Two-dimensional Triangular Lattice Antiferromagnet Research Articles

Triply Ordered 6H Halide Perovskites: A Family of Triangular Lattice Antiferromagnets.

Three new hexagonal perovskites with Cs3M+M2+RhCl9 (M+ = Na+, Ag+; M2+ = Mn2+, Fe2+) stoichiometry have been synthesized from solution precipitation reactions. These air-stable compounds crystallize as triply cation-ordered variants of the 6H perovskite structure. This structure contains octahedra that share a common face to form M2+RhCl94- dimers that are arranged on a two-dimensional triangular network. M+ cations reside in octahedral holes located between dimer layers and connect M2+RhCl94- dimers through corner-sharing linkages. The cation sites in the corner-sharing layers are fully occupied by Na+/Ag+, except for Cs3AgMnRhCl9, where a small amount of Ag+/Mn2+ antisite disorder is observed. The M2+RhCl94- dimers adopt an ordered configuration that lowers the symmetry from P63/mmc to P63mc. Optical absorption in the near ultraviolet (UV) and visible regions is dominated by Rh d-to-d transitions and metal-to-metal charge transfer transitions. Variable temperature magnetic susceptibility measurements show no sign of long-range magnetic order down to 2 K. Curie-Weiss fits reveal relatively weak antiferromagnetic interactions between M2+ ions, with Weiss constants that range from -2.3 to -5.4 K. The strength of the antiferromagnetic interactions between M2+ ions increases as the covalency of the M2+-Cl bond increases. The ordering of three different cations in the 6H perovskite structure diminishes magnetic coupling between layers, leading to a new family of two-dimensional triangular lattice antiferromagnets.

Competition between magnetic interactions and structural instabilities leading to itinerant frustration in the triangular lattice antiferromagnet LiCrSe2

LiCrSe2 constitutes a recent valuable addition to the ensemble of two-dimensional triangular lattice antiferromagnets. In this work, we present a comprehensive study of the low temperature nuclear and magnetic structure established in this material. Being subject to a strong magnetoelastic coupling, LiCrSe2 was found to undergo a first order structural transition from a trigonal crystal system (Pbar{3}m1) to a monoclinic one (C2/m) at Ts = 30 K. Such restructuring of the lattice is accompanied by a magnetic transition at TN = 30 K. Refinement of the magnetic structure with neutron diffraction data and complementary muon spin rotation analysis reveal the presence of a complex incommensurate magnetic structure with a up-up-down-down arrangement of the chromium moments with ferromagnetic double chains coupled antiferromagnetically. The spin axial vector is also modulated both in direction and modulus, resulting in a spin density wave-like order with periodic suppression of the chromium moment along the chains. This behavior is believed to appear as a result of strong competition between direct exchange antiferromagnetic and superexchange ferromagnetic couplings established between both nearest neighbor and next nearest neighbor Cr3+ ions. We finally conjecture that the resulting magnetic order is stabilized via subtle vacancy/charge order within the lithium layers, potentially causing a mix of two co-existing magnetic phases within the sample.

Nuclear and magnetic spin structure of the antiferromagnetic triangular lattice compound LiCrTe2 investigated by mu ^+SR, neutron and X-ray diffraction

Two-dimensional (2D) triangular lattice antiferromagnets (2D-TLA) often manifest intriguing physical and technological properties, due to the strong interplay between lattice geometry and electronic properties. The recently synthesized 2-dimensional transition metal dichalcogenide LiCrTe_2, being a 2D-TLA, enriched the range of materials which can present such properties. In this work, muon spin rotation (mu ^+SR) and neutron powder diffraction (NPD) have been utilized to reveal the true magnetic nature and ground state of LiCrTe_2. From high-resolution NPD the magnetic spin order at base-temperature is not, as previously suggested, helical, but rather collinear antiferromagnetic (AFM) with ferromagnetic (FM) spin coupling within the ab-plane and AFM coupling along the c-axis. The value if the ordered magnetic Cr moment is established as mu _{textrm{Cr}}= 2.36~mu _{textrm{B}}. From detailed mu ^+SR measurements we observe an AFM ordering temperature T_{textrm{N}}approx 125 K. This value is remarkably higher than the one previously reported by magnetic bulk measurements. From mu ^+SR we are able to extract the magnetic order parameter, whose critical exponent allows us to categorize LiCrTe_2 in the 3D Heisenberg AFM universality class. Finally, by combining our magnetic studies with high-resolution synchrotron X-ray diffraction (XRD), we find a clear coupling between the nuclear and magnetic spin lattices. This suggests the possibility for a strong magnon–phonon coupling, similar to what has been previously observed in the closely related compound LiCrO_2.

Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy

Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state whose low-energy behavior is described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their fractional, chargeless nature. Here we use scanning tunneling spectroscopy to image spinon density modulations arising from a spinon Fermi surface instability in single-layer 1T-TaSe$_2$, a two-dimensional Mott insulator. We first demonstrate the existence of localized spins arranged on a triangular lattice in single-layer 1T-TaSe$_2$ by contacting it to a metallic 1H-TaSe$_2$ layer and measuring the Kondo effect. Subsequent spectroscopic imaging of isolated, single-layer 1T-TaSe$_2$ reveals long-wavelength modulations at Hubbard band energies that reflect spinon density modulations. This allows direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a 2D quantum spin liquid. These results establish single-layer 1T-TaSe$_2$ as a new platform for studying novel two-dimensional quantum-spin-liquid phenomena.

Successive phase transitions and magnetization plateau in the spin-1 triangular-lattice antiferromagnet Ba2La2NiTe2O12 with small easy-axis anisotropy

The crystal structure and magnetic properties of the spin-1 triangular-lattice antiferromagnet Ba$_2$La$_2$NiTe$_2$O$_{12}$ are reported. Its crystal structure is trigonal $R\bar{3}$, which is the same as that of Ba$_2$La$_2$NiW$_2$O$_{12}$ [Y. Doi et al., J. Phys.: Condens. Matter 29, 365802 (2017)]. However, the exchange interaction $J/k_{\mathrm{B}}\simeq19$ K is much greater than that observed in the tungsten system. At zero magnetic field, Ba$_2$La$_2$NiTe$_2$O$_{12}$ undergoes successive magnetic phase transitions at $T_{\mathrm{N}1}=9.8$ K and $T_{\mathrm{N}2}=8.9$ K. The ground state is accompanied by a weak ferromagnetic moment. These results indicate that the ground-state spin structure is a triangular structure in a plane perpendicular to the triangular lattice owing to the small easy-axis-type anisotropy. The magnetization curve exhibits the one-third plateau characteristic of a two-dimensional triangular-lattice Heisenberg-like antiferromagnet. Exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate the large difference in the exchange constants between tellurium and tungsten systems and the good two-dimensionality of the tellurium system.

Hybridization and Decay of Magnetic Excitations in Two-Dimensional Triangular Lattice Antiferromagnets

Elementary quasiparticles in solids such as phonons and magnons occasionally have nontrivial interactions between them, as well as among themselves. As a result, their energy eigenvalues are renormalized, the quasiparticles spontaneously decay into a multi-particle continuum state, or they are hybridized with each other when their energies are close. As discussed in this review, such anomalous features can appear dominantly in quantum magnets but are not, a priori, negligible for magnetic systems with larger spin values and noncollinear magnetic structures. We review the unconventional magnetic excitations in two-dimensional triangular lattice antiferromagnets and discuss their implications on related issues.

Magnetic excitations in the bulk multiferroic two-dimensional triangular lattice antiferromagnet (Lu,Sc)FeO3

Noncollinear two-dimensional triangular lattice antiferromagnets (2D TLAFs) are currently an area of very active research due to their unique magnetic properties, which lead to nontrivial quantum effects that experimentally manifest themselves in the spin excitation spectra. Recent examples of such insulating 2D TLAFs include $(\mathrm{Y},\mathrm{Lu}){\mathrm{MnO}}_{3}, {\mathrm{LiCrO}}_{2}$, and ${\mathrm{CuCrO}}_{2}$. Hexagonal ${\mathrm{LuFeO}}_{3}$ is a recently synthesized 2D TLAF which exhibits properties of an ideal multiferroic material, partially because of the high spin ($S=5/2$) and strong magnetic superexchange interactions. We report the full range of spin dynamics in a bulk single crystal of $({\mathrm{Lu}}_{0.6}{\mathrm{Sc}}_{0.4}){\mathrm{FeO}}_{3}$ (Sc doping to stabilize the hexagonal structure) measured via time-of-flight inelastic neutron scattering. Modeling with linear spin-wave theory yields a nearest-neighbor exchange coupling of $J=4.0(2)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ (density functional theory calculations for $h\ensuremath{-}{\mathrm{LuFeO}}_{3}$ predicted a value of 6.31 meV) and anisotropy values of ${K}_{D}=0.17(1)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ (easy plane) and ${K}_{A}=\ensuremath{-}0.05(1)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ (local easy axis). It is observed that the magnon bandwidth of the spin-wave spectra is twice as large for $h\ensuremath{-}(\text{Lu},\mathrm{Sc}){\mathrm{FeO}}_{3}$ as it is for $h\ensuremath{-}{\mathrm{LuMnO}}_{3}$.

