Ferromagnetic critical behavior in ${\text{U(Co}}_{1-x}{\text{Fe}}_x\text{)Al}$ $(0\le x\le 0.02)$ studied by ${}^{59}\mathrm{Co}$ nuclear quadrupole resonance measurements

In order to investigate physical properties around a ferromagnetic (FM) quantum transition point and a tricritical point (TCP) in the itinerant-electron metamagnetic compound UCoAl, we have performed the ${}^{59}\mathrm{Co}$ nuclear quadrupole resonance (NQR) measurement for the Fe-substituted ${\text{U(Co}}_{1-x}{\text{Fe}}_x\text{)Al}(x=0,0.5,1,\text{and}2\%)$ in zero external magnetic field. The Fe concentration dependence of ${}^{59}\mathrm{Co}-\text{NQR}$ spectra at low temperatures indicates that the first-order FM transition occurs at least above $x=1\%$. The magnetic fluctuations along the $c$ axis detected by the nuclear spin-spin relaxation rate $1/T_2$ exhibit an anomaly at $T_{\max }\sim 20\mathrm{K}$ and enhance with increasing $x$. These results are in good agreement with theoretical predictions and indicate the presence of prominent critical fluctuations at the TCP in this system.

Figure 1

Schematic 3D [Temperature ($T$)– magnetic field ($H$)–pressure ($P$)] phase diagram for itinerant FM compounds. The pink and purple lines show the second-order and first-order transition lines, respectively. TCP, QTP, and QCEPs are denoted as a circle, a triangle, and squares, respectively. The first-order (metamagnetic) transition “wings” spreading from the first-order transition line connecting the TCP and the QTP toward the QCEPs are shown by the purple planes. The PM ground state in UCoAl at $(T,H,P)=0$ is located in the vicinity of the QTP.

Figure 2

(a) ZrNiAl-type hexagonal crystal structure (space group: $P\overline{6}2m$, No. 189) of UCoAl composed by U-Co(1) layer and Co(2)-Al layer alternately stacking along the $c$ axis. Co(1) and Co(2) are crystallographically inequivalent atomic sites. (b) U-Co(1) layer and Co(2)-Al layer from the view of the $c$ axis. U-U bonds and Al-Al bonds form the distorted Kagomé lattices in U-Co(1) layer and Co(2)-Al layer, respectively.

Figure 3

Fe concentration ($x$) dependencies of the lattice constants $a$ (squares) and $c$ (triangles) estimated by the powder x-ray diffraction peaks. The broken lines show the linear relationship expected from Vegard's law.

Figure 4

(a) ${}^{59}\text{Co-NQR}$ spectra at $T=1.4$ K for $x=0$, 0.5, 1, and 2%. The sharp peaks (light blue) represent the PM components and the broad peaks (pink) represent the FM components, respectively. (b) Numerical calculation of the resonance frequencies versus the internal field $H_{\mathrm{int}}$ along the $c$ axis. The pink broken line shows ${\mu }_0{H}_{\mathrm{int}}=1.05$ T estimated by the values of previous studies [9, 17, 18]. (c) $x$ dependence of the experimentally estimated internal field $H_{\mathrm{int}}$ along the $c$ axis at $T=1.4$ K.

Figure 5

(a) Temperature dependence of ${}^{59}\text{Co-NQR}$ spectra for $x=1$ and 2%. The sharp peaks (light blue) represent the PM components and the broad peaks (pink) represent the FM components, respectively. (b) Temperature dependence of the ${}^{59}\text{Co-NQR}$ intensity multiplied by the temperature (upper panels) and the estimated internal field $H_{\mathrm{int}}$ (lower panels) for $x=1$ and 2%.

Figure 6

Temperature dependencies of $1/\left(T_{1}T\right)$ (upper panel) and $1/T_2$ (lower panel) for $x=0$% (yellow circles), 0.5% (green diamonds), 1% (red squares), and 2% (blue triangles). These were measured at $f=12.94$ MHz (closed symbols) and $f=10.50$ MHz (open symbols). $T^{*}\sim 20$ K in $1/\left(T_{1}T\right)$ shows the temperature below which the localized behavior changes to the itinerant behavior. $T_{\max }$, pointing to the kinks or peaks in $1/T_2$, shows the characteristic temperature where magnetic fluctuaions along the $c$ axis enhance in the PM phase. 10-K anomaly in $1/T_2$ shows the robust anomaly inherent in $T_2$ as explained in the text.

Figure 7

Temperature (left axis) vs Fe concentration (lower axis) phase diagram in ${\text{U(Co}}_{1-x}{\text{Fe}}_x\text{)Al}$ and the contour plot of $1/T_2$. $T_{\mathrm{Curie}}^1\mathrm{st}$ and $T_{\max }$ experimentally determined from the ${}^{59}\text{Co-NQR}$ spectra and $1/T_2$, respectively, are denoted by open purple circles and open brown squares, respectively. The data points are extrapolated by eye to $x$ $>$ 2%. The 10-K anomaly is denoted by the gray chain line. The theoretical curves by Yamada [4] are plotted on the $T/T_{\max }$ (right axis) vs $a_0{c}_0/b_0^2$ (upper axis) phase diagram. $T_{\mathrm{Curie}}^1\mathrm{st}$, $T_{\mathrm{Curie}}^2\mathrm{nd}$, and $T_{\max }$ are denoted by black solid, broken, and dotted lines, respectively. We set the scale of axes to satisfy the conditions of $a_0{c}_0/b_0^2=0.2$ at $x$ = 0 (“pure” UCoAl), $a_0{c}_0/b_0^2=3/16$ at $x=0.75$% (QTP), and $T/T_{\max }=1$ at $T=20$ K.