Triangular Magnetic Lattice Research Articles

Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet.

Geometrically frustrated magnets can host complex spin textures, leading to unconventional electromagnetic responses. Magnetic frustration may also promote topologically nontrivial spin states such as magnetic skyrmions. Experimentally, however, skyrmions have largely been observed in noncentrosymmetric lattice structures or interfacial symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustrated centrosymmetric triangular-lattice magnet Gd2PdSi3 We observed a giant topological Hall response, indicating a field-induced skyrmion phase, which is further corroborated by the observation of in-plane spin modulation probed by resonant x-ray scattering. Our results may lead to further discoveries of emergent electrodynamics in magnetically frustrated centrosymmetric materials.

Magnetic Lattices for Ultracold Atoms

This article reviews the development in our laboratory of magnetic lattices comprising periodic arrays of magnetic microtraps created by patterned magnetic films to trap periodic arrays of ultracold atoms. Recent achievements include the realisation of multiple Bose-Einstein condensates in a 10 \(\mu\)m-period one-dimensional magnetic lattice; the fabrication of sub-micron-period square and triangular magnetic lattice structures suitable for quantum tunnelling experiments; the trapping of ultracold atoms in a sub-micron-period triangular magnetic lattice; and a proposal to use long-range interacting Rydberg atoms to achieve spin-spin interactions between sites in a large-spacing magnetic lattice.

Griffiths phase in antiferromagnetic CuCr0.95Ti0.05O2

Delafossite compound, CuCrO2, popularly known as transparent conducting oxide, has previously been reported to demonstrate antiferromagnetic ordering of the triangular magnetic lattice below 24 K. We find that mere 5% Ti-substitution at Cr-site, leads to short range magnetic correlations, manifested as non-analytical behaviour of H/M and other anomalies in the low magnetic field dc magnetization, ac magnetic susceptibility, time dependent magnetization, and isothermal remanent magnetization. The ac susceptibility measured at different applied frequencies do not show any frequency dependence, ruling out the glassy magnetic phase. The short-range magnetic correlations are observed over a wide temperature range starting from 180 K and below, until the system orders antiferromagnetically at 22 K. These correlations which are most pronounced at low values of applied magnetic field, get readily suppressed when the fields exceed 0.5 T. Signatures associated with these short-range correlations seem to fit a Griffiths-like phase description. The results of heat capacity measurement with and without magnetic field, provides additional information about the dimensionality of the magnetic interactions. Rietveld refinement of the X-ray diffraction data reveals that the highly anisotropic crystal structure remains unaffected with the substitution. A static disorder driven magnetic inhomogeneity arising in the triangular magnetic sublattice of Cr ions decreases the dimensionality of magnetic interactions, and seems to be the possible origin of this interesting magnetic behaviour.

Magnetic Ground State Crossover in a Series of Glaserite Systems with Triangular Magnetic Lattices.

The magnetic properties are reported for three members of the glaserite series of compounds, Na2BaM(VO4)2, M = Mn, Mn0.6Co0.4, and Co. Large single crystals are grown using a high-temperature hydrothermal synthesis method. This structure type exhibits a triangular magnetic lattice in which M2+O6 octahedra are interconnected with nonmagnetic (VO4)3- groups. All the structures crystallize at room temperature with rigid trigonal symmetry (space group P3̅ m1); however, at lower temperatures both Na2BaMn(VO4)2 and Na2BaMn0.6Co0.4(VO4)2 undergo a structural transition to lower symmetry (monoclinic, C2/ c). The bulk magnetic measurements indicate that Mn- and Co-structures are antiferromagnetic and ferromagnetic, respectively. Na2BaMn0.6Co0.4(VO4)2 does not show any long-range ordering down to 0.5 K, although a broad heat capacity anomaly near 1.2 K suggests short-range magnetic order or freezing into a spin-glass-like state related to the chemical disorder and resulting competing magnetic interactions. The magnetic structures of Na2BaMn(VO4)2 and Na2BaCo(VO4)2 were determined using neutron powder diffraction. At zero magnetic field, Na2BaMn(VO4)2 possesses an antiferromagnetic structure with the moments ordered in a Néel-type arrangement and aligned along the C4 axis of the octahedra. Under applied magnetic field at 0.3 K, the evolution of the magnetic structure toward a fully polarized state is observed. Na2BaCo(VO4)2 represents a ferromagnetic (FM) magnetic structure with Co moments aligned parallel to the c-axis direction. The relationships between these structures and magnetic properties are discussed.

