"Porphyria's Lover" is a narrative poem by Robert Browning.  It first appeared in print in 1836.

On a stormy night, the narrator's lover, named Porphyria,  "glides in" to his house and makes "all the cottage warm."  She sits down by her lover's side and tells him that she loves him.  There is a problem, though: 

she [was] Too weak, for all her heart’s endeavor, To set its struggling passion free From pride, and vainer ties dissever, And give herself to me forever...

Perhaps this means that she was too proud to give herself over to another person.

The lover finds a violent and disturbing solution to his problem:

all her hair

In one long yellow string I wound

Three times her little throat around 

And strangled her.

In this way, the narrator feels that Porphyria has gained her "utmost will," which was to belong to her beloved.

Most readers of this poem conclude that the narrator is insane.  However, it does not seem that his madness is an example of the psychological phenomenom known as fixation.

Fixation is defined as a strong association with a past event that triggers certain feelings or behaviors later on.  For example, if a young child is bitten by a dog, she might experience extreme anxiety whenever she sees a dog, even year's later. 

There is nothing in Browning's poem to suggest that the narrator's behavior is the result of some previous experience.  

In laymen's terms, however, we might say that he is so fixated, or obsessed, with "owning" his lover, that he will even kill her to achieve his ownership.