Loop RX antennas can have deep broadside nulls but only when the loop is quite small which means the signal output may be small, perhaps too small at LF or MF. The broadside response can be suppressed even in large loops in several ways which is the subject of this note: Download 2023 loop pattern study
Multi-turn loop receiving antennas for LFMF
For the next edition of the ARRL Antenna Book (the 25th) I've written a section on Multi-Turn Loop Antennas for LFMF reception. It will be many months before this published and available from the ARRL. I felt the topic might be of more immediate interest to the LFMF gang and have permission to post a copy of the draft: Download Chap 22 LFMF RX loops .
The ARRL note mentions direct experimental measurements of self resonant frequency. Here is a note with more detail on the measurements and modeling comparisons between different versions of NEC: Download Loop excerpt 2