Investigation of the monopole magneto-chemical potential in spin ices using capacitive torque magnetometry

The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (J_eff) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho₂Ti₂O₇, and show that the magneto-chemical potential depends on the spin sublattice (α or β), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates the J_eff for the β-sublattice. Additional simulations, including next-nearest neighbor interactions (J₂), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test for J_eff and the spin-spin interactions that contribute to it.

Magnetic-field induced phase transitions in spin-ice materials have been investigated with various experimental techniques. Here, the authors demonstrate the capability of capacitive torque magnetometry in probing magnetic interaction energies and establishing magnetic phase boundaries in Ho₂Ti₂O₇.

Spin-lattice Coupling and the Emergence of the Trimerized Phase in the S=1 Kagome Antiferromagnet Na_{2}Ti_{3}Cl_{8}

Spin-1 antiferromagnets are abundant in nature, but few theories exist to understand their properties and behavior when geometric frustration is present. Here we study the S=1 kagome compound Na_{2}Ti_{3}Cl_{8} using a combination of density functional theory, exact diagonalization, and density matrix renormalization group approaches to achieve a first principles supported explanation of its exotic magnetic phases. We find that the effective magnetic Hamiltonian includes essential non-Heisenberg terms that do not stem from spin-orbit coupling, and both trimerized and spin-nematic magnetic phases are relevant. The experimentally observed structural transition to a breathing kagome phase is driven by spin-lattice coupling, which favors the trimerized magnetic phase against the quadrupolar one. We thus show that lattice effects can be necessary to understand the magnetism in frustrated magnetic compounds and surmise that Na_{2}Ti_{3}Cl_{8} is a compound that cannot be understood from only electronic or only lattice Hamiltonians, very much like VO_{2}.

Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain

NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.

Dynamical Structure Factor of the Three-Dimensional Quantum Spin Liquid Candidate NaCaNi_{2}F_{7}

We study the dynamical structure factor of the spin-1 pyrochlore material NaCaNi_{2}F_{7}, which is well described by a weakly perturbed nearest-neighbour Heisenberg Hamiltonian, Our three approaches-molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory-reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence with the exception of the lowest energies. We discuss two surprising aspects and their implications for quantum spin liquids in general: the complete lack of sharp quasiparticle excitations in momentum space and the success of the linear spin wave theory in a regime where it would be expected to fail for several reasons.

Macroscopically Degenerate Exactly Solvable Point in the Spin-1/2 Kagome Quantum Antiferromagnet

Frustrated quantum magnets are a central theme in condensed matter physics due to the richness of their phase diagrams. They support a panoply of phases including various ordered states and topological phases. Yet, this problem has defied a solution for a long time due to the lack of controlled approximations which make it difficult to distinguish between competing phases. Here we report the discovery of a special quantum macroscopically degenerate point in the XXZ model on the spin-1/2 kagome quantum antiferromagnet for the ratio of Ising to antiferromagnetic transverse coupling J_{z}/J=-1/2. This point is proximate to many competing phases explaining the source of the complexity of the phase diagram. We identify five phases near this point including both spin-liquid and broken-symmetry phases and give evidence that the kagome Heisenberg antiferromagnet is close to a transition between two phases.

Reentrant Phase Diagram of Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ Magnetic Field

We present a magnetic phase diagram of rare-earth pyrochlore Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along ⟨111⟩ above 0.65 T. A classical Monte Carlo analysis of published Hamiltonians does account for the critical field in the low T limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.

Emergent spin excitations in a Bethe lattice at percolation

We study the spin-1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even or odd sublattice imbalance resulting in "dangling spins" [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)]. These collectively act as "emergent" spin-1/2 degrees of freedom and are responsible for the creation of a set of low-lying "quasidegenerate states." Using density matrix renormalization group calculations, we detect the presence and location of these emergent spins. We find an effective Hamiltonian of these emergent spins, with Heisenberg interactions that decay exponentially with the distance between them.

Semistochastic projector Monte Carlo method

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.