High-temperature antiferromagnetism in Yb based heavy fermion systems proximate to a Kondo insulator

Given the parallelism between the physical properties of Ce- and Yb-based magnets and heavy fermions due to the electron-hole symmetry, it has been rather odd that the transition temperature of the Yb-based compounds is normally very small, as low as $\sim 1\mathrm{K}$ or even lower, whereas Ce counterparts may often have the transition temperature well exceeding 10 K. Here, we report our experimental discovery of the transition temperature reaching 20 K in a Yb-based compound at ambient pressure. The Mn substitution at the Al site in an intermediate valence state of $\alpha \text{−}{\mathrm{YbAlB}}_4$ not only induces antiferromagnetic transition at a record high temperature of 20 K but also transforms the heavy-fermion liquid state in $\alpha \text{−}{\mathrm{YbAlB}}_4$ into a highly resistive metallic state proximate to a Kondo insulator.

Figure 1

Phase diagram as a function of temperature $T$ (vertical axis) and Mn concentration $x$ (horizontal axis) for $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$. The contour plot of the $ab$-plane resistivity $\rho$ is also provided in the same region of $T$ and $x$. Each point indicates the Néel temperature $T_{\mathrm{N}}$ determined by the anomaly found in the temperature dependence of the magnetization (squares) and specific heat (circles). The broken line schematically refers to a phase boundary due to the antiferromagnetic transition. Inset indicates the unit-cell crystal structure of $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$.

Figure 2

(a) Temperature dependence of the magnetic susceptibility measured in the magnetic field along the $ab$ plane ($B=1000\mathrm{Oe}$). Open circles and filled circles refer to the field-cooled (FC) and zero-field-cooled (ZFC) components of the susceptibility, respectively. Arrows indicate the transition temperatures defined as the onset of the bifurcation between the FC and ZFC results. Inset shows temperature dependence of the inverse susceptibility. (b) Temperature dependence of the magnetic part of the specific heat divided by temperature, $C_{\mathrm{mag}}/T$. $C_{\mathrm{mag}}$ is estimated as $C_{\mathrm{mag}}=C\left(\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4\right)-C\left(\alpha \text{−}{\mathrm{LuAlB}}_4\right)$. Inset shows the temperature dependence of the entropy calculated using the specific heat result. (c) Substitution $x\left(\mathrm{Mn}\right)$ dependence of the Weiss temperature (${\mathrm{\Theta }}_{\mathrm{W}}$), the Kondo temperature $T_{\mathrm{K}}$ (left axis) and the effective moment ($P_{\mathrm{eff}}$) (right axis). (d) Temperature dependence of the $ab$-plane resistivity. The inset indicates the semi logarithmic plot of the $1/T$ dependence of the magnetic part of the resistivity ${\rho }_{\mathrm{mag}}$ for $x=0.48$. The magnetic part ${\rho }_{\mathrm{mag}}$ is defined as ${\rho }_{\mathrm{mag}}=\rho \left(\alpha \text{−}{\mathrm{YbAl}}_{0.52}{\mathrm{Mn}}_{0.48}{\mathrm{B}}_4\right)-\rho \left(\alpha \text{−}{\mathrm{LuAl}}_{0.56}{\mathrm{Mn}}_{0.44}{\mathrm{B}}_4\right)$. Black arrows indicate the transition temperature estimated by the anomaly in the temperature derivative of the resistivity and/or the peak of the specific heat. The solid line indicates the fit to the activation law with the gap $\mathrm{\Delta }=50\mathrm{K}$ (see text).

Figure 3

(a) Experimental density of state (ExDOS) near $E_{\mathrm{F}}$ for $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$ ($x=0.39$) derived from the PES measurements. The dotted lines indicate the calculation based on the periodic Anderson model [61]. The uncertain energy region on ExDOS over $\sim 5k_{\mathrm{B}}T$ above $E_{\mathrm{F}}$ [60, 61] is shaded (over $\sim 2.2$ meV at 5 K). Inset shows ExDOS for $x=0.0$. ExDOS for other $x$ is displayed in the Fig. 5 of Appendix. E. (b) Temperature dependence of ExDOS at $E_{\mathrm{F}}$ for various compositions.

