Quantitative Test of SO(5) Symmetry in the Vortex State of ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$

By numerically solving models with competing superconducting and antiferromagnetic orders, we study the magnetic field dependence of the antiferromagnetic moment in both the weak and strong field regimes. Through a comparison with the neutron scattering results of Kang et al. and Matsuura et al. on ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$, we conclude that this system is close to a SO(5) symmetric critical point. We also make a quantitative prediction on increasing the upper critical field $B_{c2}$ and the superconducting transition temperature $T_c$ by applying an in-plane magnetic field.

Figure 1

The plot of field dependence of AF moment for different parameters. The other parameters are ${\rho }_1={\rho }_2=a^2$, $r_1=-1$, $r_2=-0.85$, $u_1=u_2=1$, and $\chi =42.4$. Here, the parameters are chosen such that the maximum SC order is 1 and the SC coherence length at zero field equals the lattice constant $a$ of our discrete model.

Figure 2

The field dependence of the AF moment. The solid squares are obtained by subtracting the intensity of $(0,0,4.4\pi )$ measured at Hahn-Meitner-Institute (HMI) [20] from the intensity of $(\pi ,\pi ,0)$ measured at National Institute of Standards and Technology [6]. The solid triangles are obtained subtracting the intensity of $(0,0,4.4\pi )$ measured at HMI [20] from the intensity of $(\pi ,\pi ,0)$ measured at HMI [6]. The parameters used in obtaining the theoretical curve are ${\rho }_1={\rho }_2=a^2$, $r_1=-1$, $r_2=-0.85$, $u_1=u_2=1$, $u_{12}=0.95$, and $\chi =42.4$.

Figure 3

The angle dependence of the $z$ component of the upper critical field, given by the solution to coupled Eqs. (9a, 9b). The parameters are the same as those used in fitting of the experimental data in Fig. 2.