We developed perpendicular magnetic tunnel junctions (MTJs) with four synthetic anti-ferromagnetically coupled Co/Pt layers (quad-SyF) and investigated their magnetic and transport properties. The quad-SyF comprised four Co/Pt layers and three 0.9 nm-thick Ru coupling layers, which consisted of Co/[Co/Pt] <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{a}$ </tex-math></inline-formula> /Ru/Co/[Co/Pt] <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{b}$ </tex-math></inline-formula> /Ru/Co/[Co/Pt] <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{c}$ </tex-math></inline-formula> /Ru/Co/[Co/Pt] <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{d}$ </tex-math></inline-formula> from top to bottom. The exchange coupling field ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ex}}$ </tex-math></inline-formula> ) reached a maximum of 1 T when the values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> were 1, 2, 2, and 1, respectively. The tunnel magnetoresistance ratio of the MTJ with the quad-SyF and the second-peak conventional double-SyF increased as the annealing temperature was increased up to 400 °C, whereas that of the MTJ with the first-peak conventional double-SyF degraded at temperatures of more than 350 °C in blanket films. A 55 nm diameter MTJ with quad-SyF was found to be stable even against an external magnetic field up to 300 mT. On the contrary, in the conventional double-SyF, the reference-layer (RL) magnetization direction flips at around 250 mT. The shift magnetic field of the MTJ with quad-SyF becomes approximately zero when the values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> are 1, 4, 1, and 2, respectively. No back-hopping of the MTJ with quad-SyF was observed even for the write pulsewidth ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{W}$ </tex-math></inline-formula> ) down to 10 ns. On the contrary, an MTJ with conventional double-SyF exhibited back-hopping. In the patterned MTJ with conventional double-SyF, as the MTJ size decreases, the coercive field of Co/Pt significantly increases and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ex}}$ </tex-math></inline-formula> decreases, causing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> curve of the RL to cross the zero magnetic field. This enables both parallel and antiparallel configurations for the top and bottom Co/Pt layers in double-SyF at the zero magnetic field, which could induce back-hopping. However, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> curves of the RL in the patterned MTJ with quad-SyF are far from the zero magnetic field owing to the high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ex}}$ </tex-math></inline-formula> and low <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{c}$ </tex-math></inline-formula> , which could lead to the suppression of back-hopping.