NaYbS2 : A planar spin- 12 triangular-lattice magnet and putative spin liquid

Platelike high-quality NaYbS$_{2}$ rhombohedral single crystals with lateral dimensions of a few mm have been grown and investigated in great detail by bulk methods like magnetization and specific heat, but also by local probes like nuclear magnetic resonance (NMR), electron-spin resonance (ESR), muon-spin relaxation ($\mu$SR), and inelastic neutron scattering (INS) over a wide field and temperature range. Our single-crystal studies clearly evidence a strongly anisotropic quasi-2D magnetism and an emerging spin-orbit entangled $S=1/2$ state of Yb towards low temperatures together with an absence of long-range magnetic order down to 260~mK. In particular, the clear and narrow Yb ESR lines together with narrow $^{23}$Na NMR lines evidence an absence of inherent structural distortions in the system, which is in strong contrast to the related spin-liquid candidate YbMgGaO$_{4}$ falling within the same space group $R\overline{3}m$. This identifies NaYbS$_{2}$ as a rather pure spin-1/2 triangular lattice magnet and a new putative quantum spin liquid.

Selective measurements of intertwined multipolar orders: Non-Kramers doublets on a triangular lattice

Motivated by the rapid experimental progress on the spin-orbit-coupled Mott insulators, we propose and study a generic spin model that describes the interaction between the non-Kramers doublets on a triangular lattice and is relevant for triangular lattice rare-earth magnets. We predict that the system supports both pure quadrupolar orders and intertwined multipolar orders in the phase diagram. Besides the multipolar orders, we explore the magnetic excitations to reveal the dynamic properties of the systems. Due to the peculiar properties of the non-Kramers doublets and the selective coupling to the magnetic field, we further study the magnetization process of the system in the magnetic field. We point out the selective measurements of the static and dynamic properties of the intertwined multipolarness in the neutron scattering, NMR and $\mu$SR probes and predict the experimental consequences. The relevance to the existing materials such as TmMgGaO$_{4}$, Pr-based and Tb-based magnets, and many ternary chalcogenides is discussed. Our results illustrate the rich physics and the promising direction in the interplay between strong spin-orbit-entangled multipole moments and the geometrical frustration.

Magnetic phase diagram of the frustrated S=1/2 triangular-lattice magnet Cu2(NO3)(OH)3

Cu2(NO3)(OH)3 (rouaite) is a frustrated triangular lattice magnet. We measured the magnetic susceptibility, specific heat, 1H-NMR and high field magnetization of a powder sample of Cu2(NO3)(OH)3 and found a clear evidence of the long range magnetic order at about 8 K. The transition temperature was found to decrease as the magnetic field H increased. An H-T phase diagram of Cu2(NO3)(OH)3 was determined by specific heat, magnetization and 1H-NMR data. The high field magnetization curve was analyzed using a simple spin model.

