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Register a new userLow-temperature properties of the dilute dipolar magnet LiHo_xY_(1-x)F_4
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We analyze recent experiments on the dilute rare-earth compound LiHo_xY_(1-x)F_4 in the context of an effective Ising dipolar model. Using a Monte Carlo method we calculate the low-temperature behavior of the specific heat and linear susceptibility, and compare our results to measurements. In our model the susceptibility follows a Curie-Weiss law at high temperature, chi ~ 1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, C_max(T) ~ x, in disagreement with recent experiments. Experimental studies do not reach a consensus on the functional form of these quantities, and in particular we do not see reported scalings of the form chi ~ T^-0.75 and chi ~ exp(-T/T_0). Furthermore we calculate the ground state magnetization as a function of dilution, and re-examine the phase diagram around the critical dilution x_c=0.24(3). We find that the spin glass susceptibility for the Ising model does not diverge below x_c, while recent experiments give strong evidence for a stable spin-glass phase in LiHo_0.167Y_0.833F_4.
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$LiHo_xY_{1-x}F_4$ is an insulating system where the magnetic Ho$^{3+}$ ions have an Ising character, and interact mainly through magnetic dipolar fields. We used the muon spin relaxation technique to study the nature of the ground state for samples with x=0.25, 0.12, 0.08, 0.045 and 0.018. In contrast with some previous works, we have not found any signature of canonical spin glass behavior down to $approx$15mK. Instead, below $approx$300mK we observed dynamic magnetism characterized by a single correlation time with a temperature independent fluctuation rate. We observed that this low temperature fluctuation rate increases with x up to 0.08, above which it levels off. The 300mK energy scale corresponds to the Ho3+ hyperfine interaction strength, suggesting that the hyperfine interaction may be intimately involved with the spin dynamics in this system.
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.
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.
In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $theta$ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that $theta = 1/2$ which is different from the zero-temperature numerical value which is close to 0.241. This result implies that unlike the $(1+1)$ system in the two-dimensional case the free energy scaling exponent is non-universal being temperature dependent.
Pyrochlore magnets are candidates for spin-ice behavior. We present theoretical simulations of relevance for the pyrochlore family R2Ti2O7 (R= rare earth) supported by magnetothermal measurements on selected systems. By considering long ranged dipole-dipole as well as short-ranged superexchange interactions we get three distinct behaviours: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, (iii) a partially ordered state with a sharp transition to paramagnetism. Thus these competing interactions can induce behaviour very different from conventional ``spin ice. Closely corresponding behaviour is seen in the real compounds---in particular Ho2Ti2O7 corresponds to case (iii) which has not been discussed before, rather than (ii) as suggested earlier.
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