Magnetic field induced phases and spin Hamiltonian in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$

Magnetic structures and spin excitations are studied across the phase diagram of the geometrically frustrated $S=3/2$ quantum antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ in magnetic fields applied along the magnetic easy axis, using neutron diffraction, inelastic neutron scattering, and terahertz absorption spectroscopy. The data are analyzed, where appropriate, using extended $\mathrm{SU}\left(4\right)$ linear spin wave theory. A minimal magnetic Hamiltonian is proposed based on measurements in the high-field paramagnetic state. It deviates considerably from the previously considered models. Additional dilatometry experiments highlight the importance of magnetoelastic coupling in this system.

Figure 1

The five nearest-neighbor magnetic interactions in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$. The nodes of the lattice are ${\mathrm{Co}}^{2+}$ ions. The boundaries of a unit cell are shown in black lines in the top-left corner.

Figure 2

A schematic representation of magnetic structures that occur in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ in magnetic fields applied along the $\mathbf{b}$ axis. Only the Co-1 and Co-3 sites that form $J_4-J_1$ zigzag ladders are shown. For these, the individual magnetic moments are in all cases confined to a plane which coincides with the local anisotropy easy plane common to Co-1 and Co-3. The red dashed lines show the range of transverse spin oscillations in this incommensurately modulated structure. The ellipses represent additional weak in-plane anisotropy [parameter $d$ in Eq. (1)].

Figure 3

Magnetic order parameter (amplitude of the corresponding Fourier component of magnetization) vs magnetic field applied along the $\mathbf{b}$ axis, as deduced from the intensities of the indicated Bragg reflections measured in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ at $T<100\mathrm{mK}$. The data for Phases A–C are from Ref. [11].

Figure 4

Calculated vs observed integrated intensities (from the D23 experiment) for magnetic Bragg peaks at 4.25 T for the spin-flop structure.

Figure 5

Calculated vs observed integrated intensities (from the D23 experiment) for magnetic Bragg peaks at 4.8 T for the fan structure.

Figure 6

(a), (c), (e), (g), (i), and (k) Inelastic neutron scattering intensity measured in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ in a magnetic field ${\mu }_{0}H=7\mathrm{T}$ applied along the crystallographic $\mathbf{b}$ axis at $T\sim 100\mathrm{mK}$, in the paramagnetic pseudopolarized phase. The data are integrated along the transverse directions in reciprocal space, as described in the text. (b), (d), (f), (h), (j), and (l) $\mathrm{SU}\left(4\right)$ spin wave theory calculation based on the minimal model parameters listed in Table 4.

Figure 7

(a), (c), (e), and (g) Inelastic neutron scattering intensity measured in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ in a magnetic field ${\mu }_{0}H=3.2\mathrm{T}$ applied along the crystallographic $\mathbf{b}$ axis at $T\sim 100\mathrm{mK}$ in the UUD-plateau phase. The data are integrated along the transverse directions in reciprocal space, as described in the text. The intensity units are consistent with those in Fig. 6. (b), (d), (f), and (h) $\mathrm{SU}\left(4\right)$ spin wave theory calculation based on the minimal model parameters listed in Table 4.

Figure 8

(a), (c), and (e) Inelastic neutron scattering intensity measured in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ in zero applied field at $T<100\mathrm{mK}$ in the Néel (stripe) phase. High- (high-contrast color map) and low-resolution (shaded) data are combined. The data are integrated along the transverse directions in reciprocal space, as described in Ref. [12]. The extra inelastic intensity seen on the left and rights sides of (a) below 0.5 meV is spurious. It originates from the neutron beam being scattered by the cryomagnet coils. (b), (d), and (f) $\mathrm{SU}\left(4\right)$ spin wave theory calculation based on renormalized minimal model parameters listed in the last column in Table 4. Dashed lines in (a) are computed dispersion relations of all SWT modes.

Figure 9

(a) Terahertz absorption spectra measured at $T=200\mathrm{mK}$ for different vales of magnetic field applied along the $\mathbf{b}$ axis. The various magnetic phases of ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ are labeled and color-coded. (b) Same data as a false color plot. (c) $\mathrm{SU}\left(4\right)$ spin wave theory calculation based on minimal model parameters listed in Table 4 for the high-field plateau and “spin flop” phases, and renormalized value for the low-field phase. Solid lines in (b) are energies of all SWT modes with line opacity representing the corresponding intensities.

Figure 10

False color plot of measured change in relative capacitance $\mathrm{\Delta }C/C$ in ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ for $\mathbf{E}\parallel \mathbf{a}$ and $\mathbf{H}\parallel \mathbf{b}$. Green solid symbols mark magnetic phase boundaries deduced from specific heat data [10].