Figure 4

(a) ZF-$\mu \mathrm{SR}$ spectra in $\alpha \text{−}{\mathrm{LuAl}}_{0.56}{\mathrm{Mn}}_{0.44}{\mathrm{B}}_4$ at 50 K and 1.7 K. Inset shows temperature dependence of the static relaxation rate $\mathrm{\Delta }$ in $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$. No significant change of $\mathrm{\Delta }$ is seen as a function of temperature. (b) de Gennes factor and the transition temperature of the $R{\mathrm{AlB}}_4$ systems with the ${\mathrm{YCrB}}_4$-type structure. ($R$ refers to rare earth elements.) $T_{\mathrm{N}}$ of $R=\mathrm{Tm}$ and $R=\mathrm{Er}$, Ho are determined by magnetic anomaly due to the hysteresis seen in the susceptibility reported in the literature [50] and [51], respectively. Solid lines indicate the naive expectation of the transition temperatures for $R{\mathrm{AlB}}_4$ based on these transition temperatures reported for $R=\mathrm{Tm}$, Er, and Ho [50, 51], assuming that the transition temperature is proportional to the de Gennes factor. (c) The Mn substitution dependence of the $\mathrm{\Delta }V/V$, which refers to the ratio of the difference $\mathrm{\Delta }V$ of the unit cell volume between $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$ and $\alpha \text{−}{\mathrm{YbAlB}}_4$ over the unit-cell volume $V$ of $\alpha \text{−}{\mathrm{YbAlB}}_4$.

Figure 5

[(a)–(f)] Experimental density of state (ExDOS) near $E_{\mathrm{F}}$ derived from the PES measurements for $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$ of $x\left(\mathrm{Mn}\right)$ = (a) 0.0, (b) 0.04, (c) 0.11, (d) 0.39, (e) 0.48, and (f) 0.57, respectively. ExDOSs in unreliable energy region above $5k_{\mathrm{B}}T$ [60] are indicated by the dashed lines. Insets show the raw PES spectra for each composition. The PES spectra are normalized by the area between –20 and 60 meV. [(g),(h)] Temperature dependence of (g) ExDOS at $E_{\mathrm{F}}$ and (h) gap size ${\mathrm{\Delta }}_{\mathrm{gap}}=\left(\right|{\mathrm{\Delta }}_{\mathrm{o}}|+|{\mathrm{\Delta }}_{\mathrm{u}}\left|\right)/2$ for $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$ estimated from the ExDOS spectra. Inset shows a schematic diagram of partial DOS in the $c\text{−}f$ hybridization model and an example of the line fit for $x=0.39$ at $T=5\mathrm{K}$. (i) Calculated DOS based on the $c\text{−}f$ hybridization model for $\alpha \text{−}{\mathrm{YbAl}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_4$ $\left[x\left(\mathrm{Mn}\right)=0.39\right]$. The parameters are $\nu =100\mathrm{meV}$ for $T=5\mathrm{K}$ and $\nu =105\mathrm{meV}$ for $T=20\mathrm{K}$ and 40 K with $T_{\mathrm{K}}=25\mathrm{K}$ for $x\left(\mathrm{Mn}\right)=0.39$, which is taken from the results shown in Fig. 2 of the main text. The dotted line denotes the calculation at $T=0\mathrm{K}$ using same parameters for $T=5\mathrm{K}$ without the experimental broadening factor. Inset shows the dispersions of the $c\text{−}f$ hybridized bands assumed in the calculation. The dashed box denotes the Brillouin zone accepted in the PES measurement with $h\nu =7\mathrm{eV}$.