Modulation of skyrmion diameter in centrosymmetric frustrated magnet

Magnetic skyrmions were first observed in a bulk B20 chiral magnet where the unit cell of the crystal lacks inversion symmetry, i. e. it is noncentrosymmetric, due to the Dzyaloshinskii-Moriya interaction (DMI). The breaking of structural inversion symmetry can also be achieved artificially in extremely thin FM layers adjacent to heavy elements, to induce a nonzero DMI. Many skyrmion properties in the DMI-based system are revealed such as the skyrmion diameters simply inversely proportional to the DMI constant. On the contrary, the triangular lattice, providing a simple realization of a high-symmetry system with six equivalent orientations for the helix, is centrosymmetric. In a two-dimensional triangular lattice magnet with the magnetocrystalline anisotropy perpendicular to the film plane, the magnetic frustration can arise from the coexistence of a nearest -neighbor ferromagnetic exchange interaction and a third-neighbor antiferromagnetic exchange interaction. When an external magnetic field is applied parallelly to the anisotropy, the non-coplanar alignments of spins are favored and even the topologically protected magnetic skyrmions also appear. Based on the Monte Carlo simulation, the dependence of magnetic-field-induced magnetic phase transitions in such magnetic frustrated magnets, including the magnetic phase of skyrmion crystals, and the skyrmion diameters on competing exchange interaction and magnetic field is studied. The results indicate that the diameters of magnetic skyrmions strongly depend on the competing exchange interactions and external magnetic field. Like the diameter features of magnetic skyrmions observed in the conventional DMI-based chiral magnets, the external magnetic field can magnetize the skyrmion periphery spins to reduce the skyrmion diameters. However, the enhanced antiferromagnetic exchange interaction can compress the entire skyrmions. In the framework of the spin wave theory and Monte Carlo simulation results, the diameters of magnetic skyrmions in exchange-interaction-frustrated systems are quantified. The skyrmion diameter decreases linearly with the increase of magnetic field for weak antiferromagnetic exchange interaction. With the increase of antiferromagnetic exchange interaction, the decrease of the skyrmion diameter with increasing magnetic field becomes slow, while the strong magnetic fields may rapidly reduce the skyrmion diameter. With the increase of antiferromagnetic exchange interaction, the maximum and median skyrmion diameters decrease to level-off roughly, while the minimum skyrmion diameters show a rapid decrease first and a great fluctuation later. The phenomena are explained through discussing the variations of configurations and magnetic energies of skyrmions. This work demonstrates the adjustability of skyrmion diameter in centrosymmetric frustrated magnet, which not only improves the understanding of origin of skyrmions, but also supports theoretically the development of new generation of skyrmion-based storage and logic devices.

Investigation of a Structural Phase Transition and Magnetic Structure of Na2BaFe(VO4)2: A Triangular Magnetic Lattice with a Ferromagnetic Ground State.

The structural and magnetic properties of a glaserite-type Na2BaFe(VO4)2 compound, featuring a triangular magnetic lattice of Fe2+ (S = 2), are reported. Temperature dependent X-ray single crystal studies indicate that at room temperature the system adopts a trigonal P3̅m1 structure and undergoes a structural phase transition to a C2/c monoclinic phase slightly below room temperature (Ts = 288 K). This structural transition involves a tilting of Fe-O-V bond angles and strongly influences the magnetic correlation within the Fe triangular lattice. The magnetic susceptibility measurements reveal a ferromagnetic transition near 7 K. Single crystal neutron diffraction confirms the structural distortion and the ferromagnetic spin ordering in Na2BaFe(VO4)2. The magnetic structure of the ordered state is modeled in the magnetic space group C2'/c' that implies a ferromagnetic order of the a and c moment components and antiferromagnetic arrangement for the b components. Overall, the Fe magnetic moments form ferromagnetic layers that are stacked along the c-axis, where the spins point along one of the (111) facets of the FeO6 octahedron.

Creation and Annihilation of Skyrmions in the Frustrated Magnets with Competing Exchange Interactions

