Session Y29: Focus Session: Disordered and Glassy Magnets

Barkhausen noise in the Random Field Ising Magnet NdFeB

With the application of a magnetic field transverse to the magnetic easy axis, sintered blocks of the rare-earth ferromagnet Nd$_{\mathrm{2}}$Fe$_{\mathrm{14}}$B form a realization of the Random-Field Ising Model at room temperature. We study domain reversal and avalanche dynamics through an analysis of the Barkhausen noise. Power-law behavior with a cutoff is observed in the avalanche energy spectrum, consistent with theoretical predictions for disordered materials. Two regimes of behavior are found, one at low temperature and high transverse field where the system shows behavior consistent with randomness-dominated dynamics, and a high-temperature, low-transverse-field regime in which thermal fluctuations dominate the dynamics. In the randomness-dominated regime, the critical exponents are consistent with mean-field predictions for heavily disordered system, whereas in the thermal-fluctuation regime, the critical exponents differ substantially from the mean-field predictions.   

Interplay of disorder and geometrical frustration in Gadolinium Gallium Garnet

We study the effects of disorder on the geometrically frustrated Heisenberg antiferromagnet Gadolinium Gallium Garnet (GGG) using neodymium doping (0.1 to 1\%) in combination with linear and nonlinear ac magnetic susceptibility. The Nd doping actually alleviates the effects of disorder due to excess Gd ions occupying Ga sites. The linear, frequency-dependent susceptibility reveals that 1\% Nd doping suppresses the appearance of any long-range order from approximately 80mK to below 30mK. The dynamics of isolated, correlated spin clusters were studied as a function of doping level using nonlinear susceptometry. In this regime, both the aggregate moment of the clustered spins and the activation field required to excite a nonlinear response were inversely correlated with the dopant density.   

Spin Glass Dynamics: Finite Size Effects

Because the spin glass lower critical dimension $2t_{co}$, spin glass dynamics cross over to two-dimensional behavior. However, even for $t>t_{co}$, there remain correlated spin glass states for which $\xi(t,T)<\ell$, but with a maximum barrier height $\Delta_{max}$. Furthermore, because of ultrametricity, the number of states separated by $\Delta_{max}$ is exponentially large. This leads to activated dynamics controlling the time dependence of the zero field cooled and thermoremanent magnetization near the glass transition temperature. We have measured these phenomena in films of a-Ge:Mn, and obtained quantitative results for (the related) $t_{co}$ and $\Delta_{max}$. These states are also responsible for the frequency dependence of the dynamic susceptibility $\chi(t)$ of Cu:Mn thin film sandwiches previously measured by Sandlung {\it et al}. We show that the spin glass temperature remains at the bulk $T_g$, and that the temperature dependence of $\chi(t)$ is a consequence of $\Delta_{max}$.   

Random Fields, Topology, and Glassy States of Matter

The debate goes on for more than forty years whether weak static random fields destroy the long-range order in condensed matter systems. A recently found answer depends on the topology of the order parameter. The $n$-component order parameter in $d$ dimensions exhibits glassy behavior at $n < d + 1$, characterized by pinning of topological defects with singularities: vortices, strings, etc. At $n = d + 1$, the presence of nonsingular topological objects, such as kinks and~skyrmions, leads to a weak metastability. At $n > d + 1$ topological objects are absent and the behavior of the system is fully reversible, characterized by the exponential decay of correlations in quantitative agreement with the Larkin-Imry-Ma argument. These findings have been confirmed numerically on lattices of up to one billion sites. (Research supported by the DOE Grant DE-FG02-93ER45487.)\\[4pt] Reference: T. C. Proctor, D. A. Garanin, and E. M. Chudnovsky, Physical Review Letters \textbf{112}, 097201 (2014).   

Improved fair sampling of ground states in Ising spin glasses

Verifying that an optimization approach can sample all solutions that minimize a Hamiltonian is a stringent test for any newly-developed algorithm. While most solvers easily compute the minimum of a cost function for small to moderate input sizes, equiprobable sampling of all ground-state configurations (within Poissonian fluctuations) is much harder to obtain. Most notably, methods such as transverse-field quantum annealing fail in passing this test for certain highly-degenerate problems. Here we present an attempt to sample ground states for Ising spin glasses based on a combination of low-temperature parallel tempering Monte Carlo combined with the cluster algorithm by Houdayer. Because the latter is rejection free and obeys details balance, the ground-state manifold is efficiently sampled. We illustrate the approach for Ising spin glasses on the D-Wave Two quantum annealer topology, known as the Chimera graph, as well as two-dimensional Ising spin glasses.   

The cumulative overlap distribution function in spin glasses: mean field vs. three dimensions

We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution in spin glasses. Using analytical and numerical mean-field results for the Sherrington-Kirkpatrick model, as well as data from toy models, we show that this approach is an effective tool to distinguish the low-temperature behavior of replica symmmetry breaking systems from that expected in the droplet picture. An application of the method to the three-dimensional Edwards-Anderson models shows agreement with the replica symmetry breaking predictions.   

