Dipolar magnets and glasses: Neutron-scattering, dynamical, and calorimetric studies of randomly distributed Ising spins

Phase diagram of a three-dimensional dipolar Ising model with textured Ising axes

We study from tempered Monte Carlo simulations the magnetic phase diagram of a textured dipolar Ising model on a face centered cubic lattice. The Ising coupling of the model follow the dipole-dipole interaction. The Ising axes are distributed with a uniaxial symmetry along the [Formula: see text] direction with a Gaussian probability density of the polar angles. This distribution provides a quenched disorder realization of the dipolar Ising model making a continuous link between the parallel axes dipoles and the random axes dipole models. As expected the phase diagram presents three distinctive phases: paramagnetic, ferromagnetic and spin-glass. A quasi long range ferromagnetic and a reentrant spin-glass phases are obtained in the vicinity of the ferromagnetic spin-glass line. This model provides a way to predict the magnetic phases of magnetic nanoparticles supracrystals in terms of the texturation of the easy axes distribution in the strong anisotropy limit.

Tuning high-Q nonlinear dynamics in a disordered quantum magnet

Quantum states cohere and interfere. Atoms arranged imperfectly in a solid rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent spin clusters by driving the system nonlinearly and measuring the resulting hole in the linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the Ising magnet LiHo0.045Y0.955F4, the quality factor Q for spectral holes can be as high as 100,000. We tune the dynamics by sweeping the Fano mixing parameter q through zero via the ac pump amplitude as well as a dc transverse field. The zero crossing of q is associated with a dissipationless response at the drive frequency. Identifying localized two-level systems in a dense and disordered magnet advances the search for qubit platforms emerging from strongly interacting, many-body systems.

Using thermal boundary conditions to engineer the quantum state of a bulk magnet

The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter-sized crystals of the Ising magnet LiHo(x)Y(1-x)F4 to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.

Novel disordering mechanism in ferromagnetic systems with competing interactions

Ferromagnetic Ising systems with competing interactions are considered in the presence of a random field. We find that in three space dimensions the ferromagnetic phase is disordered by a random field which is considerably smaller than the typical interaction strength between the spins. This is the result of a novel disordering mechanism triggered by an underlying spin-glass phase. Calculations for the specific case of the long-range dipolar LiHo(x)Y(1-x)F(4) compound suggest that the above mechanism is responsible for the peculiar dependence of the critical temperature on the strength of the random field and the broadening of the susceptibility peaks as temperature is decreased, as found in recent experiments by Silevitch et al.. [Nature (London) 448, 567 (2007)]. Our results thus emphasize the need to go beyond the standard Imry-Ma argument when studying general random-field systems.

Renormalization group study of random quantum magnets

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erdős-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.

Magnetic ordering of systems of nanodisks with quenched positional disorder

The effect of positional disorder in systems of single domain ferromagnetic nanodisks placed on a two-dimensional square lattice is studied by Monte Carlo simulations. Nanodisks are treated as magnetic dipoles pointing along one of the two principal axes of the lattice. Disorder is introduced displacing each nanodisk by (δx, δy) from its regular lattice position, where δx is randomly chosen within the interval 0 ≤ δx ≤ Δ and analogously for δy. Two different regimes are found: for Δ < Δ(0) = 0.18(2) (in units of lattice spacing) a thermally driven transition between a paramagnetic and a dipolar antiferromagnetic phase with a critical exponent α/ν changing continuously with Δ; for Δ ≥ Δ(0) a paramagnetic phase covering the whole T > 0 range. Plots of the spin-glass overlap parameter versus temperature T or lattice size L seem to exclude an equilibrium spin-glass phase in the latter regime.

