Magnetism, heat capacity, and electronic structure of ${\mathrm{EuCd}}_2{\mathrm{P}}_2$ in view of its colossal magnetoresistance

The mechanism of the peculiar transport properties around the magnetic ordering temperature of semiconducting antiferromagnetic ${\mathrm{EuCd}}_2{\mathrm{P}}_2$ is not yet understood. With a huge peak in the resistivity observed above the Néel temperature $T_{\mathrm{N}}=10.6\mathrm{K}$, it exhibits a colossal magnetoresistance effect. Recent reports on observations of ferromagnetic contributions above $T_{\mathrm{N}}$ as well as metallic behavior below this temperature have motivated us to perform a comprehensive characterization of this material, including its resistivity, heat capacity, magnetic properties, and electronic structure. Our transport measurements revealed quite different temperature dependence of resistivity with the maximum at 14 K instead of previously reported 18 K. Low-field susceptibility data support the presence of static ferromagnetism above $T_{\mathrm{N}}$ and show a complex behavior of the material at small applied magnetic fields. Namely, signatures of reorientation of magnetic domains are observed up to $T=16$ K. Our magnetization measurements indicate a magnetocrystalline anisotropy which also leads to a preferred alignment of the magnetic clusters above $T_{\mathrm{N}}$. The momentum-resolved photoemission experiments at temperatures from 24 down to 2.5 K indicate the permanent presence of a fundamental band gap without change of the electronic structure when going through $T_N$ that is in contradiction with previous results. We performed ab initio band structure calculations which are in good agreement with the measured photoemission data when assuming an antiferromagnetic ground state. Calculations for the ferromagnetic phase show a much smaller band gap, indicating the importance of possible ferromagnetic contributions for the explanation of the colossal magnetoresistance effect in the related ${\mathrm{EuZn}}_2{\mathrm{P}}_2$.

Figure 1

(a) Unit cell of the trigonal crystal structure and as-grown single crystal. (b) Temperature-dependent resistivity measured in the $a\text{−}a$ plane with an applied magnetic field oriented along the $c$ axis. The resistivity is strongly suppressed under the application of magnetic field. Large symbols mark the peak position (maximum) of the resistivity. Inset shows the zero-field resistivity up to room temperature. (c) Magnetoresistance (MR), calculated using the formula MR= $\left[\rho \right(H)-\rho (0\left)\right]/\rho \left(0\right)$, evaluated for a magnetic field of ${\mu }_{0}H=5$ T. Notably, a substantial negative MR of $99.96\%$ is observed at 14 K, followed by a gradual decline below 8 K (see inset for an enhanced view of the low-temperature behavior). Subsequently upon cooling, there is a resurgence in the MR signal, also evident in the resistivity measurements.

Figure 2

${\mathrm{EuCd}}_2{\mathrm{P}}_2$ (a) heat capacity measured with $H\parallel \left[210\right]$ and (b) with $H\parallel \left[001\right]$. The modeling of the heat-capacity data is shown in (c) for $H\parallel \left[100\right]$ and in (d) for $H\parallel \left[001\right]$. (e) No shift of the maximum is observed for $H\le 0.03\mathrm{T}$, $H\parallel \left[210\right]$. The arrow in the inset (f) shows that a kink appears for ${\mu }_{0}H=0.3\mathrm{T}$, $H\parallel \left[001\right]$. The position of the maxima in $\rho$, HC (g) and in the calculated data (h) is shown for comparison.

Figure 3

Moment versus field at 2 K for the main symmetry directions in comparison with the model.

Figure 4

(a) $M/H$ vs $H$ for increasing field at 5 K for the three main symmetry directions. The schematic drawing represents the orientation of the magnetic moments when a field is applied along an in-plane direction. In (b), the low-field region is shown. Reorientation of magnetic domains is observed below $\approx 2.5\mathrm{mT}$ for in-plane fields (arrows).

Figure 5

Magnetic moment versus temperature (a) zero-field-cooled and field-cooled moment for in-plane and out-of-plane directions at ${\mu }_{0}H\approx$ 0.1 mT. Dashed lines mark the temperatures, where the maxima in HC and resistivity appear. The dotted line marks the superconducting transition of tin. (b) Hysteresis effects in the $T$ dependence are observed for both field directions below $\approx 12.5\mathrm{K}$ (blue shaded area).

Figure 6

${\mathrm{EuCd}}_2{\mathrm{P}}_2$ (a) $d\left[\chi \right(T\left)T\right]/dT$ versus temperature measured with $H\parallel \left[001\right]$, ${\mu }_{0}H=0.0025\mathrm{T}$ (ZFC, dark red and FC, red), and ${\mu }_{0}H=0.1\mathrm{T}$ (ZFC, brown and FC, orange) in comparison with the magnetic part of the zero-field heat capacity $C^{4f}$. The blue arrows mark the temperatures of the opening and closing of the hysteresis. (b) $\chi \left(T\right)$ versus temperature for $H\parallel \left[001\right]$ and $H\parallel \left[210\right]$ at ${\mu }_{0}H=0.0025\mathrm{T}$ in comparison. The dotted line marks the superconducting transition of Sn. Dashed lines indicate the temperatures where maxima in zero-field heat capacity and resistivity appear.

Figure 7

$H\text{−}T$ phase diagram of ${\mathrm{EuCd}}_2{\mathrm{P}}_2$ for (a) $H\parallel \left[210\right]$ and (b) $H\parallel \left[001\right]$ constructed from data measured on three different samples. For very low fields and $H\parallel \left[210\right]$, we observe signatures of a domain flip (DF) in $M\left(H\right)$ (dark blue symbols, data points extracted from Fig. S3). At low fields, in the H regime (open and closed square symbols), the opening and closing of the hysteresis of the ZFC and FC susceptibility data were analyzed [blue arrows in Fig. 6]. For fields higher than $0.01\mathrm{T}$, closed squares indicate maxima in the susceptibility (Figs. S5 and S6 in [29]). Closed and open circles indicate the transition into the field-polarized (FP) state in $M\left(H\right)$ (Fig. S2 in [29]), which occurs at slightly different fields for different samples. At high temperatures the material is paramagnetic (PM). The blue and red region shows the gradual transition first from PM to the phase where the emergence of a static magnetization is observed which is assigned to the formation of ferromagnetic clusters (FMC). Below $T_N$, the material shows additional AFM order. Triangles mark the peak temperature in HC and stars the peak temperature in the resistivity for $H\parallel \left[001\right]$.

Figure 8

Computed bulk band structure of ${\mathrm{EuCd}}_2{\mathrm{P}}_2$ with (a), (b) A-type AFM and (c) FM ordering. Colors in (a) highlight the orbital composition of electronic states, while in (b) only the band dispersions are shown. Colors in (c) show the sign of the $S_z$ spin component, while the size of the colored spots denote $|S_z|$; gray spots show the states with small spin polarization.

Figure 9

(a) Calculated AFM bulk electronic states projected on the (001) surface along the $\overline{M}\text{−}\overline{K}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction. Experimental band structure along $\overline{M}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction measured with ARPES using (b) 55-eV and (c) 137-eV photons.