Session R39: Exotic Magnetic Orders and Excitations

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The compound Pb₂VO(PO₄)₂ belongs to the family of vanadyl phosphates and hosts magnetically almost isolated layers of V⁴⁺ ions which carry a spin S=½. The spins Hamiltonian approximates a square lattice with ferromagnetic nearest and anti ferromagnetic next nearest couplings. A previous neutron study has found that the antiferromagnetic ground state is less frustrated than thermodynamic measurements had initially suggested [1]. It is therefore rather surprisingly that for fields along the magnetic anisotropy axis, a new magnetic state emerges through a discontinuous transition and persists in a narrow field range just below saturation. In this talk the full H-T phase diagram, determined by means of magnetization, torque, NMR and high field neutron diffraction experiments, are presented and properties of the presaturation phase are discussed [2].

[1] S. Bettler et al, Phys. Rev. B 99, 184437 (2019)
[2] F. Landolt et al, Phys. Rev. B 102, 094414 (2020).   

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In the Shastry-Sutherland model, the ground state is expected to change from a spin dimer singlet state to a novel, intermediate 4-spin plaquette singlet state, then to an antiferromagnet state, when the relative strength of the nearest neighbor and next-nearest neighbor interactions (J/J’) is tuned. SrCu₂(BO₃)₂ realizes the Shastry-Sutherland model at ambient pressure and can be tuned to other phases by application of high pressure, thus attracting considerable interests. Recent experimental advances have revealed the presence of an intermediate ground state with signatures of a 4-spin plaquette singlet state at high pressure. However, this intermediate phase also feature signatures that clearly deviate from the prediction of the ideal Shastry-Sutherland model. Therefore, the nature of this plaquette phase and how it evolves into other phases remain unclear. Here, we report a comprehensive study of the quantum phase diagram of the plaquette state by tuning the pressure and magnetic field, using a highly sensitive magnetization measurement technique. Our results reveal the emergence of a sequence of ground states once the spin dimer singlet and the plaquette singlet phase are suppressed by the field, which are further corroborated by our theoretical simulations.   

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The order parameter of S=1 easy-plane antiferromagnets can be characterized by a complex number. The phase fluctuations of the order parameter correspond to transverse modes (magnons), whereas amplitude fluctuations produce longitudinal modes. Due to the gapless nature of the transverse mode, the longitudinal mode is kinematically allowed to decay into pairs of transverse modes. Inelastic neutron scattering measurements on an effective S=1 tetragonal lattice compound Ba₂FeSi₂O₇ reveal this decay and the consequent renormalization of the longitudinal and transverse mode dispersions. By applying a generalized linear spin wave theory with one-loop corrections, we reproduce the observed decay and the renormalization of the different modes. Moreover, by including corrections beyond one-loop, we obtain a very accurate estimate of the critical single-ion easy-plane anisotropy required to induce a quantum phase transition into a quantum paramagnetic state.   

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In this talk I will discuss signatures of interactions between magnons that show up in the dynamical spin correlations of antiferromagnets in presence of a magnetic field, focusing on the high magnetization regime. I will first present our results for the antiferromagnetic spin-1/2 chain, where we uncover the appearance of two-magnon bound states in the transverse dynamical susceptibility. This bound state feature generalizes the one arising from string states in the Bethe ansatz solution of the integrable case. I will then address higher-dimensional systems and argue that these observations are not unique to 1D.   

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Exactly solvable Hamiltonians form important cornerstones in our understanding of quantum magnetism. Recently a class of ground state solvable (GSS) frustrated quantum magnets on any lattice composed of triangular motifs has been reported¹. The exact solutions (ES) require consistent three-coloring of the lattice sites. We apply the general principle of exact coloring GSS to long-range magnetic order on the triangular and extend it to unfrustrated bipartite lattices where the ES corresponds to a two-coloring ground state (GS). For several magnetization sectors, we show how the presence of ES in the deep XY regime of the XXZ model accounts for the corresponding antiferromagnetically ordered GS. We numerically demonstrate that for square and triangular lattice, the ordered physics of the solvable points respectively at J_z /J_xy (=Δ)=-1 and Δ=-0.5 adiabatically extend close to the Heisenberg regime Δ∼1. These findings are contrasted with an anisotropic generalization of the Majumdar-Ghosh model, which is proven to have exact dimer GS and three-coloring GS at Δ=-0.5, but where only the former survives as the GS for Δ>-0.5.

1. PRL 120, 117202 (2018); PRB 99, 104433 (2019)   

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Geometrical frustration and a high magnetic field are two key factors for realizing unconventional quantum states in magnetic materials. Specifically, conventional magnetic order can potentially be destroyed by competing interactions and may be replaced by an exotic state that is characterized in terms of quasiparticles called magnons, the density and chemical potential of which are controlled by the magnetic field. Here we show that a synthetic copper mineral, Cd-kapellasite, which comprises a kagomé lattice consisting of corner-sharing triangles of spin-1/2 Cu²⁺ ions, exhibits an unprecedented series of fractional magnetization plateaus in ultrahigh magnetic fields of up to 160 T. We propose that these quantum states can be interpreted as crystallizations of emergent magnons localized on the hexagon of the kagomé lattice. [1] Okuma, R., et al. Nature communications 10.1 (2019): 1-7.   

