Metamagnetic Transition in Low-Dimensional Site-Decorated Quantum Heisenberg Ferrimagnets

TL;DR

This work investigates ultranarrow phase crossovers (UNPC) in low-dimensional site-decorated quantum Heisenberg ferrimagnets with a ferromagnetic backbone $J$ and antiferromagnetic decoration $J_{\mathrm{AF}}$. In the $J\to\infty$ limit the model reduces to a central-macrospin problem (the $a$-spins form a macroscopic spin coupled to a $b$-spin bath), yielding a ground-state with three regimes separated by $h_{c1}$ and $h_{c2}$ and two finite-temperature second-order transitions at $T_{c1}$ and $T_{c2}$ that merge at $T_0$, producing a half-ice, half-fire regime in a weak field. For finite but large $J$, a weak-field mapping leads to an effective Hamiltonian with $h_{\mathrm{eff}}=h\left[1-\frac{\widetilde{\mu_b}}{\widetilde{\mu_a}}B_{S_b}(\beta \widetilde{J_{\mathrm{AF}}})\right]$, enabling a quantitative estimate of the crossover width $2\delta T$ via $\delta T=\left[\frac{\chi_0 h \widetilde{\mu_b}}{T_0^2\widetilde{\mu_a}^2}\widetilde{J_{\mathrm{AF}}} B'_{S_b}\left(\frac{\widetilde{J_{\mathrm{AF}}}}{T_0}\right)\right]^{-1}$. The analysis shows that UNPC is viable in decorated 2D lattices due to an exponentially large initial susceptibility ($\chi_0 \propto e^{4\pi \widetilde{J}/T_0}$), whereas in 1D it is much weaker ($\chi_0 \propto J/T_0$). The results point to potential experimental realizations in decorated optical lattices and $d$-$f$ compounds and motivate further numerical tests.

Abstract

The prohibition of finite-temperature phase transition in one-dimensional (1D) Ising models and 1D/2D quantum Heisenberg models with short-range interactions fundamentally constrains the application potentials of low-dimensional magnetic materials. Recently, ultranarrow phase crossover (UNPC), which can approach a transition at a desirable finite temperature $T_0$ arbitrarily closely, was discovered in 1D decorated Ising chains and ladders. Here we present a theoretical study of similarly decorated, yet much more challenging, quantum Heisenberg ferrimagnets in a magnetic field, which features ferromagnetic backbone exchange $J$, antiferromagnetic site-decoration coupling $J_{AF}$, and different magnetic moments for the backbone and decorating spins $μ_aS_a<μ_bS_b$. We exactly solved the model in the large $J$ limit -- as a central-macrospin model -- and found two finite-temperature second-order transitions; just above $T_{c2}$ a ``half-ice, half-fire'' regime appears. Finite-$J$ weak-field results follow from an effective-field mapping, suggesting the emergence of UNPC at finite $T_0$ in 2D square lattices thanks to its exponentially strong initial magnetic susceptibility $χ_0\propto e^{4πS_a^2 J/T_0}$, though less likely in 1D chains where $χ_0\propto J/T_0$. These results may shed light on new technological applications of low-dimensional quantum spin systems and attract experimental and computational tests.

Figures (5)

• Figure 1: (a) The site-decorated model, where the $a$- and $b$-spins are the backbone and decorating spins, respectively. (b) The central-macrospin model, where the $a$-spins collapse to form one macroscopic spin in the large $J$ limit of the site-decorated model and the $b$-spins provide a bath environment.
• Figure 2: Density plots of (a) $m_a^z$, (b) $m_b^z$, (c) $\chi$, and (d) entropy / $\ln(2S+1)$ in the $h-T$ plane. $\widetilde{J}\equiv J S_a^2\to\infty$, $\widetilde{J_\mathrm{AF}}\equiv J_\mathrm{AF} S_aS_b=1$, $\widetilde{\mu_a}\equiv\mu_aS_a=1$, $\widetilde{\mu_b}\equiv\mu_bS_b=2$, $S_a=S_b=1/2$. The white solid lines indicate $T_{c1}$ and $T_{c2}$; the white dashed lines indicate $T_0$. The black dashed line in (b) is the $m_b^z=0$ contour line.
• Figure 3: Estimated $\widetilde{J}$ dependence of $\frac{\delta T}{T_0} h$ of the 1D and 2D site-decorated Heisenberg models in a weak external magnetic field $h$ for (a) $S_a\to\infty$ and $S_b\to\infty$, (b) $S_a\to\infty$ and $S_b=1/2$, (c) $S_a=1/2$ and $S_b\to\infty$, and (d) $S_a=S_b=1/2$. Here $\widetilde{J_\mathrm{AF}}=1$, $\widetilde{\mu_a}=1$, and $\widetilde{\mu_b}=2$, yielding $T_0\simeq 1.82$ for $S_b=\frac{1}{2}$ and $T_0\simeq 0.56$ for $S_b\to\infty$.
• Figure S1: Zero-temperature magnetic field dependence of (a) $m_a^z=\cos\theta_a^*$ (blue solid line) and $m_b^*=\cos\theta_b^*$ (red dashed line), and of (b) the spectral gaps of the acoustic (red solid line) and optic branches (blue dashed line) in linear spin-wave theory. $z\widetilde{J}\equiv zJ S_a^2=10$ with $z$ being the coordination number of the $a$-spins within the backbone, $\widetilde{J_\mathrm{AF}}\equiv J_\mathrm{AF} S_aS_b=1$, $\widetilde{\mu_a}\equiv\mu_aS_a=1$, $\widetilde{\mu_b}\equiv\mu_bS_b=2$, $S_a=S_b=1/2$. Vertical grid lines in (b) mark $h_{c1}=0.5$ and $h_{c2}=1.5$.
• Figure S2: Density plots of specific heat in the $h-T$ plane. $J\to\infty$, $\widetilde{J_\mathrm{AF}}\equiv J_\mathrm{AF} S_aS_b=1$, $\widetilde{\mu_a}\equiv\mu_aS_a=1$, $\widetilde{\mu_b}\equiv\mu_bS_b=2$, $S_a=S_b=1/2$. The white solid lines indicate $T_{c1}$ and $T_{c2}$; the white dashed lines indicate $T_0$.