arXiv subjects
Publications and source records attributed to M. J. P. Gingras.
We respond to the comment of Bramwell et al (arXiv:1111.4168v1) to our original publication (S. R. Dunsiger et al, Phys. Rev. Lett. 107, 207207 (2011)), detailing muon spin rotation measurements of the Spin Ice compound Dy2Ti2O7.
We use numerical linked cluster (NLC) expansions to compute the specific heat, C(T), and entropy, S(T), of a quantum spin ice model of Yb2Ti2O7 using anisotropic exchange interactions recently determined from inelastic neutron scattering measurements and find good agreement with experimental calorimetric data. In the perturbative weak quantum regime, this model has a ferrimagnetic ordered ground state, with two peaks in C(T): a Schottky anomaly signalling the paramagnetic to spin ice crossover followed at lower temperature by a sharp peak accompanying a first order phase transition to the ferrimagnetic state. We suggest that the two C(T) features observed in Yb2Ti2O7 are associated with the same physics. Spin excitations in this regime consist of weakly confined spinon-antispinon pairs. We suggest that conventional ground state with exotic quantum dynamics will prove a prevalent characteristic of many real quantum spin ice materials.
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 (muSR) experiment [S T Bramwell et al, Nature 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 muSR experiments in Dy_2Ti_2O_7 that such an effect is not observable in a TF muSR experiment. 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.
We present new high resolution inelastic neutron scattering data on the candidate spin liquid Tb2Ti2O7. We find that there is no evidence for a zero field splitting of the ground state doublet within the 0.2 K resolution of the instrument. This result contrasts with a pair of recent works on Tb2Ti2O7 claiming that the spin liquid behavior can be attributed to a 2 K split singlet-singlet single-ion spectrum at low energies. We also reconsider the entropy argument presented in Chapuis {\it et al.} as further evidence of a singlet-singlet crystal field spectrum. We arrive at the conclusion that estimates of the low temperature residual entropy drawn from heat capacity measurements are a poor guide to the single ion spectrum without understanding the nature of the correlations.
The rare earth pyrochlore magnet Yb2Ti2O7 is among a handful of materials that apparently exhibit no long range order down to the lowest explored temperatures and well below the Curie-Weiss temperature. Paramagnetic neutron scattering on a single crystal sample has revealed the presence of anisotropic correlations and recent work has led to the proposal of a detailed microscopic Hamiltonian for this material involving significantly anisotropic exchange. In this article, we compute the local sublattice susceptibility of Yb2Ti2O7 from the proposed model and compare with the measurements of Cao and coworkers [Physical Review Letters, {103}, 056402 (2009)], finding quite good agreement. In contrast, a model with only isotropic exchange and long range magnetostatic dipoles gives rise to a local susceptiblity that is inconsistent with the data.
The magnetic insulator Gd2Sn2O7 is one of many geometrically frustrated magnetic materials known to exhibit a nonzero muon spin polarization relaxation rate, $λ(T)$, down to the lowest temperature (T) studied. Such behaviour is typically interpreted as a significant level of persisting spin dynamics (PSD) of the host material. In the case of Gd2Sn2O7, such PSD comes as a surprise since magnetic specific heat measurements suggest conventional gapped magnons, which would naively lead to an exponentially vanishing $λ(T)$ as $T \rightarrow 0$. In contrast to most materials that display PSD, the ordered phase of Gd2Sn2O7 is well characterized and both the nature and the magnitude of the interactions have been inferred from the magnetic structure and the temperature dependence of the magnetic specific heat. Based on this understanding, the temperature dependence of the muon spin polarization relaxation through the scattering of spin waves (magnons) is calculated. The result explicitly shows that, despite the unusual extensive number of weakly dispersive (gapped)excitations characterizing Gd2Sn2O7, a remnant of the zero modes of the parent frustrated pyrochlore Heisenberg antiferromagnet, the temperature dependence of the calculated $λ(T)$ differs dramatically from the experimental one. Indeed, the calculation conforms to the naive expectation of an exponential collapse of $λ(T)$ at temperatures below ~ 0.7K. This result, for the first time, illustrates crisply and quantitatively the paradox that presents itself with the pervasive occurrence of PSD in highly frustrated magnetic systems as evinced by muon spin relaxation measurements.
We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.
Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many new types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band structure calculations and photoemission experiments on these systems, we include second and third neighbor hopping parameters, t' and t'', into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed, four hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4. Performing a spin wave analysis, we calculate the magnon dispersion as a function of U,t,t' and t''. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377, {2001}] for La2CuO4. The ring exchange terms are found essential, in particular to determine the relative sign of t' and t'', with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength U~8t consistent with Mott insulating behavior.
We study the ground state quantum spin fluctuations around the Néel ordered state for the one-band ($t,U$) Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian, $H_{\rm s}^{(4)}$, is generated using the canonical transformation method, expanding to order $t(t/U)^3$. $H_{\rm s}^{(4)}$ contains four-spin ring exchange terms as well as second and third neighbor bilinear spin-spin interactions. Transverse spin fluctuations are calculated to order $1/S$ using a numerical real space algorithm first introduced by Walker and Walsteadt. Additional quantum charge fluctuations appear to this order in $t/U$, coming from electronic hopping and virtual excitations to doubly occupied sites. The ground state staggered magnetization on the percolating cluster decreases with site dilution $x$, vanishing very close to the percolation threshold. We compare our results in the Heisenberg limit, $t/U \to 0$, with quantum Monte Carlo (QMC) results on the same model and confirm the existence of a systematic $x$-dependent difference between $1/S$ and QMC results away from $x=0$. For finite $t/U$, we show that the effects of both the ring exchange and charge fluctuations die away rapidly with increasing $t/U$. We use our finite $t/U$ results to make a comparison with results from experiments on La$_2$Cu$_{1-x}$(Mg/Zn)$_x$O$_4$.
