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arXiv:1907.04709 · Physical review. B./Physical review. B

Quantum phase diagram of a frustrated spin- 12 system on a trellis ladder

Debasmita Maiti, Manoranjan Kumar

Published Dec 10, 2019• 8 citations
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Abstract

We study an isotropic Heisenberg spin-$\frac{1}{2}$ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling ${J}_{3}$. ${J}_{1}$ and ${J}_{2}$ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small ${J}_{2}$ limit, a short-range striped collinear phase is found in the presence of ${J}_{3}$, whereas, in the large ${J}_{2}/{J}_{3}$ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large ${J}_{3}$ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing ${J}_{3}$. We apply this model to understand the magnetic properties of ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$ and also fit the experimental data of susceptibility and magnetization. We note that ${J}_{3}$ is a dominant interaction in this material, whereas ${J}_{1}$ and ${J}_{2}$ are approximately half of ${J}_{3}$. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.

DOI
10.1103/physrevb.100.245118

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Abstract We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropic S -type or discrete anisotropic σ -type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both S and σ -type of spins are anti-ferromagnetically aligned with each other, two nearest S spins along the rung form an anisotropic singlet bond whereas two nearest σ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heat C v ( T ), magnetic susceptibility χ ( T ) and thermal entropy S ( T ) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ ( T ) and C v ( T ) curves.
We study the ground-state (GS) properties of the frustrated spin-12\frac{1}{2}21​ J1{J}_{1}J1​--J2{J}_{2}J2​--J3{J}_{3}J3​ Heisenberg model on the two-dimensional honeycomb lattice with ferromagnetic nearest-neighbor (${J}_{1}=\ensuremath{-}1$) exchange and frustrating antiferromagnetic next-nearest-neighbor (J2>0{J}_{2}>0J2​>0) and next-next-nearest-neighbor (J3>0{J}_{3}>0J3​>0) exchanges, for the case J3=J2{J}_{3}={J}_{2}J3​=J2​. We use the coupled-cluster method implemented to high orders of approximation, complemented by the Lanczos exact diagonalization of a large finite lattice with 32 sites, in order to calculate the GS energy, magnetic order parameter, and spin-spin correlation functions. In one scenario we find a quantum phase transition point between regions characterized by ferromagnetic order and a form of antiferromagnetic (``striped'') collinear order at ${J}_{2}^{c}\ensuremath{\approx}0.1095\ifmmode\pm\else\textpm\fi{}0.0005$, which is below the corresponding hypothetical transition point at J2cl=17{J}_{2}^{\mathrm{cl}}=\frac{1}{7}J2cl​=71​ ($\ensuremath{\approx}0.143$) for the classical version of the model, in which we momentarily ignore the intervening noncollinear spiral phase in the region 110<J2<15\frac{1}{10}<{J}_{2}<\frac{1}{5}101​<J2​<51​. Hence we see that quantum fluctuations appear to stabilize somewhat the collinear antiferromagnetic order in preference to the ferromagnetic order in this model. We compare results for the present ferromagnetic case (with ${J}_{1}=\ensuremath{-}1$) to previous results for the corresponding antiferromagnetic case (with J1=+1{J}_{1}=+1J1​=+1). The magnetic order parameter is found to behave similarly for the ferromagnetic and the antiferromagnetic models for large values of the frustration parameter J2{J}_{2}J2​. However, there are considerable differences in the behavior of the order parameters for the two models for ${J}_{2}/|{J}_{1}|\ensuremath{\lesssim}0.6$. For example, the quasiclassical collinear magnetic long-range order for the antiferromagnetic model (with J1=+1{J}_{1}=+1J1​=+1) breaks down at ${J}_{2}^{{c}_{2}}\ensuremath{\approx}0.60$, whereas the ``equivalent'' point for the ferromagnetic model (with ${J}_{1}=\ensuremath{-}1$) occurs at ${J}_{2}^{c}\ensuremath{\approx}0.11$. Unlike in the antiferromagnetic model (with J1=+1{J}_{1}=+1J1​=+1), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical antiferromagnetic phases (with N\'eel and striped order) for