Helical antiferromagnetic ordering in ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ single crystals

The ${\mathrm{Eu}}^{+2}$ spins-7/2 in ${\mathrm{EuNi}}_2{\mathrm{As}}_2$ with the body-centered tetragonal ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$ structure order antiferromagnetically below the Néel temperature $T_{\mathrm{N}}=15$ K into a helical antiferromagnetic (AFM) structure with the helix axis aligned along the tetragonal $c$ axis and the Eu ordered moments aligned ferromagnetically within the $ab$ plane as previously reported from neutron diffraction measurements [T. Jin et al., Phys. Rev. B 99, 014425 (2019)]. Here we study the crystallographic, magnetic, thermal, and electronic transport properties of Bi-flux-grown single crystals using single-crystal x-ray diffraction, anisotropic magnetic susceptibility $\chi$, isothermal magnetization $M$, heat capacity $C_{{}_{\mathrm{p}}}$, and electrical resistivity $\rho$ measurements versus applied magnetic field $H$ and temperature $T$. Vacancies are found on the Ni sites corresponding to the composition ${\mathrm{EuNi}}_{1.95\left(1\right)}{\mathrm{As}}_2$. A good fit of the $\rho \left(T\right)$ data by the Bloch-Grüneisen theory for metals was obtained. The ${\chi }_{ab}\left(T\right)$ data below $T_{\mathrm{N}}$ are fitted well by molecular field theory (MFT), and the helix turn angle $kd$ and the Eu-Eu Heisenberg exchange constants are extracted from the fit parameters. The $kd$ value is in good agreement with the neutron-diffraction result. The magnetic contribution to the zero-field heat capacity below $T_{\mathrm{N}}$ is also fitted by MFT. The isothermal in-plane magnetization $M_{ab}$ exhibits two metamagnetic transitions versus $H$, whereas $M_c(T=2\mathrm{K})$ is nearly linear up to $H=14$ T, both behaviors being consistent with MFT. The $M_c(H,T),\rho (H_c,T)$, and $C_{\mathrm{p}}(H_c,T)$ data yielded a $H_c\text{−}T$ phase diagram separating the AFM and paramagnetic phases in good agreement with MFT. Anisotropic $\chi \left(T\right)$ literature data for the ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type helical antiferromagnet ${\mathrm{EuRh}}_2{\mathrm{As}}_2$ were also fitted well by MFT. A comparison is made between the crystallographic and magnetic properties of ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type $\mathrm{Eu}{M}_{2}P{n}_2$ compounds with $M=\mathrm{Fe}$, Co, Ni, Cu, or Rh, and $Pn=\mathrm{P}$ or As, where only ferromagnetic and $c$-axis helical AFM structures are found.

Figure 1

Zero-field-cooled magnetic susceptibility $\chi \left(T\right)\equiv M\left(T\right)/H$ of an ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ single crystal as a function of temperature $T$ between 1.8 to 300 K measured in magnetic field $H=0.1$ T applied in the $ab$ plane $\left({\chi }_{ab}\right)$ and along the $c$ axis $\left({\chi }_c\right)$.

Figure 2

Inverse susceptibility ${\chi }^{-1}$ versus temperature $T$ of an ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ single crystal for (a) $H=0.1$ T and (b) $H=1$ T applied in the $ab$ plane $({\chi }_{ab}^{-1},H\parallel ab)$ and along the $c$ axis $({\chi }_c^{-1},H\parallel c)$.

Figure 3

Zero-field-cooled field-dependent magnetic susceptibility $\chi \equiv M/H$ of ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ single crystal as a function of temperature $T$ for various magnetic fields $H$ applied (a) in the $ab$ plane $\left(H\parallel ab\right)$ and (b) along the $c$ axis $\left(H\parallel c\right)$. The data for $H\parallel ab=4.5,5$, and 5.5 T in (a) are offset from each other for clarity by increments of 0.$01{\mathrm{cm}}^3$/mol as indicated.

Figure 4

Isothermal magnetization $M$ of single-crystal ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ as a function of magnetic field $H$ measured at $T=2$ K with $H$ applied in the $ab$ plane $\left(M_{ab},H\parallel ab\right)$ and along the $c$ axis $\left(M_c,H\parallel c\right)$. The first-order and second-order transition fields with increasing field for $M_{ab}\left(H\right)$ are indicated by vertical arrows, respectively.

Figure 5

(a) Isothermal magnetization $M_{ab}$ of an ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ single crystal versus magnetic field $H$ applied in the $ab$ plane $\left(H\parallel ab\right)$ at the indicated temperatures $T$. (b) Derivative $d{M}_{ab}/dH$ versus $H$ at $T=2,5$, and 7 K obtained from the respective data in (a).

Figure 6

Same as Fig. 5 except with the field applied along the $c$ axis $\left(H\parallel c\right)$.

Figure 7

(a) Magnetic susceptibility $\chi$ versus temperature $T$ for fields of magnitude $H=0.1$ T parallel $\left({\chi }_c\right)$ and perpendicular $\left({\chi }_{ab}\right)$ to the tetragonal $c$ axis of single-crystal ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ at low temperatures. (b) The $\chi \left(T\right)$ data in (a) normalized by $\chi \left(T_{\mathrm{N}}\right)$. The fit of ${\chi }_{ab}\left(T\right)/\chi \left(T_{\mathrm{N}}\right)$ in (b) and of ${\chi }_{ab}\left(T\right)$ in (a) for $T\le T_{\mathrm{N}}$ by the MFT prediction in Eqs. (3) for a helix is shown as the solid curves.

