The rare-earth magnet TmMgGaO 4 is proposed to be an intrinsic quantum Ising magnet described by the antiferromagnetic transverse field Ising model (TFIM) on a triangular lattice, where the relevant degrees of freedom are the nondegenerate dipole-multipole doublets of the Tm 3+ ions and the transverse field has an intrinsic origin from the weak splitting of the doublet.We compare this special doublet of Tm 3+ with the dipole-octupole Kramers doublet.We study the proposed effective model for the Tm-based triangular lattice and consider the effects of external magnetic fields and finite temperatures.From the orthogonal operator approach, we show that the TFIM with the three-sublattice intertwined ordered state agrees with the experiments and further clarify the discrepancy in the numbers of the magnetic sublattices and the measured magnon branches.We make specific predictions for the evolution of the magnetic properties with the external magnetic field.Furthermore, we demonstrate that an emergent U(1) symmetry emerges in thermal melting of the underlying orders and at the criticality, and summarize the previously known signatures related to the finite-temperature Berezinskii-Kosterlitz-Thouless physics.We discuss the broad relevance of intrinsic quantum Ising magnets to many other systems, especially Tm-based materials.
Abstract Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations—of both equilibrium and dynamical properties—for a frustrated rare-earth magnet TmMgGaO 4 (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz–Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex–antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties.
Frustrated magnets host the promises of material realizations of new paradigm of quantum matter, while direct comparison of unbiased model calculations with experimental measurements is still very challenging. Here, we design and implement a protocol of employing many-body computation methodologies for accurate model calculation -- both equilibrium and dynamical properties -- of a frustrated rare-earth magnet TmMgGaO
4 (TMGO), which perfectly explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz-Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex-antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics and we further propose experimental detections of its intriguing properties.
Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with
C3 symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic investigations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Starting from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D
q=3 Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet
TmMgGaO4 and programmable quantum simulators are also discussed.
Transverse field Ising model is a common model in quantum magnetism and is often illustrated as an example for quantum phase transition.Its physical origin in quantum magnets, however, is actually not quite well-understood.The quantum mechanical properties of this model on frustrated systems are not well-understood either.We here clarify the physical origin, both extrinsic one and intrinsic one, for the transverse field of the quantum Ising model, and then explain the quantum effects in the kagome system.We discuss the quantum plaquette order and the quantum phase transition out of this ordered state in the rare-earth kagome magnets.Our specific results can find their relevance in the rare-earth tripod kagome magnets.
A transverse magnetic field $\mathrm{\ensuremath{\Gamma}}$ is known to induce antiferromagnetic three-sublattice order of the Ising spins ${\ensuremath{\sigma}}^{z}$ in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector
Q: $\ensuremath{\langle}{\ensuremath{\sigma}}^{z}(\stackrel{P\vec}{R}){\ensuremath{\sigma}}^{z}(0)\ensuremath{\rangle}\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{R})/{|\stackrel{P\vec}{R}|}^{\ensuremath{\eta}(T)}$ with the temperature-dependent power-law exponent $\ensuremath{\eta}(T)\ensuremath{\in}(1/9,1/4)$. Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility ${\ensuremath{\chi}}_{u}(L)$ of an $L\ifmmode\times\else\texttimes\fi{}L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular
L dependence ${\ensuremath{\chi}}_{u}(L)\ensuremath{\sim}{L}^{2\ensuremath{-}9\ensuremath{\eta}}$ when $\ensuremath{\eta}(T)$ is in the range
(1/9,2/9). This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility ${\ensuremath{\chi}}_{u}(B)$ to a uniform field
B along the easy axis is singular at intermediate temperatures in the small
B limit, ${\ensuremath{\chi}}_{u}(B)\ensuremath{\sim}{|B|}^{\ensuremath{-}\frac{4\ensuremath{-}18\ensuremath{\eta}}{4\ensuremath{-}9\ensuremath{\eta}}}$ for $\ensuremath{\eta}(T)\ensuremath{\in}(1/9,2/9)$, although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility ${\ensuremath{\chi}}_{\mathbf{Q}}$) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (
J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.
Mott-insulating transition metal oxides containing
t2g4 ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin-
21. We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using
Ru4+ as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.