Magnetism and superconductivity in ${\mathrm{M}}_c{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ ($\mathrm{M}=\mathrm{Fe}$, Co, Ni, and Cu)

Magnetic properties of ${\mathrm{M}}_c{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ $(\mathrm{M}=\mathrm{Fe},\mathrm{Co},\mathrm{Ni},\mathrm{Cu})$ have been studied using superconducting quantum interference device dc and ac magnetic susceptibility. In these systems magnetic ${\mathrm{M}}^{2+}$ ions are intercalated into van der Waals gaps between adjacent S layers of host superconductor ${\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ is a quasi-two-dimensional $XY$-like antiferromagnet on the triangular lattice. It undergoes an antiferromagnetic phase transition at $T_N$ $(=117\mathrm{K})$. The irreversible effect of magnetization occurs below $T_N$, reflecting the frustrated nature of the system. The antiferromagnetic phase coexists with two superconducting phases with the transition temperatures $T_{\mathit{cu}}=8.8\mathrm{K}$ and $T_{\mathit{cl}}=4.6\mathrm{K}$. ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ is a quasi-two-dimensional Ising-like antiferromagnet on the triangular lattice. The antiferromagnetic phase below $T_N=18.6\mathrm{K}$ coexists with a superconducting phase below $T_{\mathit{cu}}=9.1\mathrm{K}$. Both ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ and ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ are superconductors with $T_{\mathit{cu}}$ ($=8.7\mathrm{K}$ for Ni and $6.4\mathrm{K}$ for Cu) and $T_{\mathit{cl}}$ ($=4.6\mathrm{K}$ common to ${\mathrm{M}}_c{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$). Very small effective magnetic moments suggest that ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Cu}}^{2+}$ spins are partially delocalized.

Figure 1

(Color online) Derivation from ${\mathrm{Fe}}^{2+}$ spin Hamiltonian: (a) the energy levels, (b) $g$-factors $g_c^{\left(0\right)}$ and $g_a^{\left(0\right)}$ with $k$ [$=0.9$ (solid line) and 1 (dotted line)], (c) spin anisotropy parameters $p$ and $q$, and (d) $p^2∕q^2-1$, as a function of $x(={\delta }_0∕{\lambda }^{\prime })$. $x=-1.27$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. Derivation from ${\mathrm{Co}}^{2+}$ spin Hamiltonian: (e) the energy levels, (f) $g$-factors $g_c^{\left(0\right)}$ and $g_a^{\left(0\right)}$ with $k$ [$=0.9$ (solid line) and 1 (dotted line)], (g) spin anisotropy parameters $p$ and $q$, and (h) $p^2∕q^2-1$, as a function of $x(={\delta }_0∕{\lambda }^{\prime })$. $x=1.68$ for ${\mathrm{Co}}_{0.38}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 2

(Color online) $T$ dependence of (a) ${\chi }_{\mathrm{FC}}$ at $H=10\mathrm{kOe}$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$, (b) ${\chi }_{\mathrm{FC}}$ at $H=10\mathrm{kOe}$ for ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$, (c) ${\chi }_{\mathrm{FC}}$ at $H=10\mathrm{kOe}$ for ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$, and (d) ${\chi }_{\mathrm{FC}}$ at $H=500\mathrm{Oe}$ for ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. The inset shows the $T$ dependence of the reciprocal susceptibility ${({\chi }_{\mathrm{FC}}-{\chi }_{\mathrm{FC}}^0)}^{-1}$. The solid lines denote the least-squares fitting curves to the Curie–Weiss law given by Eq. (4). The fitting parameters are listed in Table .

Figure 3

(Color online) $T$ dependence of ${\chi }_{\mathrm{ZFC}}$, ${\chi }_{\mathrm{FC}}$, and $\delta (={\chi }_{\mathrm{FC}}-{\chi }_{\mathrm{ZFC}})$ for (a) ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$, (b) ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$, (c) ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$, and (d) ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. $H=1\mathrm{Oe}$. The units of (c) and (d) are the same as those of (a) and (b), respectively.

Figure 4

(Color online) $T$ dependence of (a) ${\chi }_{\mathrm{ZFC}}$ and (b) ${\chi }_{\mathrm{FC}}$ at $H$ ($=1$, 2, 5, and $10\mathrm{Oe}$) for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 5

(Color online) (a)–(f) $T$ dependence of ${\chi }_{\mathrm{ZFC}}$, ${\chi }_{\mathrm{FC}}$, and $\delta$ at various $H$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. The units of (d)–(f) are the same as those of (a)–(c).

