Anisotropic energy scale for degenerate Fermi and non-Fermi liquids near a quantum critical phase transition in ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$

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Anisotropic energy scale for degenerate Fermi and non-Fermi liquids near a quantum critical phase transition in ${YbRh}_{2} {Si}_{2}$

S. Kambe, H. Sakai, Y. Tokunaga, G. Lapertot, T. D. Matsuda, G. Knebel, J. Flouquet, and R. E. Walstedt

Phys. Rev. B 91, 161110(R) – Published 24 April 2015

Abstract

Based on ${}^{29}{Si}$ nuclear spin-lattice relaxation time $(T_{1})$ data on a single crystal of ${YbRh}_{2} {Si}_{2}$ , the coexisting Fermi liquid and non-Fermi liquid states around the quantum critical phase transition have been found to be sensitive to the direction of the applied magnetic field. Augmented scaling analysis shows that the anisotropic characteristic temperature and field are roughly ten times larger for $H ∥ c$ than for $H ∥ a$ , consistent with a previously obtained anisotropic phase diagram.

Received 19 January 2015
Revised 2 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.161110

Authors & Affiliations

S. Kambe¹, H. Sakai¹, Y. Tokunaga¹, G. Lapertot², T. D. Matsuda^1,*, G. Knebel², J. Flouquet², and R. E. Walstedt³

¹Advanced Science Research Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan
²Service de Physique Statistique, Magnétisme et Supraconductivité, Institut Nanosciences et Cryogénie, CEA-Grenoble/Université J. Fourier Grenoble I, 17 rue des Martyrs, 38054 Grenoble, France
³Physics Department, The University of Michigan, Ann Arbor, Michigan 48109, USA

^*Present address: Division of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan.

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Vol. 91, Iss. 16 — 15 April 2015

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Figure 1
Left: Crystal structure $(I 4 / m m m)$ of ${YbRh}_{2} {Si}_{2}$ . The local symmetry of the Si site is tetragonal $(4 m m)$ . The $a$ and $\bar{a}$ axes are identical crystallographically; however, they are distinguishable under magnetic field $H ∥ a$ [13]. Right: The $T − H$ phase diagram (PD) of ${YbRh}_{2} {Si}_{2}$ . Antiferromagnetic order (AFM) disappears at $H_{cr}$ . The PD for $H ∥ a$ coincides with the PD for $H ∥ c$ if $H ∥ a$ is multiplied by 11 [1].
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Figure 2
(a) Nuclear relaxation curves at $T = 45$ mK in different applied fields. Solid lines are obtained by least squares fits to Eq. (1) for 7.2 T and to Eq. (2) for 3.8, 0.66, and 0.31 T. At 7.2 T the relaxation curve is straight, indicating a homogeneous (FL) state. With decreasing field, nonlinear relaxation curves appear which are well fitted by Eq. (2), indicating the presence of two different states. (b) Nuclear magnetic relaxation curves at $H = 0.31$ T at different temperatures. Solid lines are obtained by least squares fits to Eq. (1) for 492 mK and to Eq. (2) for other temperatures. At 492 mK, the relaxation curve is a straight line, indicating a homogeneous (NFL) state. As temperature decreases, two-component relaxation curves appear, which are well fitted by Eq. (2), indicating the appearance of two different states.
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Figure 3
(a) $T$ dependence of $1 / T_{1 S} T$ (NFL state) and $1 / T_{1 L} T$ (FL state) at different fields (listed in the figure). Down to $\sim 0.1$ K no clearly resolved separate decay curves have appeared, whereas the unique $T_{1} (\equiv T_{1 L})$ depends on $H$ . As $T$ decreases below $\sim 0.1$ K at low fields, distinct values are resolved for $1 / T_{1 S} T$ and $1 / T_{1 L} T$ . The experimental error for $1 / T_{1 S} T$ is large for $T$ above $\sim 0.1$ K. At the highest field, 7.2 T, only $1 / T_{1 L} T$ appears. (b) $T$ dependence of squared static susceptibility $χ_{a}^{2}$ at 0.66 and 7 T for $H ∥ a$ with the same scale of $T$ as in (a), suggesting a simple density-of-states mechanism for the field dependence of $T_{1 L}$ . The inset shows $T$ dependence of the static susceptibility $χ_{a}$ for the same data.
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Figure 4
(a) $T$ dependence of $R$ at different fields. As shown, the experimental error at high temperatures is large, thus clearly resolved finite $R$ is only considered to appear below $\sim 0.1$ K. (b) Scaling plot for $H ∥ a$ and $H ∥ c$ cases. $R$ obeys the scaling relation $R t \sim Φ_{i} (h / t^{2.5})$ . The solid line represents the scaling function $Φ_{c}$ obtained for the $H ∥ c$ case [16]. The dashed line represents the scaling function $Φ_{a}$ for the present $H ∥ a$ case, which merges into $Φ_{c}$ for $h / t^{2.5} > 10^{2}$ . Here we adopt the estimates $T_{c}^{†} / T_{a}^{†} = H_{c}^{†} / H_{a}^{†} = 10$ . As temperature and field units, $T_{c}^{†} = 1$ K and $H_{c}^{†} = 1$ T are employed tentatively.
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Anisotropic energy scale for degenerate Fermi and non-Fermi liquids near a quantum critical phase transition in ${YbRh}_{2} {Si}_{2}$

S. Kambe, H. Sakai, Y. Tokunaga, G. Lapertot, T. D. Matsuda, G. Knebel, J. Flouquet, and R. E. Walstedt

Phys. Rev. B 91, 161110(R) – Published 24 April 2015

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Physical Review B

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Anisotropic energy scale for degenerate Fermi and non-Fermi liquids near a quantum critical phase transition in YbRh2Si2

S. Kambe, H. Sakai, Y. Tokunaga, G. Lapertot, T. D. Matsuda, G. Knebel, J. Flouquet, and R. E. Walstedt

Phys. Rev. B 91, 161110(R) – Published 24 April 2015

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Anisotropic energy scale for degenerate Fermi and non-Fermi liquids near a quantum critical phase transition in ${YbRh}_{2} {Si}_{2}$