In triangular-lattice magnets, the coexistence of third-neighbor antiferromagnetic and nearest-neighbor ferromagnetic exchange interactions can induce rich magnetic phases including noncoplanar skyrmion crystals. Based on Monte Carlo simulation, we studied the dependence of magnetic phase transition on exchange interaction strength. Under the consideration of uniaxial anisotropy and magnetic field both perpendicular to the film plane, a large antiferromagnetic exchange interaction induces a high frustration. When the value of antiferromagnetic exchange interaction is one and a half times larger than the ferromagnetic one, a magnetic phase composed of canting spin stripes, never observed in the chiral magnets, forms. Interestingly, different canting spin stripes along three 120 degree propagation directions may coexist randomly in a magnetic phase, attesting that the canting spin stripes are three-fold degenerate states akin to helices and the multiple state of canting spin stripes is a circular configuration with zero skyrmion charge number. Moreover, skyrmions and antiskyrmions can be observed simultaneously in the configuration at the low temperature nearly close to 0 K, and their configuration and diameter properties are discussed. Finally, the mechanisms of skyrmion creation and annihilation are properly interpreted by comparing exchange and Zeeman energy terms.

Trapping ultracold atoms in a sub-micron-period triangular magnetic lattice

We report the trapping of ultracold 87Rb atoms in a 0.7 micron-period 2D triangular magnetic lattice on an atom chip. The magnetic lattice is created by a lithographically patterned magnetic Co/Pd multilayer film plus bias fields. Rubidium atoms in the F=1, mF=-1 low-field seeking state are trapped at estimated distances down to about 100 nm from the chip surface and with calculated mean trapping frequencies as high as 800 kHz. The measured lifetimes of the atoms trapped in the magnetic lattice are in the range 0.4 - 1.7 ms, depending on distance from the chip surface. Model calculations suggest the trap lifetimes are currently limited mainly by losses due to surface-induced thermal evaporation following loading of the atoms from the Z-wire trap into the very tight magnetic lattice traps, rather than by fundamental loss processes such as surface interactions, three-body recombination or spin flips due to Johnson magnetic noise. The trapping of atoms in a 0.7 micrometer-period magnetic lattice represents a significant step towards using magnetic lattices for quantum tunneling experiments and to simulate condensed matter and many-body phenomena in nontrivial lattice geometries.

Rich magnetoelectric phase diagrams of multiferroic single-crystal α−NaFeO2

The magnetic and dielectric properties of the multiferroic triangular lattice magnet compound alpha-NaFeO2 were studied by magnetization, specific heat, dielectric permittivity, and pyroelectric current measurements and by neutron diffraction experiments using single crystals grown by a hydrothermal synthesis method. This work produced magnetic field (in the monoclinic ab-plane, B_ab, and along the c*-axis, B_c) versus temperature magnetic phase diagrams, including five and six magnetically ordered phases in B_ab and along B_c, respectively. Comparing the polarization direction to the magnetic structures in the different ferroelectric phases, we conclude that the extended inverse Dzyaloshinskii-Moriya mechanism expressed by the orthogonal components p1 ~ rij x (Si x Sj ) and p2 ~ Si x Sj can explain the polarization directions. Based on calculations incorporating exchange interactions up to fourth-nearest-neighbor (NN) couplings, we infer that competition among antiferromagnetic second NN interactions in the triangular lattice plane, as well as weak interplane antiferromagnetic interactions, are responsible for the rich phase diagrams of alpha-NaFeO2.

Magnetic properties of the triangular lattice magnets A4B′B2O12 ( A=Ba , Sr, La; B′=Co , Ni, Mn; B=W , Re)

The geometrically frustrated two dimensional triangular lattice magnets A${_4}$B'B${_2}$O$_{12}$ (A = Ba, Sr, La; B' = Co, Ni, Mn; B = W, Re) have been studied by x-ray diffraction, AC and DC susceptibilities, powder neutron diffraction, and specific heat measurements. The results reveal that (i) the samples containing Co$^{2+}$ (effective spin-1/2) and Ni$^{2+}$ (spin-1) ions with small spin numbers exhibit ferromagnetic (FM) ordering while the sample containing Mn$^{2+}$ (spin-5/2) ions with a large spin number exhibits antiferromagnetic (AFM) ordering. We ascribe these spin number manipulated ground states to the competition between the AFM B'-O-O-B' and FM B'-O-B-O-B' superexchange interactions; (ii) the chemical pressure introduced into the Co containing samples through the replacement of different size ions on the A site finely tunes the FM ordering temperature of the system. We attribute this effect to the modification of the FM interaction strength induced by the change of the O-B-O angle through chemical pressure.

