Magnetic-Field Induced Phase Transitions in a Weakly Coupled $s=1/2$ Quantum Spin Dimer System ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathbf{O}}_8$

By using bulk magnetization, electron spin resonance (ESR), heat capacity, and neutron scattering techniques, we characterize the thermodynamic and quantum phase diagrams of ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$. Our ESR measurements indicate that the low field paramagnetic ground state is a mixed state of the singlet and the $S_z=0$ triplet for $H\perp c$. This suggests the presence of an intradimer Dzyaloshinsky-Moriya (DM) interaction with a DM vector perpendicular to the $c$ axis.

Figure 1

(a) The first derivative of bulk magnetization ($dM/dH$) as a function of an external pulsed magnetic field ($H$) applied parallel and perpendicular to the $c$ axis, taken at $T=0.4\mathrm{K}$. Arrows indicate upper and lower critical fields determined by the positions of the peaks that appear in the second derivative, $d^{2}M/d{H}^2$, as a function of $H$ as shown in the inset. (b) Temperature dependence of the specific heat under various constant steady magnetic fields along the $c$ axis, from $H=12.5$ to 17 T. The data are consistent with recent results reported by Aczel et al. in Ref. 19.

Figure 2

(a) Elastic neutron scattering data around the magnetic $(0.5,0.5,3)$ reflection, measured at 0.15 K and with three different magnetic fields, $H=9\mathrm{T}$ (black circles), 12.5 T (blue circles), and 13.5 T (red circles). The inset shows the color contour map of the inelastic neutron scattering intensity of the $S_z=1$ triplet excitation measured with $H=14.8\mathrm{T}$. (b) The critical exponent $2\beta$ obtained from the data shown in (c). See the text for detailed description. (c) $H$ dependence of the magnetic $(0.5,0.5,3)$ Bragg reflection measured at various temperatures from 30 mK to 2.16 K. $H$ was perpendicular to the $c$ axis. The solid lines are fits to a power law. (d) Schematic figure of the structure of the transverse moments in the canted AFM phase of ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$ for $H\perp c$, obtained from our magnetic Bragg scattering data. Arrows represent the transverse magnetic moments along the $c$ axis. The magnetic unit cell is $2a\times 2b\times c$.

Figure 3

Electron spin resonance transmission spectra as a function of external magnetic field (a) at 4.2 K with $H\perp c$ (black line) and $H\parallel c$ (blue line), obtained with the frequency of $\nu =190\mathrm{GHz}$, and (b) at 1.6 K with $H\perp c$ and with two different frequencies $\nu =149.6\mathrm{GHz}$ (dotted line) and 273.9 GHz (solid line). (c) Energy level scheme of the nominal singlet and triplet states as a function of $H$. (d) Frequency dependence of the peak positions of the three modes, 1, $1^{\prime }$, 2, in $H$, which are described in the text.

Figure 4

$H\mathrm{\text{−}}T$ phase diagram (a) for $H\perp c$ determined from the elastic neutron scattering data (circles) shown in Fig. 2b and specific heat data (triangles), and (b) for $H\parallel c$ determined from the heat capacity data shown in Fig. 1b. The lines are fits to a power law (see the text for details).