Frustrated Spin Lattices Research Articles

Fluctuating magnetic droplets immersed in a sea of quantum spin liquid

The search of quantum spin liquid (QSL), an exotic magnetic state with strongly fluctuating and highly entangled spins down to zero temperature, is a main theme in current condensed matter physics. However, there is no smoking gun evidence for deconfined spinons in any QSL candidate so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report comprehensive and systematic measurements of the magnetic susceptibility, ultralow-temperature specific heat, muon spin relaxation (μSR), nuclear magnetic resonance (NMR), and thermal conductivity for NaYbSe2 single crystals, in which Yb3+ ions with effective spin-1/2 form a perfect triangular lattice. All these complementary techniques find no evidence of long-range magnetic order down to their respective base temperatures. Instead, specific heat, μSR, and NMR measurements suggest the coexistence of quasi-static and dynamic spins in NaYbSe2. The scattering from these quasi-static spins may cause the absence of magnetic thermal conductivity. Thus, we propose a scenario of fluctuating ferrimagnetic droplets immersed in a sea of QSL. This may be quite common on the way pursuing an ideal QSL, and provides a brand new platform to study how a QSL state survives impurities and coexists with other magnetically ordered states.

Mapping repulsive to attractive interaction in driven–dissipative quantum systems

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven–dissipative quantum systems. For the example of a photonic Bose–Hubbard dimer, we establish a one-to-one mapping relating cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with a time-reversal-invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and those in a non-frustrated partner lattice.

An efficient implementation of the hierarchical mean-field theory with large block

We present an efficient implementation of the hierarchical mean-field theory with large block in quantum spin systems. The wave function is a product of the large block states. Each large block state is a superposition of products of small block states. Our result is very close to that of the hierarchical mean-field in a numerical cost effective way. We test our method on a frustrated spin lattice.

Spin Frustration from cis-Edge or -Corner Sharing Metal-Centered Octahedra

A new strategy using cis-edge or -corner sharing metal-centered octahedra is described which enables interesting frustrated spin lattices to be targeted. The examination of "CuV2" triangular motifs in the two new compounds [enH2]Cu(H2O)2[V2O2F8] (1) and [Cu(H2O)(2,2'-bpy)]2[V2O2F8] (2) (where enH2 = ethylenediammonium and 2,2'-bpy =2,2'-bipyridyl) reveals that the [VOF4](2-) anions, which exhibit cis structure directing properties, lead to frustrated lattices owing to the competing ferro and antiferromagnetic interactions. There is direct coordination through two cis F(-) ligands (i.e., the F(-) ligand trans to O(2-) and one equatorial F(-) ligand) in both 1 and 2 owing to the significant π-bonding between the vanadium and the oxide ligand. We emphasize that most of triangular motifs reported in the literature are built of cis-edge or -corner sharing metal-centered octahedra, thus they can be used to target new materials exhibiting interesting magnetism such as spin frustration.

Magnetic properties of the frustrated magnet Cu5(PO4)3(OH)4 on a peculiar spin network composed of pentagons and triangles

Orthorombic Cu5(PO4)3(OH)4 (pseudomalachite) is a layered compound. Each Cu-O layer in this compound is separated by PO4 tetrahedra. The spin network in the bc-plane of a pseudomlachite is composed of triangles and pentagons, which will induce the spin frustration effect. This network may be a new type of geometrically frustrated spin lattice. Magnetic susceptibility, specific heat, high field magnetization measurements are used to study the magnetic properties of Cu5(PO4)3(OH)4 in natural mineral samples. Magnetic ordering is observed at around 4.2 K. The spin entropy change at the transition temperature is about one-fifth times smaller than that expected for a usual long-range order. A 1/5 magnetization plateau is observed in the high-field magnetization curve. The plateau is explained based on a simple model in which the spin network is assumed to be composed of chain, dimer and monomer units.

The zero-field magnetic ground state of EuC6 investigated by muon spectroscopy

The magnetic ground state of EuC6, a first-stage graphite intercalation compound, was investigated by means of zero-field muon spectroscopy. Below the Néel antiferromagnetic temperature (42K), the highly damped oscillations in the muon asymmetry could be modelled with a Bessel line shape, indicative of an incommensurate magnetic order. The internal magnetic field, as probed by the implanted muons, lies in the plane of the europium ions, has an average intensity of 150(22)mT, and seems to arise from a strong contact hyperfine interaction. The latter partially cancels out the dipolar contribution to the local field, in turn due to the localized Eu spins arranged in an antiferromagnetic triangular lattice (frustrated spin lattice) with negligible inter-layer couplings.

