Parallelizing tree creation in R using the packages data.tree and foreach

Question

I'm trying to parallelize the creation of a tree in R using the following code :

# Creation of the root
root <- Node$new("Root")

# Function to create the tree recursively
create.tree.layer.para <- function(node,depth, max_depth=2,num_children=2, num_rep=2){
  if (depth > max_depth) {
    return(NULL)
  }
  x <-
    foreach(z=1:num_rep) %:%
      foreach(i=1:num_children,
              .export = c("create.node", "sprintf", "node"),
              .packages=c("data.tree","spatstat", "sf", "sigmoid")) %dopar% {
                child <- node$AddChild(sprintf("%d,%d",i,z))
              }
  
  # Recursively build the next layer
  for (child in node$children) {
    create.tree.layer.para(child,depth+1, max_depth,num_children, num_rep)
  }
}

# Creating the tree from the root
create.tree.layer.para(node=root, depth=0, max_depth=1, num_children=2, num_rep=2)

When not parallelizing, the tree is created without problem. But when I parallelize, the tree is not built, I only get this:

  levelName
1      Root

What are your insights on this problem ?

I tried putting node$AddChildNode(Node$new(sprintf("%d,%d",i,z))) instead of child <- node$AddChild(sprintf("%d,%d",i,z)) with the same result.