get_terms to display only direct children

Hello there!

I’m trying to have get_terms to display only direct children of an specific term, but that doesn’t seem to be working.

<?php
                $current_term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
                $taxonomy_name = 'product_category';
                $termchildren = get_terms($taxonomy_name,array('child_of' => $current_term->term_id));
                ?>
                <ul>
                <?php
                foreach ( $termchildren as $child ) {
                    $term = get_term_by( 'id', $child, $taxonomy_name );
                    $image = z_taxonomy_image_url($term->term_id);
                    //var_dump($term);?>
                    <li>
                        <a href="<?php echo get_term_link($term->slug, $taxonomy_name); ?>"><img src="<?php if ($image) { echo $image; } else { echo get_bloginfo('template_directory') . '/images/placeholder.png'; } ?>" alt="<?php echo $term->name;?>"/></a>
                        <a href="<?php echo get_term_link( $term->slug, $taxonomy_name );?>"><?php echo $term->name;?></a>
                    </li>
                <?php } ?>
                </ul>

This code displays ALL children.

Anyone have a clue?

Thanks in advance!