Session A32: Disordered Magnetic Materials

Transport in strongly disordered classical spin chains

We present a numerical study of diffusion of energy at high temperature through strongly disordered arrays of interacting classicals spins with Hamiltonian dynamics. We find that quenched randomness strongly supresses transport, with diffusion constant apparently becoming smaller than any power of spin-spin interaction rescaled by randomness. We have looked for but not found signs of a classical many-body localization transition at any finite strength of disorder.   

Ferromagnetism in Melt-spun Gd$_{0.946}$Fe$_{0.054}$

The ac susceptibility and dc magnetization at various temperatures have been measured for a melt-spun Gd$_{0.946}$ Fe$_{0.054}$ alloy. The grain size was $\approx $100 nm. A sharp paramagnetic-to-ferromagnetic transition was observed at a temperature close to that of pure Gd. Effective critical exponents and the critical temperature $T_{C}$ were extracted by using modified Arrott plots and Kouvel-Fisher analysis. The values obtained were \textit{$\beta $}$_{eff}$ = 0.398 $\pm $ 0.004, \textit{$\gamma $}$_{ eff}$ = 1.24 $\pm $ 0.02, \textit{$\delta $}$_{ eff}$ = 3.83 $\pm $ 0.05, and $T_{C}$ = 290.25 $\pm $ 0.17 K. These exponent values do not satisfy the Widom scaling relation \textit{$\beta \delta $ }= (\textit{$\beta $}+\textit{$\gamma $}). The \textit{$\beta $}$_{eff}$ and \textit{$\gamma $}$_{eff}$ values for ms-Gd$_{0.946}$ Fe$_{0.054}$ are similar to those obtained for pure Gd in the same temperature interval around $T_{C}$. This is in consonance with x-ray microanalysis measurements indicating that the grains are nearly pure Gd. The lower-than-expected value of \textit{$\delta $}$_{eff}$\textit{${\rm g}$ }may be due to the effect of increased anisotropy due to the presence of Fe in the grain-boundary regions.   

Observation of spin-wave mediated Altshuler-Aronov and weak localization corrections to the conductivity in thin films of gadolinium

We present a study of quantum corrections to the conductivity tensor of thin ferromagnetic gadolinium films. Using the sheet resistance as a measure of disorder, \textit{in situ} magnetotransport studies were performed on a series of gadolinium films deposited onto sapphire substrates having sheet resistance $R_{0 }\equiv $~$R_{xx}$ (5K) varying over the range 428~$\Omega $ ($\sim $135{\AA}) to 4011 $\Omega $ ($\sim $35 {\AA}). For temperatures $T$~$<$~30 K and $R_{0} \quad <$ 4011 $\Omega $, we observe the simultaneous presence of two types of quantum correction to the Drude conductivity, $\sigma =\sigma _{Drude} +\Delta \sigma _{SpinWaveMediated} +\Delta \sigma _{WL} $. The characteristic feature of the first correction is an approximately linear increase with temperature of conductivity, and we attribute this as a spin-wave mediated Altshuler-Aronov correction to conductivity. The second correction to the Drude conductivity comes from weak localization, with a characteristic logarithmic temperature dependence of conductivity with a prefactor ${e^2} \mathord{\left/ {\vphantom {{e^2} {2\pi ^2\hbar }}} \right. \kern-\nulldelimiterspace} {2\pi ^2\hbar }$ in 2D. We observe a breakdown of this behavior at a sheet resistance $R_{0}$ =4011 $\Omega $, which is very close to the quantum of resistance, $\hbar \mathord{\left/ {\vphantom {\hbar {e^2\approx 4100\Omega }}} \right. \kern-\nulldelimiterspace} {e^2\approx 4100\Omega }$.   