Figure 8

Generic helical AFM structure [42]. Each arrow represents a layer of moments perpendicular to the $z$ axis that are ferromagnetically aligned within the $xy$ plane and with interlayer separation $d$. The wave vector k of the helix is directed along the $z$ axis. The magnetic moment turn angle between adjacent magnetic layers is $kd$, where $k$ is the magnitude of the wave vector. The top view shows the magnetic moments as viewed from the positive $z$ axis. When the moment vectors are placed tail to tail as shown, the picture is a hodograph of the magnetic moments. The MFT nearest-layer and next-nearest-layer exchange interactions $J_1$ and $J_2$ are indicated.

Figure 9

Exchange interactions $J_{\mathrm{A}},J_{\mathrm{B}}$, and $J_{\mathrm{C}}$ between the Eu spins in a body-centered-tetragonal unit cell of ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$.

Figure 10

(a) ${\chi }_{ab}$ and ${\chi }_c$ as a function of temperature $T$ in an applied magnetic field $H=1$ T and (b) ${\chi }^{-1}\left(T\right)$ and its Curie-Weiss fit by Eq. (1a) for the helical antiferromagnet ${\mathrm{EuRh}}_2{\mathrm{As}}_2$ obtained using the data in Ref. [25].

Figure 11

(a) Magnetic susceptibility $\chi$ versus temperature $T$ for fields of magnitude $H=1$ T parallel $\left({\chi }_c\right)$ and perpendicular $\left({\chi }_{ab}\right)$ to the tetragonal $c$ axis of single-crystal ${\mathrm{EuRh}}_2{\mathrm{As}}_2$ at low temperatures [25]. (b) The $\chi \left(T\right)$ data in (a) normalized by $\chi \left(T_{\mathrm{N}}\right)$. The fit of ${\chi }_{ab}\left(T\right)/\chi \left(T_{\mathrm{N}}\right)$ in (b) and of ${\chi }_{ab}\left(T\right)$ in (a) for $T\le T_{\mathrm{N}}$ by the MFT prediction for a helix with $kd=0.83\pi$ and $f=0.14$ in Eqs. (3) for a helix are shown as the solid curve.

Figure 12

(a) In-plane electrical resistivity $\rho$ of ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ as a function of temperature from 1.8 to 300 K measured in zero magnetic field. The solid black curve is the fit of the prediction of the Bloch-Grüneisen theory in Eqs. (10) to the data above 50 K and is extrapolated to $T=0$. (b) Expanded plot of $\rho \left(T\right)$ at low temperature. The black line is the fit of the data by Eq. (9) over the temperature interval $2\mathrm{K}\le T\le 14$ K with a dashed-line extrapolation to 0 K. Inset: Temperature derivative $d\rho /dT$ versus $T$.

Figure 13

In-plane electrical resistivity $\rho$ of ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ as a function of temperature between 1.8 and 300 K measured in the indicated magnetic fields $H\parallel c$.

Figure 14

(a) Temperature $T$ dependence of the heat capacity $C_{\mathrm{p}}$ for ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ and ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ [22] single crystals in $H=0$ T. The black solid curve is a fit of the data between 50 and 300 K by the Debye lattice heat capacity model in Eqs. (11). (b) Expanded plot of $C_{\mathrm{p}}\left(T\right)$ for ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ and ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ at low temperature.

Figure 15

(a) Magnetic contribution $C_{\mathrm{mag}}$ of ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ versus temperature $T$ between 1.8 and 30 K obtained by subtracting the nonmagnetic contribution $C_{\mathrm{p}}\left(T\right)$ of ${\mathrm{BaCo}}_2{\mathrm{As}}_2$. The MFT prediction for $C_{\mathrm{mag}}\left(T\right)$ with $S=7/2$ and $T_{\mathrm{N}}=14.5$ K is shown as the black solid line. (b) Plot of the data in (a) as $C_{\mathrm{mag}}\left(T\right)/T$ versus $T$, where again the MFT prediction is given by the solid black line. (c) Magnetic entropy $S_{\mathrm{mag}}\left(T\right)$ calculated from the experimental $C_{\mathrm{mag}}\left(T\right)/T$ data and the low-$T$ theoretical extrapolation in (b) using Eq. (14). The horizontal dashed line in (c) is the theoretical high-$T$ limit $S_{\mathrm{mag}}=Rln(2S+1)=Rln\left(8\right)=17.29$ J/mol K for $S=7/2$.

Figure 16

Heat capacity $C_{\mathrm{p}}$ versus temperature $T$ of single-crystal ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ in various magnetic fields applied parallel to the $c$ axis, $H\parallel c$.

Figure 17

Magnetic $H_c\text{−}T$ phase diagram containing the antiferromagnetic (AFM) and paramagnetic (PM) phases for single-crystal ${\mathrm{EuNi}}_{1.95}{\mathrm{As}}_2$ as determined from heat capacity $C_{\mathrm{p}}(H,T)$, magnetization $M_c(H,T)$, and electrical resistivity $\rho (H,T)$ measurements with fields $H_c$ parallel to the tetragonal $c$ axis. The solid curve is a MFT fit to the $T_{\mathrm{N}}(H,T)$ data in Table 5 and the $H_{\mathrm{c}\perp }\left(T\right)$ data in Table 3 by Eq. (15). The values of the fitted free parameters $T_{\mathrm{N}}$ and the critical field $H_{\mathrm{c}\perp }(T=0)$ perpendicular to the zero-field $ab$ plane of the ordered moments are given in the figure.