Magnetic and electronic properties unveil polaron formation in Eu[Formula: see text]In[Formula: see text]Sb[Formula: see text]

Abstract

The intermetallic compound Eu[Formula: see text]In[Formula: see text]Sb[Formula: see text], an antiferromagnetic material with nonsymmorphic crystalline structure, is investigated by magnetic, electronic transport and specific heat measurements. Being a Zintl phase, insulating behavior is expected. Our thermodynamic and magnetotransport measurements along different crystallographic directions strongly indicate polaron formation well above the magnetic ordering temperatures. Pronounced anisotropies of the magnetic and transport properties even above the magnetic ordering temperature are observed despite the Eu[Formula: see text] configuration which testify to complex and competing magnetic interactions between these ions and give rise to intricate phase diagrams discussed in detail. Our results provide a comprehensive framework for further detailed study of this multifaceted compound with possible nontrivial topology.

Figure 1

(a) Magnetization in dependence on magnetic field for up and down sweeps. Data at 2 K are shown for fields along all three crystallographic directions, for $H\Vert c$ also data at 5 K and 8 K are presented. Lines indicate measurements up to 14 T, markers up to 7 T. Inset: Three groups of crystallographically different Eu positions (reddish color, marked Eu1, Eu2 and Eu3) within the crystal structure of Eu${}_5$In${}_2$Sb${}_6$ (Sb in green, In not shown) viewed along the c-axis. (b,c) Temperature evolution (in steps of 1 K) of magnetization curves for $H\Vert a$ and $H\Vert b$ emphasizing the metamagnetic transitions at $H_{\text{m}}(T)$ (arrows).

Figure 2

(a) Temperature dependent ac susceptibility ${\chi }^{\prime }(T)$ for different magnetic fields H applied along the crystallographic a-axis illustrating the temperature shifts of the transitions with H. Lower inset: Slow T-sweep (0.1 K/min) reveals a small offset for different ac-field (2 Oe) drive frequencies for the low-T transition. Upper inset: suggested spin configuration. (b) $\chi \prime (T)$ for different H along the c-axis. Inset: Imaginary component of susceptibility, $\chi ″(T)$ for the same conditions. For comparison, $\chi ″(T)$ at 317 Hz and 7 T is shown. Different samples were measured in (a) and (b).

Figure 3

Magnetization in dependence on sample orientation with respect to H for two applied fields (${\mu }_{0}H=$ 0.1 T, 3 T) below and above ${\mu }_0{H}_{\text{m}}\approx 2.2$ T at $T=2$ K. The sample is rotated in the b–c plane, i.e. around the a-axis, with the alignment of the respective axis with H marked by arrows.

Figure 4

(a) Specific heat divided by temperature, $C_p/T$, in dependence on T for applied fields $H\Vert b$ up to 9 T. The insets show enlarged views of $C_p(T)$ within certain temperature ranges (in units of J/mol K). (b) $C_{\text{ph}}$ contribution from a Debye model (green curve) fitted to the experimental $C_p(T)$-data (black) within 60 K $\le T\le$ 200 K and used to estimate $C_{\text{mag}}/T$ (magenta). Inset: photograph of one representative Eu${}_5$In${}_2$Sb${}_6$ sample with the long dimension corresponding to the c axis.

Figure 5

H–T phase diagrams for magnetic fields aligned along different crystallographic directions, left: $H\Vert a$, center: $H\Vert b$, right: $H\Vert c$, as extracted from ac and dc susceptibility $\chi$, magnetization M and specific heat $C_p$ measurements. Violet arrows depict a possible magnetization orientation with respect to magnetic field (gray arrows). To enable comparison, sample demagnetization effects are taken into consideration.

Figure 6

Resistivity $\rho (T)$ in dependence on temperature for current I along different directions: (a) $I\Vert a$ and $H\Vert c$ and (b) $I\Vert c$ and $H\Vert b$. Inset in (a): Zoom into the low-T range on a logarithmic T-scale. At zero field, a kink is observed around 27 K (arrow). Inset in (b): Ratio r of resistivities for the different configurations shown in (a) and (b). The zero-field maximum near 27 K is suppressed with field. At $H=9$ T, r is of order 0.3 (green curve). All panels share the same color code for magnetic fields. (c) Ratio of resistivities measured at fields of 9 T and 0 T, as shown in (a). (d) Photographs of the sample, scale bar 400 $\mathrm{\mu }$m.