Magnetic superfluid state in the frustrated spinel oxide CdCr${}_2$O${}_4$ revealed by ultrahigh magnetic fields

We investigated the magnetic-field-induced phases of a typical three-dimensional frustrated magnet, CdCr${}_2$O${}_4$, in magnetic fields of up to 120 T using both the electromagnetic induction method and magneto-optical spectroscopy of the $d$-$d$ transitions and the exciton-magnon-phonon transitions. Anomalies were observed in the magneto-optical absorption intensity as well as the differential magnetization prior to a fully polarized magnetic phase, revealing a magnetic phase associated with changes in both the crystal and magnetic structures accompanied by the first-order phase transition. A magnetic superfluid state, such as an umbrella-like magnetic structure or a spin-nematic state, is proposed as a candidate for this phase, which is found universally in the series of chromium spinel oxides, $A$Cr${}_2$O${}_4$ ($A$ $=$ Zn, Cd, Hg).

Figure 1

Magnetization and $dM/dH$ curves of CdCr${}_2$O${}_4$ at 4.2 K in magnetic fields up to 120 T obtained by the electromagnetic induction method. Black arrows show anomalies observed in the vicinity of the fully polarized magnetic phase. Gray arrows indicate canted 3:1 and fully polarized magnetic structures.

Figure 2

Magneto-optical absorption spectra obtained at 6 K in a region of wavelengths where ${}^4{A}_2\to {}^4{T}_2$ and EMP transitions occur in CdCr${}_2$O${}_4$. The spectra were measured at several magnetic fields (up to 100 T) obtained by streak spectroscopy. Absorption intensity of EMP transitions is multiplied by 4. Dotted arrows show wavelengths at which the absorption intensities in magnetic fields are plotted in Fig. 3.

Figure 3

Magneto-optical absorption intensity at wavelengths of 610 nm (${}^4{A}_2\to {}^4{T}_2$ transition) and 675 nm (EMP transition) as a function of magnetic field. Dotted lines show anomalies observed in the absorption intensity.

Figure 4

Magnetic phase diagram of chromium spinel oxides. Phase transition points were taken from Ref. 13 for ZnCr${}_2$O${}_4$ and from Ref. 28 for HgCr${}_2$O${}_4$.