Monte Carlo study of the three-dimensional Coulomb glass

The memory and hysteresis effects found in strongly-disordered electron systems can be explained by the existence of a glassy phase, the Coulomb glass. Efros and Shklovskii have predicted the emergence of a soft Coulomb gap, resulting from the long-range interactions between the localized electrons. However, the relationship between the soft Coulomb gap in the density of states and the electron's glassy behavior has been a long-standing unresolved question. Only recently has it been surmised within the framework of a mean field theory that the disordered electron system undergoes a replica symmetry breaking transition at a finite temperature, similar to the Sherrington-Kirkpatrick model of spin glasses. Because it is not clear, however, whether the transition persists beyond the mean-field approximation, we study in detail the critical behavior and the shape of the Coulomb gap in three space dimensions using Monte Carlo methods. Furthermore, we compare our results for the (random-energy) Coulomb glass model to previous results on a random lattice version of the model. Since these models possess different symmetries, the equivalence of the phase diagrams is far from obvious, contrary to previous claims.   

Reentrant spin-glass behavior and enhanced Curie temperature in epitaxial MnSi

We grew single crystal MnSi(111) thin films on Si(111) substrates by molecular beam epitaxy. The 3{\%} lattice mismatch created an in-plane tensile strain of $\varepsilon _{\vert \vert }$ = 0.005 $\pm $ 0.001, as measured by transmission electron microscopy, and induced an out-of-plane compressive strain $\varepsilon _{\bot }$= -0.0033 $\pm $ 0.0001, as determined by x-ray diffraction. The MnSi(111) films displayed two magnetic phases. The first transition from a paramagnetic phase to a phase with long range magnetic order occurs with an enhanced Curie temperature T$_{C}$ = 40 K as compared to bulk MnSi, which develops helical magnetic structure below T$_{C}$ = 29.5~K. This increase in T$_{C}$ can be explained by an in-plane strain. A second phase transition to spin glass, below T$_{f}$ = 35 K, maybe due to geometric frustration created by the compressive out-of-plain strain. We propose a relationship between the reentrant spin-glass behavior and the partial magnetic order reported for bulk MnSi under pressure.   

Dynamical behavior of spin clusters in La$_{1-x}$Sr$_{x}$CoO$_{3}$

Previous work has provided evidence for magnetic glassy behavior in the hole-doped cobaltite system La$_{1-x}$Sr$_{x}$CoO$_{3 }$(LSCO). Models proposed to describe the interesting and unusual magneto-transport properties of LSCO involve hole-rich clusters in a hole-poor matrix. The glassy properties, which are not well understood, have variously been interpreted in terms of spin glass and cluster glass components. The present $^{139}$La NMR spectral lineshape measurements on single crystal LSCO, that map the hyperfine field distribution in the x$-T$ plane, confirm the presence of magnetic clusters, identified as spin polarons, and provide a phase inhomogeneity diagram. NMR relaxation rates have been used to probe the dynamical behavior of the system at the nanoscale level in macroscopically insulating and metallic samples as a function of temperature in the range 4-280 K. For x less than the metal-insulator critical concentration x$_{C }$= 0.17 evidence has been obtained for two classes of glassy component with different characteristic correlation time distributions and freezing temperatures. The magnetic glass properties persist above x$_{C}$. A spin polaron model is used to explain the results.   

Local field distributions in spin glasses

Numerical results for the local field distributions of a family of Ising spin-glass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range power-law-modulated interactions that interpolate between a nearest-neighbor Edwards-Anderson system in one dimension and the infinite-range Sherrington-Kirkpatrick model. Remarkably, the local field distributions only depend weakly on the range of the interactions and the dimensionality and show strong similarities except for near zero local field.   

The Antiferromagnetic SO(3) Heisenberg Quantum Spin-Glass with Short Range Interaction

We study the quenched disordered magnetic system which is obtained from the 2D SO(3) quantum Heisenberg model, with nearest neighbors interaction, by taking the random values of the exchange couplings as given by a Gaussian probability distribution centered in a value of the coupling that corresponds to anti-ferromagnetic order. Using coherent states, we map this system onto a generalization of the SO(3) nonlinear sigma model, containing different flavors, which correspond to the replicas and a quartic interaction. We then integrate over the transverse components and perform a mean-field calculation of the free energy density in the limit of zero replicas. The phase diagram of the system is then obtained and shows a critical curve, starting at a quantum critical point at T=0 separating a paramagnetic from a spin-glass phase. The stability of the phases is demonstrated by an analysis of the Hessian matrix of the free energy.   

