Spin-singlet dimer phase in a frustrated square lattice under a magnetic field

TL;DR

The paper addresses how frustration and quantum fluctuations in a spin-$1/2$ Heisenberg model on an anisotropic square lattice under a magnetic field can stabilize nontrivial quantum phases. The authors apply a cluster mean-field method with eight-site clusters to capture short-range correlations while treating intercluster couplings at the mean-field level, focusing on six exchange couplings $J_n$ and the field $h^z$. They find that modest adjustments of the exchange parameters can enhance frustration and drive a field-induced phase in which chain 1 is ferromagnetic and chain 2 forms spin-singlet dimers, producing a robust $M/M_{ ext{sat}}=1/2$ plateau with singlet-dimer correlations. Spin-spin correlations reveal the emergence of dimerized order in chain 2 and a persistent polarization in chain 1, with the plateau persisting at low temperatures and melting as temperature increases. The results provide microscopic insights into FM-dimerized phases and offer guidance for interpreting experiments in verdazyl-based low-dimensional quantum magnets.

Abstract

We investigated the isotropic spin-1/2 Heisenberg model on an anisotropic square lattice with competing exchange interactions, motivated by the unconventional magnetic behavior observed in the verdazyl-based compound (o-MePy-V)PF6. Using a cluster mean-field approach, we explore a field-induced phase stabilized by the interplay between frustration and quantum fluctuations, focusing on the role of exchange interactions. We identify: (i) the formation of spin singlet pairs, signaled by enhanced spin-spin correlations in specific field regimes; and (ii) a one-half magnetization plateau, emerging from a subtle balance between competing exchange couplings and field-enhanced quantum fluctuations. Our results reveal that an enhancement of frustration, achieved by tuning small variations in the spatially anisotropic exchange interactions of the compound (o-MePy-V)PF6, can stabilize a field-induced quantum phase where ferromagnetism coexists with antiferromagnetic dimers. Our results provide microscopic insight into the mechanisms driving these nontrivial phases and offer theoretical support for interpreting experimental observations in this class of low-dimensional quantum magnets.

Figures (7)

• Figure 1: Schematic representation of the eight-site CMF approach applied to an anisotropic square lattice with six distinct exchange couplings $J_{n}$ ($n = 1,\dots,6$). Solid and dashed lines denote FM and AF exchange interactions, respectively. The gray sites form a FM chain connected by couplings $J_{1}$ and $J_{6}$ (referred to as chain 1), while the black sites form chain 2, composed of AF and FM couplings $J_{2}$ and $J_{5}$. The two chains are coupled via AF interactions $J_{3}$ and $J_{4}$, resulting in a frustrated square lattice geometry. Frustration arises in square plaquettes containing an odd number of AF bonds. Arrows indicate the bonds treated at the mean-field level within the CMF framework.
• Figure 2: Longitudinal (dashed lines) and transverse (solid lines) components of the eight local magnetizations in the ground state under an external magnetic field for: (a) and (b) Reference system , (c) and (d) $J_{2}/ J_{1}=-1.0$, (e) and (f) $J_{3}/ J_{1}=-0.40$ , (g) and (h) $J_{6}/ J_{1}=0.40$ . The left column displays the local moments of chain 1, while the right column shows the local moments of chain 2.
• Figure 3: Normalized total magnetization as a function of the external magnetic field, with the exchange parameters of the compound ($o$-MePy-V)PF$6$ kept fixed except for one, which is varied: (a) $|J_{2}|/J_{1}$ , (b) $|J_{3}|/J_{1}$, (c) $J_{5}/J_{1}$, and (d) $J_{6}/J_{1}$. The dashed lines represent the reference values for the exchange interactions of the compound ($o$-MePy-V)PF$_6$. The one-half magnetization plateau is depicted as a broad white region in the diagram.
• Figure 4: Ground state of the CMF model under magnetic field and different exchange interaction. (a) Total magnetization curve normalized by the saturation, (b) average local moments of chain 1 $m_{c1}$, and (c) average local moments of chain 2 $m_{c2}$. The dashed line indicates the exchange interactions of the reference compound ($o$-MePy-V)PF$_{6}$.
• Figure 5: Field dependence of spin-spin correlation functions computed using eight-site CMF model at $T/J_{1}$=0 for (a) Reference compound , (b) $J_{2}/J_{1}=-1.0$, (c) $J_{3}/J_{1}=-0.40$ and (d) $J_{6}/J_{1}=0.40$. Some correlations have been omitted from the figure as they are nearly equivalent to those already shown, e.g., the correlations $C_{01}\approx C_{23}$, $C_{45}\approx C_{67}$, $C_{46}\approx C_{57}$ and the interchain correlations $C_{07}\approx C_{16} \approx C_{25} \approx C_{34}$.