Motivated by recent experimental results on GdRu$_2$Si$_2$ [Khanh, N.D., Nakajima, T., Yu, X. et al., \emph{Nat. Nanotechnol.} \textbf{15}, 444-449 (2020)], where nanometric square skyrmion lattice was observed, we propose simple analytical mean-field description of the high-temperature part of the phase diagram of centrosymmetric tetragonal frustrated antiferromagnets with dipolar interaction in the external magnetic field. In the reciprocal space dipolar forces provide momentum dependent biaxial anisotropy. It is shown that in tetragonal lattice in the large part of the Brillouin zone for mutually perpendicular modulation vectors in the $ab$ plane this anisotropy has mutually perpendicular easy axes and collinear middle axes, what leads to double-Q modulated spin structure stabilization. The latter turns out to be a square skyrmion lattice in the large part of its stability region with the topological charge $\pm 1$ per magnetic unit cell, which is determined by the frustrated exchange coupling, and, thus, nanometer-sized. In the presence of additional single-ion easy-axis anisotropy, easy and middle axes can be swapped, which leads to different phase diagram. It is argued that the latter case is relevant to GdRu$_2$Si$_2$.
Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（复杂系统理论物理中心，基础科学研究院）；National Research University “Higher School of Economics”（国立高等经济大学）；The Faculty of Physics of St. Petersburg State University（圣彼得堡国立大学物理系）
The quantum Heisenberg model is studied in the geometrically frustrated body-centered tetragonal lattice(BCT lattice) with antiferromagnetic interlayer coupling J1 and intralayer first and second neighbor coupling J2 and J3. We introduce a variational method: each interaction term can be decoupled partially in the purely magnetic Weiss and in the spin-liquid (SL) mean-field channels. We find that the most stable variational solutions correspond to the three different possible long range magnetic orders that are respectively governed by J1, J2, and J3. We characterize three different purely SL …
We report single-crystal neutron diffraction studies on a spinel antiferromagnet GeCo$_2$O$_4$, which exhibits magnetic order with a trigonal propagation vector and tetragonal lattice expansion ($c/a\simeq1.001$) below $T_{\rm N}=21$ K. For this inconsistency between spin and lattice in symmetry, magnetic Bragg reflections with a tetragonal propagation vector were discovered below $T_{\rm N}$. We discuss spin and orbital states of Co$^{2+}$ ion underlying the new magnetic component.
Recently synthesized metastable tetragonal CoSe, isostructural to the FeSe superconductor, offers a new avenue for investigating systems in close proximity to the iron-based superconductors. We present magnetic and transport property measurements on powders and single crystals of CoSe. High field magnetic susceptibility measurements indicate a suppression of the previously reported 10 K ferromagnetic transition with the magnetic susceptibility exhibiting time-dependence below the proposed transition. Dynamic scaling analysis of the time-dependence yields a critical relaxation time of $τ^{*} = …
An $SU({\rm n})$-symmetric generalization of the Heisenberg model for quantum spin $S$ operators is used to investigate the geometrically frustrated body-centered tetragonal (BCT) lattice with antiferromagnetic interlayer coupling $J_1$ and intralayer first and second neighbor coupling $J_2$ and $J_3$. Using complementary representations of the spin operators, we study the phase diagram characterizing the ground state of the system. For small n, we find that the most stable solutions correspond to four different families of possible long range magnetic orders that are governed by $J_1$, $J_2$,…
A novel general method of describing the spin-lattice interactions in magnetic solids was proposed in terms of first principles calculations. The spin exchange and Dzyaloshinskii-Moriya interactions as well as their derivatives with respect to atomic displacements can be evaluated efficiently on the basis of density functional calculations for four ordered spin states. By taking into consideration the spin-spin interactions, the phonons, and the coupling between them, we show that the ground state structure of a representative spin-frustrated spinel, MgCr2 O4, is tetragonally distorted, in agr…
We investigate the crystal structure, magnetic properties, and crystalline-electric field of tetragonal, $I4_1/amd$, NaCeO$_2$. In this compound, Ce$^{3+}$ ions form a tetragonally elongated diamond lattice coupled by antiferromagnetic interactions ($Θ_{CW} = -7.69$ K) that magnetically order below $T_N = 3.18$ K. The Ce$^{3+}$ $J = 5/2$ crystalline-electric field-split multiplet is studied via inelastic neutron scattering to parameterize a $J_{eff} = 1/2$ ground state doublet comprised of states possessing mixed $|m_z \rangle$ character. Neutron powder diffraction data reveal the onset of $A$…
Frustration of harmonic and solitonic helimagnetism on the body-centered tetragonal lattice of GdAlSi
