Experimental benchmark of the quantum-classical crossover in a spin ladder

Abstract

We report a spin-(1/2, 5/2) three-leg ladder realized in a radical-Mn polymer, exhibiting an antiferromagnetic transition and magnetization curves accurately described by classical mean-field theory. Although the underlying spin model intrinsically supports strong quantum fluctuations, as confirmed by quantum Monte Carlo simulations, the real system shows an anomalously complete suppression of quantum behavior. These findings provide a key experimental benchmark for the quantum-classical crossover and suggest that lattice topology can play a crucial role in tuning the balance between quantum and classical physics in strongly correlated systems.

Figures (4)

• Figure 1: (a) Crystal structure of [Mn($p$-Py-V)$_2$(NO$_3$)$_2$]$_n$ forming the three-leg ladder along the $a$ axis. Hydrogen atoms are excluded to enhance clarity. The green nodes represent the spin-1/2 of the radicals. The thick lines represent exchange interactions. (b) Spin-(1/2,5/2) three-leg ladder comprising $J_{\rm{1}}$, $J_{\rm{2}}$, and $J_{\rm{3}}$. $\boldsymbol{s}$ and $\boldsymbol{S}$ denote the spins on the radical and Mn$^{2+}$, respectively.
• Figure 2: (a) Temperature dependence of magnetic susceptibility ($\chi$ = $M/H$) of [Mn($p$-Py-V)$_2$(NO$_3$)$_2$]$_n$ at 0.1 T. The solid line represents the QMC result for $J_{1}/k_{\rm{B}}$ = 29 K, $J_{2}/k_{\rm{B}}$ = 2.5 K, $J_{3}/k_{\rm{B}}$ = 1.1 K. (b) Temperature dependence of the specific heat $C_{\rm{p}}$ of [Mn($p$-Py-V)$_2$(NO$_3$)$_2$]$_n$. The arrow indicates the phase transition temperatures at zero field. For clarity, the values for 3, 5, 7, and 9 T have been shifted up by 4, 6.5, 9, and 12 J/mol K, respectively. (c) Magnetization curve of [Mn($p$-Py-V)$_2$(NO$_3$)$_2$]$_n$ at 1.3 and 4.2 K. The broken line represents the MF result with $D/k_{\rm{B}}$ = 0.1 K, averaged over field directions for the powder sample. A radical purity of 95 ${\%}$ is considered. The inset shows the low-field region with $dM/dH$ at 1.3 K, and the arrow indicates the spin-flop transition at $H_{\rm{c}}$.
• Figure 3: (a) Frequency dependence of ESR absorption spectra of [Mn($p$-Py-V)$_2$(NO$_3$)$_2$]$_n$ at 1.7 K. Closed symbol marks the AF resonance fields, while open symbol marks the paramagnetic resonance fields caused probably by impurities. (b) Frequency-field plot of the resonance fields. The closed and open circles correspond to the resonance fields indicated by the closed and open symbols in Fig. 3(a), respectively. Solid and broken lines indicate the calculated easy-axis AF resonance modes and paramagnetic resonanse line, respactively. The vertical broken line indicates the spin flop transition field $H_{\rm{c}}$.
• Figure 4: (a) Schematic views of the spin configurations. The larger pink and smaller blue arrows represent the sublattices associated with $\boldsymbol{S}$ and $\boldsymbol{s}$, respectively. The spins form a collinear AF structure at zero field, while for $H\parallel z$ with $H \textgreater H_{\rm{c}}$ and for $H\perp z$, the spins exhibit canted configurations. Two sublattice pairs, composed of $\boldsymbol{s}$-$\boldsymbol{s}$ and $\boldsymbol{S}$-$\boldsymbol{S}$, polarize toward the field direction with different canting angles. (b) Magnetization curve for $H\parallel z$, calculated using the MF approximation with $J_{1}/k_{\rm{B}}$ = 29 K, $J_{2}/k_{\rm{B}}$ = 2.5 K, $J_{3}/k_{\rm{B}}$ = 1.1 K, $D/k_{\rm{B}}$ = 0.1 K. The illustration depicts the tilt of the sublattice pairs toward the external field, with canting angles defined as 90°for parallel alignment. The inset shows the low-field region for $H\parallel z$ and $H\perp z$. (c) Calculated magnetization curves of the present ladder, showing the effects of removing $J_{2}$ or $J_{3}$, and comparison between MF and QMC results, assuming $D$ =0. The result for the $s$=1/2 chain is calculated by using QMC with $H_{\rm{in}} \approx -4.7$ T, and the magnetization is offset by 5/7.