J2c1<J2<J2c2{J}_{2}^{{c}_{1}}<{J}_{2}<{J}_{2}^{{c}_{2}}J2c1​​<J2​<J2c2​​, with ${J}_{2}^{{c}_{1}}\ensuremath{\approx}0.47$, we find no clear indications at all in the ferromagnetic model for an intermediate magnetically disordered phase between the corresponding phases exhibiting ferromagnetic and striped order. Instead the evidence for the ferromagnetic model (with ${J}_{1}=\ensuremath{-}1$) points to one of two scenarios: either there is a direct first-order transition between the two magnetically ordered phases, as mentioned above; or there exists an intervening phase between them in the very narrow range $0.10\ensuremath{\lesssim}{J}_{2}\ensuremath{\lesssim}0.12$, which is probably a remnant of the spiral phase that exists in the classical counterpart of the model over the larger range 110<J2<15\frac{1}{10}<{J}_{2}<\frac{1}{5}101​<J2​<51​.
The quantum phases of two-leg spin-12\frac{1}{2}21​ ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density-matrix renormalization-group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange J2>0{J}_{2}>0J2​>0 between first neighbors in the legs, variable isotropic AF exchange J1{J}_{1}J1​ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when ${J}_{1}\ensuremath{\gg}{J}_{2}$. Ladders with skewed rungs and variable J1{J}_{1}J1​ have frustrated AF interactions leading to multiple quantum phases: AF at small J1{J}_{1}J1​, either ferromagnetic or AF at large J1{J}_{1}J1​, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate J1{J}_{1}J1​.
Abstract In this work, we consider a frustrated two‐leg spin‐1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin‐1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non‐collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin‐1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of phase and calculate the pitch angle in the NCF phase.
Using the coupled-cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-12\frac{1}{2}21​ J1{J}_{1}J1​-J2{J}_{2}J2​ model on the square lattice with plaquette structure. We consider antiferromagnetic (J1>0{J}_{1}>0J1​>0) as well as ferromagnetic (J1<0{J}_{1}<0J1​<0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction J2>0{J}_{2}>0J2​>0. The strength of interplaquette interaction $\ensuremath{\lambda}$ varies between $\ensuremath{\lambda}=1$ (which corresponds to the uniform J1{J}_{1}J1​-J2{J}_{2}J2​ model) and $\ensuremath{\lambda}=0$ (which corresponds to isolated frustrated 4-spin plaquettes). While on the classical level ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) both versions of models (i.e., with ferro- and antiferromagnetic J1{J}_{1}J1​) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case s=1/2s=1/2s=1/2. For the antiferromagnetic case (J1>0{J}_{1}>0J1​>0) N\'eel antiferromagnetic long-range order at small J2/J1{J}_{2}/{J}_{1}J2​/J1​ and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.47$ as well as collinear striped antiferromagnetic long-range order at large J2/J1{J}_{2}/{J}_{1}J2​/J1​ and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.30$ appear which correspond to their classical counterparts. Both semiclassical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing $\ensuremath{\lambda}$. For the ferromagnetic case (J1<0{J}_{1}<0J1​<0) we have the trivial ferromagnetic ground state at small J2/∣J1∣{J}_{2}/|{J}_{1}|J2​/∣J1​∣. By increasing J2{J}_{2}J2​ this classical phase gives way for a semiclassical plaquette phase, where the plaquette block spins of length s=2s=2s=2 are antiferromagnetically long-range ordered. Further increasing of J2{J}_{2}J2​ then yields collinear striped antiferromagnetic long-range order for $\ensuremath{\lambda}\ensuremath{\gtrsim}0.38$, but a nonmagnetic quantum paramagnetic phase $\ensuremath{\lambda}\ensuremath{\lesssim}0.38$.
We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either SSS or σσσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both SSS and σσσ-type of spins are anti-ferromagnetically aligned with each other, two nearest SSS spins along the rung form an anisotropic singlet bond whereas two nearest σσσ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like Cv(T)Cv(T)Cv(T), χ(T)χ(T)χ(T) and S(T)S(T)S(T) are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from χ(T)χ(T)χ(T) and Cv(T)Cv(T)Cv(T) curves.