first order phase transitions.

Relationship of the inhomogeneous broadenings in the triplet state optical and ODMR spectra of NaNO2/Ag+

The triplet state optical and ODMR spectra associated with a perturbed NO−2 anion in crystals of NaNO2 doped with AgNO2 are shown to be inhomogeneously broadened at T ≲ 4.2 K. The energies of the trap triplet state D ± E ODMR transitions depend linearly on the optical detector energy monitoring at ≲ 1 cm−1 optical resolution across a phosphorescence vibronic line whose width is ≲ 5 cm−1. The observed dimensionless slopes are ≈10−4. The corresponding ODMR linewidths are a minimum detecting at the center of the optical line and increase several-fold detecting in the wings of the optical line. A simplified model is presented, based on perturbations by random local electric fields, which accounts for the major observations. The coupling coefficients to the electric field (dipole moment changes) were independently determined from the optical and ODMR Stark shifts in an external electric field, and these appear consistent with the observed slopes for the variation of the ODMR energies with optical detector energy. The origin of the non-zero coupling coefficients for the ODMR transitions is discussed in terms of the spin—orbit interactions in the trap.

Random field effects in disordered anisotropic antiferromagnets

A uniform magnetic field is shown to generate random local fields in uniaxially anisotropic antiferromagnets with random exchange interactions. This leads to a stronger divergence of the temperature derivative of the static susceptibility even at zero field, and to a drastic change in the critical exponents at the Ising-like antiferromagnetic transition as well as at the tricritical or bicritical points occurring at finite fields.

Effect of slow molecular motion on damping of transverse nuclear magnetization in amorphous polymers

The NMR pulse method was used to study the variation of the form of damping of transverse magnetization (DTM) in polybutadiene, polyisobutylene and natural rubber in the range of glass temperature of polymer up to 200° and in polyethyleneglycol at 75°, according to molecular weight. To describe the relations derived a simple model was introduced, in which relaxation was caused by random local fields, these fields having two components—a rapid and a slow fluctuation component. It is assumed furthermore, that fluctuations are Gaussian random Markoff processes. The ratios derived give a satisfactory description of all experimental curves of DTM.

On the character of local electric fields in amorphous semiconductors

On the basis of the agreement of calculated and measured parameters of some amorphous semiconductors, an argument is stated in favour of the central-symmetric type of random local electric fields. A possible mechanism of the transport of electrons is discussed.

Effects of random local magnetic fields in the ising model (S = 1, 3/2)

Effects of random local magnetic fields in the ising model (S = 1, 3/2)

The electric susceptibility and specific heat of praseodymium magnesium nitrate

The zero-field splittings of the praseodymium non-Kramers ground state doublet in PrMN have been studied by specific heat and electric susceptibility measurements down to 0.1K. The electric dipole moment of the Pr ion in the plane perpendicular to the three fold symmetry axis was found to be 0.73*10-31 C m, much too small to provide significant electric dipole-dipole interactions between Pr ions. The zero-field splittings are attributed to random local fields due to crystal imperfections, but the susceptibility data could not be well fitted with a gaussian distribution. Instead, satisfactory agreement was obtained with a Holtsmark distribution, as expected for the local fields due to a random configuration of charged defects. The conclusions are in broad agreement with those obtained in EPR studies by Sells and Bloor (1976). The magnitudes of the splittings ( approximately 0.1 cm-1) imply the suppression of long-range order by random local fields.

Magnetic anisotropy in amorphous metals

Abstract A model hamiltonian incorporating random local crystal fields, and appropriate to the description of the magnetic properties of amorphous rare-earth transition metal alloys [5], has recently been extended to describe a possible “spin-glass-like” phase in these materials [6]. We propose that a model hamiltonian of similar form can be derived for amorphous metals without localized spins, and for which the magnetic anisotropy is due to the spin-orbit interaction. We suggest that the magnitude of such anisotropy may be large enough to explain, for example [1] the anomalous properties of amorphous YFe2 in terms of a “spin-glass-like” ordering. Discussion of this alloy was specifically outside the scope of the older model [5].

Effects of External Magnetic Fields on Optical Spin Orientation in GaSe

Optical spin orientation experiments have been made in GaSe under longitudinal and transverse magnetic fields at 4.2 K. From the results, the lifetime and the spin relaxation time of the direct exciton are determined to be of the order of 10 -9 s at zero magnetic field. The polarized luminescence spectrum due to the difference of the thermalized populations and that due to the spin memory have been obtained separately under longitudinal magnetic field. This makes it possible for the first time to determine the depolarization factor due to the origins other than the spin relaxation in the emitting state and also the correlation time of the random local field modulation which is responsible for the spin relaxation. Theoretical magnetic field dependence of the degree of polarization of luminescence is derived and compared with experiments for the free exciton line.

Generalized Locator‐Coherent‐Potential Approach to Ferromag‐netic Systems with Random Local Magnetic Fields and Moments

AbstractThe locator formulation of the coherent‐potential approximation (CPA) is generalized and applied to a Hamiltonian with diagonal and off‐diagonal disorder where the latter comprises additional terms of the type a and ajak. The random variables can take an arbitrary number of values. The off‐diagonal elements are assumed to be separable. The resulting CPA‐equations are represented by relations between 2 × 2‐matrices. The formalism is applied in particular to the problem of inhomogeneous broadening of ferromagnetic resonance lines in polycrystalline materials. Taking into account the usual simplifications, a transcendental equation for the reduced, complex frequency shift is derived. The used approach comprises the results previously obtained by other methods.

Ultrasonic attenuation due to the neutral acceptor indium in silicon

We have measured the temperature and frequency dependencies of the u.s.-attenuation of a longitudinal u.s. wave in [111] excited by an evaporated CdS-transducer in the frequency range 0.38 to 4 GHz in silicon doped with the deep acceptor indium (p = 5. 1015 cm−3) for comparison with the results of the attenuation measurements in GaAs due to the deep acceptor Mn /1/ /2/. There we have seen that this deep acceptor ground state may be characterized by a distribution of splittings δ of the two Kramers levels due to random local fields and with a level 3 meV above, which may be connected to a dynamic Jahn Teller effect.