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Register a new userNon-monotonic residual entropy in diluted spin ice: a comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results
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Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, have been the subject of much interest for over the past fifteen years. Their low temperature strongly correlated state can be mapped onto the proton disordered state of common water ice and, consequently, spin ices display the same low temperature residual Pauling entropy as water ice. Interestingly, it was found in a previous study [X. Ke {it et. al.} Phys. Rev. Lett. {bf 99}, 137203 (2007)] that, upon dilution of the magnetic rare-earth ions (Dy^{3+} and Ho^{3+}) by non-magnetic Yttrium (Y^{3+}) ions, the residual entropy depends {it non-monotonically} on the concentration of Y^{3+} ions. In the present work, we report results from Monte Carlo simulations of site-diluted microscopic dipolar spin ice models (DSIM) that account quantitatively for the experimental specific heat measurements, and thus also for the residual entropy, as a function of dilution, for both Dy2Ti2O7 and Ho2Ti2O7. The main features of the dilution physics displayed by the magnetic specific heat data are quantitatively captured by the diluted DSIM up to, and including, 85% of the magnetic ions diluted (x=1.7). The previously reported departures in the residual entropy between Dy2Ti2O7 versus Ho2Ti2O7, as well as with a site-dilution variant of Paulings approximation, are thus rationalized through the site-diluted DSIM. For 90% (x=1.8) and 95% (x=1.9) of the magnetic ions diluted, we find a significant discrepancy between the experimental and Monte Carlo specific heat results. We discuss some possible reasons for this disagreement.
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Water ice and spin ice are important model systems in which theory can directly account for zero point entropy associated with quenched configurational disorder. Spin ice differs from water ice in the important respect that its fundamental constituents, the spins of the magnetic ions, can be removed through replacement with non-magnetic ions while keeping the lattice structure intact. In order to investigate the interplay of frustrated interactions and quenched disorder, we have performed systematic heat capacity measurements on spin ice materials which have been thus diluted up to 90%. Investigations of both Ho and Dy spin ices reveal that the zero point entropy depends non-monotonically on dilution and approaches the value of Rln2 in the limit of high dilution. The data are in good agreement with a generalization of Paulings theory for the entropy of ice.
Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction x of all L^3 sites of a simple cubic lattice that point up or down along a given crystalline axis. For x < 0.65 these systems are known to exhibit an equilibrium spin-glass phase below a temperature T_sg proportional to x. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter q that are strongly sample-dependent. We focus on spikes associated with large excitations. From cumulative distributions of q and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. This is compared with the behaviour found for the Sherrington-Kirkpatrick model.
It is a salient experimental fact that a large fraction of candidate spin liquid materials freeze as the temperature is lowered. The question naturally arises whether such freezing is intrinsic to the spin liquid (disorder-free glassiness) or extrinsic, in the sense that a topological phase simply coexists with standard freezing of impurities. Here, we demonstrate a surprising third alternative, namely that freezing and topological liquidity are inseparably linked. The topological phase reacts to the introduction of disorder by generating degrees of freedom of a new type (along with interactions between them), which in turn undergo a freezing transition while the topological phase supporting them remains intact.
In classical and quantum frustrated magnets the interactions in combination with the lattice structure impede the spins to order in optimal configurations at zero temperature. The theoretical interest in their classical realisations has been boosted by the artificial manufacture of materials with these properties, that are of flexible design. This note summarises work on the use of vertex models to study bidimensional spin-ices samples, done in collaboration with R. A. Borzi, M. V. Ferreyra, L. Foini, G. Gonnella, S. A. Grigera, P. Guruciaga, D. Levis, A. Pelizzola and M. Tarzia, in recent years. It is an invited contribution to a J. Stat. Phys. special issue dedicated to the memory of Leo P. Kadanoff.
Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects.
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