Figure 6

(Color online) (a)–(c) $T$ dependence of ${\chi }_{\mathrm{ZFC}}$ (emu/Fe mole) at $H$ ($=5$, 20, and $300\mathrm{Oe}$) for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 7

(Color online) (a) $H$ dependence of $M$ at $T=1.9\mathrm{K}$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. The measurement of $M$ was made by changing $H$ in sequence from $0\text{to}1\mathrm{kOe}$ ($M$ coincides with $M_{\mathrm{ZFC}}$), from $1\text{to}-1\mathrm{kOe}$, and from $-1\text{to}1\mathrm{kOe}$, after the sample was cooled from $298\text{to}1.9\mathrm{K}$ in the absence of $H$. The inset shows the $H$ dependence of $M_{\mathrm{ZFC}}$ at $T=1.9\mathrm{K}$. (b) $H$ dependence of $M_{\mathrm{FC}}$ at various $T$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 8

(Color online) $T$ dependence of (a) ${\chi }^{\prime }$ and (b) ${\chi }^{″}$ at $f(=0.05–100\mathrm{Hz})$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. $h=1\mathrm{Oe}$. $T$ dependence of (c) ${\chi }^{\prime }$ and (d) ${\chi }^{″}$ at various $H$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. $f=0.1\mathrm{Hz}$. $h=1\mathrm{Oe}$. The units of (c) and (d) are the same as those of (a) and (b), respectively. Note that the background part of ${\chi }^{\prime }$ and ${\chi }^{″}$ at $f=0.1\mathrm{Hz}$ and $h=1\mathrm{Oe}$ in (a) and (b) is different from those in (c) and (d). These two measurements were carried out independently. The method of the measurements is different: (a) and (b) for the $f$ scan at each fixed $T$ and (c) and (d) for the $T$ scan at $f=0.1\mathrm{Hz}$ as $T$ was increased at each $H$ (after each $T$ scan, $H$ was increased at $14\mathrm{K}$ and then $T$ was decreased to $1.9\mathrm{K}$ in the presence of $H$).

Figure 9

(Color online) $H–T$ diagram of ${\mathrm{M}}_c{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. (a) The line $H_{\mathit{cl}}\left(T\right)$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ [peak temperatures of ${\chi }_{\mathrm{ZFC}}$ vs $T$ (●), ${\chi }_{\mathrm{FC}}$ vs $T$ (∎), and ${\chi }^{\prime }$ vs $T$ (▴) as a function of $H$], ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ [peak temperatures of ${\chi }_{\mathrm{ZFC}}$ vs $T$ (엯) and ${\chi }_{\mathrm{FC}}$ vs $T$ (◻) as a function of $H$], and ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ [peak temperatures of ${\chi }_{\mathrm{FC}}$ vs $T$ (▵) as a function of $H$]. (b) The line $H_{\mathit{cu}}\left(T\right)$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$: peak temperatures of ${\chi }_{\mathrm{ZFC}}$ vs $T$ (●) and ${\chi }^{\prime }$ vs $T$ (▴) as a function of $H$. (c) The lines $H_N^{\prime }\left(T\right)$ and $H_N\left(T\right)$ for ${\mathrm{Fe}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$: peak temperatures of ${\chi }_{\mathrm{ZFC}}$ vs $T$ (●) as a function of $H$. The solid lines of (a) and (b) denote least-squares fitting curves of the data to the power law form Eq. (5).

Figure 10

(Color online) (a) Magnetization curve ($M$ vs $H$) at $T=1.9\mathrm{K}$ for ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. (b) Detail of $M_{\mathrm{ZFC}}$ vs $H$ at $T=1.9$ and $6.0\mathrm{K}$.

Figure 11

(Color online) $T$ dependence of (a) ${\chi }^{\prime }$ and (b) ${\chi }^{″}$ at various $H$ for ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$. $f=1\mathrm{Hz}$. $h=0.5\mathrm{Oe}$. $T$ dependence of (c) ${\chi }_{\mathrm{ZFC}}$ and (d) ${\chi }_{\mathrm{FC}}$ at various $H$ for ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 12

(Color online) $T$ dependence of $\delta$ for ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 13

(Color online) (a) $H–T$ diagram for ${\mathrm{Co}}_{0.33}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$: $H_{\mathit{cu}}\left(T\right)$ determined from the data of ${\chi }^{\prime }$ vs $T$ (closed circles) and $\delta$ vs $T$ (open circles) with $H$. (b) $H–T$ phase diagram for ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$: $H_{\mathit{cu}}\left(T\right)$ determined from the data of $\delta$ vs $T$ with $H$. (c) $H–T$ phase diagram for ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$: $H_{\mathit{cu}}\left(T\right)$ determined from the data of $d\delta ∕dT$ vs $T$ (closed circle) and $d{\chi }_{\mathrm{ZFC}}∕dT$ vs $T$ (open circle) with $H$. The solid lines denote least-squares fitting curves to the power law form Eq. (5).

Figure 14

(Color online) $T$ dependence of (a) ${\chi }_{\mathrm{ZFC}}$ and (b) ${\chi }_{\mathrm{FC}}$ for ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ at various $H$.

Figure 15

(Color online) $T$ dependence of $\delta$ for ${\mathrm{Ni}}_{0.25}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$ at various $H$. Note that it is difficult to derive the value of $T$ at which $\delta$ tends to zero for each $H$, since the value of $\delta$ is plotted in a logarithmic scale, as a function of $T$.

Figure 16

(Color online) (a)–(f) $T$ dependence of ${\chi }_{\mathrm{ZFC}}$, ${\chi }_{\mathrm{FC}}$, and $\delta$ at various $H$ for ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.

Figure 17

(Color online) $T$ dependence of (a) $\delta$ and (b) ${\chi }_{\mathrm{FC}}$ at various $H$ for ${\mathrm{Cu}}_{0.60}{\mathrm{Ta}}_2{\mathrm{S}}_2\mathrm{C}$.