The University of Tokyo（东京大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 新兴物质科学中心）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；High Energy Accelerator Research Organization（高能加速器研究机构）；Nagoya University Synchrotron Radiation Research Center (NUSR), Nagoya University（名古屋大学同步辐射研究中心）
We report the discovery of a spin one diamond lattice in NiRh2O4. This spinel undergoes a cubic to tetragonal phase transition at T = 440 K that leaves all nearest neighbor interactions equivalent. In the tetragonal phase, magnetization measurements show a Ni2+ effective moment of p(eff) = 3.3(1) and dominant antiferromagnetic interactions with Θ(CW) = -11.3(7) K. No phase transition to a long-range magnetically ordered state is observed by specific heat measurements down to T = 0.1 K. Inelastic neutron scattering measurements on sub-stoichiometric NiRh2O4 reveal possible valence-bond behavior…
We present a microscopic model of the spin-gap quantum magnet (CuCl)LaNb2O7 that was previously suggested as a realization of the spin-1/2 frustrated square lattice. Taking advantage of the precise atomic positions from recent crystal structure refinement, we evaluate individual exchange integrals and construct a minimum model that naturally explains all the available experimental data. Surprisingly, the deviation from tetragonal symmetry leads to the formation of spin dimers between fourth neighbors due to a Cu-Cl-Cl-Cu pathway with a leading antiferromagnetic exchange J4 ~ 25 K. The total in…
The structurally simplest high-temperature superconductor FeSe exhibits an intriguing superconducting nematic paramagnetic phase with unusual spin excitation spectra that are different from typical spin waves; thus, determining its effective magnetic exchange interactions is challenging. Here we report neutron scattering measurements of spin fluctuations of FeSe in the tetragonal paramagnetic phase. We show that the equal-time magnetic structure factor, $\mathcal{S}(\textbf{Q})$, can be effectively modeled using the self-consistent Gaussian approximation calculation with highly frustrated near…
Above 40K, the magnetic susceptibility of the heavy Fermion spinel LiV2O4 has many features in common with those of geometrically frustrated magnetic insulators, while its room temperature resistivity comfortably exceeds the Mott-Regel limit. This suggests that local magnetic moments, and the underlying geometry of the pyrochlore lattice, play an important role in determining its magnetic properties. We extend a recently introduced tetragonal mean field theory for insulating pyrochlore antiferromagnets to the case where individual tetrahedra contain spins of different lengths, and use this as …
We present a computational study of the layered copper oxychloride [CuCl]LaNb(2)O(7) that has been recently proposed as a spin-1/2 frustrated square lattice compound. Our results evidence an orbitally degenerate ground state for the reported tetragonal crystal structure and reveal a Jahn-Teller-type structural distortion. This distortion heavily changes the local environment of copper -- CuO(2)Cl(2) plaquettes are formed instead of CuO(2)Cl(4) octahedra -- and restores the single-orbital scenario typical for copper oxides and oxyhalides. The calculated distortion is consistent with the availab…
Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large…
Motivated by the proposal of topological quantum paramagnet in the diamond lattice antiferromagnet NiRh$_2$O$_4$, we propose a minimal model to describe the magnetic interaction and properties of the diamond material with the spin-one local moments. Our model includes the first and second neighbor Heisenberg interactions as well as a local single-ion spin anisotropy that is allowed by the spin-one nature of the local moment and the tetragonal symmetry of the system. We point out that there exists a quantum phase transition from a trivial quantum paramagnet when the single-ion spin anisotropy i…
We present extensive Monte Carlo simulations for a classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice coupled to the lattice degrees of freedom. The Ising-like phase transition, that appears for $J_2/J_1>1/2$ in the pure spin model, is strengthened by the spin-lattice coupling, and is accompanied by a lattice deformation from a tetragonal symmetry to an orthorhombic one. Evidences that the universality class of the transition does not change with the inclusion of the spin-lattice coupling are reported. Implic…
It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings ({\it e.g.} on a body-centered tetragonal lattice) generically exhibits two thermal phase transitions with lowering temperature -- an upper transition at $T_{TO}$ (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower Néel transition at $T_{N}$ at which spin-rotation symmetry is broken. Although this is the same sequence of transitions observed in La$_2$CuO$_4$, in the Heisenberg model (without additional lattic…
We report the characterisation of natural samples of the cubic pyrite mineral MnS2 using very high resolution synchrotron X-ray diffraction techniques. At low temperatures we find a new low temperature polymorph, which results from coupling between magnetic and lattice degrees of freedom. Below the magnetic ordering temperature T_N= 48 K, we detect a pseudo-tetragonal distortion with a tiny c/a ratio of 1.0006. The structure can be refined in the space group Pbca. The symmetry lowering reduces magnetic frustration in the fcc Mn2+ lattice and is likely responsible for the previously reported lo…