Lattice distortion effects on the frustrated spin-1 triangular-antiferromagnet A3NiNb2O9 ( A=Ba , Sr, and Ca)

In the geometrically frustrated materials with the low-dimensional and small spin moment, the quantum fluctuation could interfere with the complicated interplay of the spin, electron, lattice and orbital interactions, and host exotic ground states such as nematic spin-state and chiral liquid phase. While the quantum phases of the one-dimensional chain and S - 1/2 two-dimensional triangular-lattice antiferromagnet (TLAF) had been more thoroughly investigated by both theorists and experimentalists, the work on S = 1 TLAF has been limited. We induced the lattice distortion into the TLAFs, A3NiNb2O9 (A = Ba, Sr, and Ca) with S (Ni2+) = 1, and applied the thermodynamic, magnetic and neutron scattering measurements. Although A3NiNb2O9 kept the non-collinear 120{\deg} antiferromagnetic phase as the ground state, the Ni2+-lattice changed from the equilateral triangle (A = Ba) into isosceles triangle (A = Sr and Ca). The inelastic neutron scattering data were simulated by the linear spin-wave theory, and the competition between the single-ion anisotropy and the exchange anisotropy from the distorted lattice was discussed.

Berezinskii-Kosterlitz-Thouless type scenario in the molecular spin liquid ACr2O4(A=Mg,Zn,Cd)

The spin relaxation in chromium spinel oxides $A$Cr$_{2}$O$_{4}$ ($A=$ Mg, Zn, Cd) is investigated in the paramagnetic regime by electron spin resonance (ESR). The temperature dependence of the ESR linewidth indicates an unconventional spin-relaxation behavior, similar to spin-spin relaxation in the two-dimensional (2D) chromium-oxide triangular lattice antiferromagnets. The data can be described in terms of a generalized Berezinskii-Kosterlitz-Thouless (BKT) type scenario for 2D systems with additional internal symmetries. Based on the characteristic exponents obtained from the evaluation of the ESR linewidth, short-range order with a hidden internal symmetry is suggested.

Neutron scattering study of Ag, Mg and Al substitution effects on the magnetic excitations in CuCrO2

CuCrO2 is a quasi two-dimensional triangular-lattice antiferromagnet with S = 3/2. Recently, it was found that small amount of element substitution strongly affects magnetic and transport properties. In the present study, we studied magnetic excitations in powder samples of CuCrO2,Cu0.85Ag0.15CrO2,CuCr0.97Mg0.03CrO2 and CuCr0.85Al0.15O2 by inelastic neutron scattering using the chopper spectrometer AMATERAS at J-PARC. We observed a variety of the magnetic excitations induced by different types of the element substitutions, and they should be keys to understand the magnetic and transport properties.

Traces of Z2-Vortices in CuCrO2, AgCrO2, and PdCrO2

The spin-spin relaxation of the two-dimensional triangular lattice antiferromagnets CuCrO 2 , AgCrO 2 , and PdCrO 2 is investigated by electron spin resonance spectroscopy. The data proof excellent agreement with very recent predictions for the Z 2 -vortex ordering scenario in triangular Heisenberg antiferromagnets derived by Okubo and Kawamura.

High-Field and Multi-Frequency ESR in the Quasi Two-Dimensional Triangular-Lattice Antiferromagnet CuCrO2

We have performed high-field and multi-frequency electron spin resonance (ESR) and magnetization measurements in magnetic fields up to about 53 T on single crystals of a delafossite triangular-lattice antiferromagnet CuCrO2, which has been proposed to show an out-of-plane 120° spiral spin structure below about 24 K. We calculated ESR resonance modes and magnetization curves assuming an Ising-like Heisenberg Hamiltonian with a spiral spin structure by a mean-field theory. The experimental results can be well reproduced using the following parameters, the intralayer exchange constant J/kB=26.9 K, the easy-axis anisotropy D/kB=−0.47 K, and the in-plane g-factor gab=2.0.

Partially disordered antiferromagnetic state in two-dimensional triangular-lattice antiferromagnet

The partially disordered antiferromagnetic (PDA) state, as an exotic phase peculiar to the antiferromagnet with Ising spin in triangular lattice, is investigated by using Monte Carlo simulations of Wang–Landau algorithm and Glauber algorithm. It is revealed that PDA state, as the ground state of the triangular antiferromagnetic system, presents the complicated spin configuration due to geometrical frustration. The formation of multi-domain structure within the framework of honeycomb antiferromagnet results in the high degeneracy of PDA state. And this degeneracy of ground state can be lifted by a small magnetic field. Consequently the system shows the ferrimagnetic state, and the magnetization plateau of 1/3 saturate value ( M s ) is observed in many experiments. Moreover, due to the multi-domain structure of PDA state and those spins on domain walls, the metastable steps may manifest themselves superposed on the 1 / 3 M s plateau in some special cases.

