Magnetic-field effects on the fragile antiferromagnetism in YbBiPt

We present neutron-diffraction data for the cubic-heavy-fermion YbBiPt that show broad magnetic diffraction peaks due to the fragile short-range antiferromagnetic (AFM) order persist under an applied magnetic-field $\mathbf{H}$. Our results for $\mathbf{H}\perp \left[\overline{1}10\right]$ and a temperature of $T=0.14\left(1\right)\mathrm{K}$ show that the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak can be described by the same two-peak line shape found for ${\mu }_{0}H=0\mathrm{T}$ below the Néel temperature of $T_{\text{N}}=0.4\mathrm{K}$. Both components of the peak exist for ${\mu }_{0}H\lesssim 1.4\text{T}$, which is well past the AFM phase boundary determined from our new resistivity data. Using neutron-diffraction data taken at $T=0.13\left(2\right)\mathrm{K}$ for $\mathbf{H}\parallel \left[001\right]$ or $\left[110\right]$, we show that domains of short-range AFM order change size throughout the previously determined AFM and non-Fermi liquid regions of the phase diagram, and that the appearance of a magnetic diffraction peak at $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ at ${\mu }_{0}H\approx 0.4\mathrm{T}$ signals canting of the ordered magnetic moment away from $\left[111\right]$. The continued broadness of the magnetic diffraction peaks under a magnetic field and their persistence across the AFM phase boundary established by detailed transport and thermodynamic experiments present an interesting quandary concerning the nature of YbBiPt's electronic ground state.

Figure 1

(a) Temperature-dependent electrical resistivity $\rho \left(T\right)$ of YbBiPt for a current I with a frequency of $16\mathrm{Hz}$ applied along $\left[100\right], \left[110\right]$, or $\left[\overline{1}\overline{1}1\right]$. The curves are normalized to 1 at $T=1\mathrm{K}$, and the legend indicates the direction of I and the sample number corresponding to each plot. Data for I $\parallel \left[001\right]$ are from Ref. [7]. (b)–(d) $\rho \left(T\right)$ curves for various values of magnetic field applied along the $\left[001\right]$ (b), $\left[\overline{1}10\right]$ (c), or $\left[111\right]$ (d) directions with $\mathbf{I}$ applied $\perp \mathbf{H}$. (e) Transverse magnetoresistivity ($\mathbf{I}\perp \mathbf{H}$) at $T=0.1\mathrm{K}$ for $\mathbf{H}\parallel \left[001\right], \left[\overline{1}00\right]$, or $\left[111\right]$

Figure 2

Magnetic phase diagrams based on resistivity data for $\mathbf{I}\perp \mathbf{H}$ with $\mathbf{H}\parallel \left[001\right]$ (a), $\left[\overline{1}10\right]$ (b), or $\left[111\right]$ (c). Open symbols are from Ref. [7] and closed symbols are new data. Lines are guides to the eye. AFM stands for antiferromagnetic, nFL labels the non-Fermi-liquid region, characterized by $\rho \sim T^{1.5}$, and FL marks the Fermi-liquid region, characterized by $\rho \sim T^2$. $T_{\text{N}}$ labels the Néel temperature and $T_{\text{FL}}$ marks the boundary of the Fermi-liquid region.

Figure 3

(a) $\mathrm{\Delta }\rho \left(T\right)=\rho \left(T\right)-\rho (T=0\mathrm{K})$ versus $T^{1.5}$ and (b) $\mathrm{\Delta }\rho \left(T\right)$ versus $T^2$ for $\mathbf{H}\parallel \left[001\right], \left[\overline{1}10\right]$, or $\left[111\right]$. I was applied $\perp \mathbf{H}$, along the directions indicated in Fig. 1. Solid lines are guides to the eye.

Figure 4

The Fermi-liquid coefficient $A=\mathrm{\Delta }\rho \left(T\right)/T^2$ for $\mathbf{H}\parallel \left[100\right], \left[\overline{1}10\right]$, or $\left[111\right]$. $\mathbf{I}$ was applied $\perp \mathbf{H}$, along the directions indicated in Fig. 1. Data from Ref. [7] (for $\mathbf{H}\parallel \left[001\right]$) are included for comparison. The solid line is a fit to $A\propto 1/(H-H_{\text{c}})$, where $H_{\text{c}}$ corresponds to the magnetic field at which $T_{\text{N}}$ extrapolates to $0\mathrm{K}$. Note that the values of $A$ are for values of $H$ and $T$ corresponding to the FL region.

Figure 5

Intensity of the scattering at $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ versus magnetic field for various temperatures and $\mathbf{H}\parallel \left[\overline{1}10\right]$. Data were taken on SPINS. Vertical dotted lines mark the boundaries identified in Fig. 2 at $T=0.14\mathrm{K}$ determined from resistivity data.

Figure 6

Rocking curves for the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak at $T=0.13\mathrm{K}$ for ${\mu }_{0}H=0$ (a) and $0.6\mathrm{T}$ (b) applied parallel to $\left[\overline{1}10\right]$. Data were taken on SPINS using $\lambda =5.504\AA$ neutrons. Solid curves are fits to the two-Gaussian line shape described in the text, and the line shape's components are shown by dashed curves. The small peak at $\approx {10}^{\circ }$ is due to residual Bi flux from the crystal synthesis process and was masked while performing fits. Data for ${\mu }_{0}H=0$, 0.6, and $1.6\mathrm{T}$ are plotted altogether in (c). A scaled rocking curve for the (1,1,1) structural Bragg peak at $T=0.13\mathrm{K}$ is also shown in (a).

