Session B8: Focus Session: Frustrated magnetism - Spin ice

Spin dynamics in the frozen state of the dipolar spin ice material Dy$_2$Ti$_2$O$_7$

Low temperature magnetic ac susceptibility measurements of single crystal dipolar spin ice Dy$_2$Ti$_2$O$_7$ are presented. The measured dynamics qualitatively agree with simulations based on current magnetic monopole theory, but not with thermal relaxation measurements, whose dynamics freeze out at a slower rate. The relaxation is found to exhibit thermally activated Arrhenius behavior with an activation energy of 9.79\,K. A comparison between the measurement results of Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$ will also be made.   

Anderson-Higgs transition in quantum spin ice Yb$_{2}$Ti$_{2}$O$_{7}$

We have carried out polarized elastic neutron-scattering experiments on single crystals Yb$_{2}$Ti$_{2}$O$_{7}$ from 1 K to 0.04 K. The results reveal that the diffuse [111]-rod scattering [1] is suppressed below T$_{c}$ $\sim $ 0.21 K, where magnetic Bragg peaks and a full depolarization of neutron spins are observed with the thermal hysteresis, indicating a first-order ferromagnetic transition. Theoretically, a quantum spin ice state [2] above T$_{c }$ has been realized from an effective classical model where $<$111$>$ Ising moments, i.e., pseudospin-1/2 interact mainly through a magnetic dipolar interaction [3], and a transition from magnetic Coulomb phase to Higgs phase has emerged at T$_{c }$ in Yb$_{2}$Ti$_{2}$O$_{7}$. [1] K. A. Ross \textit{et al.}, Phys. Rev. Lett. \textbf{103}, 227202 (2009). [2] S. Onoda \textit{et al.}, J. Phys.: Conf. Series, in press. [3] S. T. Bramwell and M. J. P. Gingras, Science \textbf{294}, 1495 (2001).   

Schwinger-boson approach to spin-liquid and Higgs phases in quantum spin ice: Yb$_2$Ti$_2$O$_7$ and Pr$_2$Zr$_2$O$_7$

The most generic pseudospin-$1/2$ quantum spin ice model for rare-earth magnetic pyrochlore oxides, that include Yb$_2$Ti$_2$O$_7$ and Pr$_2TM_2$O$_7$ (TM=Sn, Zr, Hf, and Ir), is studied by means of a Schwinger-boson approach. From a projective symmetry group and a mean-field analysis on this magnetically anisotropic model, we classify and analyze quantum spin liquid phases in the space of four coupling constants, including both U(1) and $Z_2$ spin liquids that are characterized by power-law decaying and exponentially decaying spin correlations, respectively, as well as Higgs phases showing long-range orders. We apply the analysis to cases of the model parameters extracted from both microscopic arguments and the fitting to neutron-scattering experiments of some of the above materials and clarify the dynamical magnetic excitation spectra that take the continuum form due to the deconfined monopolar spinons. The relevance to recent experimental results is discussed.   

Dynamical strings in quantum spin ice

Spin ice is a highly frustrated ferromagnet displaying rich emergent phenomena. Recently, new spin ice materials such as Yb$_2$Ti$_2$O$_7$ and Pr$_2$Zr$_2$O$_7$ have stood out as possible candidates for quantum spin ice, in which quantum fluctuations could play a major role. In this talk, we discuss new emergent phenomena in quantum spin ice in an external magnetic field applied along the (100) lattice direction. When quantum monopoles are confined by the external field, the open string binding a monopole pair (Dirac string) becomes a dynamical object with a field-dependent tension. The motion of an open string includes longitudinal expansion and contraction and transverse fluctuations. The emergent quantum string theory in this context allows for simple analytical solution and straightforward numerical simulation. Moreover, vibrational modes of the string can be detected by experimental techniques such as neutron scattering and THz spectroscopy.   

