Basal-plane anisotropy of field-induced multipolar order in tetragonal CeRh$_2$As$_2$

TL;DR

This study reveals a pronounced basal-plane anisotropy in the field-induced multipolar order of CeRh$_2$As$_2$, pointing to a coupling between magnetic and quadrupolar (or higher) order that may influence superconductivity. By combining resistivity and heat-capacity measurements with fields oriented in the basal plane, the authors map how the ordering temperature $T_{0}$ and the I–II transition field $H_{ ext{cr}}$ depend on field direction, finding a stronger enhancement for $H \parallel [110]$ than for $H \parallel [100]$. A microscopic framework based on a quasi-quartet crystal-field scheme is developed to explain the anisotropy, highlighting the role of field-induced intra-doublet quadrupolar matrix elements in both $O_{xy}$ and $O_{x^2-y^2}$ components. The results motivate refinements to the crystal-field scheme and advance the understanding of multipolar ordering in Ce-based tetragonal heavy-fermion systems, with implications for the mechanism of unconventional superconductivity in CeRh$_2$As$_2$.

Abstract

Unconventional superconductivity in Ce-based Kondo-lattice materials emerges almost exclusively in the vicinity of weak dipolar magnetic orders, while higher multipolar orders are only known to occur in a few Pr-based unconventional superconductors and possibly URu$_2$Si$_2$. The multiphase superconductor CeRh$_2$As$_2$ appears to be a notable exception from this trend. Showing clear signatures of magnetism, this tetragonal system is suspected to host a concomitant quadrupolar order, which could be causing the strong enhancement of the ordering temperature when a magnetic field is applied perpendicular to the fourfold ($c$) axis of the lattice. In this work, we show that the field-temperature phase diagram of CeRh$_2$As$_2$ has a remarkable basal-plane anisotropy. This finding supports the scenario of coupled magnetic and multipolar ordering, which may have implications for the pairing mechanism of the superconductivity, and guides the development of the next iteration of theoretical models.

Figures (9)

• Figure 1: Phase diagrams of CeRh$_2$As$_2$ as functions of temperature ($T$) and magnetic field ($\mu_{\textrm{0}}H$, where $\mu_{\textrm{0}}$ is the vacuum permeability), applied along the [100] and [110] crystallographic directions. Phases I and II are indicated. The critical temperature ($T_{\textrm{0}}$) and fields ($H_{\textrm{0}}$, $H_{\textrm{cr}}$) were extracted from measurements of $T$ and $H$ dependence of electrical resistivity, respectively. Solid grey lines are guides for the eye. The hysteretic regions are shaded in light-grey. The superconducting phase is omitted. Inset: an extension of the phase diagrams to higher fields according to heat capacity [$C(T)$] data.
• Figure 2: Left: tetragonal unit cell of CeRh$_2$As$_2$. The crystallographic $a$ and $c$ axes as well as selected directions, labeled by Miller indices, are shown. Middle: photograph of the CeRh$_2$As$_2$ sample used for the resistivity measurements of this work. The yellow arrow indicates the direction of the current $J$. The scale bar marks a 1 mm distance. Right: orientation of the sample in the middle panel. In this study, a magnetic field $H$ was applied perpendicular to the $c$ axis, at a varied angle $\phi$ with respect to the [100] orientation.
• Figure 3: Electrical resistivity ($\rho$) of CeRh$_2$As$_2$ along the [110] crystallographic direction as a function of temperature $T$ (a,b) and magnetic field $\mu_{\textrm{0}}H$ (c,d) at fixed fields and temperatures, respectively. The field is applied along the [100] (a,c) and [110] (b,d) directions. The downward (upward) arrows mark the points of inflection (extremal curvature), defining the critical temperatures and fields of phase I (II) of CeRh$_2$As$_2$.
• Figure 4: Heat capacity $C(T)$ of CeRh$_2$As$_2$ divided by temperature $T$ at high magnetic fields applied along the [100] (a) and [110] (b) crystallographic directions. The yellow stars mark the critical temperatures $T_{\textrm{0}}$ of phase II, according to the equal entropy analysis. Panel (a) inset provides a comparison with $C(T)$ at zero field. The inset in panel (b) shows the corresponding heat capacity jump sizes $\Delta C/T$ at $T_{\textrm{0}}$. The arrow marks the zero-field jump size
• Figure 5: Magnetic-field-orientation dependence of the critical temperatures $T_{\textrm{0}}$ of phases I and II (a) and of the critical field $H_{\textrm{cr}}$ of the I--II transition (b) in CeRh$_2$As$_2$. The angle $\phi$ measures the basal-plane orientation of the field with respect to the [100] crystallographic direction. Measurements of $T_{\textrm{0}}$ were done at 5.3 and 9.0 T, when the system could only enter either phase I or phase II, respectively. The two values of $H_{\textrm{cr}}$ plotted for each angle correspond to the transitions encountered in the upward and downward field sweeps. The solid black lines are guides to the eye. The data used for extracting the $T_{\textrm{0}}$ and $H_{\textrm{cr}}$ values are provided in Supplemental Material.