P.B. Chakraborty {\it et al.}, Phys. Rev. B {\bf 70}, 144411 (2004)) study of the LiHoF$_4$ Ising magnetic material in an external transverse magnetic field $B_x$ show a discrepancy with the experimental results, even for small $B_x$ where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature $T$, versus transverse field phase diagram of LiHoF$_4$ in the regime of weak $B_x$. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF$_4$, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at $B_x=0$. Via this effective classical Hamiltonian, we study the $B_x-T$ phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. For example, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the $B_x-T$ phase diagram is modified when using different microscopic crystal field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small $B_x$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a $B_x-T$ phase diagram compatible with the experiments in the small semi-classical $B_x$ regime.
We present analytical and numerical evidence for the validity of an effective S=1/2 approach to the description of random field generation in S>=1, and especially in an S=1, dipolar spin glass models with strong uniaxial Ising anisotropy and subject to weak external magnetic field Bx transverse to the Ising direction. Explicitely Bx-dependent random fields are shown to naturally emerge in the effective low-energy description of a microscopic S=1 toy model. We discuss our results in relation to recent theoretical studies pertaining to the topic of Bx-induced random fields in the LiHo$_x$Y$_{1-x}$F$_4$ magnetic materials with the Ho$^{3+}$ Ising moments subject to a transverse field. We show that the S_{eff}=1/2 approach is able to capture both the qualitative and quantitative aspects of the physics at small Bx, giving results that agree with those obtained using conventional second order perturbation theory.
We have measured the low-temperature specific heat of the geometrically frustrated pyrochlore Heisenberg antiferromagnet Gd2Sn2O7 in zero magnetic field. The specific heat is found to drop exponentially below approximately 350 mK. This provides evidence for a gapped spin-wave spectrum due to an anisotropy resulting from single ion effects and long-range dipolar interactions. The data are well fitted by linear spin-wave theory, ruling out unconventional low energy magnetic excitations in this system, and allowing a determination of the pertinent exchange interactions in this material.
We investigate the problem of inelastic x-ray scattering in the spin$-{1/2}$ Heisenberg model on the square lattice. We first derive a momentum dependent scattering operator for the $A_{1g}$ and $B_{1g}$ polarization geometries. On the basis of a spin-wave analysis, including magnon-magnon interactions and exact-diagonalizations, we determine the qualitative shape of the spectra. We argue that our results may be relevant to help interpret inelastic x-ray scattering experiments in the antiferromagnetic phase of the cuprates.
The LiHo$_x$Y$_{1-x}$F$_4$ magnetic material in a transverse magnetic field $B_{x}\hat x$ perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the $B_{x}-$induced magnetization along the $\hat x$ direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho$^{3+}$ ions, {\it random fields} along the Ising $\hat z$ direction. This identifies LiHo$_x$Y$_{1-x}$F$_4$ in $B_x$ as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin glass transition with increasing $B_{x}$, and render the $B_{x}-$induced quantum criticality in LiHo$_x$Y$_{1-x}$F$_4$ likely inaccessible.
Motivated by various spin-1/2 compounds like Cs$_2$CuCl$_4$ or $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, we derive a Raman-scattering operator {\it à la} Shastry and Shraiman for various geometries. For T=0, the exact spectra is computed by Lanczos algorithm for finite-size clusters. We perform a systematic investigation as a function of $J_2/J_1$, the exchange constant ratio: ranging from $J_2=0$, the well known square-lattice case, to $J_2/J_1=1$ the isotropic triangular lattice. We discuss the polarization dependence of the spectra and show how it can be used to detect precursors of the instabilities of the ground state against quantum fluctuations.
We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U) to intermediate coupling limit ({\it i.e.} away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U)^3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U -> 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S=1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U, despite the fact that the moment of the spin Hamiltonien, which depends on transverse spin fluctuations only, in an increasing function of t/U. We also comment on quantitative aspects of the t/U and 1/S expansions.
Dy2Ti2O7 has been advanced as an ideal spin ice. We present a neutron scattering investigation of a sample of 162Dy2Ti2O7. The scattering intensity has been mapped in zero applied field in the hhl and hk0 planes at temperatures between 0.05 K and 20 K. The measured diffuse scattering (in the static approximation) has been compared to that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.
The pyrochlore antiferromagnet Tb2Ti2O7 has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local <111> Ising antiferromagnet at low temperatures, T < 10 K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2 K. However, muon spin resonance experiments reveal a paramagnetic structure down to tens of milli-Kelvin. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagnetic correlations can not be described without including the higher crystal field states. However, these fluctuations treated within the random phase approximation (RPA) fail to account for the lack of ordering in this system below 2 K. In this work, we briefly review the experimental evidence for the collective paramagnetic state of Tb2Ti2O7. The basic theoretical picture for this system is discussed, where results from classical spin models are used to motivate the investigation of quantum effects to lowest order via the RPA. Avenues for future experimental and theoretical work on Tb2Ti2O7 are presented.