Study of the ground state properties of LiHo(x)Y(1-x)F4 using muon spin relaxation

LiHo(x)Y(1-x)F4 is an insulator where the magnetic Ho3+ ions have an Ising character and interact mainly through magnetic dipolar fields. We used the muon spin relaxation technique to study the nature of its ground state for samples with x ≤ 0.25. In contrast with some previous works, we did not find canonical spin glass behavior down to ≈ 15 mK. Instead, below ≈300 mK we observed temperature-independent dynamic magnetism characterized by a single correlation time. The 300 mK energy scale corresponds to the Ho3+ hyperfine interaction strength, suggesting that this interaction may be involved in the dynamic behavior of the system.

Glassy dynamics in thermally activated list sorting

Sorting the integers 1 through N into an ordered list is a simple task that can be done rapidly. However, using an algorithm based on the thermally activated pairwise exchanges of neighboring list elements, we find sorting can display many features of a glass, even for lists as small as N=5. This includes memory and rejuvenation effects during aging-two hallmarks of glassy dynamics that have been difficult to reproduce in standard glass simulations.

Spectral responses in granular compaction

The slow compaction of a tapped granular packing is reminiscent of the low-temperature dynamics glasses. Here, I study the dynamics of granular compaction by means of a volumetric spectroscopy. While the specific packing volume v displays glassy aging and memory effects at low tapping amplitudes Gamma, the dynamic volumetric susceptibility chi(v)= partial differentialv/ partial differentialGamma displays minimal glassy effects, and its frequency spectrum gives no indication of a rapidly growing time scale. These features are contrast sharply with that found in the dielectric and magnetic susceptibilities of structural and spin glasses. Instead, chi(v) appears to exhibit the behavior of a dynamic configurational specific heat, such as that obtained from computer simulations of spin-glass models. This suggests that the glassy dynamics of granular compaction is controlled by statistically rare processes that diverge from the typical dynamics of the system. From modifications of the dynamical spectrum by finite system size, I suggest that these glassy processes derive from large-scale collective particle rearrangements.

Switchable hardening of a ferromagnet at fixed temperature

The intended use of a magnetic material, from information storage to power conversion, depends crucially on its domain structure, traditionally crafted during materials synthesis. By contrast, we show that an external magnetic field, applied transverse to the preferred magnetization of a model disordered uniaxial ferromagnet, is an isothermal regulator of domain pinning. At elevated temperatures, near the transition into the paramagnet, modest transverse fields increase the pinning, stabilize the domain structure, and harden the magnet, until a point where the field induces quantum tunneling of the domain walls and softens the magnet. At low temperatures, tunneling completely dominates the domain dynamics and provides an interpretation of the quantum phase transition in highly disordered magnets as a localization/delocalization transition for domain walls. While the energy scales of the rare earth ferromagnet studied here restrict the effects to cryogenic temperatures, the principles discovered are general and should be applicable to existing classes of highly anisotropic ferromagnets with ordering at room temperature or above.

Spin-glass transition at nonzero temperature in a disordered dipolar Ising system: the case of LiHoxY(1-x)F4

The physics of the spin-glass (SG) state, with magnetic moments (spins) frozen in random orientations, is one of the most intriguing problems in condensed matter physics. In LiHoxY(1-x)F4, the Ho3+ moments, which are well described by Ising spins with only discrete "up or down" directions, interact predominantly via the inherently frustrated magnetostatic dipole-dipole interactions. The random frustration causing the SG behavior originates from the random substitution of dipole-coupled Ho3+ by nonmagnetic Y3+. In this Letter, we provide compelling evidence from extensive computer simulations that a SG transition at nonzero temperature occurs in a realistic microscopic model of LiHoxY(1-x)F4. This resolves the long-standing, and still ongoing, controversy about the existence of a SG transition in disordered dipolar Ising systems.