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The Ising model, with simple short-range interactions between constituents (e.g., spins), is a basic mathematical model in statistical mechanics for describing phase transitions in various many-body systems. It was rigorously proven that in one dimension, phase transitions do not exist in this model at any nonzero temperature because the free energy is analytic. Here I show that a family of strongly frustrated one-dimensional Ising model can exhibit a first-order-like phase transition at finite temperature via a virtual level crossing in the free energy, resulting in a large latent heat and an ultranarrow peak in the specific heat [1]. The critical temperature goes to zero as the transition width goes to zero; therefore, this ultranarrow phase transition does not violate the existing theorems and is an extension of the zero-temperature phase transition to the finite temperature regime, thus named marginal phase transition. These exact results expose a mathematical structure and unconventional order parameters that have not appeared before in phase transition problems, shedding new light not only on our understanding of phase transitions and the dynamic actions of frustration but also on one-dimensional device applications. [1] W. Yin, arXiv:2006.08921; arXiv:2006.15087 (2020).   

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Spin-nematic (quadrupolar) order is a typical less-visible order in magnetic systems. Proposing an efficient experimental way of detecting spin-nematic (SN) order is important to deepen the understanding of spin nematicity and frustrated magnetism. Several theoretical works have shown that in forced fully polarized states of SN ordered magnets, magnon pairs (molecule of two magnons) generally appear in addition to usual magnons. Moreover, a SN order is usually shown to occur as the result of the Bose-Einstein condensation of magnon pairs in a broad class of SN magnets. Therefore, the detection of magnon pairs can provide an indirect but strong evidence for the emergence of SN order. Since magnon pairs have angular momentum 2hbar, they can be excited through two-photon absorption with strong electromagnetic (EM) waves. Based on these backgrounds, we theoretically consider the magnon-pair resonance driven by strong EM wave in a fully polarized state of SN magnets. Using the quantum master equation for a nano spin model, we predict that magnon-pair resonance peak can be detected with currently available terahertz laser. I explain the essential aspects of our proposal.   

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The Axial Next Nearest Neighbor Ising model predicts a fractal (infinite) set of phases with incommensurate wave vectors that are separated by 1st order phase boundaries. This behavior emerges from a simple frustration condition between nearest and next-nearest neighbors along a chain of Ising spins. Here, we probe the dynamics of this scenario using Monte Carlo simulations and compare to X-ray photon correlation spectroscopy (XPCS) measurements in Lu2CoMnO6. We resonantly probe the dynamics of speckle within Mn and Co L3-edge antiferromagnetic Bragg peaks. Bragg peaks of incommensurate order slide towards commensurate `up up down down' spin order with decreasing temperature and increasing time. Analysis of the speckle dynamics supports a counter-intuitive dependence of the dynamics on temperature that is consistent with our simulations.   

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The standard paradigm of magnetic-saturation-by-BEC-of-magnons breaks down close to a classical ferro-antiferromagnetic transition [1]. Upon decreasing the external magnetic field the fully polarized state collapses before the single magnon instability is reached. New quantum presaturation phases with unusual long range orders may emerge, including spin density waves, nematics and chiral states.

Strong frustration of FM and AFM interactions is uncommon in materials. Among the most interesting candidates are the layered vanady phosphates ABVO(PO₄)₂ (proximate J₁-J₂ square lattices) and linear-chain molybdates (Rb, Cs)₂Cu₂Mo₃O₁₂ (J₁-J₂ spin chains). Both families are known for quite some time, but their investigation were hampered by a lack of single crystals. In recent breakthoughs, large crystals of BaCdVO(PO₄)₂ , Pb₂VO(PO₄)₂ , SrZnVO(PO₄)₂ were synthesized. The spin Hamiltonians was determined in neutron spectroscopy experiments [2] and the behavior in applied fields was studied in detail [3-5]. Indeed, novel presaturation phases were found in each of these materials, but seem to vary considerably between species.
Smaller single crystals of the molybdates are now also available [6,7]. The Cs system shows an entire cascade of field-induced transitions with a very distinctive presaturation phase [7]. The Rb material has a presaturation phase as well. It is more subtle and is only revealed in highly sensitive dielectric experiments.

It is a good moment in time for theorists to step in and help classify the animals in the zoo of new quantum presaturation phases in these compounds.

[1] H. T. Ueda and T. Momoi, Phys. Rev. B 87, 144417 (2013).
[2] Bettler et al., Phys. Rev. B 99, 184437(2019).
[3] Povarov et al., Phys. Rev. B 99 024413 (2019).
[4] Bhartiya et al., Phys. Rev. Research 1, 033078 (2019).
[5] Landolt et al., Phys. Rev. B 102, 094414 (2020).
[6] Hayashida et al., Phys. Rev. B 100, 134427 (2019).
[7] Flavian et al., Phys. Rev. B 101, 224408 (2020).   

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The rare earth element neodymium exhibits a series of complex magnetic phases as a function of temperature and applied magnetic fields. Neodymium crystallizes in a double hexagonal closed packed structure consisting of triangular nets of Nd stacked along the c-axis. Here we report the observation of a new set of magnetic modulation vectors through small angle neutron scattering (SANS) and single-crystal neutron diffraction measurements. While we find distinct modulations occur in different phases, this talk focuses on the modulations occurring for 5.9(1) ≤ T ≤ 7.6(1) K and µ₀H ≤ 1.0(1) T for fields applied along the c-axis. Within this phase, the modulation vectors are found to occur at 0.06 a* implying a characteristic length scale of ~52 Å. We discuss the possibility that these additional modulation vectors indicate the presence of frustration driven spin texture in the element Nd.