We present an experimental study of the two-dimensional S=1/2 square-lattice antiferromagnet Cu(pz)$_2$(ClO$_4$)$_2$ (pz denotes pyrazine - $C_4H_4N_2$) using specific heat measurements, neutron diffraction and cold-neutron spectroscopy. The magnetic field dependence of the magnetic ordering temperature was determined from specific heat measurements for fields perpendicular and parallel to the square-lattice planes, showing identical field-temperature phase diagrams. This suggest that spin anisotropies in Cu(pz)$_2$(ClO$_4$)$_2$ are small. The ordered antiferromagnetic structure is a collinear arrangement with the magnetic moments along either the crystallographic b- or c-axis. The estimated ordered magnetic moment at zero field is m_0=0.47(5)mu_B and thus much smaller than the available single-ion magnetic moment. This is evidence for strong quantum fluctuations in the ordered magnetic phase of Cu(pz)$_2$(ClO$_4$)$_2$. Magnetic fields applied perpendicular to the square-lattice planes lead to an increase of the antiferromagnetically ordered moment to m_0=0.93(5)mu_B at mu_0H=13.5T - evidence that magnetic fields quench quantum fluctuations. Neutron spectroscopy reveals the presence of a gapped spin excitations at the antiferromagnetic zone center, and it can be explained with a slightly anisotropic nearest neighbor exchange coupling described by J_1^{xy}=1.563(13)meV and J_1^z=0.9979(2)J_1^{xy}.
We analyze the zero temperature phase diagrams of the spin S quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem from the large S limit. Our primary focus is on determining the extent to which the existence and character of any quantum disordered phases can be inferred from this approach.
The magnetic structure of the double perovskite compound Sr$_2$CuTeO$_6$ was determined from neutron powder diffraction data. This material is magnetically described as an $S\,{=}\,1/2$ quasi-two-dimensional square-lattice Heisenberg model with antiferromagnetic nearest-neighbor and next-nearest-neighbor interactions. Sr$_2$CuTeO$_6$ undergoes a magnetic phase transition at $T_{\rm N}\,{\simeq}\,29\,$ K. The spin structure below $T_{\rm N}$ is Néel antiferromagnetic on the square lattice, which means that the nearest-neighbor interaction ($J_1$) is stronger than the next-nearest-neighbor inter…
We develop a simple and unbiased numerical method to obtain the uniform susceptibility of quantum many body systems. When a Hamiltonian is spatially deformed by multiplying it with a sine square function that smoothly decreases from the system center toward the edges, the size-scaling law of the excitation energy is drastically transformed to a rapidly converging one. Then, the local magnetization at the system center becomes nearly size independent; the one obtained for the deformed Hamiltonian of a system length as small as L=10 provides the value obtained for the original uniform Hamiltonia…
The isostructural double perovskites Ba$_2$CuTeO$_6$ and Ba$_2$CuWO$_6$ are shown by theory and experiment to be frustrated square-lattice antiferromagnets with opposing dominant magnetic interactions. This is driven by differences in orbital hybridisation of Te$^{6+}$ and W$^{6+}$. A spin-liquid-like ground state is predicted for Ba$_2$Cu(Te$_{1-x}$W$_x$)O$_6$ solid solution similar to recent observations in Sr$_2$Cu(Te$_{1-x}$W$_x$)O$_6$.
Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose …
We numerically study optical conductivity $σ(ω)$ near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections, and to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature- and $ω$-dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the …
We investigate the spin dynamics of the square-lattice spin-1/2 Heisenberg antiferromagnet by means of an improved mean field Schwinger boson calculation. By identifying both, the long range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean field triplet excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this triplet excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low and high energy spectral weight feat…
We discuss spin-$\frac12$ Heisenberg antiferromagnet on simple square lattice in magnetic field $H$ using recently proposed bond-operator technique. It is well known that magnetically ordered phases of quantum magnets are well described at least qualitatively by the conventional spin-wave theory that only introduces quantum corrections into the classical solution of the problem. We observe that quantum fluctuations change drastically dynamical properties of the considered model at $H$ close to its saturation value: the dynamical structure factor shows anomalies corresponding to Green's functio…
Sr$_2$CuTeO$_6$ presents an opportunity for exploring low-dimensional magnetism on a square lattice of $S=1/2$ Cu$^{2+}$ ions. We employ ab initio multi-reference configuration interaction calculations to unravel the Cu$^{2+}$ electronic structure and to evaluate exchange interactions in Sr$_2$CuTeO$_6$. The latter results are validated by inelastic neutron scattering using linear spin-wave theory and series-expansion corrections for quantum effects to extract true coupling parameters. Using this methodology, which is quite general, we demonstrate that Sr$_2$CuTeO$_6$ is an almost realization …
We successfully synthesize single crystals of the verdazyl radical $α$-2,3,5-Cl$_3$-V. $Ab$ $initio$ molecular orbital calculations indicate that the two dominant antiferromagnetic interactions, $J_{\rm{1}}$ and $J_{\rm{2}}$ ($α=J_{\rm{2}}/J_{\rm{1}}\simeq 0.56$), form an $S$ = 1/2 distorted square lattice. We explain the magnetic properties based on the $S$ = 1/2 square lattice Heisenberg antiferromagnet using the quantum Monte Carlo method, and examine the effects of the lattice distortion and the interplane interaction contribution. In the low-temperature regions below 6.4 K, we observe ani…
