Tl;dr: Use the PDF icon or , and drop the text.
Given your comment (thanks!) the icon tells users it is a PDF, and is, practically, universally recognizable (not meaningfully increasing cognitive debt).
Opening in a new tab is appropriate for PDFs because:
- Research showed the standard user action after finishing a PDF in a browser window is to close the window.
- Often, the browser will launch the default PDF reader on the machine and abort opening the new window.
Both of these feel the about the same to the user, and are expected behavior. "Opens in a new window" will actually be confusing for users if their browser is configured to open files in a desktop application automatically.
The icon prepares the user that something uncommon will happen when the click the link. It is both communicative and inconspicuous.
The better question may be to ask why the link should open in a new window as a default interaction.
Standard UX for browser links is to target SELF. Users right-click select "Open in a new Tab" or "... Window" when they want to open a new tab or window. This has been a commonly supported interaction on all major browsers for many major versions of each.
For further reading, see this SO question, Jakob Nielsen (#9), and a talk from Jared Spool.
The one exception I'd make, which Nielsen empirically observes, is that links to PDFs or non-HTML files (anything that isn't a web page) should be opened in a new window.
If it is necessary:
Adoption of the icon will likely be effected by the demographics of the site users. Browser demographics can help:
- If the majority of users access using modern, latest-version browsers, the users may be younger or more tech-savvy.
- If the majority of the users access using older browsers, the user base may be older or not "digital native".
However, as pointed out here, browser demographics cannot be the only metric by which you make decisions.
The middle ground for your client may be to add "Opens in a new window" as the roll-over text for those links, in addition to using the icon.
And, since you're only using these links for PDFs and other documents/files, use the icon for the most recognizable application that will open that file (the Word logo, PDF logo, etc). That will be instantly recognizable.