High-field electron spin resonance spectroscopy of singlet-triplet transitions in the spin-dimer systems ${\text{Sr}}_3$${\text{Cr}}_2$${\text{O}}_8$ and ${\text{Ba}}_3$${\text{Cr}}_2$${\text{O}}_8$

Magnetic excitations in the isostructural spin-dimer systems ${\text{Sr}}_3$${\text{Cr}}_2$${\text{O}}_8$ and ${\text{Ba}}_3$${\text{Cr}}_2$${\text{O}}_8$ are probed by means of high-field electron spin resonance at subterahertz frequencies. Three types of magnetic modes were observed. One mode is gapless and corresponds to transitions within excited states, while two other sets of modes are gapped and correspond to transitions from the ground to the first excited states. The selection rules of the gapped modes are analyzed in terms of a dynamical Dzyaloshinskii-Moriya interaction, suggesting the presence of phonon-assisted effects in the low-temperature spin dynamics of ${\text{Sr}}_3$${\text{Cr}}_2$${\text{O}}_8$ and ${\text{Ba}}_3$${\text{Cr}}_2$${\text{O}}_8$.

Figure 1

(a) Unit cell of $A_3$${\text{Cr}}_2$${\text{O}}_8$($A=\text{Sr}$,Ba) in the low-temperature monoclinic phase with space group $C2/c$. (b) Layered structure of spin dimers with anisotropic exchange interactions from Ref. [9]. $J_0$ is the intradimer exchange interaction. Cr pairs are labeled by $\left(12\right)$, $\left(1^{\prime }{2}^{\prime }\right),$ and $\left(1^{\prime \prime }{2}^{\prime \prime }\right)$ in accord with (a). (c) Symmetry elements of the space group $C2/c$: inversion center $-$1, twofold rotation 2, and glide plane $c$ with glide vector (0,0,1/2) marked in the crystalline ac plane [29]. (d) The Cr${}^{5+}$ ($s=1/2$) spin dimer composed of two ${\text{CrO}}_4$ tetrahedra with local inversion center $-$1. Green, red, and gray spheres denote Cr, O, and Sr/Ba ions, respectively.

Figure 2

${\text{Sr}}_3$${\text{Cr}}_2$${\text{O}}_8$ (a) schematic singlet-triplet excitations in an external magnetic field. 1 and 3 are the acoustic modes, and $1^{\prime }$ and $3^{\prime }$ are the optical modes. The two types of modes originate from the two inequivalent layers in the unit cell. Mode 2 denotes the intratriplet excitations. The singlet-triplet excitations are measured with no polarization analysis (b) and with polarization analysis ($E^{\omega },H^{\omega }$) (c)–(f) for different orientations of applied magnetic field $H$ at 2 K. The vertical dashed lines indicate artifacts due to spark lines from the BWOs.

Figure 3

${\text{Ba}}_3$${\text{Cr}}_2$${\text{O}}_8$ (a) singlet-triplet excitations. Polarized transmission spectra measured at 2 K (b) and at 1.4 K (c),(d). In (c), $H^{\omega }$ is parallel to the $a_h{b}_h$ plane. Inset: enlarged view of the spectrum for $H\parallel c_h$, $E^{\omega }\parallel c_h$, and $H^{\omega }\parallel b_h$.

Figure 4

Illustration of the coupling constants $A_{ca}\sim 0$, $A_{cb}\ne 0$, and $A_{cc}\sim 0$. The spin dimer ${\text{Cr}}_2$${\text{O}}_8$ distorts in the radiation electric field $E^{\omega }\parallel c$ with associated instantaneous Dzyaloshinskii-Moriya vectors $d^a$, $d^b$, and $d^c$.