Evidence of spin glass dynamics in dilute LiHoxY1-xF4

ac susceptibility measurements are presented on the dilute, dipolar coupled, Ising magnet LiHoxY1-xF4 for a concentration x=0.045. The frequency and temperature dependences of the susceptibility show characteristic glassy relaxation. The absorption spectrum is found to broaden with decreasing temperature suggesting that the material is behaving as a spin glass and not as an exotic spin liquid as was previously observed. A dynamical scaling analysis suggests a spin glass transition temperature of 43+/-2 mK with an exponent znu=7.8+/-0.2.

Quantum and classical glass transitions in LiHoxY1-xF4

When performed in the proper low-field, low-frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in a transverse field LiHo(x)Y(1-x)F(4) prove the existence of a spin-glass transition for x=0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.

Quantum projection in an Ising spin liquid

A transverse magnetic field is used to scan the diagonal and off-diagonal susceptibility of the uniaxial quantum magnet, LiHo(0.045) Y(0.955)F(4). Clusters of strongly coupled spins act as the primary source for the response functions, which result from a field-induced quantum projection of the system into a classically forbidden (meaning non-Ising) regime. Calculations based on spin pairs reproduce only some features of the data and fail to predict the measured off-diagonal response, providing evidence of a multispin collective state.

A ferromagnet in a continuously tunable random field

Most physical and biological systems are disordered, even though the majority of theoretical models treat disorder as a weak perturbation. One particularly simple system is a ferromagnet approaching its Curie temperature, T(C), where all of the spins associated with partially filled atomic shells acquire parallel orientation. With the addition of disorder by way of chemical substitution, the Curie point is suppressed, but no qualitatively new phenomena appear in bulk measurements as long as the disorder is truly random on the atomic scale and not so large as to eliminate ferromagnetism entirely. Here we report the discovery that a simply measured magnetic response is singular above the Curie temperature of a model, disordered magnet, and that the associated singularity grows to an anomalous divergence at T(C). The origin of the singular response is the random internal field induced by an external magnetic field transverse to the favoured direction for magnetization. The fact that ferromagnets can be studied easily and with high precision using bulk susceptibility and a large variety of imaging tools will not only advance fundamental studies of the random field problem, but also suggests a mechanism for tuning the strength of domain wall pinning, the key to applications.

Absence of conventional spin-glass transition in the Ising dipolar system LiHo(x)Y(1-x)F(4)

The magnetic properties of single crystals of LiHo(x)Y(1-x)F(4) with x = 16.5% and x = 4.5% were recorded down to 35 mK using a micro-SQUID magnetometer. While this system is considered as the archetypal quantum spin glass, the detailed analysis of our magnetization data indicates the absence of a phase transition, not only in a transverse applied magnetic field, but also without field. A zero-Kelvin phase transition is also unlikely, as the magnetization seems to follow a noncritical exponential dependence on the temperature. Our analysis thus unmasks the true, short-ranged nature of the magnetic properties of the LiHo(x)Y(1-x)F(4) system, validating recent theoretical investigations suggesting the lack of phase transition in this system.

Specific heat of the dilute Ising magnet LiHoxY1-xF4

We present specific heat data on three samples of the dilute Ising magnet LiHoxY1-xF4 with x=0.018, 0.045, and 0.080. Previous measurements of the ac susceptibility of an x=0.045 sample showed the Ho3+ moments to remain dynamic down to very low temperatures, and the specific heat was found to have unusually sharp features. In contrast, our measurements do not exhibit these sharp features in the specific heat and instead show a broad feature, for all three samples studied, which is qualitatively consistent with a spin glass state. Integrating C/T, however, reveals an increase in residual entropy with lower Ho concentration, consistent with recent Monte Carlo simulations showing a lack of spin glass transition for low x.

