spalten
to split
To separate something lengthwise into two or more parts with a targeted blow or pressure, especially wood.
Im Winter spaltet er jeden Tag Holz für den Kaminofen.
In winter, he splits wood for the fireplace every day.

to split
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to split
To separate something lengthwise into two or more parts with a targeted blow or pressure, especially wood.
Im Winter spaltet er jeden Tag Holz für den Kaminofen.
In winter, he splits wood for the fireplace every day.

The verb 'spalten' (to split) is closely related to the noun 'der Spalt' (gap/crack) or 'die Spalte' (column/split). When you split something, you create a gap or a column.
Durch den Spalt in der Wand konnte man Licht sehen.
You could see light through the crack in the wall.
'Spalten' (to split/divide) can be used transitively or reflexively. 'Jemand spaltet eine Gruppe' (someone splits/divides a group) means that a person actively causes the separation. 'Die Gruppe spaltet sich' (the group splits) means that the group divides by itself.
Seine radikalen Ansichten spalten die Diskussionsteilnehmer.
His radical views are dividing the participants in the discussion.
The past participle 'gespalten' (split/divided) is very often used as an adjective. It can mean 'divided' or 'ambivalent.' A 'gespaltene Persönlichkeit' (split personality) is a psychological technical term.
Ich habe zu diesem Thema eine gespaltene Meinung.
I have mixed feelings about this topic.
In its literal meaning, 'spalten' (to split) is almost always used in the combination 'Holz spalten' (to split wood), often with the tool 'mit einer Axt' (with an axe).
Mein Großvater hat früher jeden Morgen Holz für den Ofen gespalten.
My grandfather used to split wood for the stove every morning.
In the figurative, social meaning, typical objects are 'die Gesellschaft' (society), 'eine Partei' (a party), 'eine Familie' (a family), or 'die Nation' (the nation). It is always about the separation of a social group.
Das Thema Migration spaltet die europäische Gesellschaft.
The topic of migration is dividing European society.
The meaning 'Atomkerne oder Moleküle zerlegen' (to break down atomic nuclei or molecules) is limited to the technical language of physics and chemistry. Typical objects are 'Atome' (atoms) or 'Atomkerne' (atomic nuclei).
Bei der Kernspaltung wird eine enorme Menge an Energie freigesetzt.
During nuclear fission, an enormous amount of energy is released.
to share / divide
'teilen' and 'spalten' can both mean that something is separated into several parts. 'teilen' is neutral and very general. It works for things, groups, or sections. 'spalten' is stronger and more specific: with wood, it means splitting it lengthwise, often with force. With people or groups, 'spalten' means that conflict or different opinions arise. You can confuse the words because both describe dividing something up. But 'teilen' often sounds normal and practical, while 'spalten' often sounds stronger, more physical, or more conflict-related.

Mein Vater hat das Holz für den Ofen mit einer Axt gespalten.
My father split the wood for the stove with an axe.
Die Lehrerin teilt die Klasse für die Gruppenarbeit in vier Teams.
The teacher divides the class into four teams for the group work.