Vortex dynamics and frustration in two-dimensional triangular chromium lattices

The spin dynamics of the two-dimensional (2D) triangular lattice antiferromagnets ${\text{HCrO}}_{2}$, ${\text{LiCrO}}_{2}$, and ${\text{NaCrO}}_{2}$ is investigated by electron spin resonance. In these oxides, on approaching the N\'eel temperature ${T}_{\text{N}}$ from above, the divergence of the temperature dependent linewidth is well described in terms of a Berezinskii-Kosterlitz-Thouless scenario due to magnetic vortex-antivortex pairing. A refined analysis suggests analogies to the melting scenario of a 2D triangular lattice described by Nelson, Halperin, and Young.

Spin Disorder on a Triangular Lattice

As liquids crystallize into solids on cooling, spins in magnets generally form periodic order. However, three decades ago, it was theoretically proposed that spins on a triangular lattice form a liquidlike disordered state at low temperatures. Whether or not a spin liquid is stabilized by geometrical frustration has remained an active point of inquiry ever since. Our thermodynamic and neutron measurements on NiGa2S4, a rare example of a two-dimensional triangular lattice antiferromagnet, demonstrate that geometrical frustration stabilizes a low-temperature spin-disordered state with coherence beyond the two-spin correlation length. Spin liquid formation may be an origin of such behavior.

High-field magnetization of triangular lattice antiferromagnet: GdPd 2Al 3

Magnetic properties of GdPd 2Al 3 single-crystalline samples where Gd 3+ ions form the triangular lattice have been studied by high field magnetization measurements. Large magnetic anisotropic features were observed in the ordered state in spite of the 8 S 7/2 state for Gd 3+ ions. These anomalous properties of GdPd 2Al 3 are discussed in terms of a two-dimensional triangular lattice antiferromagnet.

Critical behavior of antiferromagnets with chiral symmetry

The quasi-one-dimensional and two-dimensional triangular lattice antiferromagnets give rise to new critical behavior which is due to an additional symmetry of chirality. Experiments performed recently on easy-axis and easy-plane compounds, notably specific-heat experiments of high accuracy, clearly demonstrate that critical exponents and amplitude ratios of the specific heat are in good agreement with predictions for chiral behavior. It is also possible to observe a crossover induced, e.g. by magnetic fields, from non-chiral to chiral universality classes.

Optical Investigation of the Magnetic Excitations in Two-Dimensional Triangular Lattice Antiferromagnets

We have investigated exciton-magnon absorption spectra in VX 2 (X=Cl, Br and I) and LiCrO 2 known as two-dimensional Heisenberg triangular lattice antiferromagnets (2DH TAL-AF) in order to study the effect of the peculiar spin frustration on the magnetic elementary excitations. In VX 2 (X=Cl and Br) and LiCrO 2 , the temperature dependence of the line width of the exciton-magnon absorption resembles closely that of the density of the characteristic point defects known as Z 2 -vortex in 2DH TAL-AF. Thus the line width of the exciton magnon absorption in 2DH TAL-AF exhibits Z 2 -vortex induced broadening. We also reported the magnetic Raman scattering in VCl 2 and VI 2 .

Ferromagnetic Short-Range Correlations in a Two-Dimensional Triangular Lattice Antiferromagnet with S=1/2 LiNiO2

We have demonstrated that a two-dimensional triangular lattice antiferromagnet with spin=1/2 LiNiO 2 reveals ferromagnetic short-range spin correlations in forward scattering below T N1 ∼240 K, unlike other two-dimensional trianglar lattice antiferromagnets. The intensity of diffuse scattering in the forward direction appears below T N1 , and monotonically increases as the temperature is lowered, then shows a sharp divergence at T N2 ∼35 K. The present results suggest that a frozen spin pattern with the ferromagnetic short-range correlation similar to the spin glass phase is realized at the low-temperature phase below T N2 . In contrast, no appreciable intensity was detected around the (\(\frac{1}{3}\), \(\frac{1}{3}\), n ) positions, being consistent with early studies.

Z2Vortex-Induced Broadening of the EPR Linewidth in the Two-Dimensional Triangular Lattice Antiferromagnets, HCrO2and LiCrO2

The title compounds are the family of the AMO 2 -type (R\bar3m) crystal which has a pronounced layer structure and are promising candidates for the two-dimensional Heisenberg triangular lattice antiferromagnet (2DH TAL-AF). The interesting observation is that a singular point of the EPR signal is located around T KM =0.66 J S 2 for the critical temperature of phase transition associated with the pairing-dissociation of the Z 2 vortices, suggesting the present system behaves as 2DH TAL-AF down to very close to T KM . The EPR linewidth exhibits Z 2 vortex-induced broadening above the critical temperature which is inversely proportional to the thermally excited vortex density, n v ∝exp (- E v / k B T ) with the activation energy \(E_{\text{v}}{\cong}4k_{\text{B}}T_{\text{KM}}\).