Magnetic properties of epsilon-Fe(3)N-GaN core-shell nanowires

epsilon-Fe(3)N-GaN core-shell nanowires are synthesized by the wet chemical route and by nitridation of the Fe-Ga-oxide nanowires in flowing NH(3) (g). The encapsulation by the GaN shell protects the epsilon-Fe(3)N core and spin-glass-like cooperative ordering is observed at low temperatures. Magnetic disorder occurs at the epsilon-Fe(3)N-GaN interface, giving rise to the spin-glass-like state below 50 K because of the presence of anti-ferromagnetic (AF) mixed oxynitrides and ferromagnetic (FM) epsilon-Fe(3)N nitride and the random distribution of epsilon-Fe(3)N in the interface region. The spin-glass-like ordering is probed by relaxation and ac susceptibility experiments.

Quantum magnets with anisotropic infinite range random interactions

Using exact diagonalization techniques, we study the dynamical response of the anisotropic disordered Heisenberg model for systems of S=1/2 spins with infinite range random exchange interactions at temperature T=0. The model can be considered as a generalization, to the quantum case, of the well-known Sherrington-Kirkpatrick classical spin glass model. We also compute and study the behavior of the Edwards Anderson order parameter and energy per spin as the anisotropy evolves from the Ising to the Heisenberg limits.

Entangled quantum state of magnetic dipoles

Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors and certain rare-earth intermetallics, the 1/T law is replaced by a power law T(-alpha) with alpha < 1. Here we show that a much simpler material system-namely, the insulating magnetic salt LiHo(x)Y(1-x)F(4)-can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects-entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom-becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.

Quantum and thermal fluctuations in the SU(N) Heisenberg spin-glass model near the quantum critical point

We solve for the SU(N) Heisenberg spin glass in the limit of large N focusing on small S and T. We study the effect of quantum and thermal fluctuations in the frequency dependent response function and observe interesting transfers of spectral weight. We compute the T dependence of the order parameter and the specific heat and find an unusual T2 behavior for the latter at low temperatures in the spin-glass phase. We find remarkable qualitative agreement with various experiments on the quantum frustrated magnet SrCr(9p)Ga(12-9p)O19.

Coherent spin oscillations in a disordered magnet

Most materials freeze when cooled to sufficiently low temperature. We find that magnetic dipoles randomly distributed in a solid matrix condense into a spin liquid with spectral properties on cooling that are the diametric opposite of those for conventional glasses. Measurements of the nonlinear magnetic dynamics in the low-temperature liquid reveal the presence of coherent spin oscillations composed of hundreds of spins with lifetimes of up to 10 seconds. These excitations can be labeled by frequency and manipulated by the magnetic fields from a loop of wire and can permit the encoding of information at multiple frequencies simultaneously.

Nuclear spin driven quantum relaxation in LiY0.998Ho0.002F4

Staircaselike hysteresis loops of the magnetization of a LiY0.998Ho0.002F4 single crystal are observed at subkelvin temperatures and low field sweep rates. This behavior results from quantum dynamics at avoided level crossings of the energy spectrum of single Ho3+ ions in the presence of hyperfine interactions. Enhanced quantum relaxation in constant transverse fields allows the study of the relative magnitude of tunnel splittings. At faster sweep rates, nonequilibrated spin-phonon and spin-spin transitions, mediated by weak dipolar interactions, lead to magnetization oscillations and additional steps.

Dynamical response of quantum spin-glass models at t = 0

We study the behavior of two archetypal quantum spin glasses at T = 0 by exact diagonalization techniques: the random Ising model in a transverse field and the random Heisenberg model. The behavior of the dynamical spin response is obtained in the spin-glass ordered phase. In both models it is gapless and has the general form chi(")(omega) = qdelta(omega)+chi(")(reg)(omega), with chi(")(reg)(omega) approximately omega for the Ising and chi(")(reg)(omega) approximately const for the Heisenberg, at low frequencies. The method provides new insight to the physical nature of the low-lying excitations.

Quantum annealing of a disordered magnet

Traditional simulated annealing uses thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. Thermal and quantum annealing are compared in a model disordered magnet, where the effects of quantum mechanics can be tuned by varying an applied magnetic field. The results indicate that quantum annealing hastens convergence to the optimum state.