Residual entropy and magnetocaloric effect in a diluted sawtooth spin model of hole-doped CuO chains

Ground-state and magnetocaloric properties of a site-diluted sawtooth magnetic chain in the presence of an external magnetic field are exactly investigated by using the transfer-matrix method. The model captures the main magnetic interactions along CuO chains present in some hole-doped cuprates. The ground-state diagram is exhibited and analytical expressions for the residual entropy within each ground state and along the transition lines are derived. We explicitly discuss the role of the underlying pairing correlations and the entropy maximization principle. The isothermal entropy change is determined as a function of interaction parameters, doping concentration, and magnetic-field amplitude. Normal and inverse magnetocaloric effects are reported. Adiabatic demagnetization curves are discussed in connection with configurational and spin contributions to the residual entropy.

Figure 1

(top panel) Diagrammatic representation of the randomly decorated spin model of a hole-doped CuO chain. The sites with Ising spins $S_i$ (blue cubes) are all occupied by magnetic atoms and interact through an antiferromagnetic exchange coupling $J_2$. The oxygen sites (orange circles) are randomly occupied with a fraction $p$ of Ising spins and interact with the nearest-neighbor $S$ spins through a ferromagnetic coupling $J_1$. (bottom panel) The equivalent diluted sawtooth spin chain.

Figure 2

Ground-state diagram in the external field $H/J_1$ versus ratio between exchange couplings $-J_2/J_1$ plane. The transitions lines can be obtained by comparing the energies per unit cell of each phase. We sketch the unit-cell configuration for the three possible ground states. $g{\mu }_B=1$ units were used.

Figure 3

Cell magnetization $m=\langle S_i+{\sigma }_i\rangle$ at finite magnetic fields as a function of the fraction $p$ of decorated cells for all three possible ground states F-F, AFM-F, and AFM-Fr and along the two transition lines. Notice the nonlinear dependence at the transitions on which $q\left(p\right)=(m_{\text{F-F}}-m_{\text{F-F}\text{to}\text{AFM-F}})/2$ and $\epsilon \left(p\right)=m_{\text{AFM-F}\text{to}\text{AFM-Fr}}-m_{\text{AFM-Fr}}$.

Figure 4

Entropy per unit cell as a function of the degree of dilution for two representative values of the magnetic field and different values of the ratio between exchange couplings $J_2/J_1$. (a) $H/J_1=0$ and (b) $H/J_1=1.0$.

Figure 5

Field dependence of the entropy per unit cell for three representative values of the degree of dilution $p$. Here we use $J_2/J_1=-1.5$ for which the zero-temperature ground state is antiferromagnetic frustrated state AFM-Fr.

Figure 6

Isothermal entropy change $-\mathrm{\Delta }S/k_B=-[S(T,H)-S(T,0)]/k_B$ as a function of the magnetic field for representative values of the temperature. The arrow indicates the increase in the degree of dilution $p$. Here we use $J_2/J_1=-1.5$.

Figure 7

Isothermal entropy change $-\mathrm{\Delta }S/k_B$ as a function of temperature for fixed external magnetic-field amplitude. The arrow indicates increasing degree of dilution $p$. Here we use $J_2/J_1=-1.5$.

Figure 8

Entropy density plot evincing curves of isoentropy for the particular case of decoration degree $p=0.2$. (a) $J_2/J_1=-0.5$ for which the zero-field ground state is AFM-F. A single critical field is observed. Dashed line corresponds to $s(T,H)/k_B=s(0,0)/k_B=0.5004\cdots$. (b) $J_2/J_1=-1.5$ for which the zero-field ground state is AFM-Fr. This case presents two critical fields. Dashed line corresponds to $s(T,H)/k_B=s(0,0)/k_B=0.639\cdots$. Notice that maxima adiabatic cooling rates take place near $H=0$ as well as near the critical magnetic fields.