Experimental signatures of quantum and topological states in frustrated magnetism

Abstract

Frustration in magnetic materials arising from competing exchange interactions can prevent the system from adopting long-range magnetic order and can instead lead to a diverse range of novel quantum and topological states with exotic quasiparticle excitations. Here, we review prominent examples of such emergent phenomena, including magnetically-disordered and extensively degenerate spin ices, which feature emergent magnetic monopole excitations, highly-entangled quantum spin liquids with fractional spinon excitations, topological order and emergent gauge fields, as well as complex particle-like topological spin textures known as skyrmions. We provide an overview of recent advances in the search for magnetically-disordered candidate materials on the three-dimensional pyrochlore lattice and two-dimensional triangular, kagome and honeycomb lattices, the latter with bond-dependent Kitaev interactions, and on lattices supporting topological magnetism. We highlight experimental signatures of these often elusive phenomena and single out the most suitable experimental techniques that can be used to detect them. Our review also aims at providing a comprehensive guide for designing and investigating novel frustrated magnetic materials, with the potential of addressing some important open questions in contemporary condensed matter physics.

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• Fermionic response from fractionalization in an insulating two-dimensional magnet
• A centrosymmetric hexagonal magnet with superstable biskyrmion magnetic nanodomains in a wide temperature range of 100K to 340K
• Emergent properties hidden in plane view: Strong electronic correlations at oxide interfaces
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• Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3
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• Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO${}_4$
• Universal quantum critical dynamics of two-dimensional antiferromagnets
• Dimensional reduction at a quantum critical point
• Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice
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• Fast non-thermal switching between macroscopic charge-ordered quantum states induced by charge injection
• $\mu$SR evidence for the U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO${}_4$
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
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• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
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• Two-dimensional fluctuations at the quantum-critical point of CeCu_{6-x}Au_x
• Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition
• Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
• Muon spin rotation and relaxation in magnetic materials
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• Why spin ice obeys the ice rules
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• From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
• Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2
• Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice
• NaYbS${}_2$ - a new planar spin-$\frac{1}{2}$ triangular-lattice magnet and putative spin liquid
• Bubble and Skyrmion Crystals in Frustrated Magnets with Easy-Axis Anisotropy
• Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
• The Chemistry of Quantum Spin Liquids
• A new high-temperature quantum spin liquid with polaron spins
• Gapless spin-liquid state in the structurally disorder-free triangular antiferromagnet NaYbO${}_2$
• An anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Choreographed entangle dances: topological states of quantum matter
• Quantum Ice : a quantum Monte Carlo study
• Multiferroicity and skyrmions carrying electric polarization in GaV4S8
• Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu${}_3$(OH)${}_6$Cl${}_2$