Effect of substrate rotation on domain structure and magnetic relaxation in magnetic antidot lattice arrays

Microdimensional triangular magnetic antidot lattice arrays were prepared by varying the speed of substrate rotation. The pre-deposition patterning has been performed using photolithography technique followed by a post-deposition lift-off. Surface morphology taken by atomic force microscopy depicted that the growth mechanism of the grains changes from chain like formation to island structures due to the substrate rotation. Study of magnetization reversal via magneto optic Kerr effect based microscopy revealed reduction of uniaxial anisotropy and increase in domain size with substrate rotation. The relaxation measured under constant magnetic field becomes faster with rotation of the substrate during deposition. The nature of relaxation for the non-rotating sample can be described by a double exponential decay. However, the relaxation for the sample with substrate rotation is well described either by a double exponential or a Fatuzzo-Labrune like single exponential decay, which increases in applied field.

Magnetic and ESR studies in a Quasi-two-dimensional Triangular magnet Ba3MnNb2O9

We report the magnetic, specific heat and electron spin resonance (ESR) studies on Ba3MnNb2O9, as one of quasi-two-dimensional triangular–lattice magnet. The magnetic susceptibility and specific heat measurement show that it undergoes an magnetic transition at TN=3.2K. The magnetic capacity (Cmag) follows T2 dependence, and magnetic entropy (Smag) reaching to 14.5JK−1mol−1 at 32K satisfactorily agrees with the theoretical estimations of Mn2+ ion in high-spin configuration with S=5/2. From the ESR spectra, the Landé factor (geff), the linewidth (ΔHpp) and the ESR intensity (I) are derived and analyzed as a function of temperature. As temperature decreases to T⁎~18K, the g-factor shows a minima with geff=1.984(2) before shifts to larger value at lower temperatures, and the ESR intensity starts to be suppressed below this temperature. This anomalous phenomenon is explained in terms of the establishment of short-range AFM spin correlations at much higher temperatures above TN.

Synthesis and magnetic properties of a new series of triangular-lattice magnets, Na2BaMV2O8 (M = Ni, Co, and Mn)

A new series of triangular-lattice magnets, Na2BaMV2O8 (M = Ni, Co, and Mn), are reported. These three compounds crystallize with the Ag2BaMnV2O8 type structure, where the magnetic M2+ ions form a two-dimensional triangular lattice. The magnitude of the exchange interactions in these compounds is moderate because the nonmagnetic VO4 tetrahedra interrupt direct connections between MO6 octahedra. The magnetic susceptibilities of Na2BaNiV2O8 and Na2BaCoV2O8 reveal ferromagnetic transitions at 8.4 and 3.9 K, respectively. In contrast, the magnetic susceptibility of Na2BaMnV2O8 exhibits a broad maximum at around 2.3 K, which suggests antiferromagnetic nearest-neighbour interactions and a significant effect of geometric frustration. The specific heat and magnetization curve of Na2BaMnV2O8 indicate that magnetic long-range ordering appears below 1.5 K.

Spin nematic ground state of the triangular latticeS=1biquadratic model

Motivated by the spate of recent experimental and theoretical interest in Mott insulating S=1 triangular lattice magnets, we consider a model S=1 Hamiltonian on a triangular lattice interacting with rotationally symmetric biquadratic interactions. We show that the partition function of this model can be expressed in terms of configurations of three colors of tightly-packed, closed loops with {\em non-negative} weights, which allows for efficient quantum Monte Carlo sampling on large lattices. We find the ground state has spin nematic order, i.e. it spontaneously breaks spin rotation symmetry but preserves time reversal symmetry. We present accurate results for the parameters of the low energy field theory, as well as finite-temperature thermodynamic functions.

