Session V18: Focus Session: Low D/Frustrated Magnetism - Spin Ice, et al.

Magneto-optical Kerr Effect Studies of Artificial Frustrated Magnets

We use the magneto-optical Kerr effect (MOKE) to study the collective magnetic behavior of geometrically frustrated arrays of single-domain ferromagnetic islands. By varying the island spacing, lattice geometry and the orientation relative to the magnetic field, we probe the properties of the arrays via MOKE measurements of the net moment of the arrays. We study the influence of local geometry and frustration on the collective magnetization reversal process, using the switching field as a measure. Further, angle-resolved MOKE measurements probe the influence of individual island shape anisotropy on the collective anisotropy of interacting arrays. Finally, we present preliminary measurements in an oscillating magnetic field. The results are compared to the results of micromagnetic simulation. We thank M. Ericson and C. Leighton for sample preparation. This research was supported by the US Dept. of Energy.   

Measuring Disorder in Artificial Kagome Ice

Artificial spin ice is proving to be a valuable tool in understanding magnetic interactions on the nanoscale. It can directly show the interactions responsible for geometric frustration, and different geometries have been used to model real pyrochlore spin ice compounds and other lattices. The strength in the approach lies in the ability of a synthetic material, fabricated from macroscopic artificial ``atoms,'' to mimic real materials, where atoms are essentially identical with low disorder from lattice site to lattice site. However, in artificial spin ice materials there can be substantial variation among the artificial atoms in relevant quantities such as coercive field, with some systems showing standard deviations as high as 20{\%}. By carefully studying the reversal process of artificial kagome ice along specific crystallographic directions, we can directly measure the distribution of coercivities of the individual nanoscale magnets. ~By using a lattice of connected magnets fabricated from Ni80Fe20, we find that the coercivity distribution can have a deviation of less than 5{\%}. These narrow deviations should allow the observation of behavior that mimics more closely what would be expected in real spin ice materials.   

Dynamics of magnetization in artificial spin ice on kagome

We model magnetization dynamics in artificial spin ice on kagome under an applied magnetic field. Magnetization reversal is mediated by domain walls carrying two units of magnetic charge emitted from and absorbed by lattice junctions and propagating along the wires. The Coulomb interaction between magnetic charges induces avalanches in magnetization reversal. Distributions of avalanche lengths for various angles between the initial magnetization and the applied magnetic field were considered. We used a Gaussian distribution in the magnitude of the links' critical fields to mimic disorder in a real system [1]. An asymmetric distribution of topological defects at a wire junction gives rise to an offset angle $\alpha$ in the reversal field $H(\theta)=H_{c}/\cos{(\theta+\alpha)}$ where $\theta$ is the angle between the link and the applied magnetic field [2]. The model reproduces the salient features of magnetization reversal curves observed experimentally. \\[4pt] [1] Y. Qi, T. Brintlinger, and J. Cumings, Phys. Rev. B \textbf{77,} 094418 (2008). \\[0pt] [2] P. Mellado, O. Petrova, Y. Shen, and O. Tchernyshyov, Phys. Rev. Lett. \textbf{105,} 187206 (2010).   

Disorder and field-induced dynamics in artificial spin ice

Artificial spin ices are athermal systems for which dynamics are induced by a time varying applied field. The field induced dynamics have received a lot of attention, both experimental and theoretical (see, e.g., [1,2]), but these studies have not dealt explicitly with the effects of disorder. We show, through numerical simulations and studies of the phase space of the system, that disorder in fact has a strong and fundamental effect on the field-induced dynamics. This highlights the fact that an understanding of the dynamics of artificial spin ice must take into account both the sequence of applied fields and the spin ice lattice. \\[4pt] [1] X. Ke, J. Li, C. Nisoli, P. E. Lammert, W. McConville, R. F. Wang, V. H. Crespi, and P. Schiffer, Phys. Rev. Lett. 101, 037205 (2008).\\[0pt] [2] Z. Budrikis, P. Politi, and R. L. Stamps, Phys. Rev. Lett. 105, 017201 (2010).   

Control of Ground State Order in Artificial Square Ice

Anisotropy in nanomagnet arrays can be tailored to enforce geometrical frustration, so that analogs of spin-ice materials can be fabricated [1-2]. We have studied artificial square ice, which consists of interlinked vertices of four Ising moments. Previously, energy minimisation via ac demagnetization has received significant attention, however, the long-range ordered ground state (GS) is inaccessible via this method. Furthermore, equilibriation is disallowed in the athermal limit so far explored. We show it is possible to realise GS order in as-prepared arrays, fabricated via electron beam lithography and evaporation, due to early-growth thermalization [3]. Monopole and string-like excitations from the GS are seen to be Boltzmann factor-weighted. Monopole propagation and interactions can be inferred within an energy band structure. Lattice spacing and buffer material allow control of ordering. \\[4pt] [1] Wang et al., Nature (2006), \textbf{439}, 303-306 \\[0pt] [2] Harris et al., PRL (1997), \textbf{79}, 2554-2557 \\[0pt] [3] Morgan et al., Nature Phys. (at press)   