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• Imaging spinon density modulations in a 2D quantum spin liquid
• Observation of spin current in quantum spin liquid
• Topography of Spin Liquids on a Triangular Lattice
• Reservoir Computing with Random Skyrmion Textures
• Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na2Co2TeO6
• Magnetic-Moment Fragmentation and Monopole Crystallization
• Magnetic Skyrmions on a Two-Lane Racetrack
• The planar thermal Hall conductivity in the Kitaev magnet α-RuCl3
• Rewritable Artificial Magnetic Charge Ice
• Correlated impurities and intrinsic spin liquid physics in the kagome material Herbertsmithite
• Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu${}_3$Zn(OH)${}_6$FBr
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• Amperean Pairing Instability in the U(1) Spin Liquid State with Fermi Surface and Application to $\kappa -(BEDT-TTF{)}_{2}C{u}_2(CN{)}_3$
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• Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Sample dependence of the half-integer quantized thermal Hall effect in the Kitaev candidate $\alpha$-RuCl${}_3$
• Experimental Observation of Bethe Strings
• Weak-field induced nonmagnetic state in a Co-based honeycomb
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• Unconventional Dynamics in Triangular Heisenberg Antiferromagnet NaCrO2
• Quantum spin liquid ground state in the disorder free triangular lattice NaYbS${}_2$
• Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS${}_2$
• Fractional Spin Fluctuation as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Candidate Quantum Spin Liquid in the Ce\textsuperscript{3+} Pyrochlore Stannate Ce${}_2$Sn${}_2$O${}_7$
• Realization of the kagome spin ice state in a frustrated intermetallic compound
• A quantum liquid of magnetic octupoles on the pyrochlore lattice
• Phonon and crystal field excitations in geometrically frustrated rare earth titanates
• Quantum phases of SrCu2(BO3)2 from high-pressure thermodynamics
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Topological quantum computation away from the ground state with Majorana fermions
• Possible itinerant excitations and quantum spin state transitions in the effective spin-1/2 triangular-lattice antiferromagnet Na${}_2$BaCo(PO${}_4$)${}_2$
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• Fluctuations and all-in$-$all-out ordering in dipole-octupole Nd2Zr2O7
• Weak Mott insulators on the triangular lattice: possibility of a gapless nematic quantum spin liquid
• Universal quantum computation based on nanoscale skyrmion helicity qubits in frustrated magnets
• Quantum spin liquid in the Ising triangular-lattice antiferromagnet neodymium heptatantalate
• Large topological Hall effect in a geometrically frustrated kagome magnet Fe${}_3$Sn${}_2$
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Witnessing entanglement in quantum magnets using neutron scattering
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Electric dipoles on magnetic monopoles in spin ice
• Gapless excitations in the ground state of 1T-TaS${}_2$
• Anisotropic susceptibilities in the honeycomb Kitaev system $\alpha$-RuCl${}_3$
• Pressure-Tuned Exchange Coupling of a Quantum Spin Liquid in the Molecular Triangular Lattice $\kappa$-(ET)${}_2$Ag${}_2$(CN)${}_3$
• Barlowite: A Spin-1/2 Antiferromagnet with a Geometrically Perfect Kagome Motif
• Bond disordered spin liquid and the honeycomb iridate H${}_3$LiIr${}_2$O${}_6$ $-$ abundant low energy density of states from random Majorana hopping
• Emergent Order in the Kagome Ising Magnet Dy3Mg2Sb3O14
• Topological frustration of artificial spin ice
• Coexisting localized and itinerant gapless excitations in a quantum spin liquid candidate 1T-TaS${}_2$
• Absence of magnetic thermal conductivity in the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2 -- revisited
• Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO${}_3$
• Static and dynamic properties of bimerons in a frustrated ferromagnetic monolayer
