High-field phase diagram of the heavy-fermion metal ${\mathrm{CeIn}}_3$: Pulsed-field NMR study on single crystals up to 56 T

The heavy-fermion antiferromagnet ${\mathrm{CeIn}}_3$ exhibits a field-induced anomaly associated with Fermi surface reconstruction at $H^{*}\sim 45$ T, well below the antiferromagnetic (AFM) critical field that exceeds 60 T. In order to explore the origin of this anomaly, we have measured ${}^{115}\mathrm{In}$ NMR spectra in pulsed magnetic fields up to 56 T using high-quality single crystals. To within experimental resolution, we do not detect any change in the NMR spectra that could suggest a modification in either the character of the hyperfine field or the electric field gradient at In sites through $H^{*}$. This strongly suggests that the 45 T anomaly cannot be simply ascribed to a field-induced change in the magnetic structure of the AFM state. Neither do we find any evidence of changes in the crystallographic structure or in the distribution of charge density at $H^{*}$. The field dependence of the NMR shift implies the existence of a field-induced anomaly in the hyperfine coupling above $H^{*}$.

Figure 1

Temperature–magnetic-field phase diagram for fields applied along the $\langle 100\rangle$ direction in ${\mathrm{CeIn}}_3$ [5]. An anomaly was observed in TDO measurements at $H^{*}\approx 45$ T [6].

Figure 2

The field-swept ${}^{115}\mathrm{In}$ NMR spectra obtained in (a) PM and (b) AFM states in fields below 15 T. Here the spin-echo signals were recorded at a fixed frequency of 101.8 MHz by changing $H$ in equally spaced steps. The spectra were then obtained by adding the Fourier transforms of spin-echo signals at each field value. The spectrum in the PM state consists of two sets of sharp peaks; one set separated by about 1 T (labeled 1), the other separated by about 0.5 T (labeled 2). On the other hand, the spectrum in the AFM state contains only nine sharp peaks separated by about 1 T. In the lower panel, we show the results of numerical simulations for (c) ${\mathrm{In}}^{\perp }(\theta ={90}^{\circ })$ and (d) ${\mathrm{In}}^{\parallel }(\theta =0^{\circ })$. The numerical simulations were performed using a diagonalized total Hamiltonian matrix consisting of EFG and Zeeman terms, where the EFG parameters are fixed at ${\nu }_Q=9.61$ MHz and $\eta =0$, respectively [12, 13, 14, 15]. The simulations include the effect of the hyperfine field due to the field-induced magnetization along the field direction, shown in Fig. 6.

Figure 3

Crystal and magnetic structures of ${\mathrm{CeIn}}_3$. The local symmetry of the In site is tetragonal, and therefore the asymmetry parameter of the EFG is $\eta =0$. The local principal axis of the EFG ($V_{zz}$) for each In site, denoted by a green arrow, is perpendicular to the plane of the four nearest-neighbor Ce atoms. The direction of the applied field $H$ is denoted by black arrows. $\theta$ is the angle between $V_{zz}$ and $H$. Below $T_N=10$ K, Ce moments ($M_{\text{AF}}$) order antiferromagnetically with the zero-field propagation vector (1/2, 1/2, 1/2) [16], which generates hyperfine fields $H_{\mathrm{hf}}$ (red arrows) parallel to the Ce-In plane [12]. The numbering scheme shown for In sites is referenced in the text.

Figure 4

Temperature dependence of the field-swept NMR spectrum obtained in the pulsed magnet with a fixed NMR frequency 494.4 MHz.

Figure 5

Field dependence of the NMR spectrum. The horizontal axis is $\mathrm{\Delta }H=H_{\mathrm{ext}}-H_{\mathrm{res}}$, where $H_{\mathrm{res}}$ is the field value of the central peak in each spectrum, i.e., (a) 10.7 T, (b) 36.4 T, and (c) 52 T, respectively.

Figure 6

Field dependence of the NMR shift, $\mathrm{\Delta }{H}^{\parallel }=H_{\mathrm{bare}}-H_{\mathrm{res}}$ plotted together with the magnetization, $M^{\parallel }$, of a powder sample cited from Ref. [3] (solid line, right vertical axis). The $H_{\mathrm{res}}$ values were extracted from the field values of the center (solid square) and satellite (open square) peaks in several NMR spectra measured in different field regions.