augenblicklich
immediately
Without any delay; right away or at once.
Als der Feueralarm losging, verließen alle augenblicklich das Gebäude.
When the fire alarm went off, everyone left the building immediately.

immediately / currently
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immediately
Without any delay; right away or at once.
Als der Feueralarm losging, verließen alle augenblicklich das Gebäude.
When the fire alarm went off, everyone left the building immediately.

The word derives from 'der Augenblick' (the moment), which means 'moment'. Literally, it means something like 'happening in a moment' or 'applying for the moment'.
Ein Augenblick der Unaufmerksamkeit kann zu Fehlern führen.
A moment of inattention can lead to mistakes.
As an adverb, 'augenblicklich' can stand at the beginning of the sentence (position 1) or inside the sentence. If it is in position 1, the verb follows in position 2 (inversion).
Augenblicklich habe ich leider keine Zeit für dich.
Unfortunately, I currently don't have time for you.
The meaning 'sofort' (immediately) usually describes a quick reaction to an event. The meaning 'momentan' (currently) describes a current state that does not have to be permanent. The sentence context and tense help distinguish between them.
Nach dem Anruf fuhr er augenblicklich los. (sofort)
After the call, he left immediately. (right away)
'Augenblicklich' can sound somewhat more formal or elevated. In everyday language, other words are often used for the two meanings.
Der Minister trat augenblicklich von seinem Amt zurück.
The minister resigned from his office immediately.
now
'jetzt' and 'augenblicklich' can both point to the current moment. 'jetzt' is the normal everyday word for 'at this moment' and can also strengthen a clear demand. 'augenblicklich' sounds more formal and often means 'immediately, without waiting'. It can also mean 'currently', but in everyday speech people usually say 'jetzt' or 'zurzeit' for that. The words can be confused because both have to do with the present moment. If you are simply talking about the moment, 'jetzt' is usually more natural. If something is supposed to happen immediately, 'augenblicklich' is more precise.

Bitte verlassen Sie augenblicklich den Raum.
Please leave the room immediately.
Ich habe jetzt keine Zeit, aber später können wir reden.
I don't have time now, but we can talk later.