Avocado Stem Leaf Death

If the symptoms started out with yellowing between the leaf veins, this could be a fungal disease called Verticillium wilt, but its hard to say for certain with a photo. You can cut the dead twig and look for the characteristic brown color in the center of the stem where the water carrying tissues have been infected and are no longer able to function, starving the affected stems, and consequently the leafs, of water. Unfortunately, there is not cure for this wilt disease. However, you can avoid having it affect other trees in the future. We've included a link about Avocados for your reference. (You'll see the link on this page for Verticillium wilt). Just to narrow down the possibilities of cause, you will also want to look for any oozing cankers on the trunk or stems, as these are signs of some of the other issues that could cause this kind of damage. We do recommend using a fertilizer formulated for Avo's - they usually need Nitrogen and Iron, and as you say, maybe some Zinc, especially if its in a pot with potting soil rather than in the ground, but Palm fertilizers are usually higher in Magnesium, which if in high enough concentrations and in the presence of calcium, can cause toxicity to Avocados. We've included another link with an article about Mg toxicity just in case.
http://www.ipm.ucdavis.edu/PMG/GARDEN/FRUIT/avocados.html
http://ucce.ucdavis.edu/files/repositoryfiles/ca1407p5-67224.pdf