Figure 7

Rocking scan data from SPINS ($\lambda =5.504\AA$) for the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ (a)–(f) and $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ (g)–(l) reciprocal-lattice positions taken at $T=0.13$ and $0.14\mathrm{K}$, respectively, for various values of $\mathbf{H}\parallel \left[\overline{1}10\right]$. Data in (g)–(l) are subtracted by data for ${\mu }_{0}H=0\mathrm{T}$. The solid curves are fits to either a two-Gaussian [$(\frac{1}{2},\frac{1}{2},\frac{3}{2})$] or Gaussian [$(\frac{1}{2},\frac{1}{2},\frac{1}{2})$] line shape.

Figure 8

The integrated intensities (a) and magnetic-correlation lengths (b) versus field for $\mathbf{H}\parallel \left[\overline{1}10\right]$ and $T=0.14\left(1\right)\mathrm{K}$ from fits to the rocking curves for the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ and $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ magnetic diffraction peaks shown in Figs. 6, 7, and 11. Narrow and broad refer to the components of the two-Gaussian line-shape fit to the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ peak, and total refers to the sum of the integrated intensities of the two components. Vertical dotted lines mark the boundaries identified in Fig. 2 at $T=0.14\mathrm{K}$ determined from resistivity data. Solid lines are guides to the eye.

Figure 9

Diagram showing the region for which magnetic diffraction peaks are found for $\mathbf{H}\parallel \left[\overline{1}10\right]$. The AFM and FL boundaries determined via resistivity are also shown. Squares (triangles) mark the onset temperatures and magnetic fields of the broad (narrow) component of the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak, and the shaded region indicates where short-range AFM exists. Lines are guides to the eye. nFL and FL label the non-Fermi-liquid and Fermi-liquid regions, respectively.

Figure 10

Data from transverse scans taken on FLEXX, using $\lambda =5.464\AA$ neutrons, showing the temperature dependence of the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak for ${\mu }_{0}H=0.4\mathrm{T}$. Data are successively offset by 400 counts per minute. Solid red curves are fits to the two-Gaussian lineshape described in the text. The lineshape's components are shown by dashed curves. Bragg peaks due to residual Bi flux from the crystal synthesis process are also marked.

Figure 11

(a) Rocking curves taken on SPINS, using $\lambda =5.504\AA$ neutrons, for the $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ reciprocal-lattice position at $T=0.14\mathrm{K}$ for ${\mu }_{0}H=0$ and $0.6\mathrm{T}$ applied $\parallel \left[\overline{1}10\right]$. (b) Difference of the ${\mu }_{0}H=0.6$ and $0\mathrm{T}$ data. The solid line is a fit to a Gaussian line shape.

Figure 12

Intensity of the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak versus magnetic field at $T=0.13\left(2\right)\mathrm{K}$ for a vertical field applied along $\left[\overline{1}10\right]$ (a), or a horizontal field applied within the scattering plane along either $\left[110\right]$ (b) or $\left[001\right]$ (c). Data are scaled to 1 at ${\mu }_{0}H=0\mathrm{T}$ and 0 at $2\mathrm{T}$, as described in the text. Data in (a) are the SPINS data shown in Fig. 5, and data in (b) and (c) were taken on E-4. Vertical dotted lines correspond to the boundaries at $T=0.14\mathrm{K}$ given in Figs. 2 and 2.

Figure 13

Diagram of the $(h,h,l)$ reciprocal-lattice plane showing structural (squares) and magnetic (circles) Brillouin zone centers, as well as the AFM propagation vectors connecting them. $\mathbf{Q}=(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ is also shown. A circle with an $\times$ in its interior indicates a magnetic zone center with zero diffraction intensity due to the associated magnetic moments being oriented along $\mathit{\tau }$, as occurs for ${\mu }_{0}H=0\mathrm{T}$.

Figure 14

Diagram showing the angles between $\mathbf{H}, \mathbf{Q}$, and $\mathit{\mu }$ for $\mathbf{Q}=(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ and $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, and $\mathbf{H}\parallel \left[\overline{1}10\right]$. ${\mathbf{\mu }}_{{\mathbf{\tau }}_{\mathit{\text{1}}}}$ and ${\mathit{\mu }}_{{\mathit{\tau }}_2}$ refer to moments associated with domains corresponding to ${\mathit{\tau }}_1$ and ${\mathit{\tau }}_2$, respectively. $\beta$ is the angle by which $\mathit{\mu }$ is rotated out of the $(h,h,l)$ plane by $\mathbf{H}$.

Figure 15

(a) The ratio of the integrated intensity of the narrow component of the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak to the integrated intensity of the $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ magnetic diffraction peak for $\mathbf{H}\parallel \left[\overline{1}10\right]$ and $T=0.14\left(1\right)\mathrm{K}$. (b) The angle $\beta$ by which the field causes $\mathit{\mu }$ to rotate out of the scattering plane. A point at ${\mu }_{0}H=1.2\mathrm{T}$ is absent, because $\sqrt{32/(33N-1)}$ is outside of the valid range for ${sin}^{-1}$ [see Eqs. (4) and (5)]. Vertical dotted lines correspond to the boundaries identified in Figs. 2 and 2 for $T=0.14\mathrm{K}$, which were determined from resistivity data. Solid lines are guides to the eye.