Powershell - get all default values for a document library

Question

I am attempting to write a powershell script that will iterate through all document libraries and provide me with the default values for specific columns.

I am successfully iteration through the sites, and their respective lists, but for a column named "NH Department" I would like to know if a default value has been set or not, and if so, what the default value is. I have tried the following with no success (partial, applicable code below):

foreach ($list in $subWeb.Lists)
{
  $listname = $list.Title

  $FieldName = $list.Fields["NH Department"]
  Write-Output $("NH Department: " + $FieldName.value)

}

I guess I don't know how to query the VALUE of the field I am targeting. I am not even confident I am finding the field properly above (probably not).

The fields in question are Managed Metadata fields that are part of a site column, which in turn is part of a content type applied to the document library.

EDIT: Complete code

$webApplicationURL = "http://www.site.com/"
$webApp = Get-SPWebApplication $webApplicationURL

if($webApp -ne $null)
{
  $webAppName = $webApp.name
  Write-Output "Web Application : $webAppName"

  foreach($siteColl in $webApp.Sites)
    { 
     if($siteColl -ne $null)
      {
        $siteCollName = $siteColl.Url
         Write-Output "Site Collection : $siteCollName"

         foreach($subWeb in $siteColl.AllWebs)
          {
            if($subWeb -ne $null)
              {
              $subWebName = $subWeb.Title
              Write-Output "Site : $subWebName"

              foreach ($list in $subWeb.Lists)
              {
                $listname = $list.Title
                if($lastlistname -ne $listname){Write-Output "List: $listname"}

                $FieldName = $list.Fields["NH Department"]
                Write-Output $("NH Department: " + $FieldName.DefaultValue)

              }
                 $subWeb.Dispose()
              }
           else
              {
                Echo $subWeb "does not exist"
              }
          }
            $siteColl.Dispose()
       }
     else
         {
            Echo $siteColl "does not exist"
         }
     }
} else
     {       Echo $webApplicationURL "does not exist, check the WebApplication name"
     }

Answer 1

There is property called DefaultValue.

$FieldName = $list.Fields["NH Department"]
Write-Output $("NH Department - Default Value " + $FieldName.DefaultValue)