Logs, woodchip, straw, sawdust,
cardboard will increase the fertility of your
land too. I sometimes prefer straw over hay because straw have no seed that will sprout and compete with my spring planting. Logs/woodchip and other TREE sources of
carbon take longer to breakdown than dry grass (hay/straw). So hay will improve your soil faster.
There is quite a few way to increase the fertility of your land.
1) Add new mineral: artificial fertilizer, rockdust, sea90, rockdust,
compost
2) Increase the air pockets in your soil,
roots need air too
3) Increase how much
water your soil hold and how long it holds it
4) Increase the carbon in your soil, holds water and like activated charcoal holds mineral
5) Increase the bio-availability of the minerals in your soil, with peeing-pooping worms and other critters and bacteria, fungi that will "dissolve" rocks to trade with plant roots, fix nitrogen from the air, change the localized PH
Personally I cover my fruit tree/shrub area with woodchip
And the garden area i just let the plant reamains stay right there in the garden with it looking super messy. Leaf litter works too, and straw if some presents itself at the frontdoor.