Ground States of a Disordered Frustrated Quantum Dimer Magnet

We present results of thermodynamic measurements of the site-diluted spin-dimer magnet Ba$_3($Mn$_{1-x}$V$_x)_2$O$_8$, including magnetization, torque magnetometry, and AC susceptibility. The parent compound Ba$_3$Mn$_2$O$_8$ is a frustrated $S=1$ quantum dimer-magnet with a singlet ground state, and triplet and quintuplet excitations. A magnetic field can be used to tune the energy spectrum of this system, yielding successive triplet and quintuplet condensates at low temperatures. Site substitution with $S=0$ V breaks Mn-dimers, introducing site disorder into the high-field ordered states. This substitution also introduces unpaired $S=1$ Mn ions, and it has been an open question whether such spins order at low temperatures. Here, we present evidence of the spin-freezing of unpaired Mn ions below 240mK for all compositions measured, from $x$=0.05 to 0.85. We also present the evolution of the high field ordered state with increasing disorder.   

Absence of Magnetic Order and Persistent Spin Dynamics in Tb$_2$Ge$_2$O$_7$

The terbium pyrochlores exhibit many unique magnetic properties, which has generated significant interest in this family of frustrated materials. A candidate spin liquid, Tb$_2$Ti$_2$O$_7$ fails to magnetically order, despite strong antiferromagnetic correlations. The application of external pressure has been found to produce partial antiferromagnetic order in Tb$_2$Ti$_2$O$_7$. Recently, we synthesized a new member of this family, Tb$_2$Ge$_2$O$_7$. Due to the large ionic radii decrease from titanium to germanium, Tb$_2$Ge$_2$O$_7$ can be considered a chemical pressure analog of Tb$_2$Ti$_2$O$_7$. However, neutron scattering measurements revealed an absence of magnetic order in Tb$_2$Ge$_2$O$_7$ down to 20 mK and dominant ferromagnetic correlations. Now, we have investigated the low temperature magnetism of Tb$_2$Ge$_2$O$_7$ with muon spin rotation. Our zero field $\mu$SR measurements confirm an absence of static order in Tb$_2$Ge$_2$O$_7$. We find a sharp increase in magnetic correlations below 10 K and persistent spin dynamics down to 25 mK. Our longitudinal field $\mu$SR measurements on Tb$_2$Ge$_2$O$_7$ at 25 mK are consistent with a system of fluctuating moments, with a fluctuation rate of 11 MHz. This fluctuation rate is nearly temperature independent below 2.5 K.   

Local Probe Study of S=1 Spin Liquid Candidate Ba$_3$NiSb$_2$O$_9$

The family of hexagonal perovskites, Ba$_3M$Sb$_2$O$_9$, has attracted a considerable amount of attention in recent years, with the discovery of several spin liquid candidates. For $M=$Cu, the material is fairly disordered and likely exhibits a honeycomb-like lattice whereas in other cases the structure consists of triangular planes of spins. Three different structural phases of Ba$_3$NiSb$_2$O$_9$ have been discovered, depending on synthesis pressure [1]. Two of these phases (6HA and 6HB) consist of triangular planes of $S=1$ moments, and differ primarily by the stacking of these planes. Here, we present muon spin rotation ($\mu$SR) and $^{121}$Sb nuclear magnetic resonance (NMR) results on a high-pressure synthesis of this material, 6HB-Ba$_3$NiSb$_2$O$_9$. Most importantly, we demonstrate that there are no signs of magnetic ordering or spin freezing down to temperatures as low as 20 mK, making this material a plausible spin liquid candidate. Furthermore our NMR results are indicative of gapless excitations, consistent with previous specific heat and magnetic susceptibility results [1].\\[4pt] [1] J. G. Cheng \emph{et al.}, PRL {\bf 107}, 197204 (2011).   

Giant anisotropic interactions in frustrated quantum magnet BiCu2PO6

I will discuss a series of comprehensive inelastic neutron scattering measurements which uncover the full magnetic excitation spectrum in the valence bond ordered compound BiCu$_2$PO$_6$. Owing to its frustrated geometry and potential to realize unique quantum phase transitions in high magnetic fields, BiCu$_2$PO$_6$ has received significant attention in recent literature. However, the true nature of the magnetic Hamiltonian responsible for the high field phenomena has not been known until now. I will present measurements of the spin excitation spectrum in BiCu$_2$PO$_6$ from which the magnetic Hamiltonian is elucidated. The spectrum is unique to the frustrated two-leg ladder geometry in BiCu$_2$PO$_6$ and we have been able to correctly describe the lowest energy excitations within the framework of a bond-operator theory, incorporating anisotropic magnetic exchange interactions which are comparable to the Heisenberg exchange terms. The anisotropic exchange interactions originate from spin orbit coupling and are of an unexpectedly large magnitude for a Cu based magnetic compound, potentially indicating the relevance of Bismuth in the superexchange pathway. BiCu$_2$PO$_6$ is a complex and unique quantum magnet combining frustration and anisotropic exchange; the discovery of such large anisotropic interactions in BiCu$_2$PO$_6$ hints at new routes for incorporating spin anisotropies in 3d transition metal based magnets.