On the ordering of Ising spin glasses in a field

We study the existence of a spin-glass phase in a magnetic field in three space dimensions using a novel approach where the Monte Carlo simulations are performed along a nontrivial path in the magnetic field--temperature plane which must cross any putative de Almeida-Thouless line. The method is first tested on the mean-field version of the Edwards-Anderson Ising spin glass on a Bethe lattice where we compute analytically the instability line that separates the spin glass from the paramagnetic state. While the de Almeida-Thouless line is clearly reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model. We thus conclude that there is no such instability line for three-dimensional short-range Ising spin glasses.   

Spin glass of a diluted Ising dipolar system

The diluted dipolar Ising system has been regarded as a standard example which exhibits spin glass properties. Recent studies have challenged the existence of spin glass phase transition in one of the materials in this category, $LiHo_{x}Y_{1-x}F_{4}$. Using Monte Carlo simulations, we calculate various quantities to address the current controversy of a possible spin glass phase transition in this material. Beside the conventional method to locate the spin glass transition by observing the crossing of Binder ratios of magnetization moments, another crucial probe for the nature of spin glass, order parameter fluctuations, is studied via the so-called fluctuation sensitive parameters. Crossing is observed in the Binder ratio of overlap order parameter, and non-trivial structures of overlap order parameter are obtained at low temperature.   

Nonlinear and ac Susceptibility of the Dilute Ising Magnet LiHo$_x$Y$_{1-x}$F$_4$

Recent work has called into question the existence of a spin glass transition in the dilute dipolar Ising magnet LiHo$_x$Y$_{1-x}$F$_4$ [1]. Other work has suggested that there is an exotic spin liquid phase found at a Ho concentration of $x = 0.045$ [2]. In order to carefully study the dynamics of this system, we have put together a SQUID magnetometer which allows for measurements of ac susceptibility and nonlinear susceptibility over a large frequency range. We present results from measurements on single crystals of LiHo$_x$Y$_{1-x}$F$_4$, particularly on an $x = 0.045$ sample, in an attempt to either reproduce the exotic ``anti-glass'' physics that was previously observed or to detect a spin glass transition. [1] P. E. Jonnson et al. PRL 98, 256403 (2007) [2] S. Ghosh et al. Science 296, 2195 (2002)   

Low-temperature properties of the dilute dipolar magnet LiHo$_x$Y$_{1-x}$F$_4$

The phase diagram of the rare-earth compound LiHo$_x$Y$_{1-x}$F$_4$ is considered as a function of dilution. At low temperatures the material is a good realization of a dipolar Ising magnet. The net magnetization vanishes at high dilution and the glassy behavior that ensues has several interesting features, including a proposed anti-glass phase and anomalous peaks in the specific heat. In this talk we will show results obtained with Monte Carlo techniques and compare them with recent experimental data.   

Quantum and Classical Glass Transitions in $\mathrm{LiHo}_x\mathrm{Y}_{1-x}\mathrm{F}_4$

When performed in the proper low field, low frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in transverse field, $\mathrm{LiHo}_x\mathrm{Y}_{1-x}\mathrm{F}_4$, prove the existence of a spin glass transition in both the classical and quantum limits for x = 0.167 and 0.198. The classical behavior tracks for the two concentrations, but the quantum glasses differ because of the competing effects of entangled spins and local random fields.   

Study of the dipolar coupled Ising system $\mathrm{LiHo_xY_{1-x}F_4}$ using muon spin relaxation.

In $\mathrm{LiHo_xY_{1-x}F_4}$ magnetic Ho ions have an Ising character and interact mainly through the magnetic dipolar interaction. For $x=1$ the ground state of the system is ferromagnetic and as $x$ decreases a disordered ground state with glassy properties arises. If $x$ is decreased further, the system enters a phase sometimes referred to as ``antiglass". Both the non-canonical glassy state and the not yet understood ``antiglass", have never been systematically studied using a microscopic probe. We performed muon spin relaxation measurements in five samples (x=0.018, 0.045, 0.08, 0.12 and 0.25) which span these disordered phases. In this talk we will show from the microscopic point of view, how does the glassy state manifests itself as well as how does the evolution from the glass to the ``antiglass" occurs.