Entropy of the quantum soliton lattice and multiple magnetization steps in ${\mathrm{BiCu}}_2{\mathrm{PO}}_6$

${\mathrm{BiCu}}_2{\mathrm{PO}}_6$, a spin-gapped material in a frustrated two-leg ladder lattice, exhibits a complex $(H,T)$ phase diagram in external magnetic fields. We have characterized the field-induced phases through specific heat, magnetocaloric effect, Faraday rotation, and magnetization measurements in fields up to 120 T. In addition to observing a magnetic phase above 60 T which we attribute to the crystallization of triplet excitations, our measurements reveal the emergence and the subsequent disappearance of a high-entropy (short-range-ordered) phase at first and second critical magnetic fields, respectively. This is in good agreement with the theoretical prediction of a quantum soliton lattice at intermediate fields.

Figure 1

(a)–(c) Contour map of $S(T,H)$ for $H\parallel a$ (left), $H\parallel b$ (middle), and $H\parallel c$ (right). The contour plot of $S_M(T,H)$ is constructed through linear interpolation of a series of $T(H,S_M)$ traces. The phase boundaries determined by MCE and specific heat are also shown as open circles and open triangles, respectively. The solid dots are the phase boundaries reported in Ref. [5]. The phase boundaries above 60 T detected by $M$ and Θ${}_M$ are not shown for clarity.

Figure 2

Specific heat of ${\mathrm{BiCu}}_2{\mathrm{PO}}_6$ for field applied to the $a$ axis. (a) Field dependence of $C_p$ at two temperatures. The results are plotted in arbitrary units. (b) ${\mathrm{C}}_M$T${}^{-1}$ as a function of $T$ as obtained in pulsed magnetic fields (solid squares). Below 34 T, ${\mathrm{C}}_M$T${}^{-1}$ was also collected under static fields (curves).

Figure 3

(a) Selected magnetocaloric effect (MCE) traces measured in the adiabatic condition for ${\mathrm{BiCu}}_2{\mathrm{PO}}_6$. Circles correspond to phase boundaries deduced from MCE experiments. (b) Magnetic entropy $\left(S_M\right)$ as a function of $H$. The solid (dashed) arrows indicate the phase boundaries (see the text). $S_M$ was estimated by subtracting the lattice entropy of ${\mathrm{BiZn}}_2{\mathrm{PO}}_6$ [12] from the total entropy.

Figure 4

(a) Magnetization of ${\mathrm{BiCu}}_2{\mathrm{PO}}_6$. Thin curves were obtained in a single turn coil. Thick curves were measured in a 75 T nondestructive magnet. The inset is a magnification showing $M$ as a function of $H$ for $H\parallel a$. (b) Faraday rotation angle Θ${}_M$ at different temperatures. For this measurement, the magnetic field was applied along the $a$ axis.