We present observations of highly frustrated quasi-two-dimensional (2D) magnetic correlations in the honeycomb lattice layers of the ${S}_{\text{eff}} =1/2$ compound $\ensuremath{\gamma}\ensuremath{-}{\mathrm{BaCo}}_{2}{({\mathrm{PO}}_{4})}_{2}$ ($\ensuremath{\gamma}$-BCPO). Specific heat shows a broad peak comprised of two weak kink features at ${T}_{N1}\ensuremath{\sim}6$ K and ${T}_{N2}\ensuremath{\sim}3.5$ K, the relative weights of which can be modified by sample annealing. Neutron powder diffraction measurements reveal short range quasi-2D order that is established below ${T}_{N1}$ and ${T}_{N2}$, at which two separate, incompatible, short range magnetic orders onset: commensurate antiferromagnetic correlations with correlation length ${\ensuremath{\xi}}_{c}=60\ifmmode\pm\else\textpm\fi{}2$ \AA{} (${T}_{N1}$) and in quasi-2D helical domains with ${\ensuremath{\xi}}_{h}=350\ifmmode\pm\else\textpm\fi{}11$ \AA{} (${T}_{N2}$). The ac magnetic susceptibility response lacks frequency dependence, ruling out spin freezing. Inelastic neutron scattering data on $\ensuremath{\gamma}$-BCPO is compared with linear spin wave theory, and two separate parameter regions of the XXZ ${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ model with ferromagnetic nearest-neighbor exchange ${J}_{1}$ are favored, both near regions of high classical degeneracy. High energy coherent excitations ($\ensuremath{\sim}10$ meV) persist up to at least 40 K, suggesting strong in-plane correlations persist above ${T}_{N}$. These data show that $\ensuremath{\gamma}$-BCPO is a rare highly frustrated, quasi-2D ${S}_{\text{eff}} =1/2$ honeycomb lattice material which resists long range magnetic order and spin freezing.

https://link.aps.org/accepted/10.1103/PhysRevB.97.134409

Short-range order in the quantum XXZ honeycomb lattice material BaCo 2 ( PO 4 ) 2

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto several three-dimensional Ising models with complicated many-spin interactions. This hierarchy of Ising-like models is studied by means of analytic and Monte Carlo techniques. We demonstrate that the sequence of these Ising models can be used to calculate accurately the thermodynamics of the two-dimensional spin-1/2 XY model. By calculating the specific heat, spin correlation functions, susceptibilities and a disorder parameter, we address the question of the nature of the phase transition in the two-dimensional spin-1/2 XY model.

/pdf/thermodynamics-of-the-two-dimensional-spin-1-2-xy-model-2vlxe9tnnd.pdf

Thermodynamics of the two-dimensional spin-1/2 XY model

Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo2(AsO4)2 frustrated honeycomb-lattice magnet.

The T=0K phase diagram of the Heisenberg model for finite S on the square lattice with exchange interaction up to third neighbours is studied. The nearest-neighbour interaction is assumed to be ferromagnetic. In the classical (S to infinity ) approximation the model has, in addition to the ferromagnetic phase, an antiferromagnetic and two non-equivalent helical phases depending on the amount of competition between the interactions. To lowest order in 1/S these phases are still present but quantum fluctuations bring a significant modification to the phase diagram: with the exception of the ferro-helix transition line, all the phase boundaries are shifted with a considerable enhancement of the region with antiferromagnetic order. In addition, between the two non-equivalent helices a new phase sets in which is characterised by an infinite degeneracy of the ground state with absence of long-range order even at T=0K. In the S to infinity limit this phase collapses into line in the parameter space.

http://iopscience.iop.org/article/10.1088/0022-3719/19/33/011/pdf

Quantum fluctuations and phase diagram of Heisenberg models with competing interactions

Elastic and quasielastic neutron scattering measurements have been performed in the S=1/2 square Heisenberg antiferromagnet copper(II) deuteroformate tetradeuterate, Cu(DCO2)2.4D2O. The sublattice magnetization was measured below TN=16.54(5) K, and the critical exponent beta was found to cross over from 0.23(1) to 0.32(2) at a reduced temperature epsilon =(TN-T)/TN of 0.06 as TN was approached from below. The temperature dependence of the inverse correlation length of the two-dimensional antiferromagnetic correlations and of the sublattice susceptibility above TN was consistent with the predictions of the quantum non-linear sigma model of Chakravarty (1989) and co-workers for a spin-wave stiffness of 13.4(4) K.

http://iopscience.iop.org/article/10.1088/0953-8984/4/4/003/pdf

Magnetic ordering and fluctuations in the S=1/2 square Heisenberg antiferromagnet Cu(DCO2)2.4D2O

We measured the magnetic specific heat of two quasi-two-dimensional (2-D), XY helimagnets, BaCo2 (AsO4)2 and BaCo2(PO4)2. At temperatures T < 2 K, C is proportional to T2 as expected from spin wave theory. At higher temperatures C has an exponential form characteristic of a potential barrier. The specific heat of BaCo2 (AsO4)2 exhibits a sharp anomaly at TN = 5.29 K whereas only a bump is observed around 5.5 K in BaCo2(PO4)2.

https://hal.archives-ouvertes.fr/jpa-00217789/document

J. Rossat-Mignod

Papers

SPECIFIC HEAT OF THE QUASI 2D-XY HELIMAGNETS BaCo2(AsO4)2 AND BaCo2 (PO4)2