Programmable　magnetic　field-free　manipulation　of　perpendicular　magnetization　switching　is　essential　for　the　development　of　ultralow-power　spintronic　devices.　However,　the　magnetization　in　a　centrosymmetric　single-layer　ferromagnetic　film　cannot　be　switched　directly　by　passing　an　electrical　current　in　itself.　Here,　we　demonstrate　a　repeatable　bulk　spin-orbit　torque　(SOT)　switching　of　the　perpendicularly　magnetized　CoPt　alloy　single-layer　films　by　introducing　a　composition　gradient　in　the　thickness　direction　to　break　the　inversion　symmetry.　Experimental　results　reveal　that　the　bulk　SOT-induced　effective　field　on　the　domain　walls　leads　to　the　domain　walls　motion　and　magnetization　switching.　Moreover,　magnetic　field-free　perpendicular　magnetization　switching　caused　by　SOT　and　its　switching　polarity　(clockwise　or　counterclockwise)　can　be　reversibly　controlled　in　the　IrMn/Co/Ru/CoPt　heterojunctions　based　on　the　exchange　bias　and　interlayer　exchange　coupling.　This　unique　composition　gradient　approach　accompanied　with　electrically　controllable　SOT　magnetization　switching　provides　a　promising　strategy　to　access　energy-efficient　control　of　memory　and　logic　devices.　A　major　challenge　of　spintronics　is　achieving　magnetic　field　free　electrical　control　of　magnetisation.　Here,　Xie　et　al.　achieve　perpendicular　magnetisation　switching　in　a　CoPt　alloy,　breaking　inversion　symmetry　by　varying　the　composition　of　the　alloy　in　the　growth　direction.