Areal density improvement of perpendicular magnetic recording (PMR) write head by tuning magnetic flux loops

A PMR writer, comprising:

• (a) a first trailing shield layer formed on a write gap and adjoining an air bearing surface (ABS), the write gap contacts a top surface of a front portion of a main pole layer at the ABS;
• (b) a second (PP3) trailing shield that adjoins a top surface of the first trailing shield layer and extends toward a back end of the PMR writer where the PP3 trailing shield contacts a top yoke formed on a top surface of a back portion of the main pole layer;
• (c) a leading shield with a top surface contacting a bottom surface of a leading gap at the ABS, the leading gap has a top surface adjoining a bottom surface of the front portion of the main pole layer at the ABS;
• (d) a leading shield connector (LSC) that contacts a bottom surface of the leading shield and extends from the ABS toward a back end of the PMR writer;
• (e) a shield section that is recessed from the ABS and adjoins a bottom surface of the LSC and a top surface of a return path layer (RTP);
• (f) the RTP with an ABS facing side that is recessed from the ABS and with a top surface that is parallel to the main pole layer bottom surface;
• and
• (g) a back gap connection (BGC) that is a via filled with a magnetic material and connects the top surface of the RTP to a bottom surface of the back portion of the main pole layer wherein a magnitude of magnetic flux in a return pathway from a magnetic medium through the leading shield, LSC, shield section, RTP, and BGC to the main pole layer forming a leading loop, is substantially less than a magnitude of magnetic flux returning from the magnetic medium to the main pole layer through the first trailing shield and PP3 trailing shield because of enhanced magnetic impedance in the leading loop resulting from one or both of the BGC having a cross-sectional area of about 6 micron2 or less from a top-down view, and a magnetization saturation (Ms) value less than 10 kG in the RTP.