I use the Petzl Am'D, but any D carabiner works. Locking belay devices such as the Cinch and GriGri are best paired with D carabiners rather than HMS carabiners, such as the Petzl Attache.

My favourite carabiner for use with the Cinch, or any belay device, is the Simond Spider+BLC


Snag-free nose and no cross-loading!

I hate cross-loading with a passion - nothing to do with concerns for safety and everything to do with my tendency to be a control freak.

IME the D end such as on a positron will catch on the ring of a cinch or gri that causes it to bind. Why would you say a D is best?

The Cinch will not bind on a standard D carabiner any more or less than it will on an HMS carabiner. I said a D carabiner is best because that is what D carabiners are designed for. HMS carabiners are primarily designed to be used with ATCs. They feature a gently rounding top so as to create a bar to block the ATC. However, that feature is completely useless for a device such as a Cinch and it only increases the chances of the Cinch inadvertently loading the nose. None the less, it does not matter, you can use an HMS carabiner, a D carabiner, an oval, a quicklink, whatever.

You need to brush up on your carabiner history.

The "D" shape is a modification of the symmetrical oval shape to give it more strength by moving more of the load toward the spine and away from the gate.

HMS is short for Halbmastwurfsicherung, German for "half clove hitch" and describes the Munter/Italian hitch. The wide basket end of a pear-shaped HMS is designed for use with a Munter hitch.

Sorry, when I said that D carabiners are designed for that use, I was not specifically referring to use with a locking belay device. I meant they are designed to be used in applications where the load can appropriately be placed along the spine. Let me try to have a run at carabiner history. So, class X carabiners (oval) are often used for pulleys where the load must be applied evenly to both brackets in order to prevent uneven loading of the sheave, and they have also been traditionally used in aid climbing to prevent the biner shift noise that scares some climbers. Class K carabienrs are almost always used for via ferrata lanyards, and they are designed to withstand loading over an edge. They also have a reduced security locking mechanism to enable faster opening of the gate. Class D carabiners (directional) are often used in quickdraws or other applications where the user wants to fix one end of the biner to a sling permanently. Class H or HMS carabiners are used to create clove hitches as you said, but most commonly they are used in conjunction with plate belay devices. I believe you when you said they were designed for use with clove hitches, but in their current state, they are most commonly used with plate belay devices. Class Q carabiners are not actually carabiners, they are quicklinks, and they are used in specialty applications. They are very common in slacklining and highlinging. And lastly, class B carabiners, AKA D carabiners, are used in scenarios where increased strength is required, and where it is appropriate to force the load towards the spine of the carabiner. Most commonly, they are used on quickdraws, slings, and trad gear. Of course, that list is nonexclusive, the range of usages appropriate to one type of carabiner are endless.