Quantum magnetization plateau and sign change of the magnetocaloric effect in a ferrimagnetic spin chain.

The magnetocaloric effect in the $(5∕2,1)$ ferrimagnetic chain is investiagted using a finite-cluster solver with central spin selection to reduce finite-size effects. We found that an enhanced magnetocaloric effect occurs at the boundary of the ground-state magnetization plateau. The calculated magnetic Grüneisen parameter ${\Gamma }_H$ exhibits strong signatures of a field-induced quantum phase transition at the critical magnetic field $H_c$ destroying the plateau. We obtain the characteristic increase ${\Gamma }_H\sim T^{-1∕\nu z}$ near $H_c$ and the sign change ${\Gamma }_H\approx -G_r∕(H-H_c)$, in accordance with scaling theory predictions.

Figure 1

Construction of the superblock from two blocks of size $N=4$ and one central site. The latter has the spin-1 value. The spin-$5∕2$ and spin-1 are denoted by odd and even numbers, respectively.

Figure 2

Schematic picture of the valence-bond-solid ground state in an external magnetic field for the ferrimagnetic chain $(5∕2,1)$. The arrows denote spins $1∕2$. The dotted (solid) lines correspond to singlet (triplet) pairs. The ovals represent a construction of spins $5∕2$ or 1 by a symmetrization of five (two) spins inside.

Figure 3

Lowest cluster energy levels as a function of the applied magnetic field (a). $T=0$ magnetization curve (solid line) of the $(5∕2,1)$ ferrimagnetic chain. The magnetization jump at the critical field $H_c$ is marked by the arrow. The result of DPIR calculation (dotted line) for $T={10}^{-4}J$ is shown for comparison (b). The magnetization $m\left(H\right)=-{(\partial F∕\partial H)}_T$ found with aid of the block partition function at $T={10}^{-3}J$ (dotted line) and via the envelope of the lowest cluster levels (solid line) (c).

Figure 4

Curves of constant entropy for the $(5∕2,1)$ ferrimagnetic chain on large (a) and small (b) scales. The values of the cluster entropy $\mathcal{S}$ measured in units of $k_B$ are shown by numbers at the end of each line. The tilt near the putative quantum critical point is shown by the arrow. Inset in (b): Isoentropy curve $(\mathcal{S}=1.0k_B)$ calculated with the cluster energies $E_{iSM}$ exhibits strong finite-size features.

Figure 5

(Color online) Magnetocaloric effect of the $(5∕2,1)$ ferrimagnetic chain near the critical field $H_c$ for a temperature sweep in the low-temperature regime at constant control parameter $r$: $0.66\times {10}^{-3}$ (○), $1.76\times {10}^{-3}$ (▵), $2.76\times {10}^{-3}$ (◻) (a); log-log plot of ${\Gamma }_H$ vs temperature in the quantum critical regime $r=0$ (b). The cluster entropy values $\mathcal{S}∕k_B$ are given near each point.

Figure 6

Magnetocaloric effect of the $(5∕2,1)$ ferrimagnetic chain near the critical field $H_c$ as a function of the control parameter $r$ for a temperature sweep at constant magnetic field. The cluster entropy in units of $k_B$ is marked by an arrow for each curve.

Figure 7

(Color online) The same as Fig. 6 but for the inverse of ${\Gamma }_H$. The direction of the change of entropy from $0.70k_B$ to $0.78k_B$ with the step $0.02k_B$ is shown by arrows. The data for the curve with $\mathcal{S}=0.70k_B$ are fitted by $3.5785(H-H_c)-0.0004$ (dotted line).

Figure 8

(Color online) The entropy per block (in units of $k_B$) $\mathcal{S}∕N$ vs $T$ for $H=H_c$ (◻) and the square-root approximation (solid line).