Orbitally relieved magnetic frustration inNaVO2

The magnetic properties of NaVO2 are investigated using full-potential linearized augmented plane wave method. We perform calculations for three structures. For the rhombohedral structure at 100 K, the t2g orbitals of V ions are split into upper a1g and lower e'g orbitals by a trigonal distortion of compression. For the monoclinic structure at 91.5 K, the system behaves like a frustrated spin lattice with spatially anisotropic exchange interactions. For another monoclinic structure at 20 K, the magnetic frustration is relieved by a lattice distortion which is driven by a certain orbital ordering, and the long-range magnetic ordering is thus formed. Moreover, the small magnetic moment originates from the compensation oforbital moment for the spin moment.

Exact eigenstates of highly frustrated spin lattices probed in high fields

Strongly frustrated antiferromagnets such as the magnetic molecule {Mo72Fe30}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M = Ns − n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T = 0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined.

Magnetic field-induced transitions in geometrically frustratedCo3V2O8single crystal

Magnetization and specific heat of the $S=3∕2$ antiferromagnet on a kagome staircase, ${\mathrm{Co}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, were investigated as a function of temperature and magnetic field. The low temperature magnetization data revealed unusual features related to the strongly frustrated spin lattice. Of particular interest were magnetic field induced phase transitions observed for various orientations of the magnetic field. Abrupt macroscopic magnetization jumps induced by a magnetic field directed along the $\mathbit{c}$-axis have been observed below $6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This effect was also observed for a high enough magnetic field applied in the $\mathbit{a}\text{\ensuremath{-}}\mathbit{c}$ plane. It is suggested that the jump, observed for $H\ensuremath{\parallel}\mathbit{c}$ is due to a spin reorientation phase transition. It was shown that ${\mathrm{Co}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ crystals are characterized by a strong magnetocrystalline anisotropy of an easy-plane type. This anisotropy is due to the presence of ${\mathrm{Co}}^{2+}$ ions in octahedral positions.

Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields

We consider the quantum spin-$s$ $XXZ$ Heisenberg antiferromagnet on the two- and three-dimensional pyrochlore lattices and examine a spin-Peierls mechanism of lowering the total energy by a lattice distortion in a high magnetic field. For the exact eigenstates consisting of several independent localized magnons in a ferromagnetic environment we show the existence of a spin-Peierls instability by rigorous analytical calculations. In addition we report on exact diagonalization data for finite two-dimensional pyrochlore lattices up to N=64 sites. We discuss a scenario of the field-tuned changes in the ground-state properties of the frustrated spin lattices due to the coupling between spin and lattice degrees of freedom.

Localized-magnon states in strongly frustrated quantum spin lattices

Recent developments concerning localized-magnon eigenstates in strongly frustrated spin lattices and their effect on the low-temperature physics of these systems in high magnetic fields are reviewed. After illustrating the construction and the properties of localized-magnon states we describe the plateau and the jump in the magnetization process caused by these states. Considering appropriate lattice deformations fitting to the localized magnons we discuss a spin-Peierls instability in high magnetic fields related to these states. Last but not least we consider the degeneracy of the localized-magnon eigenstates and the related thermodynamics in high magnetic fields. In particular, we discuss the low-temperature maximum in the isothermal entropy versus field curve and the resulting enhanced magnetocaloric effect, which allows efficient magnetic cooling from quite large temperatures down to very low ones.

Generalized Elitzur’s theorem and dimensional reductions

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are of current interest. These include liquid crystalline phases of Quantum Hall systems, orbital systems, geometrically frustrated spin lattices, Bose metals, and models of superconducting arrays.

Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spinlattices

For a class of frustrated spin lattices including for example the 1D sawtooth chain, the 2DKagomé and checkerboard, as well as the 3D pyrochlore lattices, we construct exact producteigenstates consisting of several independent, localized one-magnon states in aferromagnetic background. Important geometrical elements of the relevant lattices aretriangles being attached to polygons or lines. Then the magnons can be trapped on thesepolygons/lines. If the concentration of localized magnons is small, they can be distributedrandomly over the lattice. On increasing the number of localized magnons, theirdistribution over the lattice becomes more and more regular, and finally the magnonscondense in a crystal-like state.The physical relevance of these eigenstates emerges in high magnetic fields where theybecome groundstates of the system. As a result a macroscopic magnetization jumpappears in the zero-temperature magnetization curve just below the saturationfield. The height of the jump decreases with increasing spin quantum numberand vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices.

For a class of frustrated spin lattices including the Kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the Kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.