php simpleXml generate a invalid XML - php

Question

i have tryed some things to figure out what wrong with my code, but i dont see the problem.
Simply i have a structured assoziative Array like this:
$data = array(
'field1' => array(
'filed11' => '',
'field12' => array(
'field121' => 'blub'
)
),
'field2' => 'foo',
'field3' => array(
'field31' => 'val',
'field32' => 'other value'
)
);
i have writen a small recursive method to generate an xml from the Array:
protected function buildXmlFromArray(SimpleXMLElement $xml, $data)
{
if(is_array($data)) {
foreach($data as $key => $value) {
if(is_array($value)) {
$child = $xml->addChild($key);
$this->buildXmlFromArray($child, $value);
} else {
$xml->addChild($key, $value);
}
}
}
}
So i generate the root-node and put it in the method:
$xml = new SimpleXMLElement('<root />');
$res = $this->buildXmlFromArray($xml, $data);
print_r($xml->asXML());
exit;
i would expect that iam getting somthing like this:
<?xml version="1.0"?>
<root>
<field1>
<filed11 />
<field12>
<field121>blub</field121>
</field12>
</field1>
<field2>foo</field2>
<field3>
<field31>val</field31>
<field32>other value</field32>
</field3>
</root>
but iam getting an invalid XML:
<?xml version="1.0"?>
<root>
<field1>
<filed11>
<field12>
<field121>blub</field121>
</field12>
</field1>
<field2>foo</field2>
<field3>
<field31>val</field31>
<field32>other value</field32>
</field3>
</root>
so field11 is not closed
Whats wrong with this?
My PHP Version is 7.2.10-0ubuntu0.18.04.1