Pressure-Tuned Metamagnetism and Emergent Three-Body Interactions in CsFeCl$_3$

TL;DR

This work reveals that CsFeCl$_3$ under high magnetic fields and pressure cannot be captured by a single spin-1 description. Instead, low-to-intermediate fields are described by a spin-1 XXZ+$D$ model, while high-field metamagnetism requires a projected spin-$\tfrac{1}{2}$ model built from Zeeman-select crystal-field states from different $J$ manifolds, which permits emergent three-body interactions on triangular plaquettes and yields asymmetric fractional magnetization plateaus. Pressure tunes exchange and single-ion anisotropies, driving a sign change in the next-nearest-neighbor coupling and enriching the high-field phase diagram with states such as 1/3, 1/2, 1/5, and 1/8 plateaus, in good agreement with ESR, magnetization, and PDO measurements. The findings highlight a broader principle: when crystal-field multiplets are brought into resonance by Zeeman splitting, the resulting low-energy Hamiltonians can include odd-body terms, opening pathways to exotic high-field phases in multiplet-based quantum magnets.

Abstract

We present a combined experimental and theoretical study of the triangular-lattice quantum antiferromagnet CsFeCl$_3$ under high magnetic fields and high pressure. Pulsed-field magnetization for the magnetic field along the symmetric $c$ direction at ambient pressure reveals a magnetization process from a nonmagnetic singlet ground state with a nearly linear increase between 3.7 and 10.7 T, a plateau-like region, and then a sharp stepwise metamagnetic transition near 32 T. Wide frequency--field range electron spin resonance indicates that the low-field regime originates from the $J = 1$ manifold, while the high-field metamagnetic transition suggests a level crossing between the $J = 1$ and $J = 2$ lowest states. Pulsed-field magnetic susceptibilities measured with a proximity detector oscillator under high pressure show that the low-field nonmagnetic singlet phase is gradually suppressed, while the high-field metamagnetic transition evolves into an increasingly rich pattern of fractional steps. While the observations at low to intermediate fields can be understood within the established spin-1 description, the high-field regime requires a new perspective, which we provide through a projected spin-1/2 framework built from Zeeman-selected crystal-field states not related by time reversal. This construction naturally allows emergent three-body interactions on triangular plaquettes and explains the asymmetric evolution of the fractional steps in the magnetization. Our findings reveal that high-field effective spin models in quantum magnets with separated yet accessible crystal-field multiplets are not constrained to even-body couplings, but can naturally host odd-body terms, opening a broader avenue for realizing field-asymmetric magnetization processes and exotic phases beyond conventional even-body physics.

Figures (14)

• Figure 1: (a) Crystal structure of CsFeCl$_3$ depicted using VESTA momma2011vesta. (b) Schematic view of the energy levels of the Fe$^{2+}$ ion hori1989magnetization.
• Figure 2: (a) Sketch of the magnetization curve of CsFeCl$_3$ for fields applied along the $c$-axis at ambient pressure CHIBA1987427tsuboi1988magnetization. (b) Enlarged view of the high-field regime. Here, $\tilde{M}$ and $\tilde{H}$ denote the rescaled magnetization and effective field defined within the spin-1/2 model description, which are shifted from the physical magnetization and field origin of the full system.
• Figure 3: (a) Magnetization ($M$) and its field derivative ($dM/dH$) of CsFeCl$_3$ at 1.4 K for $H \parallel c$ at ambient pressure. Broken lines are the extrapolations of the magnetization slope above $H_{\rm c2}$ and $H_{\rm m2}$ toward zero field. (b) Enlarged view of $M$ and $dM/dH$ around $H_{\rm m1}$ and $H_{\rm m2}$. The arrows indicate the field-ascending and descending processes.
• Figure 4: ESR absorption spectra of CsFeCl$_3$ at 4.2 K for $H \parallel c$ taken between 326 and 1839 GHz (red) at AHMF and between 60 and 120 GHz (green) at HLD. As the transmission of the spectra at 1017, 1481, 1565, and 1839 GHz is weak, their spectra are plotted by a factor of 10 times larger than the other spectra. The resonance fields are indicated by upward and downward triangles, diamonds, circles, squares, and crosses. Gray arrows point to the signal of the ESR standard marker DPPH (2,2-diphenyl-1-picrylhydrazyl).
• Figure 5: Frequency vs resonance-field plot obtained by ESR measurements. Red and green symbols are the resonance fields taken from Fig. \ref{['ESR']}. Open colored symbols are resonance fields taken from Refs. motokawa1989submillimetermitsudo2003highokubo2023high. The red solid line indicates the linear fit of the solid diamond symbols corresponding to the transitions between the ground $m_{J1}^z$ = $+1$ and the excited $m_{J1}^z$ = 0 states(see text). The red and purple broken lines are linear fits to the red circles at 326-1287 GHz and 1392-1481 GHz, respectively. The field at the gray broken line is approximately 33 T, which is close to the metamagnetic transition field. The inset indicates the resonance fields related to the transition between the ground state and $m_{J2}^z$ = +2 state. The ground state in magnetic fields is considered to change from $m_{J1}^z$ = 0 to $m_{J1}^z$ = $+1$, and then to $m_{J2}^z$ = $+2$ as indicated by green, blue, and red hatching, respectively. These resonance fields were obtained at the ESR wave vector $\hbox{\boldmath $k$}$ = (0, 0, 0).