No Arabic abstract
We report thermodynamic properties, magnetic ground state, and microscopic magnetic model of the spin-1 frustrated antiferromaget Li$_{2}$NiW$_{2}$O$_{8}$ showing successive transitions at $T_{rm N1}simeq 18$ K and $T_{rm N2}simeq 12.5$ K in zero field. Nuclear magnetic resonance and neutron diffraction reveal collinear and commensurate magnetic order with the propagation vector $mathbf k=(frac12,0,frac12)$ below $T_{rm N2}$. The ordered moment of 1.8 $mu_B$ at 1.5 K is directed along $[0.89(9),-0.10(5),-0.49(6)]$ and matches the magnetic easy axis of spin-1 Ni$^{2+}$ ions, which is determined by the scissor-like distortion of the NiO$_6$ octahedra. Incommensurate magnetic order, presumably of spin-density-wave type, is observed in the region between $T_{rm N2}$ and $T_{rm N1}$. Density-functional band-structure calculations put forward a three-dimensional spin lattice with spin-1 chains running along the $[01bar 1]$ direction and stacked on a spatially anisotropic triangular lattice in the $ab$ plane. We show that the collinear magnetic order in Li$_2$NiW$_2$O$_8$ is incompatible with the triangular lattice geometry and thus driven by a pronounced easy-axis single-ion anisotropy of Ni$^{2+}$.
Magnetic frustration in three dimensions (3D) manifests itself in the spin-$frac12$ insulator Li$_2$CuW$_2$O$_8$. Density-functional band-structure calculations reveal a peculiar spin lattice built of triangular planes with frustrated interplane couplings. The saturation field of 29 T contrasts with the susceptibility maximum at 8.5 K and a relatively low Neel temperature $T_Nsimeq 3.9$ K. Magnetic order below $T_N$ is collinear with the propagation vector $(0,frac12,0)$ and an ordered moment of 0.65(4) $mu_B$ according to neutron diffraction data. This reduced ordered moment together with the low maximum of the magnetic specific heat ($C^{max}/Rsimeq 0.35$) pinpoint strong magnetic frustration in 3D. Collinear magnetic order suggests that quantum fluctuations play crucial role in this system, where a non-collinear spiral state would be stabilized classically.
Spin density waves, based on modulated local moments, are usually associated with metallic materials, but have recently been reported in insulators which display coupled magnetic and structural order parameters. We discuss one such example, the multiferroic Cu$_3$Nb$_2$O$_8$, which is reported to undergo two magnetic phase transitions, first to a spin density wave phase at $T_N approx 26.5K$, and then to a helicoidal structure coupled to an electric polarization below $T_2 approx 24K$ [R. D. Johnson, et al., Phys. Rev. Lett., 107, 137205 (2011)] which breaks the crystallographic inversion symmetry. We apply spherical polarimetry to confirm the low-temperature magnetic structure, yet only observe a single magnetic phase transition to helicoidal order. We argue that the reported spin density wave originates from a decoupling of the components of the magnetic order parameter, as allowed by symmetry and driven by thermal fluctuations. This provides a mechanism for the magnetic, but not nuclear, structure to break inversion symmetry thereby creating an intermediate phase where the structure imitates a spin density wave. As the temperature is reduced, this intermediate structure destabilizes the crystal such that a structural chirality is induced, as reflected by the emergence of the electric polarization, and the imitation spin density wave relaxes into a generic helicoid. This provides a situation where the magnetic structure breaks inversion symmetry while the crystal structure remains centrosymmetric.
We have grown single crystals of Na$_2$BaNi(PO$_4$)$_2$, a new spin-1 equilateral triangular lattice antiferromagnet (ETLAF), and performed magnetic susceptibility, specific heat and thermal conductivity measurements at ultralow temperatures. The main results are (i) at zero magnetic field, Na$_2$BaNi(PO$_4$)$_2$ exhibits a magnetic ordering at 430 mK with a weak ferromagnetic moment along the $c$ axis. This suggests a canted 120$^circ$ spin structure, which is in a plane including the crystallographic $c$ axis due to the existence of an easy-axis anisotropy and ferromagnetically stacked along the $c$ axis; (ii) with increasing field along the $c$ axis, a 1/3 magnetization plateau is observed which means the canted 120$^circ$ spin structure is transformed to a up up down (UUD) spin structure. With even higher fields, the UUD phase further evolves to possible V and V phases; (iii) with increasing field along the $a$ axis, the canted 120$^circ$ spin structure is possibly transformed to a umbrella phase and a V phase. Therefore, Na$_2$BaNi(PO$_4$)$_2$ is a rare example of spin-1 ETLAF with single crystalline form to exhibit easy-axis spin anisotropy and series of quantum spin state transitions.
We report the first detailed investigation of K$_2$MnS$_2$ and K$_2$MnSe$_2$ from the K$_2$MnS$_2$ structure type and their magnetic solid solution K$_2$MnS$_{2-x}$Se$_x$ and find that compounds of this structure type consist of strongly-coupled pseudo-one-dimensional antiferromagnetic chains that collectively represent a frustrated two-dimensional triangular antiferromagnet. Bulk samples of K$_2$MnS$_{2-x}$Se$_x$ with $0 leq x leq 2$ are characterized using X-ray diffraction, neutron diffraction, magnetization and heat capacity measurements. An incommensurate cycloid magnetic structure with a magnetic propagation vector $k = [0.58~0~1]$ is observed for all samples in K$_2$MnS$_{2-x}$Se$_x$, and the ordering is robust despite a 12% increase in cell volume. Geometric frustration of chains results in incommensurability along $a$ and a two-step magnetic transition. The varying geometries accessible in compounds of this structure type are presented as promising avenues to tune frustration.
The layered {beta}-NaMnO2, a promising Na-ion energy-storage material has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated q= (0.077(1), 0, 0) structure. Here, Mn3+ Jahn-Teller distorted MnO6 octahedra form corrugated layer stacking sequences of the {beta}-NaMnO2 type, which are interrupted by flat sheets of the {alpha}-like oxygen topology. Spontaneous long-range collinear antiferromagnetic order, defined by the propagation vector k= (1/2, 1/2, 1/2), appears below TN1= 200 K. Moreover, a second transition into a spatially modulated proper-screw magnetic state (k+-q) is established at TN2= 95 K, with an antiferromagnetic order parameter resembling that of a two-dimensional (2D) system. The evolution of 23Na NMR spin-lattice relaxation identifies a magnetically inhomogene-ous state in the intermediate T-region (TN2 <T< TN1), while its strong suppression below TN2 indicates that a spin-gap opens in the excitation spectrum. High-resolution neutron inelastic scattering confirms that the magnetic dynamics are indeed gapped ({Delta}~5 meV) in the low-temperature magnetic phase, while simulations on the basis of the single-mode approximation suggest that Mn-spins residing on ad-jacent antiferromagnetic chains, establish sizable 2D correlations. Our analysis points that novel struc-tural degrees of freedom promote, cooperative magnetism and emerging dielectric properties in this non-perovskite-type of manganite.