Phenomenological model of multiferroic properties in langasite-type crystals with a triangular magnetic lattice

The conditions for occurrence of the magnetoelectric, magnetoelastic, and piezomagnetic effects in crystals of the langasite family with a triangular magnetic lattice are considered on the basis of the phenomenological model. It is shown that the iron-containing langasites with a triangular magnetic lattice may have piezoelectric properties above the N\`eel temperature ${T}_{\mathrm{N}}$, but they are not ferroelectrics. Occurrence of either ferroelectric or both ferroelectric and piezoelectric states is possible below ${T}_{\mathrm{N}}$, and these crystals can be considered as multiferroics with a helicoid of magnetic moments oriented along the $c$ axis. The observation of electric polarization ${p}_{z}$ in these crystals at $T<{T}_{N}$ is possible at sufficiently large values of piezocoefficients ${e}_{zyz}$ (class 2) or ${e}_{zxx}$ (class 3) and as a result of mechanical deformations occurring due to magnetostriction. Moreover, because of magnetoelastic interactions (appearing due to lowering symmetry $P$321 \ensuremath{\rightarrow} $P$3 below ${T}_{\mathrm{N}}$), the electric polarization and the axis of the magnetic helicoid can both be parallel to the $z$ axis even in the absence of the Dzyaloshinskii-Moriya (DM) effect. Possible ferroelastic and ferroelectric transitions are considered at $T<{T}_{\mathrm{N}}$. The occurrence of the magnetic helicoid with its axis in the $ab$ plane is also discussed. It may appear due to the spin-orbit interaction (DM effect). In this case, electric polarization must appear also in the $ab$ plane.

A (3, 4, 14)-connected framework with various distorted triangular magnetic lattices exhibiting field-induced metamagnetism, spin competition and spin reorientation

A (3, 4, 14)-connected framework with complicated distorted triangular magnetic lattices, {[Co(7)(H(2)O)(4)(trz)(8)(sip)(2)]·3H(2)O}(n) (trz = 1,2,4-triazolate, sip = 5-sulfoisophthalate), exhibits continuous field-induced metamagnetic transition from an antiferromagnetic ordering to a ferrimagnetic state at 15 kOe, spin competition at 26 kOe and spin reorientation at 50 kOe, respectively.

Magnetic and non-magnetic phases of a quantum spin liquid

A quantum spin-liquid phase is an intriguing possibility for a system of strongly interacting magnetic units in which the usual magnetically ordered ground state is avoided owing to strong quantum fluctuations. It was first predicted theoretically for a triangular-lattice model with antiferromagnetically coupled S = 1/2 spins. Recently, materials have become available showing persuasive experimental evidence for such a state. Although many studies show that the ideal triangular lattice of S = 1/2 Heisenberg spins actually orders magnetically into a three-sublattice, non-collinear 120° arrangement, quantum fluctuations significantly reduce the size of the ordered moment. This residual ordering can be completely suppressed when higher-order ring-exchange magnetic interactions are significant, as found in nearly metallic Mott insulators. The layered molecular system κ-(BEDT-TTF)(2)Cu(2)(CN)(3) is a Mott insulator with an almost isotropic, triangular magnetic lattice of spin-1/2 BEDT-TTF dimers that provides a prime example of a spin liquid formed in this way. Despite a high-temperature exchange coupling, J, of 250 K (ref. 6), no obvious signature of conventional magnetic ordering is seen down to 20 mK (refs 7, 8). Here we show, using muon spin rotation, that applying a small magnetic field to this system produces a quantum phase transition between the spin-liquid phase and an antiferromagnetic phase with a strongly suppressed moment. This can be described as Bose-Einstein condensation of spin excitations with an extremely small spin gap. At higher fields, a second transition is found that suggests a threshold for deconfinement of the spin excitations. Our studies reveal the low-temperature magnetic phase diagram and enable us to measure characteristic critical properties. We compare our results closely with current theoretical models, and this gives some further insight into the nature of the spin-liquid phase.