Currently if you use SOLR for search and deploy it with search API module you can index Title field as fulltext so you can make better use of it and find parts of it when searching. But then you can't sort by title in search api sorts module, what to do? Well use
Under the Workflow tab, select 'aggregated fields' and select the field you want to use for a sort, make sure you index that aggregated field on the Fields tab (as First) and sort on string fields. You can also do it other way around. Use default fields as string and use them for sorting and use aggregated fields as fulltext and use them for searching, where you can add few fields in combination and have even more power and options.