We report the magnetic properties of the double perovskites SrLaCuSbO$_6$ (SLCSO) and SrLaCuNbO$_6$ (SLCNO). The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an $S\,=\,1/2$ square lattice Heisenberg antiferromagnet. Magnetic ordering occurs at $T_{\rm N}\,{=}\,13.6$ and 15.7 K for SLCSO and SLCNO, respectively. Neutron powder diffraction measurements reveal contrasting spin structures in both compounds. The spin structures of SLCSO and SLCNO below $T_{\rm N}$ are Néel antiferromagnetic and collinear antiferromagnetic, respect…
We investigate the ground-state and the finite-temperature properties of the bond-random $s=1/2$ Heisenberg model on a square lattice with frustrating nearest- and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration ($J_2/J_1$) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like s…
We explore the interplay between randomness and magnetic frustration in the series of $S = 1/2$ Heisenberg square-lattice compounds Sr$_2$CuTe$_{1-x}$W$_x$O$_6$. Substituting W for Te alters the magnetic interactions dramatically, from strongly nearest-neighbor to next-nearest-neighbor antiferromagnetic coupling. We perform neutron scattering measurements to probe the magnetic ground state and excitations over a range of $x$. We propose a bond-disorder model that reproduces ground states with only short-ranged spin correlations in the mixed compounds. The calculated neutron diffraction pattern…
Spin reorientation in the square-lattice antiferromagnets RMnAsO (R = Ce, Nd): Density functional analysis of the spin exchange interactions between the rare-earth and transition-metal ions
We implement the coupled cluster method to very high orders of approximation to study the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ Heisenberg model on a cross-striped square lattice. Every nearest-neighbour pair of sites on the square lattice has an isotropic antiferromagnetic exchange bond of strength $J_{1}>0$, while the basic square plaquettes in alternate columns have either both or neither next-nearest-neighbour (diagonal) pairs of sites connected by an equivalent frustrating bond of strength $J_{2} \equiv αJ_{1} > 0$. By studying the magnetic order parameter (i.e., the average local on-site m…
We predict that spin-waves in an ordered square quantum antiferromagnet in a transverse magnetic field (h) may demonstrate three modes of spin excitations. Starting from the self-consistent rotation-invariant Green's function method, a new mean-field theory is constructed for h not equal to 0. The method preserves the translational and the axial symmetries, and provides exact fulfillment of the single-site constraint for each of the three modes. We examine the dynamical structure factors S(aa)(k,w), a= x, y, z. It is shown, that the introduction of h leads to the hybridization of two degenerat…
Quantum Phase Transitions of a Square-Lattice Heisenberg Antiferromagnet with Two Kinds of Nearest-Neighbour Bonds: A High-Order Coupled-Cluster Treatment
The Heisenberg model for S=1/2 describes the interacting spins of electrons localized on lattice sites due to strong repulsion. It is the simplest strong-coupling model in condensed matter physics with wide-spread applications. Its relevance has been boosted further by the discovery of curate high-temperature superconductors. In leading order, their undoped parent compounds realize the Heisenberg model on square-lattices. Much is known about the model, but mostly at small wave vectors, i.e., for long-range processes, where the physics is governed by spin waves (magnons), the Goldstone bosons o…
We studied the low-temperature specific heats of two antiferromagnets with the two-dimensional square-kagome structure, i.e., KCu$_6$AlBiO$_4$(SO$_4$)$_5$Cl (KCu6) and Na$_6$Cu$_7$BiO$_4$(PO$_4$)$_4$[Cl,(OH)]$_3$ (NaCu7) with the structural differences that there are interlayer Cu$^{2+}$ ions in NaCu7. Both materials show no magnetic ordering down to 50 mK. At zero field, the $C/T$ of KCu6 has a finite value when the temperature is close to zero K. Under the magnetic field, a seemingly $T^2$ dependence appears and its coefficient is progressively suppressed by the field. For NaCu7, the specifi…
We study the Néel to four-fold columnar valence bond solid (cVBS) quantum phase transition in a sign free $S=1$ square lattice model. This is the same kind of transition that for $S=1/2$ has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square lattice $S=1/2$ Néel-VBS transition have found consistency with the DCP scenario with no direct evidence for first order behavior. In contrast to the $S=1/2$ case, in our quantum Monte Carlo simulations for the $S=1$ model, we present unambiguous evidence for a direct conventional first-order qu…
We report results of magnetization and $^{31}$P NMR measurements under high pressure up to 6.4~GPa on RbMoOPO$_4$Cl, which is a frustrated square-lattice antiferromagnet with competing nearest-neighbor and next-nearest-neighbor interactions. Anomalies in the pressure dependences of the NMR shift and the transferred hyperfine coupling constants indicate a structural phase transition at 2.6~GPa, which is likely to break mirror symmetry and triggers significant change of the exchange interactions. In fact, the NMR spectra in magnetically ordered states reveal a change from the columnar antiferrom…
