For the toasts: Place an oven rack in the center of the oven. Preheat the oven to 375 degrees F. Arrange the bread slices in a single layer on a heavy baking sheet. Drizzle both sides of the bread with the oil. Season with salt and bake until light golden, about 10 minutes. Cool for 1 minute, and then rub the toasts with the cut side of the garlic.
For the crab: In a small bowl, gently combine the crab, lemon juice, chives, and salt.
For the mayonnaise: In a small bowl, combine the mayonnaise, yogurt, lemon zest, salt, and cayenne pepper.
Divide the crabmeat evenly and place on top of the toasts. Dollop with about 1 teaspoon of the mayonnaise mixture and serve immediately.