Add-Type -Path (Resolve-Path "$env:CommonProgram FilesCommon FilesMicrosoft SharedWeb Server Extensions16ISAPIMicrosoft.SharePoint.Client.dll")
Add-Type -Path (Resolve-Path "$env:CommonProgram FilesCommon FilesMicrosoft SharedWeb Server Extensions16ISAPIMicrosoft.SharePoint.Client.Runtime.dll")

#Site collection URL
$siteurl = "https://**********.sharepoint.com/sites/I*******/"

$userName ="admin@******.onmicrosoft.com"
$password ="**********"

#client context object and setting the credentials
[Microsoft.SharePoint.Client.ClientContext]$clientContext = New-Object Microsoft.SharePoint.Client.ClientContext($siteurl)

# convert password into secure string
$securedpassword = ConvertTo-SecureString $password -AsPlainText -Force

$clientContext.Credentials = New-Object Microsoft.SharePoint.Client.SharePointOnlineCredentials($userName, $securedpassword)

#get the rootweb
$site = $clientContext.Site
$web = $site.RootWeb

#Get fields collection
$fields = $web.Fields

$clientContext.Load($web)
$clientContext.Load($fields)

$clientContext.ExecuteQuery()

#your field xml
$fieldXML = "<Field Type='Choice'
Name='Department'
Description=''
DisplayName='Department'
StaticName='Department'
Group='Custom Columns'
Hidden='FALSE'
Required='TRUE'
Sealed='FALSE'
ShowInDisplayForm='TRUE'
ShowInEditForm='TRUE'
ShowInListSettings='TRUE'
ShowInNewForm='TRUE'>
<CHOICES>
<CHOICE>other</CHOICE>
</CHOICES>
</Field>"
$fields.AddFieldAsXml($fieldXML, $true, [Microsoft.SharePoint.Client.AddFieldOptions]::AddToDefaultContentType)
$clientContext.Load($fields)
$clientContext.ExecuteQuery()

Exception calling "ExecuteQuery" with "0" argument(s): "A duplicate field name "Department" was found."
At line:20 char:1
+ $clientContext.ExecuteQuery()
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (:) [], MethodInvocationException
    + FullyQualifiedErrorId : ServerException