I'm also in the GTA and am working through a similar problem right now. In addition to the points raised by the previous posters, the issue that I've come across is that the banks look at your income when determining mortgage amount, because they need to know that you will be able to cover both mortgages even if your rental property is vacant. As a PhD student, will your salary/grant/income source be enough to cover both mortgages in any given month, in the worst case scenario where you are not receiving a rental income?
We've rented our condo out for four years, with only a one month vacancy in that period. Now that we're considering purchasing a second rental condo, the banks worry that we can't cover both mortgages, especially because our incomes are still only mediocre. Our solid four-year rental history doesn't seem to play much of a role (though obviously it's not hurting the mortgage application). So banks tend to offer a smaller mortgage. One way to work around it is to apply for a line of credit against your first property - in our case, we've built up enough equity (first mortgage is almost paid off) to qualify for a pretty hefty line of credit. The interest rate is slightly higher than a mortgage, but still pretty decent.
From my experience, you don't have to pay all cash for a second property. You do have to get a bit more creative with financing. Talking to the bank that holds your mortgage will likely be helpful since they can run numbers for you and tell you how much of a mortgage you qualify for. I've found it is also helpful to build a relationship with a particular branch/branch manager.
Please note that I am by no means an expert on this. I'm just sharing my own experience as a Torontonian with a mortgage and mediocre income trying to buy a second condo in TO. Would love to hear how it all turns out for you.