We study the influence of the spin lattice distortion on the properties of frustrated magnetic systems and consider the applicability of the spin-1/2 frustrated square lattice model to materials lacking tetragonal symmetry. We focus on the case of layered vanadium phosphates AA'VO(PO4)2 (AA' = Pb2, SrZn, BaZn, and BaCd). To provide a proper microscopic description of these compounds, we use extensive band structure calculations for real materials and model structures and supplement this analysis with simulations of thermodynamic properties, thus facilitating a direct comparison with the experi…
We study geometrically frustrated antiferromagnets with magnetoelastic coupling. Frustration in these systems may be relieved by a structural transition to a low temperature phase with reduced lattice symmetry. We examine the statistical mechanics of this transition and the effects on it of quenched disorder, using Monte Carlo simulations of the classical Heisenberg model on the pyrochlore lattice with coupling to uniform lattice distortions. The model has a transition between a cubic, paramagnetic high-temperature phase and a tetragonal, Neel ordered low-temperature phase. It does not support…
The $A$-site spinel NiRh$_2$O$_4$ is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here, we carry out resonant inelastic x-ray sc…
We present our theoretical and numerical results on thermodynamic properties and the microscopic mechanism of two successive transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) obtained by Monte Carlo calculations of an effective spin-orbital-lattice model in the strong correlation limit. Geometrical frustration in the pyrochlore lattice structure of V cations suppresses development of spin and orbital correlations, however, we find that the model exhibits two transitions at low temperatures. First, a discontinuous transition occurs with an orbital ordering assisted by the …
Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{\text 2}$O$_{\text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applying a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-$S$ magnets, we find that systems with $S \geq 3/2$ reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments $S$=1…
Depending on the crystal growth conditions, an orthorhombic (O-type) or a tetragonal (T-type) structure can be found in the solid solution Cs2CuCl4-xBrx (0 < x < 4). Here we present measurements of the temperature-dependent magnetic susceptibility and isothermal magnetization on the T-type compounds x = 1.6 and 1.8 and compare these results with the magnetic properties recently derived for the O-type variant by Cong et al., Phys. Rev. B 83, 064425 (2011). The systems were found to exhibit quite dissimilar magnetic properties which can be assigned to differences in the Cu coordination in these …
We report on the quasi-two-dimensional magnetism of the natural mineral diaboleite Pb2Cu(OH)4Cl2 with a tetragonal crystal structure, which is closely related to that of the frustrated spin-1/2 magnet PbVO3. Magnetic susceptibility of diaboleite is well described by a Heisenberg spin model on a diluted square lattice with the nearest-neighbor exchange of J~35 K and about 5% of non-magnetic impurities. The dilution of the spin lattice reflects the formation of Cu vacancies that are tolerated by the crystal structure of diaboleite. The weak coupling between the magnetic planes triggers the long-…
Spin nematic liquid crystal and scalar spin chirality in tetragonal lattice YbMnBi$_2$
Rice University（莱斯大学）；Chongqing University（重庆大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Soongsil University（崇实大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Oak Ridge National Laboratory（橡树岭国家实验室）
We discuss the ground state properties of a spin 1/2 magnetic ion with threefold $t_{2g}$ orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti$^{3+}$ ion in B-spinel MgTi$_2$O$_4$. We formulate an effective spin-orbital Hamiltonian and study its low energy sector by constructing several exact-eigenstates in the limit of vanishing Hund's coupling. We find that orbital degrees of freedom modulate the spin-exchange energies, release the infinite spin-degeneracy of pyrochlore structure, and drive the system to a non-magnetic spin-singlet manifold. The latter is a collection of spi…
Antiferromagnetic insulators on the diamond lattice are candidate materials to host exotic magnetic phenomena ranging from spin-orbital entanglement to degenerate spiral ground-states and topological paramagnetism. Compared to other three-dimensional networks of magnetic ions, such as the geometrically frustrated pyrochlore lattice, the investigation of diamond-lattice magnetism in real materials is less mature. In this work, we characterize the magnetic properties of model A-site spinels CoRh2O4 (cobalt rhodite) and CuRh2O4 (copper rhodite) by means of thermo-magnetic and neutron scattering m…