Monopole Dynamics in Spin Ice

The last couple of years have witnessed intense interest in spin ice materials due to the unique nature of its low energy excitations, which take the form of emergent magnetic monopoles. Through combined theoretical and experimental work, it has become increasingly apparent that an effective description of these excitations in terms of free, Coulomb interacting point-like quasiparticles is essential to develop an understanding of the thermodynamic properties of these materials beyond numerical simulations. On the other hand, we are only just beginning to unravel the repercussions of such exotic excitations on the dynamics of spin ice, in relation for instance to how the system relaxes when driven out of equilibrium, or in relation to thermal transport experiments. In this talk we review some of the latest theoretical and experimental results on the out of equilibrium properties of spin ice materials, ranging from thermal and field quenches [Castelnovo, Moessner, \& Sondhi, PRL 104, 107201 (2010) and ongoing work] to thermal runaways in response to a varying magnetic field [Slobinsky \textit{et al.}, arXiv:1010.4143v1]. In particular, we discuss how these phenomena can be understood as consequences of the specific nature of the low energy excitations.   

Magnetic Monopoles in Matter: An Analytic Theory

Transport theory is presented which, starting from the microscopic field equations, incorporates the magnetic monopole physics occurring in materials such as spin ice. Hall effect, Landau levels, and thermopower are calculated for magnetic charges. Magnetic charge currents in elementary lattices are shown to exist even in the absence of geometrical frustration.   

Theoretical and computational models of emergent magnetic monopoles and Dirac strings in kagome spin-ice

Magnetic monopoles and their associated Dirac strings have recently been experimentally observed as emergent quasiparticles in frustrated magnetic spin-ice systems. Detection of reciprocal signatures of monopoles were reported for 3D pyrochlore systems, and subsequently, direct real-space observations of monopoles and their associated Dirac strings were made in 2D artificial kagome lattices. In contrast to conventional domain growth, the magnetization process in these spin ice systems proceeds through nucleation and avalanche-type propagation of overturned dipoles - physical versions of a Dirac string. The 1D nature of these avalanches in a 2D system provides an example of dimensional reduction through frustration. We establish a theoretical model and perform Monte Carlo simulations which faithfully reproduce the observed hysteresis, string-avalanche statistics and monopole densities.   

Hunting a [111] magnetization plateau to test the quantum spin ice model in Tb2Ti2O7

The pyrochlore magnet Tb2Ti2O7 may be described by a quantum spin ice model. This model predicts a magnetization plateau will occur for weak fields applied along the [111] axis at low-temperature. We have carried out muon-spin relaxation measurements to test this hypothesis. Features are observed at 15 and 65mT, agreeing with the predicted boundaries of the magnetization plateau. In the intermediate region the field dependence of the muon relaxation rate suggests a constant distribution of local magnetic fields of 10mT, and a constant fluctuation time of 20ns. ac susceptibility measurements are being carried out to investigate the bulk response on a longer timescale.   

Creation and Measurement of Magnetic Charge Currents in Spin Ice

The recent discovery of magnetic charge in spin ice raises the question of whether long-lived currents of magnetic ``monopoles'' can be created and manipulated by applying magnetic fields. Here we show that they can; by applying a magnetic field pulse to a Dy$_2$Ti$_2$O$_7$ spin ice crystal at 0.36 Kelvin, we create a relaxing magnetic current that lasts for several minutes. We measure the current by means of the electromotive force it induces in a solenoid coupled to a susceptometer and quantitatively describe it using a chemical kinetic model of point-like charges obeying the Onsager-Wien mechanism of carrier dissociation and recombination.   

$d$-wave Metal phase of itinerant electrons with ring exchange on a 2-leg ladder

I will present recent results in the search for theoretical insights into non-Fermi liquid phases in two dimensions. In particular, we propose a novel conducting phase for itinerant electrons on the square lattice with strong $d$-wave correlations (i.e. a ``$d$-wave metal''; see [1] for the bosonic analog of this phase) and a candidate Hamiltonian (hopping plus four-site electron ring exchange), which we examined in search of this phase (at $T=0$) over some portion of the phase diagram. For numerical tractability, we specialize to the 2-leg ladder and study this model using variational Monte Carlo (VMC) and the density matrix renormalization group (DMRG). For the VMC, we construct trial wavefunctions corresponding to a particular slave particle decomposition of the electrons and consistent with the properties of the proposed $d$-wave metal as well as for the ``normal'' Fermi liquid phase to map out a VMC phase diagram for the candidate Hamiltonian. Meanwhile, DMRG is employed as a quasi-exact probe of this Hamiltonian and the successes and failures of the trial wavefunctions, relative to the unbiased DMRG results, will be presented. [1] O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B, {\bf 75}, 235116 (2007).   

Entanglement Hamiltonians for quantum spin chains

We report on our analysis of entanglement phenomena in gapped and gapless quantum spin chains. In particular we discuss criteria of correspondence between entanglement spectra and Hamiltonian spectra with respect to symmetries, spectral gaps, and eigenstate properties. We find that the structure of the entanglement Hamiltonian associated with the ground state is helpful to discover various spectral properties of the full system.