rnorm in R not iid

I'm generating small samples (e.g. 24 obs) of normally distributed variable in R. It seems that the resulting variable has a systematically negative autocorrelation.

Code below generates 1000 samples of 24 observations of x and calculates the first three autocorrelations. These are not huge on average (-0.075 to 0.045) but the averages are always negative. Increasing sample size (N) decreases the autocorrelation towards zero. However, my questions is: Why are the random numbers in a small sample negatively autocorrelated?

K <- 1000
N <- 24
ac <- NULL
for (k in 1:K) {
  x <- rnorm(n=N)
  ac <- rbind(ac, pacf(x, plot=F)$acf[1:3,1,1])
}
apply(ac, 2, mean)
[1] -0.04925651 -0.07523400 -0.04542514

Thanks!