• Thermodynamic Evidence of Proximity to a Kitaev Spin-Liquid in Ag${}_3$LiIr${}_2$O${}_6$
• Phase diagram of the Shastry-Sutherland Compound SrCu2(BO3)2 under extreme combined conditions of field and pressure
• Absolute cross-section normalization of magnetic neutron scattering data
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Theory of two-dimensional nonlinear spectroscopy for the Kitaev spin liquid
• Magnetic Monopole Noise
• Thermal conductivity of the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2: No evidence of mobile gapless excitations
• Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4
• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Spin Liquid Ground State in the Frustrated Kagome Antiferromagnet MgCu3(OH)6Cl2
• Breakdown of magnetic order in the pressurized Kitaev iridate $\beta$-Li${}_2$IrO${}_3$
• Field-Induced Freezing of a Quantum Spin Liquid on the Kagome Lattice
• A magnetic continuum observed by terahertz spectroscopy in a quantum spin liquid candidate BaCo${}_2$(AsO${}_4$)${}_2$
• Dzyaloshinsky-Moriya interaction in vesignieite: A route to freezing in a quantum kagome antiferromagnet
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Spin dynamics and disorder effects in the S=1/2 kagome Heisenberg spin liquid phase of kapellasite
• Identification of Nuclear Relaxation Processes in a Gapped Quantum Magnet: Proton NMR in the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4
• Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7
• Sleuthing out exotic quantum spin liquidity in the pyrochlore magnet Ce${}_2$Zr${}_2$O${}_7$
• Ground-state phase diagram of an anisotropic spin-$1/2$ model on the triangular lattice
• The mother of all states of the kagome quantum antiferromagnet
• Theory of quantum impurities in spin liquids
• Dynamic properties of a diluted pyrochlore cooperative paramagnet (Tb_pY_{1-p})_2Ti_2O_7
• Anomalous Hall effect in the noncollinear antiferromagnet Mn5Si3
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Statistics of fractionalized excitations through threshold spectroscopy
• Re-entrance of Gapless Quantum Spin Liquids Observed in a Newly Synthesized Spin-1/2 Kagome Antiferromagnet $ZnC{u}_3(OH{)}_{6}S{O}_4$
• Heat transport study of the spin liquid candidate 1T-TaS2
• Heat capacity evidence for proximity to the Kitaev QSL in A${}_2$IrO${}_3$ ($A=$ Na, Li)
• Magnetic and transport anomalies in R2RhSi3 (R= Gd, Tb, and Dy), resembling those of an exotic magnetic skyrmion Gd2PdSi3
• Functional-renormalization-group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice
• Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T-TaSe${}_2$
• Emergence of spin singlets with inhomogeneous gaps in the kagome Heisenberg antiferromagnets Zn-barlowite and herbertsmithite
• Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid
• Multiphase Magnetism in Yb2Ti2O7
• Coherent Transmutation of Electrons into Fractionalized Anyons
• Coexistence of magnetic order and persistent spin dynamics in a quantum kagome antiferromagnet with no intersite mixing
• Quantum-disordered state of magnetic and electric dipoles in a hydrogen-bonded Mott system
• Materializing Rival Ground States in the Barlowite Family of Kagome Magnets: Quantum Spin Liquid, Spin Ordered, and Valence Bond Crystal States
• Topological magnons in a kagome lattice spin system with $XXZ$ and Dzyaloshinskii-Moriya interactions
• Two-dimensional Vortices in Superconductors
• Mott Transition and Superconductivity in Quantum Spin Liquid Candidate NaYbSe${}_2$
• Skyrmions in magnetic materials
• Quantum spin ice on the breathing pyrochlore lattice
• Controlling the helicity of magnetic skyrmions by electrical field in frustrated magnets
• Origin of Magnetic Ordering in a Structurally-Perfect Quantum Kagome Antiferromagnet
• Nature of the spin liquid ground state in a breathing kagome compound studied by NMR and series expansion
• Low-Energy Excitations and Ground State Selection in Quantum Breathing Pyrochlore Antiferromagnet Ba${}_3$Yb${}_2$Zn${}_5$O${}_{11}$
