Spin resistivity in frustrated antiferromagnets

In this paper we study the spin transport in frustrated antiferromagnetic FCC films by Monte Carlo simulation. In the case of the Ising spin model, we show that the spin resistivity versus temperature exhibits a discontinuity at the phase transition temperature: an upward jump or a downward fall, depending on how many parallel and antiparallel localized spins interacting with a given itinerant spin. The surface effects as well as the difference of two degenerate states on the resistivity are analyzed. A comparison with nonfrustrated antiferromagnets is shown to highlight the frustration effect. We also show and discuss the results of the Heisenberg spin model on the same lattice.

Figure 1

Ground-state spin configuration of the fcc cell at the film surface (basal $\mathit{xy}$ plane). The horizontal (vertical) axis is the $x$ ($z$) axis. (top) Ground state when $\left|J_s\right|<0.5\left|J\right|$. (middle and bottom) First and second ground states when $\left|J_s\right|>0.5\left|J\right|$.

Figure 2

Collapse phase diagram in the space $(K_0,D)$. The black zone is the collapse region. $D_1=D_2=a$. See text for comments.

Figure 3

Staggered magnetization of antiferromagnetic fcc thin film of thickness $N_z=8$ versus $T$. The transition temperature $T_C\simeq 1.79$.

Figure 4

Different physical quantities versus $D_1$ in units of the lattice constant $a$ in the case of the first degenerate configuration. From top to bottom: Resistivity, velocity on the $x$ axis, difference of up- and down-spin numbers, energy of an itinerant spin. In each plot circles corresponds to $T=1.65$ and diamonds to $T=2$. $N_z=8$, $N_0=1600$, $J_s=J=-1.0$, and $D=0.35$.

Figure 5

Resistivity of thin film of size $N_x=N_y=20$ and $N_z=8$ for $N_0=1600$ itinerant spins versus $T$ for $D_1=a$ (black circles) and $D_1=1.25a$ (white circles), $a$ being the lattice constant. Case of the first degenerate state $J_s=J=-1.0$, $I_0=K_0=0.5$, $D=0.35$.

Figure 6

Resistivity versus $T$ for two values of magnetic field $B$ with $D_1=a$, $N_z=8$, $N_0=1600$, and $J_s=J=-1.0$. Black circles correspond to $B=0.75$ and white circles to $B=0.25$.

Figure 7

Resistivity, spin velocity, $\Delta N_{\uparrow \downarrow }$, and energy of itinerant spin versus $D_1$ (in units of the lattice constant $a$) at temperatures $T=1.65$ (black circles) and $T=2.0$ (white diamonds) in the case of second degenerate configuration. $N_z=8$, $N_0=1600$, and $J_s=J=-1.0$.

Figure 8

Resistivity versus temperature in the case of second degenerate state for $D_1=a$ (black circles) and $D_1=1.25a$ (white circles) with $N_z=8$, $N_0=1600$, $J_s=J=-1.0$, $I_0=K_0=0.5$, and $D=0.35$.

Figure 09

Layer magnetizations versus $T$ for $J_s=J_p=-0.5$ and $J=-1$. Other parameters: $D_1=a$, $N_z=8$, $N_0=1600$, $I_0=K_0=0.5$, and $D=0.35$. The surface transition is at $T_1\simeq 1.2$. The vertical dotted line is a guide to the eye indicating the discontinuous fall of interior layer magnetization.

Figure 10

Resistivity versus temperature $T$ in the case shown in Fig. 09. There are two anomalies occurring, respectively, at the surface transition temperature and at the bulk one.

Figure 11

Energy landscape at $T=1$ in a cubic box of $2a\times 2a\times 2a$ dimension where $a$ is the lattice parameter, for the first and second degenerate configurations (left and right, respectively). The energy scale is indicated on the figure.

Figure 12

Three-dimensional antiferromagnetic fcc lattice at $T=1$, where lattice down spins are presented in red, up spins in yellow, and itinerant spins (which are up) in white. The plane shown is the $\mathit{xy}$ plane with the $x$ direction (spin flow direction) being horizontal. Left: snapshot in the case $D_1=a$. Right: snapshot in the case $D_1=1.4a$.

Figure 13

Travel path of an itinerant spin at $T=1$ in the first degenerate state (top) and in the second degenerate state (bottom) during an equal travel time with $D_1=a$. As seen, spins move more easily in the first degenerate configuration than in the second one. Other parameters are $N_0=1600$, $I_0=K_0=0.5$, $D=0.35$, $J_s=J=-1.0$

Figure 14

Heisenberg case. Resistivity, spin velocity, and energy of itinerant spin versus $D_1$ (in units of the lattice constant $a$) at temperatures $T=0.75$ (black circles) and $T=0.85$ (white diamonds) for first (top) and second (bottom) degenerate configurations. $A=-1$, $N_z=8$, $N_0=1600$, and $J_s=J=-1.0$.

Figure 15

Heisenberg case. Resistivity of thin film of size $N_x=N_y=20$ and $N_z=8$ for $N_0=1600$ itinerant spins versus $T$ for $D_1=a$ (black circles) and $D_1=1.25a$ (white circles) in units of the lattice constant $a$ for first (top) and second (bottom) degenerate states. $A=-1$, $J_s=J=-1.0$, $I_0=K_0=0.5$, and $D=0.35$.