Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

Abstract

The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic nearest- and next-nearest neighbour interactions (the $J_1$--$J_2$ model) has long been studied as a paradigm of a two-dimensional frustrated quantum magnet. Only very recently, however, have the first experimental realisations of such systems been synthesized. The newest material, Pb${}_2$VO(PO${}_4$)${}_2$ seems to have mixed ferro-- and antiferromagnetic exchange couplings. In the light of this, we extend the semiclassical treatment of the $J_1$--$J_2$ model to include ferromagnetic interactions, and present an analysis of the finite temperature properties of the model based on the exact diagonalization of 8, 16 and 20 site clusters. We propose that diffuse neutron scattering can be used to resolve the ambiguity inherent in determining the ratio and sign of $J_1$ and $J_2$ from thermodynamic properties alone, and use a finite temperature Lanczos algorithm to make predictions for the relevant high temperature spin-spin correlation functions. The possibility of a spin-liquid phase occurring for ferromagnetic $J_1$ is also briefly discussed.

18 pages, 26 figures. Replaced Figures 22 and 23, slight changes to the text. Accepted for publication in European Physical Journal B

References in corpus (2)

• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Determination of the exchange energies in Li2VOSiO4 from a high-temperature series analysis of the square lattice J1-J2 Heisenberg model

Cited by in corpus (42)

• Magnetic properties of BaCdVO(PO_4)_2: a strongly frustrated spin-1/2 square lattice close to the quantum critical regime
• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Frustrated two dimensional quantum magnets
• Extension of the spin-1/2 frustrated square lattice model: the case of layered vanadium phosphates
• Magnetocaloric effect in the frustrated square lattice J1-J2 model
• Octupolar order in the multiple spin exchange model on a triangular lattice
• Intertwined nematic orders in a frustrated ferromagnet
• Strong frustration due to competing ferromagnetic and antiferromagnetic interactions: magnetic properties of M(VO)2(PO4)2 (M = Ca and Sr)
• Second-order quantum corrections for the frustrated, spatially anisotropic, spin-1/2 Heisenberg antiferromagnet on a square lattice
• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Antiferromagnetism of Zn${}_2$VO(PO${}_4{)}_2$ and the dilution with Ti${}^{4+}$
• Adiabatic demagnetization refrigeration to mK temperatures with the distorted square lattice magnet NaYbGeO${}_4$
• Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice
• Quantum fluctuations in high field magnetization of 2D square lattice J1-J2 antiferromagnets
• Effective One-Dimensional Coupling in the Highly-Frustrated Square-Lattice Itinerant Magnet CaCo${}_{2-y}$As${}_2$
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• Ground-state phase diagram and magnetic properties of a tetramerized spin-1/2 J_1-J_2 model: BEC of bound magnons and absence of the transverse magnetization
• Square-lattice magnetism of diaboleite Pb2Cu(OH)4Cl2
• Utilizing frustration in Gd- and Yb-based oxides for milli-Kelvin adiabatic demagnetization refrigeration
• Quantum fluctuations in anisotropic triangular lattices with ferro- and antiferromagnetic exchange
• Putative spin-nematic phase in BaCdVO(PO${}_4$)${}_2$
• Spin nematic phase in (quasi-)one-dimensional frustrated magnet in strong magnetic field
• Ordered moment in the anisotropic and frustrated square lattice Heisenberg model
• Néel temperature and reentrant H-T phase diagram of quasi-2D frustrated magnets
• Magnetic phase diagram of spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice
• Deformed spin-$\frac{1}{2}$ square lattice in antiferromagnetic NaZnVOPO${}_4$(HPO${}_4$)
• The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
• Realising square and diamond lattice $S=1/2$ Heisenberg antiferromagnet models in the $\alpha$ and $\beta$ phases of the coordination framework, KTi(C${}_2$O${}_4$)${}_2\cdot$\textit{x}H${}_2$O
• Stability of the 1/3 magnetization plateau of the $J_1-J_2$ kagome Heisenberg model
• Contrasting Magnetic Structures in SrLaCuSbO${}_6$ and SrLaCuNbO${}_6$: Spin-1/2 Quasi-Square-Lattice $J_1-J_2$ Heisenberg Antiferromagnets
• Short-range order of Br and three-dimensional magnetism in (CuBr)LaNb2O7
• Peculiarities of magnetic ordering in the S = 5/2 two-dimensional square-lattice antimonate NaMnSbO4
• Isothermal and adiabatic magnetization processes of the spin-$\frac{1}{2}$ Heisenberg model on an anisotropic triangular lattice
• Pressure-induced phase transition in the $J_1$-$J_2$ square lattice antiferromagnet RbMoOPO${}_4$Cl
• Spin and density excitations in the triangular-lattice $t$-$J$ model with multiple-spin exchange interactions: ${}^3$He on graphite
• Two dimensional frustrated magnets in high magnetic field
• Quasi two-dimensional magnetism in spin-$\frac{1}{2}$ square lattice compound Cu[C${}_6$H${}_2$(COO)${}_4$][H${}_3$N-(CH${}_2$)${}_2$-NH${}_3$]$\cdot$3H${}_2$O
• Two-dimensional frustrated spin systems in high magnetic fields
• Spin dynamics in itinerant antiferromagnet SrCr${}_2$As${}_2$
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice
• A Green's function method for the two-dimensional frustrated spin-1/2 Heisenberg magnetic lattice
• Frustration-induced diffusive scattering anomaly and dimension change in $\mathrm{FeG}{\mathrm{e}}_2$