• Negative-vector-chirality 120${}^{\circ }$ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu${}_3$(OH)${}_6$Cl${}_3$
• Increased lifetime of metastable skyrmions by doping
• Partial up-up-down order with the continuously distributed order parameter in the triangular antiferromagnet TmMgGaO4
• Absence of zero-point entropy in a triangular Ising antiferromagnet
• On the multiferroic skyrmion-host GaV4S8
• Current-driven skyrmionium in a frustrated magnetic system
• Frustration-induced nanometre-scale inhomogeneity in a triangular antiferromagnet
• Quantum Kagome Ice
• Spinon Fractionalization from Dynamic Structure Factor of Spin-1/2 Heisenberg Antiferromagnet on the Kagome Lattice
• Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin liquid states in the frustrated triangular lattice
• Local Magnetism and Spin Dynamics of the Frustrated Honeycomb Rhodate Li2RhO3
• The Kondo effect in bosonic spin liquids
• From magnetic order to quantum disorder: a $\mu$SR study of the Zn-barlowite series of $S=\frac{1}{2}$ kagomé antiferromagnets, Zn${}_x$Cu${}_{4-x}$(OH)${}_6$FBr
• Dynamical fractal and anomalous noise in a clean magnetic crystal
• Development of short and long-range magnetic order in the double perovskite based frustrated triangular lattice antiferromagnet Ba2MnTeO6
• Electron spin resonance in S=1/2 antiferromagnets at high temperature
• Kondo impurities in the Kitaev spin liquid: Numerical renormalization group solution and gauge-flux-driven screening
• Unveiling contextual realities by microscopically entangling a neutron
• Signatures of a spin-1/2 cooperative paramagnet in the diluted triangular lattice of Y${}_2$CuTiO${}_6$
• Role of Antisymmetric Exchange in Selecting Magnetic Chirality in Ba${}_3$NbFe${}_3$Si${}_2$O${}_{14}$
• Magnetic excitations of the field induced states in BaCo2(AsO4)2 probed by time-domain terahertz spectroscopy
• Kondo screening in a charge-insulating spinon metal
• Optically probing symmetry breaking in the chiral magnet Cu2OSeO3
• Resonating valence bond liquid physics on the triangular lattice
• Multifarious skyrmion phases on a trilayer triangular lattice
• Effect of structural disorder on the Kitaev magnet Ag${}_3$LiIr${}_2$O${}_6$
• Effective Magnetic Hamiltonian at Finite Temperatures for Rare Earth Chalcogenides
• Magnetic impurity in a $U(1)$-Spin Liquid with a Spinon Fermi-Surface
• Instabilities of Spin-Liquid States in a Quantum Kagome Antiferromagnet
• Magnetic phases of skyrmion-hosting GaV${}_4$S${}_{8-y}$Se${}_y$ ($y=0,2,4,8$) probed with muon spectroscopy
• Ground State of the Easy-Axis Rare-Earth Kagomé Langasite Pr${}_3$Ga${}_5$SiO${}_{14}$
• Phonon-modulated magnetic interactions and spin Tomonaga-Luttinger liquid in the p-orbital antiferromagnet CsO2
• Novel magnetism on a honeycomb lattice in a-RuCl3 studied by muon spin rotation
• Field-Induced Instability of a Gapless Spin Liquid with a Spinon Fermi Surface
• Optically driven collective spin excitations and magnetization dynamics in the Néel-type skyrmion host GaV${}_4$S${}_8$
• Persistent spin dynamics intrinsic to amplitude-modulated long-range magnetic order
• Nuclear Magnetic Resonance in High Magnetic Field: Application to Condensed Matter Physics
• Crystallizing Kagome artificial spin ice
• Stabilization of magnetic skyrmions by RKKY interactions
• Field-induced pseudo-skyrmion phase in the antiferromagnetic kagome lattice
• Hall Effect of La2/3(Ca,Pb)1/3MnO3 Single Crystals near the Critical Temperature
• $\mu$SR Insight into the Impurity Problem in Quantum Kagome Antiferromagnets
• Measuring the Formation Energy Barrier of Skyrmions in Zinc Substituted Cu${}_2$OSeO${}_3$
• A field trip through spin ice
• Transverse field muon-spin rotation signature of the skyrmion lattice phase in Cu2OSeO3
• Multiple Spin-Orbit Excitons and the Electronic Structure of $\alpha$-RuCl${}_3$
• Dynamical spin correlations of the kagome antiferromagnet
• Fractionalization on the Surface: Is Type-II Terminated $1T$-TaS${}_2$ Surface an Anomalously Realized Spin Liquid?