Higgs transitions of spin ice

Spin ice is a frustrated magnetic material displaying a variety of interesting phenomena. At low temperature, it exhibits a ``Coulomb phase'', in which there is no magnetic order and correlations have power-law forms at long distances. In this talk, I will describe the effects of applying perturbations that favor ordered states and show that the resulting phase transitions cannot be described by the standard Landau paradigm. They are instead naturally viewed as Higgs transitions of an emergent gauge theory; this perspective leads to long-wavelength theories for the critical properties. I will present specific examples of transitions described by this approach that result from perturbations such as an applied magnetic field or additional spin--spin interactions.   

Loop statistics in the Coulomb phase

The Coulomb phase is a classical gauge field theory arising in frustrated systems with ``divergence free'' constraints, such as spin ice [1]. In this talk, we show how this phase can be understood as a loop model, and characterized by their loop length distribution and fractal dimensions [2]. Comparing similar models in 2- and 3-dimensions allows us to extract insights from connections to Stochastic-Loewner Evolution (SLE) processes, percolation and polymer physics. We mention implications of these results for related models and experiments (Heisenberg magnets, itinerant electrons [3]). \\[4pt] [1] Henley, Annual Review of Condensed Matter Physics {\bf 1}, 179 (2010).\\[0pt] [2] Jaubert, Haque, Moessner, Phys. Rev. Lett. {\bf 107}, 177202 (2011)\\[0pt] [3] Jaubert, Pitaecki, Haque \& Moessner, in preparation (2012).   

Similarities and differences between spin and water ice models

In the present contribution we provide a brief survey of the amazing analogy between spin and water ice basically from the water ice physics point of view. Special attention is paid to the following question: which of the theoretical concepts developed in ice physics could be applied to the study of spin ice and other frustrated systems. We show that the analogy between ground states of these systems can be extended other properties. In Section 1 we outline the history and present state of the analogy, and thoroughly investigate the similarity between quasi-particle excitations in ordinary ice (point defects in the ice proton system) and in spin ice (magnetic monopoles). The magnetic monopole concentration is shown to have a break in its temperature dependence arising due the magnetic Coulomb interaction (melting of the Coulomb phase). In Section 2 we develop a theory of magnetic charge transport, study the magnetic relaxation as well as the screening of magnetic field in spin ice. The transport analogy between spin and water ice is shown to be of limited nature: it is impossible to produce a stationary magnetic current in the commonly accepted model of spin ice. An extended spin ice model is suggested which is free from this disadvantage. In Section 3 we discuss the problem of how the magnetic ordering is modified near the free surface of spin ice or near its interface with other magnets. The study is based on the concepts previously used in water ice physics. In concluding Section 4 we discuss the differences between water and spin ice models (differences in numerical relations between appropriate constants, limited nature of transport analogy) and indicate some other problems which are not considered in this contribution (thermal effects of charge currents, quantum properties of the models, effect of frustrations on electron energy spectrum).   

Spin Ice correlations in a macroscopic system

We report the realization of spin ice like correlations in a macroscopic array of ferromagnetic rods arranged in a honeycomb lattice. We found that this system has a rich dynamics that can be rationalized as the result of the interplay between the viscous rotation of each rod and Coulomb like interactions between magnetic charges located at the ends of the magnets. The dynamical response of this system has also been explored by using an external magnetic dipole moving at a distance $h$ from the lattice. A clear separation between the interaction strengths permitted us to observe localized as well as a collective dynamics depending on the value of two dimensionless numbers; one associated with the two relevant time scales of the system and the other related with the strength of internal and external magnetic forces. This new spin-ice realization will allow the manipulation of parameters almost impossible to control on its microscopic relatives, such as inertia, vacancies, and quenched geometrical disorder between others.   

Internal field distribution in spin ice materials

At low temperatures, spin ice is populated by a finite density of magnetic monopoles --- point like topological defects with a mutual magnetic Coulomb interaction. Here we study the distribution of magnetic fields inside spin ice. This is of conceptual importance as it reflects the monopolar fields set up by defects in a spin ice configuration. We discuss its manifestations in experiments involving local field probes, such as NMR or muon spin rotation. Averaged over the bulk of the sample, this distribution resembles one set up by a random spin arrangement. However, somewhat counter intuitively, the density of low-field locations decreases as the local ferromagnetic correlations imposed by the ice rules develop. The $1/r^2$ Coulomb field of a single monopole is visible in (magnetic) voids of the lattice where lattice-scale effects due to the immediate proximity of other spins are supressed.   

