Crystal electric field excitations and spin dynamics in a spin-orbit coupled distorted honeycomb magnet BiErGeO$_5$

Abstract

The magnetic properties and crystal electric field (CEF) scheme of BiErGeO$_5$ are investigated via magnetization, heat capacity, muon spin relaxation (muSR), and inelastic neutron scattering (INS) experiments on a polycrystalline sample. The Er$^{3+}$ ions form a quasi-two-dimensional distorted honeycomb network with a Kramers doublet ground state. Magnetic susceptibility and heat capacity reveal short-range antiferromagnetic correlations, manifested as a broad maximum around 1.4 K. Heat-capacity data further confirm the onset of a magnetic long-range order at $T_ N = 0.4$ K. The INS spectra exhibit eight CEF excitations and the CEF analysis yields the $g$-factor anisotropy with $g_{xy}/g_{z} = 1.38$ and exchange anisotropy with $J_{xy} = 2.96$ K and $J_{z} = 1.56$ K. The experimental temperature and field dependent magnetization and heat capacity are also reproduced by the simulation using CEF energy scheme. Zero-field muSR measurements down to 30 mK, do not exhibit coherent oscillations or a static 1/3 tail. The spectra are well described by two exponential relaxation components, indicating two magnetically inequivalent muon environments. The relaxation rates display a nearly temperature-independent plateau below $T_{\rm N}$ and follow an Orbach-type activated behavior at higher temperatures involving excited CEF levels, consistent with the INS results. Longitudinal-field $μ$SR measurements reveal only weak decoupling up to 1.5 T, indicating persistent slow spin fluctuations below $T_{\rm N}$.

Figures (12)

• Figure 1: (a) Crystal structure of BiErGeO$_5$ viewed along the $a$-axis, showing the separation of adjacent honeycomb layers. (b) A section of the honeycomb layer in the $ac$-plane formed by edge-shared ErO$_7$ polyhedra and highlights the anisotropic bond lengths.
• Figure 2: Powder XRD pattern (open circles) at $T = 300$ K for (a) BiErGeO$_5$ and (b) BiYGeO$_5$. The black solid line represents the Rietveld fit of the data. Expected Bragg positions are indicated by green vertical bars and the solid blue line at the bottom denotes the difference between experimental and calculated intensities. The goodness-of-fit is achieved to be $\chi^{2} \simeq 2$ and 3, respectively.
• Figure 3: (a) $\chi(T)$ of BiErGeO$_5$ measured in different magnetic fields. The dot-dashed lines are the calculated $\chi_{\rm CEF}$ in different magnetic fields. Inset: $\chi(T)$ measured at $\mu_0H=0.01$ T in both ZFC and FC protocols. (b) High-$T$ CW fit to $1/\chi$ data (at $\mu_0H=0.1$ T) extrapolated down to low temperatures. Inset: The low-$T$ CW fit after subtracting the Van-Vleck contribution.
• Figure 4: (a) $M$ vs $H$ measured at different temperatures The solid line represents a linear fit to the high-field data for $T=0.4$ K. The dot-dashed lines are the calculated $M_{\rm CEF}$ in different temperatures. (b) ($M-M_{\rm VV}$) vs $\mu_0H/T$ at different temperatures to observe the scaling of magnetization curves in the correlated regime. Inset: d$M$/d$H$ vs $\mu_0H$ plot to highlight the field induced feature.
• Figure 5: (a) $C_{\rm p}$ vs $T$ for BiErGeO$_5$ measured in different applied fields. The dot-dashed line represents $C_{\rm ph}(T)$ of the nonmagnetic analog BiYGeO$_5$. (b) Magnetic heat capacity $C_{\rm mag}$ vs $T$ in different magnetic fields. The solid line represents a combination of power law and nuclear Schottky fit to the low-$T$ data. Inset: Magnetic entropy $S_{\rm mag}$ vs $T$ in zero field. (c) Zero field $C_{\rm mag}$ vs $T$ highlighting different anomalies. The blue and red solid lines indicate the ED simulation of XXZ model and calculated $C_{\rm CEF}$ in zero field, respectively. The dot-dashed line is the sum of both. (d) Calculated $C_{\rm CEF}$ vs $T$ in different magnetic fields, as discussed in the text.