• NMR Investigation on Honeycomb Iridate Ag${}_3$LiIr${}_2$O${}_6$
• Megahertz dynamics in skyrmion systems probed with muon-spin relaxation
• Unusual spin dynamics in the low-temperature magnetically ordered state of Ag${}_3$LiIr${}_2$O${}_6$
• Specific Heat of the Kagome Antiferromagnet Herbertsmithite in High Magnetic Fields
• Skyrmion instabilities and distorted spiral states in a frustrated chiral magnet
• Emergent particles and gauge fields in quantum matter
• Skyrmions and Hopfions in 3D Frustrated Magnets
• Behavior of the breathing pyrochlore lattice Ba${}_3$Yb${}_2$Zn${}_5$O${}_{11}$ in applied magnetic field
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Freezing of the Lattice in the Kagome Lattice Heisenberg Antiferromagnet Zn-barlowite ZnCu${}_3$(OD)${}_6$FBr
• Magnetism and Néel skyrmion dynamics in GaV${}_4$S${}_{8-y}$Se${}_y$
• Stability and Metastability of Skyrmions in Thin Lamellae of Cu${}_2$OSeO${}_3$
• Multiple Magnetic Bilayers and Unconventional Criticality without Frustration in BaCuSi${}_2$O${}_6$
• Proposal to detect emergent gauge field and its Meissner effect in spin liquids using NV Centers
• Persistent spin dynamics in the pressurized spin-liquid candidate YbMgGaO${}_4$
• A Discrepancy in Thermal Conductivity Measurement Data of Quantum Spin Liquid $\beta$'-EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ (dmit = 1,3-Dithiol-2-thione-4,5-dithiolate)
• Kondo physics in the algebraic spin liquid
• Emergence of the spin polarized domains in the kagome lattice Heisenberg antiferromagnet Zn-barlowite (Zn${}_{0.95}$Cu${}_{0.05}$)Cu${}_3$(OD)${}_6$FBr
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• First demonstration of tuning between the Kitaev and Ising limits in a honeycomb lattice
• Resistivity and Thermal Conductivity of an Organic Insulator beta'-EtMe3Sb[Pd(dmit)2]2
• Heat conduction in herbertsmithite: field dependence at the onset of the quantum spin liquid regime
• Thermal Hall conductivity of $\alpha$-RuCl${}_3$
• Active orbital degree of freedom and potential spin-orbit-entangled moments in Kitaev magnet candidate BaCo${}_2$(AsO${}_4$)${}_2$
• Raman fingerprints of fractionalized Majorana excitations in honeycomb iridate Ag${}_3$LiIr${}_2$O${}_6$
• Inelastic light scattering in the spin cluster Mott insulator Cu${}_2$OSeO${}_3$

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• Spin dynamics and 1/3 magnetization plateau in a coupled distorted diamond chain compound K2Cu3(MoO4)4
• Magnetic properties and field-induced phenomena in the Jeff = 1/2 distorted kagome antiferromagnet
• Coexistence of anomalous spin dynamics and weak magnetic order in a chiral trillium lattice K2FeSn(PO4)3
• Spin-Energy Entanglement of a Time-Focused Neutron
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• Glassy disordered ground states in the frustrated pyrochlore and fluorite antiferromagnets NaCd$M_2$F${}_7$ ($M$ = Ni${}^{2+}$, Mn${}^{2+}$)
• The nature of low-temperature spin-freezing in frustrated Kitaev magnets
• High-temperature series expansion of the dynamic Matsubara spin correlator
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects
• Coexistence of static and dynamic local magnetic fields in an S = 3/2 honeycomb lattice antiferromagnet Co2Te3O8
• Incommensurate magnetic order arising from frustrated interchain interactions in the spin-1/2 chain compound AgCuVO${}_4$
• Spin-liquid-like spin dynamics in the frustrated antiferromagnet TbBO3
• Possible Bose-Einstein condensation of magnons in a S = 5/2 honeycomb lattice
• Multistage spin correlations in the $s$ = 1/2 stuffed hyper-star lattice Li${}_2$Cu${}_2$(MoO${}_4$)${}_3$
• Antitopological magnetic textures in an antiferromagnetically coupled bilayer with frustration
• Spin liquid state in a three-dimensional pyrochlore-like frustrated magnet
• Magnetic and thermodynamic studies on the distorted kagome magnet Pr${}_3$BWO${}_9$
• Magnetic ground state of a Jeff = 1/2 based frustrated triangular lattice antiferromagnet
• Canted ferromagnetic order in a distorted triangular-lattice magnet Na${}_2$SrCo(VO${}_4$)${}_2$
• Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2