Probing the spin ice state in the cubic pyrochlore Ho$_{2}$Ge$_{2}$O$_{7}$

Spin ices are a remarkable magnetic ground state that can arise in geometrically frustrated pyrochlores, A$_{2}$B$_{2}$O$_{7}$, when magnetic rare earth ions are situated on the vertices of a lattice of corner sharing tetrahedra. Competing nearest-neighbor and long-range dipolar interactions result in a short-range ordered ground state for each tetrahedron in which two spins point in and two spins point out [1]. The excitations in spin ices are equally remarkable; spin ices are the only known hosts of magnetic monopoles, emergent quasiparticles with a net magnetic charge. The cubic pyrochlore Ho$_{2}$Ge$_{2}$O$_{7}$ was prepared with a high temperature and high pressure technique. Preliminary DC susceptibility, heat capacity and X-ray diffraction experiments confirmed that Ho$_{2}$Ge$_{2}$O$_{7}$ has the bulk properties of a spin ice including residual entropy equal to the Pauling value for water ice [2]. The results of a polarized neutron scattering experiment performed at ILL as well as AC susceptibility and heat capacity measurements will be presented, and compared to the canonical spin ices.\\[4pt] [1] S. T. Bramwell \textit{et al.}, Phys. Rev. Lett. \textbf{87}, 047205 (2001). \newline [2] H. Zhou \textit{et al.}, Nature Communications \textbf{2}, 478 (2011).   

Far infrared time domain terahertz spectroscopic study of Ho2Ti2O7

We report a far infrared time domain terahertz spectroscopic study of the spin ice material holmium titanate. The complex dielectric constant was obtained in the terahertz frequency range. Several low energy excitations were identified from the optical spectra. We will discuss the possible nature of those excitations and their relevance to the spin ice physics.   

Calorimetric Study of Diluted Spin Ice Materials

Spin ice materials Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ have been the subject of ongoing interest for over ten years. The cooperative magnetic ground state can be mapped onto the proton disordered ground state in water ice, and its residual entropy follows the same Pauling's estimate. Interestingly it was found in a previous study that, upon dilution of the magnetic rare earth ions Dy$^{3+}$ and Ho$^{3+}$ by non-magnetic substitutes Y$^{3+}$, the residual entropy depends non-monotonically on the dilution level. In this work we investigate through Monte Carlo simulations microscopic models to account quantitatively for the calorimetric experimental measurements, and thus also the residual entropies as a function of dilution. Features of the dilution physics in the specific heat are captured quantitatively by the microscopic models and the interplay between dilution and frustration is understood on the basis of a Bethe lattice calculation. The effect of the dipolar interactions between magnetic spins are exposed numerically for various dilution concentrations. Our work explains the previous discrepancy of the residual entropy between different species of rare earth ions and the generalized Pauling's estimate.   

Spin Ice: Magnetic Excitations without Monopole Signatures using Muon Spin Rotation

Theory predicts the low-temperature magnetic excitations in spin ices consist of deconfined magnetic charges, or monopoles. A recent transverse-field (TF) muon spin rotation ($\mu$SR) experiment [S T Bramwell {\it et al}, Nature {\bf 461}, 956 (2009)] reports results claiming to be consistent with the temperature and magnetic field dependence anticipated for monopole nucleation $-$ the so-called second Wien effect. We demonstrate via a new series of $\mu$SR experiments in Dy$_2$Ti$_2$O$_7$ that such an effect is not observable in TF $\mu$SR. Rather, as found in many highly frustrated magnetic materials, we observe spin fluctuations which become temperature independent at low temperatures, behavior which dominates over any possible signature of thermally nucleated monopole excitations.